text:
中央办公室
公司№201334002R,60巴耶利巴尔路,#09-40巴耶利巴尔广场,大堂2,新加坡,409051
办公室1306,19Razzakova街,比什凯克,吉尔吉斯共和国,720030
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Rare Earth Metals
Neon Mining has recently applied for and is currently in the process of acquiring the license for the KUTESSAY II RARE EARTH PROPERTY, located in the Aktyuz Ore Field, Kemin District, Chui Oblast, Kyrgyz Republic, 140 km east of Bishkek, the Kyrgyz capital, and 43 km from the nearest rail station in Kemin.
HISTORY OF THE KUTESSAY II PROPERTY
The Kutessay-II rare earth deposit was discovered in 1943. Initial exploration of the deposit started in 1956 and ended late in 1958. Initially, Kutessay II was considered a polymetallic, then a thorium deposit, and since 1956, a rare earth-polymetallic deposit. The first historic reserve estimate of the Kutessay-II rare earth deposit was approved by the USSR State Committee Reserves in 1959.
Development of the deposit began in 1958 by underground mining method for the first two years, and by the open pit in all following years. Until 1966 the mine operated primarily as a lead mine, with less attention paid to rare earth ores. From 1966 to closure in 1991 the mine operated primarily as a rare-earth-polymetallic mine with the production of rare earth concentrates (including yttrium), accompanied by the recovery of lead, molybdenum, silver, and bismuth.
Mining and rare-earth production was conducted under the management of Kyrgyz Mining and Metallurgical Combine from 1958 through 1991, and particular mining was conducted by its subsidiary Aktyuz Mine Group. Ore was milled and rare earth concentrates were sent for processing to the Chemical-Metallurgical Plant of the Kyrgyz Mining and Metallurgical Combine at Orlovka village, about 43 km west from Kutessay II. Concentrates of other metals were sent to other enterprises.
It is reported that during the Kutessay II combined underground and open pit mine life from 1958 to 1991 a total of 5.454 million t of ore were mined out to produce 22,109 t of TR2O3, at an average grade of 0.41%.
During the period 1962 to 1990 the plant processed 5.314 million t ore containing 19,980 t of rare earths at a weighted average grade of 0.376% of TR2O3, including 0.114% yttrium oxide. Kutessay II was also the source of 21,100 t lead, 167 t molybdenum, 17.3 t silver, and 25 t bismuth, with much of this metal production coming from the upper levels of the deposit.
For the last ten years of operation from 1980 to 1990, the recovery of total rare earths ranged from 62.04% to 64.0%, and averaged 63.4% from an annual feed ranging from 180,000 t to 300,000 t ore, with an average grade ranging from 0.29% to 0.34% _RE2O3.
Officially exploitation of the Kutessay II deposit was stopped at the beginning of 1995, and following the Governmental regulation dated 1 June 1995, all operations were temporarily suspended. Up to 1990, the deposit was the principal supplier of the yttrium and lanthanides requirements for the former USSR.
HISTORIC MINERAL RESERVE ESTIMATE
On January 1, 1992, the staff of the Aktyuz Mine Group (S. Isaev and T. Beregovaya, 1992) published a mineral reserve estimate of total rare earth oxides (ΣTR2O3) for the unmined portion of the Kutessay II deposit, between the horizons 2,353-2,153 m above sea level. The mineral reserve estimate was approved by the State Reserve Committee of the Kyrgyz Republic on October 1, 1995. The estimate was done using horizontal slices, polygonal estimation methodology based on the results of analyses from channel samples and core samples conducted from a system of underground workings on four horizons of the Kutessay II deposit.
The Historic 1992 Mineral Reserve estimate for Kutessay II was 16.9 million t of ore including 44,800 t _RE2O3 at a grade of 0.27% of the B + C1 Category; and 1.8 million t including 3,900 tones _RE2O3 at a grade of 0.22% of the C2 Category.
The 1992 estimate was classified as Mineral Reserves, designated as B, C1, and C2 reserve categories, using the Soviet resource and mineral reserve classification system prevailing at the time.
In 2011 Kutessay II Mineral Resource Estimate as of March 21, 2011, was prepared by Kutisay Mining LLC in accordance with JORC 2004 Code Standards.
Metric tones
Grade ΣTR2O3
ΣTR2O3
Resource Classification
1,000 t
Northern Zone
Measured + Indicated
Inferred
Total Northern & Central Zones
Mineral Resources were classified in accordance with JORC 2004 Code Standards.
Cut-off-Grade – 0.1% ΣTR2O3, minimum width of mineralization – 3 m, and a maximum thickness of below cut-off interbeds of 3 m.
A rock density ranging from 2.68 to 2.81 was normally used depending on the rock type hosting mineralization, equivalent, respectively to a tonnage factor of 0.373 m3/t and 0.356 m3/t.
High grades have not been cut for the Mineral Resource Estimate.
A long term price of US$100.00/kg total rare earth oxides is used for the Mineral Resource Estimate.
No Mineral Reserves have been estimated for the Kutessay II deposit.
DISTRIBUTION OF THE ELEMENTS
The distribution of the elements composition of the 15 individual REEs in the Kutessay II mineralization is given below. This historic 1959 estimate is from the Kutessay II open pit and the 1992 estimate is from the Kutessay II deposit. The distribution between the rare earths was made based on X-ray spectral analysis (Doroshenko, 1959 and Isaev and Beregovaya, 1992).
Grade of ΣTR2O3, %
Isaev and Beregovaya
Samples from Kutessay II
Open-pit
Year reported
Cerium group
Total Cerium group:
Yttrium group
Dу
Total Yttrium group:
Total ΣTR2O3
Doroshenko (1959) reported that a characteristic feature of the rare earth mineralization accessed by the open pit is the approximate equal distribution in the ores of the Cerium group, the Light REEs, and the Yttrium group, the Heavy REEs, with the Yttrium group varying between 40% and 47% of the total rare earth oxides and the Cerium group varying between 49% and 60% of the total rare earth oxides. For the Kutessay II underground deposit, Isaev and Beregovaya (1992) reported a ratio of the Yttrium HREEs to Cerium LREEs of 43.9% to 54.1%, respectively, as shown in Table above.
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Mueller's Request To Drop Restraining Order Illustrates Domestic Violence Dilemma
According to an article just released from CNN, Brooke Mueller, wife of actor Charlie Sheen, has reportedly asked a judge to modify a restraining order restricting Sheen's contact with Mueller. Sheen was arrested on Christmas Day on charges of domestic violence after he allegedly attacked Mueller in a drunken fight and held a knife to her throat. According to Mueller's 911 call to police, Sheen attacked her because she told him she wanted a divorce. Follow this link to a CBS article reporting on these details.
At first glance, Mueller may not appear to be the typical (or, perhaps, stereotypical) victim of domestic violence. Prior to her marriage to Sheen in May 2008, Mueller was a real estate investor, apparently successful in her own right. She also has enough funds at her disposal to hire celebrity lawyer, Yale Galanter, who made her request to drop the restraining order against Sheen.
And yet, by asking the judge to lift the restraints on Sheen, Mueller illustrates a sad, but all-too-familiar dilemma in domestic violence cases – the victim that returns to the abuser. According to Mueller's lawyer, the Christmas Day incident was merely "one bad night." One bad night?!? If Mueller's account of the evening's events is correct, Sheen attacked her with a knife because she wanted a divorce! That is not something to be dismissed as "one bad night." Moreover, the couple was reported in celebrity gossip rags as having domestic problems almost immediately after they wed. You can link to an article here from June 2008 discussing the rumor that the couple cut short their honeymoon in Costa Rica because of incessant fighting.
Unfortunately, because the Mueller-Sheen case has received so much attention in the press, Mueller's decision to reconcile with Sheen may be setting a dangerous example for women everywhere. To illustrate this very real danger, here are some sobering statistics on domestic violence against women in the U.S.:
One in four women (25%) has experienced domestic violence in her lifetime.
(The Centers for Disease Control and Prevention and The National Institute of Justice, Extent, Nature, and Consequences of Intimate Partner Violence, July 2000. The Commonwealth Fund, Health Concerns Across a Woman's Lifespan: 1998 Survey of Women's Health, 1999)
Estimates range from 960,000 incidents of violence against a current or former spouse, boyfriend, or girlfriend to 3 million women who are physically abused by their husband or boyfriend per year. (U.S. Department of Justice, Violence by Intimates: Analysis of Data on Crimes by Current or Former Spouses, Boyfriends, and Girlfriends, March 1998. The Commonwealth Fund, Health Concerns Across a Woman's Lifespan: 1998 Survey of Women's Health, 1999)
Women of all races are about equally vulnerable to violence by an intimate partner.
(Bureau of Justice Statistics, Violence Against Women: Estimates from the Redesigned Survey, August 1995)
Intimate partner violence affects people regardless of income. However, people with lower annual income (below $25K) are at a 3-times higher risk of intimate partner violence than people with higher annual income (over $50K).* (Bureau of Justice Statistics, Intimate Partner Violence in the U.S. 1993-2004, 2006.)
Nearly three out of four (74%) of Americans personally know someone who is or has been a victim of domestic violence. (Allstate Foundation National Poll on Domestic Violence, 2006. Lieberman Research Inc., Tracking Survey conducted for The Advertising Council and the Family Violence Prevention Fund, July – October 1996)
On average, more than three women are murdered by their intimate partners in this country every day. (Bureau of Justice Statistics Crime Data Brief, Intimate Partner Violence, 1993-2001, February 2003. Bureau of Justice Statistics, Intimate Partner Violence in the U.S. 1993-2004, 2006.)
In a national survey of American families, 50% of the men who frequently assaulted their wives also frequently abused their children. (Strauss, Murray A, Gelles, Richard J., and Smith, Christine. 1990. Physical Violence in American Families; Risk Factors and Adaptations to Violence in 8,145 Families. New Brunswick: Transaction Publishers)
These statistics were obtained from the Domestic Violence Resource Center. You can link to more statistics at their website here. The United Nations also regards violence against women as a human rights issue. You can link to more information about the UNITE campaign here.
This entry was posted in human rights, violence against women and children and tagged Brooke Mueller, Charlie Sheen, Domestic violence, women's rights. Bookmark the permalink.
2 responses to "Mueller's Request To Drop Restraining Order Illustrates Domestic Violence Dilemma"
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Annette | January 2, 2010 at 5:25 pm |
Good points, I think I will definitely subscribe!🙂. I'll go and read some more!

redpajama_set_name: RedPajamaCommonCrawl


A couple of weeks back I had been driving for about 10 minutes, when my car started chugging/hesitating on acceleration. After driving for a few more minutes, the CEL came on and the message center flashed the messages 'anti-skid service required' and 'engine maintenance required'. This was accompanied by the transmission locking into third gear (I'm assuming some sort of limp mode) and the 'D' on the gauge cluster being replaced with a '-'.
I let it sit for about 10 hours and had the same occurrences on the way home, but the issue was so bad that it stalled three times at stop lights. I took it to a trusted (but technically lacking) mechanic who told me to take it to the dealership. The battery and alternator tested fine, but there were 19 codes on the OBD scanner, seen below.
I am at a TOTAL loss and have absolutely no idea what to do. Any help or guidance would be amazing.
Re: 2006 V70R (automatic) throwing 19 error codes!!!
First step is to get a scanner and clear all those codes and see what comes back, and when.
You are going to need 5-10 hours of researching to troubleshoot this successfully ifVolvo is new to you.
How many miles are on it and what's the service history?
You might try the battery disconnect reset as well.
Thanks guys. I should have mentioned that I have indeed cleared the codes twice - once through a scanner and once through a battery disconnect. Issues persist as described shortly thereafter.
Im not knowledgeable with your year, but you would have to assume bad engine ground, bad ECU, bad alternator. I know you checked it, but a bad alternator will light the dash warning lights up like a Christmas tree. You can have 14 volts but it may be AC if the diodes are bad, or it could be shorting if the bearings are gone. has it been noisy?
Can you do the ad,in work of googling each code with the word Volvo, Andy then putting the code description NextDoor to each code in a new post?
Very confusing. There is no skip shift solenoid on Volvos.
There is no bank 2 on a 5 cylinder.
I am thinking the scan tool is not interpreting Volvo codes correctly.
Some of those alphanumeric strings can exist with a three character module acronym in Volvo code language. Some of the strings can exist in multiple modules.
I am scheduled to take it to the dealership in two days for a VIDA scan. Hopefully that will shed a bit more light on it, and I will update when I find out more. Thanks!
Skip shift solenoid.. Generic OBD codes get a little 'lost in the translation' sometimes.. especially if the definition was pulled off a website linked from a search engine.
You said the issue is intermittent? Meaning sometimes you can restart the car and it'll run/drive fine for at least a short period of time before going haywire again, correct??
If that is the case first thing I would rule out would be the engine management system relay under the hood. And while you're at it make sure every fuse/relay on that panel is pushed down/seated fully. I am aware of a friend's coworker whose V70 was acting like this and it turned out one of those relays had worked itself partway out/wasn't fully seated down into the panel. He didn't say exactly which relay it was.
If those are all ok you're probably looking at a bad ground or power connection somewhere. Unless you're experienced/already highly familiar with the P2 Volvo electrical systems you might find letting the dealer sort it to be your better/faster option.


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Zlatko Komadina (ur. 24 października 1958 w Lublanie) – chorwacki polityk, inżynier i samorządowiec, wiceprzewodniczący Socjaldemokratycznej Partii Chorwacji, parlamentarzysta, żupan, w latach 2011–2012 minister spraw morskich, transportu i infrastruktury.

Życiorys
Z wykształcenia inżynier, specjalista w zakresie termoenergetyki. Studia ukończył na Uniwersytecie w Rijece. Pracował w przemyśle okrętowym, prowadził też własną działalność gospodarczą, był dyrektorem przedsiębiorstw Conkom i KD Energo.

W 1990 dołączył do założonej w tym samym roku Socjaldemokratycznej Partii Chorwacji. W 2000 stanął na czele tego ugrupowania w żupanii primorsko-gorskiej, a w 2004 został wiceprzewodniczącym krajowych struktur socjaldemokratów. W 1990 wybrany do zgromadzenia miejskiego w Rijece, w samorządzie miejskim zasiadał do 1997. Następnie przez rok był radnym żupanii. W latach 1997–2001 posłował do ówcześnie istniejącej wyższej izby chorwackiego parlamentu. W latach 2001–2011 był żupanem żupanii primorsko-gorskiej. W 2007 i 2011 uzyskiwał mandat deputowanego do Zgromadzenia Chorwackiego, który z uwagi na niepołączalność funkcji faktycznie wykonywał tylko w latach 2012–2013.

W grudniu 2011 został ministrem spraw morskich, transportu i infrastruktury w rządzie Zorana Milanovicia. Ustąpił z tego stanowiska już w kwietniu 2012, motywując to względami zdrowotnymi. W 2013 powrócił na stanowisko żupana (reelekcja w 2017 i 2020). W 2020 ponownie wybrany na deputowanego do chorwackiego parlamentu (zawiesił wykonywanie mandatu, pozostając na funkcji żupana). W tym samym roku czasowo wykonywał obowiązki przewodniczącego socjaldemokratów, gdy po słabym wyniku wyborczym skupionej wokół SDP koalicji z kierowania partią zrezygnował Davor Bernardić.

Przypisy

Chorwaccy ministrowie spraw morskich, transportu i infrastruktury
Deputowani do Zgromadzenia Chorwackiego
Politycy Socjaldemokratycznej Partii Chorwacji
Ludzie urodzeni w Lublanie
Urodzeni w 1958

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ScholarWorks@UARK highlights a growing collection of faculty publications, presentations, student work and teaching materials. The University of Arkansas is committed to disseminating its research and scholarship as widely as possible.
We welcome you to contribute your own work. Just follow the guidelines, and let us know how we can assist you.


If anyone has a complete vn 800 engine they would like to sell please let me know.
If you have a blown engine that could have parts please let me know. Looks like I have dropped a valve on the rear cylinder. Your engine may have the parts I need.
All times are GMT +12. The time now is 22:17.


text:
Chicomurex laciniatus är en snäckart som först beskrevs av G. B. Sowerby II 1841.  Chicomurex laciniatus ingår i släktet Chicomurex och familjen purpursnäckor. Inga underarter finns listade i Catalogue of Life.

Bildgalleri

Källor

Externa länkar

Purpursnäckor
laciniatus


A 58-year-old man has been arrested today in Elbasan. Flamur Alterziu, a resident in the 11th-November suburb of Elbasan, was put in a shackle after a serious accident occurred at the Rolling Mill of 'Kurum' metallurgical plant, Elbasan, where he was in charge as responsabile.
Yesterday at around 15:00 has died citizen Naim Dërstila, 63-year-old, electrician, resident in village Dërstilë of Gjinar Administrative Unit.
Oculus News sources suggest that the arrest of the person in charge came due to the disrespect of the rules of safety at work.
Meanwhile three days ago another accident was recorded in another industrial facility in the industrial area of the former Metalurg in Elbasan. We recall here that a worker died earlier in the Cement Factory and another was seriously injured.
In all cases, accidents have come about due to lack of safety rules. Meanwhile, the state labor inspectorate did not penalize abusive entities under law even though the occurred incidents are flagrant.


AIMA of Nashua, PLLC is on the 3rd floor (Suite 310) of the Telegraph Building, which sits on the edge of the Nashua River. Our office is on the top floor and is accessible via elevator. We offer an on-site parking lot for patrons which includes spaces for persons with disabilities. To park in the lot, which is located behind the building, take Pearson Ave off of Main Street. The Telegraph Building is the large brick building to your left. Pearson Ave is a two way street, and it is accessible if you are coming either North or South on Main Street. Take a left off of Pearson Ave into the rear parking lot, and then take the elevator or stairs to the 3rd floor. AIMA of Nashua, PLLC is on the left, adjacent to the elevator.
Please call us at 603-231-2478 if you need further assistance.


text:
Q: Generate Json file after order is confirmed I need to generate a Json file containing information about Order just right after a customer finish his checkout and the order is generated in admin using orderIdThis json file will contain data about products shipping methods ... related to this  order.if you can help

A: You need to do following things :

*

*create the events.xml file on following location.

app\code\Vendor\Extension\etc\events.xml

<?xml version="1.0"?>
<config xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:Event/etc/events.xsd">
      <event name="sales_order_place_after">
           <observer name="vendor_sales_order_place_after" instance="Vendor\Extensoin\Observer\OrderObserver" />
      </event>
</config>

*Now create OrderObserver.php on following location.

app\code\Vendor\Extension\Observer\OrderObserver.php

<?php
namespace Vendor\Extension\Observer;

use Magento\Framework\Event\ObserverInterface;

class OrderObserver implements ObserverInterface
{
    public function execute(\Magento\Framework\Event\Observer $observer)
    {
        $Orderdata = $observer->getEvent()->getOrder();

        //Write your logic to create Json file withh the Order information
    }
}

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Living room is the center of every home.
Whenever you have guests, they will judge your house based on its cleanliness, design and overall feeling they have while being in this room. This is why you should do everything in your power to make a nice impression.
However, changing up your living room is not only important because of your guests; it is something you should do for yourself. There are some minor adjustments that you can make and which can have a major impact on the design.
Check them out and see if any one of them fits for your home!
Whenever we talk about walls, we usually focus on paintings.
Historically, this was a common ornament for walls all over the world. As the times changed, so did our taste. Having paintings can come off as tacky and even arrogant. Instead, people opt to decorate their walls with some other items.
Among the most popular wall decoration it is necessary to mention photos, posters and mirrors. Basically, each one of them gives a different impression and can fit different design. Nevertheless, there is one thing in common for all of them: they fit perfectly for modern homes.
So, next time you decide to get a Hollywood mirror (check out the collection at hollywoodmirrors.co.uk), you should definitely consider using it as an ornament.
According to modern interior design, minimalism is one of the best things that happened to modern homes. But, although this approach makes your living room look clean it also takes away from its persona.
As a way to restore its previous charm, you need to consider adding small items.
What do I mean when I say small items? Well, practically anything.
A lot of people like collecting souvenirs from their trips and using them as ornaments. Book shelves are another great addition (when filled with books of course) that gives fullness to your living room. If these two options don't work for you, you can always get small pottery items.
Drapes are not as popular as they were some 30 years ago.
Nowadays, according to minimalistic views, people are opting for some other stuff and forgetting these seemingly cool ornaments. However, that doesn't mean that drapes will not have resurgence.
Basically, drapes may seem a bit retro but they fit perfectly for certain homes. The fact that they are no longer as popular makes them much more valuable. In times where everything is the same, take a chance and be different.
Not only that! Drapes also restore mystery to your home. If you wish to try your living room with them, they are rather easy to install and cheap. Even if you don't like them, you can easily remove them.
As everything else, certain things always come back to trend.
Instead of waiting for other to make a move and copy it, why don't you take a chance and use some ideas that are unique or retro.


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FAQ: Where Are All The Good Christmas Songs For Church Choirs?
1 What are the top 10 Christmas hymns?
2 What is the most recognized sacred Christmas song?
3 What are the top 3 Christmas songs?
5 What is the best Christmas hymn?
6 What is the most beautiful Christmas song?
7 What is the most popular Christmas song ever written?
8 What are Christmas songs about Jesus called?
9 What is a religious or holiday song called?
10 What is the least popular Christmas song?
11 What is the most played Christmas song 2020?
12 What is the easiest Christmas song to sing?
13 What is the No 1 Christmas song of all time?
14 What are the top 50 Christmas songs of all time?
15 What's the oldest Christmas Carol?
What are the top 10 Christmas hymns?
If less traditional holiday music is more your style, check out Come On And Jingle Bell Rock to These Holiday Albums.
"God Rest You Merry, Gentlemen"
"Children, Go Where I Send Thee"
What is the most recognized sacred Christmas song?
22 Best Religious Christmas Songs to Spread Holiday Joy
1 "Mary's Boy Child" by Harry Belafonte.
2 "I Wonder as I Wander" by Harry Connick Jr.
3 "It Came Upon a Midnight Clear" by Norah Jones.
4 "Angels We Have Heard on High" by Josh Groban.
6 "O Little Town of Bethlehem" by Nat King Cole.
What are the top 3 Christmas songs?
Ariana Grande, "Santa Tell Me"
Brenda Lee, "Rockin' Around the Christmas Tree"
Band Aid, "Do They Know It's Christmas?" (
John Lennon & Yoko Ono, "Happy Xmas (War Is Over)"
Chris Rea, "Driving Home for Christmas "
Elvis Presley, "Blue Christmas "
Coldplay, " Christmas Lights"
You might be interested: Often asked: Songs For Good Friday Church Service?
It's Beginning To Look A Lot Like
Have Yourself A Merry Little Christmas – Remastered Frank Sinatra
2 Hallelujah Carrie Underwood, John Legend 4:35
3 Silent Night The Temptations 2:24
4 Rockin' Around The Christmas Tree – Single Version Brenda Lee 2:06
5 Deck The Hall Nat King Cole 1:08
What is the best Christmas hymn?
Top 10 Christmas Carols of All Time
O Come All Ye Faithful.
O Holy Night.
We Three Kings.
The First Noel.
Away in a Manger.
O Little Town of Bethlehem.
Joy to the World.
What is the most beautiful Christmas song?
As the festive season approaches, we've donned our Christmas hats and found the most beautiful performances of these enduring carols.
Silent Night.
In the Bleak Mid-Winter – Gustav Holst version.
In the Bleak Mid-Winter – Harold Darke version.
O Come, O Come Emmanuel.
Coventry Carol.
What is the most popular Christmas song ever written?
According to the Guinness Book of World Records, "White Christmas " by Bing Crosby is not only the best -selling Christmas /holiday single in the United States, but also the best -selling single of all time, with estimated sales in excess of 50 million copies worldwide.
What are Christmas songs about Jesus called?
Christian Christmas Songs
Silent Night. Lyrics for this song from genius.com.
Oh, Come, All Ye Faithful.
Once in Royal David's City.
It Came Upon the Midnight Clear.
You might be interested: Question: Lakewood Church Worship Songs?
What is a religious or holiday song called?
Songs which are traditional, even some without a specific religious context, are often called Christmas carols.
What is the least popular Christmas song?
LIST: What Are Your Least Favorite Christmas Songs?
"Merry Xmas Everybody" – Slade.
"Last Christmas – Wham!"
"Fairytale of New York" – The Pogues and Kirsty MacColl.
"Baby It's Cold Outside" – Tom Jones & Cerys Matthews.
"Santa Claus is Coming to Town" – Jackson 5.
"Santa Baby" – Eartha Kitt.
"Jingle Bells" – Andrews Sisters.
What is the most played Christmas song 2020?
45 Best Modern Christmas Songs You Need on Your Holiday Playlist
1 "Santa Tell Me" by Ariana Grande.
2 "All I Want for Christmas Is You" by Mariah Carey.
3 "Like It's Christmas " by the Jonas Brothers.
4 "Mistletoe" by Justin Bieber.
5 "8 Days of Christmas " by Destiny's Child.
6 "My Gift Is You" by Gwen Stefani.
What is the easiest Christmas song to sing?
Easiest Christmas Songs To Sing For Beginners
White Christmas.
Rockin' Around The Christmas Tree.
Rudolph The Red-Nosed Reindeer.
Jingle Bells.
Winter Wonderland.
We Wish You A Merry Christmas.
Driving Home For Christmas.
What is the No 1 Christmas song of all time?
The first version of Do They Know It's Christmas? is the biggest selling Christmas Number 1 of all time, with over 3.8 million copies sold. Mary's Boy Child has been a Christmas Number 1 twice for totally different artists.
What are the top 50 Christmas songs of all time?
Count down our 50 favourite Christmas songs
'Stay Another Day' – East 17.
' All I Want For Christmas Is You' – Mariah Carey.
'Last Christmas ' – Wham!
' Christmas (Baby Please Come Home)' – Darlene Love.
'White Christmas ' – Bing Crosby.
'Fairytale of New York' – The Pogues and Kirsty MacColl.
You might be interested: Quick Answer: What Are Songs For Church On Mother's Day?
What's the oldest Christmas Carol?
More and more slow, solemn hymns started to emerge in the fourth century, and by the 12th, songs referring to Nativity themes and creatures had emerged. According to Oxford Dictionaries, one of the oldest printed carols is the 'Boar's Head Carol ', which dates from 1521.
Readers ask: What Is The Name Of The Book That Contains Songs Sung In Church Called?
Quick Answer: Church Wedding Recessional Songs?
FAQ: Christian Church Where Songs Are Sung?
FAQ: Church How Many Songs?
Readers ask: How Many Songs Should A Church Use?


text:
Zolder 6-timmars är en långdistanstävling för sportvagnar som körs på Circuit Zolder i Belgien.

Historia
Sportvagnstävlingen på Zolder var under 2000-talet en deltävling i FIA GT.

Vinnare

Externa länkar
Racingsportscars.com

FIA GT
Motorsportevenemang i Belgien


NIC's internship program aligns talented university students with leading firms in the seniors housing and care industry. These internships provide hands-on experience in the industry as well as insight into what it takes from a capital and service commitment perspective to give seniors quality housing and care so they can live meaningful, purposeful lives.
To review the internships currently available and the host companies, click the buttons on the right.
The seniors housing and care industry provides both housing and an array of services to seniors, generally to those over the age of 75. Care segments are commonly divided into four categories: independent living, assisted living, memory care, and nursing care. Nursing care typically has been provided in an institutional-style setting, though there is a growing movement toward more home-like surroundings. The other care segments are typically provided in a multifamily setting.
Seniors housing and care properties also include continuing care retirement communities (CCRCs), which typically offer all care segments, including independent living, assisted living and nursing care.
In the United States, there currently are approximately 21,100 investment-grade seniors housing and care properties containing nearly 2.8 million units. "Investment grade" is defined as those age-restricted properties with at least 25 units/beds that charge market rates for the housing and services offered. The total market capitalization of this investment-grade seniors housing and care property market is estimated at $300 billion.
Besides housing, including both shelter and recreational activities, seniors housing and care properties offer hospitality services (meals, transportation, housekeeping, entertainment and concierge services), care services (assistance with bathing, grooming, dressing, eating, medication management and other activities of daily living [ADLs]) and medical services (skilled nursing, rehab therapy). The care and medical service mix at the property increases with the resident's need. Independent living typically serves the most able residents and offers primarily hospitality services. Nursing care, on the other hand, serves higher acuity residents and accordingly, has the most intensive services.


text:
Celebrate 23 books authored by Arts and Sciences faculty in 2018
Written by Haley Herfurth
Writing a book is no small feat, and the faculty in the College of Arts and Sciences are taking the publishing world by storm. Twenty-three faculty from the departments of anthropology, biology, chemistry, communication studies, computer science, criminal justice, English, history, music, philosophy and psychology wrote books of poetry and children's books plus texts about tech in James Bond fiction, globalism in higher education and the behavioral science of peace.
Click through the slideshow below to learn more about each book.
Jonathan Amsbary, Ph.D.
Will Byrd, Ph.D.
Loretta Cormier, Ph.D.
Alan Franks, MFA
Denise Gainey, DMA
Hayden Griffin, Ph.D.
Ragib Hasan, Ph.D.
Mark Hickson, Ph.D.
Josh May, Ph.D.
Kevin McCain, Ph.D.
Steve McCornack, Ph.D.
Andy Millard, Ph.D.
Chris Minnix, Ph.D.
Kelly Morrison, Ph.D.
Larry Powell, Ph.D.
Trygve Tollefsbol, Ph.D., D.O.
Zina Trost, Ph.D.
Peter Verbeek, Ph.D.
Adam Vines, MFA
Sergey Vyazovkin, Ph.D.
Jeff Walker, Ph.D.
Brynn Welch, Ph.D.
Professor, Department of Communication Studies
"Interviewing in a Changing World"
Co-authored with Larry Powell, Ph.D., a fellow professor in the department, the second edition of "Interviewing in a Changing World," published by Routledge, can help students develop strong interview skills for various situations and contexts — from job interviews to persuasive interviews, performance and appraisal interviews and media interviews for radio, television, newspapers and political reporting. It also includes two chapters on interview skills needed for qualitative and quantitative research.
"Becoming John Wayne: The Early Westerns of a Screen Icon, 1930-1939"
Also co-authored with Powell, "Becoming John Wayne," published by McFarland & Co., explores the early movies of screen legend John Wayne, from his first starring role in "The Big Trail" to his breakthrough in John Ford's "Stagecoach." Amsbary and Powell trace the actor's transformation into the carefully crafted film persona that made him famous.
Researcher, Department of Computer Science
"The Reasoned Schemer"
The second edition of "The Reasoned Schemer," published by The MIT Press, explores ways to implement a relational programming language in scheme or any other functional language and demonstrates the remarkable flexibility of the resulting programs. This edition features simplified programming language and explicit rules to ease translations of scheme functions into relations.
Associate Professor, Department of Anthropology
"The Primate Zoonoses: Culture Change and Emerging Diseases"
Co-authored with Pauline Jolly, Ph.D., professor in UAB's Department of Epidemiology, "The Primate Zoonoses," published by Routledge, offers an accessible and up-to-date reference on primate zoonoses, infectious diseases spread between primates and humans. Recent years have seen a rise in human diseases zoonotically transferred from animals, and wild primates are implicated in the spread of numerous newly emerging infections. The book goes beyond providing just an inventory of diseases and helps readers understand how and why they are transmitted, with consideration given to the contemporary cultural and ecological factors.
Assistant Professor, Department of Communication Studies
"#Media: A History of Media in America"
Co-authored with Department of Communication Studies professors Larry Powell, Ph.D., and Mark Hickson, Ph.D., and published by Kendell Hunt, "#Media" is a comprehensive look at the history of mass media, from the beginning of writing to modern social media and includes discussion of the history of telegraphs, telephones, newspapers, film, radio and television.
"Kalmen Opperman: A Legacy of Excellence"
"Kalmen Opperman," published by Carl Fischer Music, combines interviews with the American clarinetist's former students with personal essays and reflections from those closest to the master teacher and performer; Gainey was a longtime student and research colleague. The book explores Opperman's life, pedagogy and contributions to the clarinet's canon.
Associate Professor, Department of Criminal Justice
"Routledge Handbook of Corrections in the United States"
Co-authored with the University of West Georgia's Vanessa Woodward, Ph.D., the "Routledge Handbook of Corrections in the United States," published by Routledge, brings together original contributions from leading scholars in criminology and criminal justice to provide an in-depth, state-of-the-art look at the most important topics in corrections. The book discusses the foundations of U.S. corrections, philosophical issues that guided historical movements in the field, varying types of punishment and supervision, among other things, and is an essential reference for both students and academicians and practitioners working in corrections and related agencies.
Associate Professor, Department of Computer Science
"Amazing Stories of Scientists"
"Amazing Stories of Scientists" includes interesting anecdotes about scientists and mathematicians, born out of bedtime stories Hasan told to his 7-year-old son — about an absent-minded Albert Einstein, how a melted pack of chocolates led to the invention of the microwave, how Thomas Edison was kicked out of school for being 'dim-witted' and how Charles Friedrich Gauss once pranked his kindergarten teacher with his mathematical prowess. The goal of "Amazing Stories of Scientists" is to show children that science is fun.
Co-authored with Department of Communication Studies Professor Larry Powell, Ph.D., and Assistant Professor Alan Franks, and published by Kendell Hunt, "#Media" is a comprehensive look at the history of mass media, from the beginning of writing to modern social media and includes discussion of the history of telegraphs, telephones, newspapers, film, radio and television.
Associate Professor, Department of Philosophy
"Regard for Reason in the Moral Mind"
"Regard for Reason in the Moral Mind," published by Oxford University Press, is an accessible defense of the rationality of moral thought and action and rebuts the scientific debunking of morality, engaging critically with both the science and philosophy of morality.
"Believing in Accordance with the Evidence: New Essays on Evidentialism"
"Believing in Accordance with the Evidence," published by Springer and edited by McCain, explores evidentialism, a major theory of epistemic justification, and contains more than 20 papers examining its nuances, challenges and future directions written by leading and up-and-coming epistemologists. The book includes insightful discussion on such issues as the ontology of evidence, phenomenal dogmatism, how experiences yield evidence, the new evil demon problem probability and more.
"The Essential Guide to Interpersonal Communication"
Co-authored with department Professor Kelly Morrison, Ph.D., and published by Bedford/St. Martin's, "The Essential Guide to Interpersonal Communication" is the third edition of a brief and inexpensive supplemental text designed for combination with other guides for larger survey courses. The guide is up-to-date on today's interpersonal scholarship and includes experiential examples and quizzes to engage students in self-reflection.
Professor, Department of History
"Equipping James Bond: Guns, Gadgets and Technological Enthusiasm"
In "Equipping James Bond," Millard chronicles the hundred-year history of espionage technology through the lens of Ian Fleming's infamous character James Bond and his ingenious spyware. Beginning with the creation of MI6, the Secret Intelligence Service, Millard traces the development of espionage tech from 19th-century weaponry to the evolving threat of computer hacking and surveillance and describes how Bond transitions from protecting 1950s England from criminal activity to saving a world threatened by nuclear bombs, poison gas and attacks from space.
Associate Professor, Department of English
"Rhetoric and the Global Turn in Higher Education"
Drawing on an analysis of the way discourses of security, economy and ethics shape the rhetoric of global higher education and that of its populist and nationalist critics, "Rhetoric and the Global Turn in Higher Education" studies the role of rhetoric in the expansive movement for global higher education in the United States and will appeal to scholars and students of rhetoric and composition studies, communication and education plus faculty and administrators working in global higher education or internationalization programs.
Co-authored with department Professor Steve McCornack, Ph.D., and published by Bedford/St. Martin's, "The Essential Guide to Interpersonal Communication" is the third edition of a brief and inexpensive supplemental text designed for combination with other guides for larger survey courses. The guide is up-to-date on today's interpersonal scholarship and includes experiential examples and quizzes to engage students in self-reflection.
"Political Campaign Communication: Inside and Out"
Co-authored with retired political consultant J. Cowart, the second edition of "Political Campaign Communication," published by Pearson, examines the intricacies of political campaigning through the eyes of academia and political consulting. The book discusses theories and principles, political socialization and the roles of money, ethics and critical events.
Co-authored with Department of Communication Studies Professor Mark Hickson, Ph.D., and Assistant Professor Alan Franks, and published by Kendell Hunt, "#Media" is a comprehensive look at the history of mass media, from the beginning of writing to modern social media and includes discussion of the history of telegraphs, telephones, newspapers, film, radio and television.
Co-authored with Jonathan Amsbary, Ph.D., a fellow professor in the department, the second edition of "Interviewing in a Changing World," published by Routledge, can help students develop strong interview skills for various situations and contexts — from job interviews to persuasive interviews, performance and appraisal interviews and media interviews for radio, television, newspapers and political reporting, plus two full chapters on interview skills needed for qualitative and quantitative research.
Also co-authored with Amsbary, "Becoming John Wayne," published by McFarland & Co., explores the early westerns of screen star John Wayne, from his first starring role in "The Big Trail" to his breakthrough in John Ford's "Stagecoach." Powell and Amsbary trace the actor's transformation into the carefully crafted film persona that made him famous.
"Epigenetics in Human Disease"
The second edition of "Epigenetics in Human Disease," published by Academic Press, examines the diseases and conditions — such as cancer, autoimmune disorders and aging — researchers and clinicians know have epigenetic factors, plus diabetes, neurobiological disorders and cardiovascular disease, which are yielding exciting breakthroughs in the field. With its translational focus, "Epigenetics" will is a valuable reference for both scientists and clinicians.
Assistant Professor, Department of Psychology
"Social and Interpersonal Dynamics in Pain: We Don't Suffer Alone"
Trost's book "Social and Interpersonal Dynamics in Pain: We Don't Suffer Alone" is an international collaboration co-edited by Tine Vervoort, Ph.D., research professor at Ghent University in Belgium, Kai Karos, a doctoral student the Katholieke Universiteit Leuven in Belgium, and Kenneth Prkachin, professor emeritus of psychology at the University of Northern British Columbia. The book explores new research that acknowledges that pain occurs in a social context; while not a new concept in psychology or behavioral therapies, it is a newcomer to mainstream pain research. "Social and Interpersonal Dynamics in Pain" takes work from the top pain researchers studying these new developments and compiles it into one volume, designed to keep readers up-to-date on the trends.
Read more in the UAB Reporter.
"Peace Ethology: Behavioral Processes and Systems of Peace"
With contributions from experts representing a variety of scholarly fields, from philosophy to economics, "Peace Ethology," published by Wiley-Blackwell, offers social-psychological perspective on the causation of peaceful behavior, information on children's peacekeeping and peacemaking, ideas for overcoming social tensions for police and civilians and recent thinking on the behavioral science of peace. Written for students and academics of the behavioral and social sciences, the book explores the development, nature and current state of peace.
"Day Kink"
Co-authored with Cirque du Soleil's The Beatles LOVE show aerialist Tristan Allen Jih and published by Unicorn Press, "Day Kink" explores the unusual, small, out-of-place details of modern life, such as a mother impersonating Gene Simmons, or a suitcase dumped into a river. Reviewers have called its poems "memorials to those beloved suburban otherworlds" and the book a "freaky burlesque show."
"Out of Speech"
Grounded in technical mastery, the poems in "Out of Speech," published by LSU Press, explore themes of exile, family, disease, desire and isolation through 20th and 21st century painters such as Picasso, Hopper, Rothko, de Kooning, Warhol, Lichtenstein and Artschwager. Vines also explores characters set in present-day museums, such as a bored docent to a misinformed "explainer" of an artwork's meaning. By combining those two perspectives, "Out of Speech" provides insights into the complexity of being human.
Professor, Department of Chemistry
"Handbook of Thermal Analysis and Calorimetry: Recent Advances, Techniques and Applications"
The sixth edition of the handbook, co-edited with Hiroshima University's Nobuyoshi Koga, Ph.D., and the University de Rostock's Christoph Schick and published by Elsevier Science, covers recent advances in techniques and applications that complement earlier volumes. After recent years yielded tremendous progress in the field, "Handbook of Thermal Analysis" compiles 19 chapters on high-impact topics such as biomass conversion, sustainable polymers, nonmetallic glasses and phase change materials and provides a broad overview of recent progress in the field.
Professor and Chair, Department of Criminal Justice
"Foundations of Crime Analysis: Data, Analyses and Mapping"
Co-authored with the University of Arkansas' Grant Drawve, Ph.D., and published by Routledge, "Foundations of Crime Analysis" offers a theoretical and methodological introduction to crime analysis, covering its theoretical roots and development of the profession, pertinent statistical methods, spatio-temporal applications and the intersection of crime analysis and police work. It features case studies and specific examples and has a companion website with more resources for students.
Assistant Professor, Department of Philosophy
"Bennie Goes Up! Up! Up!"
Inspired by the adoption of the author's 5-year-old son, "Bennie," which is self-published, follows the adventures of Bennie and his dreams of soaring and reaching for the stars. The book is full of details not often present in popular children's literature; much like the real-life family that inspired them, the book's mother-son duo is unconventional, with her red hair and his dark skin. The goal of "Bennie" is to provide a more realistic depiction of the world the authors and illustrators saw daily — full of people with varied family structures, abilities and skin colors.
Published in Publications
Maligned brain cells get an overdue closeup in Parpura's 'Neuroglia'
New textbook by neurobiology professor, the first of its kind, details emerging role in Alzheimer's, Parkinson's, autism spectrum disorder and more.
Here's a playbook for stopping deadly cytokine storm syndrome
A new textbook by Randy Cron, M.D., Ph.D., the first of its kind, can help physicians diagnose and treat an often-puzzling condition with a host of causes.
Parcak's book offers a peek into a life spent in ruins
In her latest book, space archeologist and anthropology Professor Sarah Parcak reveals what it is like to be a scientist traveling the globe to study ancient civilizations and protect the world's ancient treasures.
Event Date July 18
Smith's 'How to Know the Flowers' explores natural dyeing, healing processes
English Instructor Jessica Smith wrote the book of poetry as she was leaving a job, helping a student learn to trust again, and discovering a new skill.
This past year, CAS faculty wrote books on everything from technology in James Bond fiction to globalism in higher education.
Madden-Lunsford's new book pays homage to her 'mountain mother'
"Ernestine's Milky Way" tells the story of a determined 5-year-old girl in the early 1940s, who sets off on a journey to deliver two Mason jars of milk to her neighbors in the holler.
Trost's new book puts cutting-edge pain research 'in a social context'
Psychology's Zina Trost and several international colleagues have compiled a valuable resource for clinicians, students and researchers studying the practice, management, processes and psychology of pain.


Are Teenage Truck Drivers the Answer to the Truck Driver Shortage?
Trucking groups are backing legislation (DRIVE Safe Act) that would allow truck drivers younger than 21 years old to cross state borders to help fill a driver shortage, as safety groups argue younger drivers are more likely to be involved in fatal accidents and that the bill's training requirements are inadequate.
Under the legislation, younger drivers would have to meet the requirements to obtain a commercial driver's license. Then, they would receive training that would include two probationary periods. While on probation they would be permitted to drive outside state lines only when accompanied by an experienced driver.
The teenage truck drivers would have to complete a 120-hour probationary period of "on-duty time," in which 80 of those hours must be spent driving. Then, they would have to undergo a second 280-hour probationary period when the teen would drive for a total of 160 hours.
Companies and organizations including UPS, the International Foodservice Distributors Association, and American Trucking Associations (ATA) support the legislation, referred to as the DRIVE Safe Act, because of the additional training, and argue it would expand the recruitment pool to help alleviate a truck driver shortage.
ATA predicted last year the industry would lack about 50,000 truck drivers by the end of 2017 and 174,000 drivers by 2026 if current trends continue.
The group also has argued that over the next 10 years, 890,000 new truck drivers must be brought into the industry, given certain factors such as retirement, retention and demand.
However, safety groups such as Advocates for Highway and Auto Safety are fighting the legislation because younger drivers are more likely to be involved in fatal crashes. In 2015, drivers between the ages of 16 and 19 were nearly three times more likely to be involved in a fatal accident than those older than 20, according to the Insurance Institute for Highway Safety.
Peter Kurdock, director of regulatory affairs at Advocates for Highway and Auto Safety, also said that drivers of large trucks between the ages of 19 to 21 were six times more likely to be involved in fatal accidents compared to the overall rate for all truck drivers, according to a 1991 study that was published in the public health journal Accident Analysis & Prevention. Those under the age of 19 were four times more likely to be involved in fatal crashes than the overall rate.
Kurdock says the training requirements in the legislation are not adequate to ensure a new truck driver can properly operate a commercial motor vehicle, adding that they're not a substitute for experience and would not alleviate safety concerns.
"We are talking about significant public safety concerns with this bill," Kurdock said.
During the probationary training periods, teenage truck drivers must meet certain benchmarks, in which they are evaluated on matters including speed and space management, right and left turns, and night driving. But meeting the benchmarks is subject to the employer's satisfaction, which Kurdock said is cause for concern.
Additionally, Kurdock pushes back on claims the trucking industry is facing recruitment challenges. He says the industry actually is struggling to keep drivers.
Kurdock said he believes other truck driver groups will become vocal in opposing the legislation.
"I think you're going to hear from a lot of groups that have serious concerns with this bill," Kurdock said.
Truck drivers do horrible shifts, sometimes even 24-hour shifts in order to make send meet and are treated horribly by the industry and carriers. We have to do better and work together with drivers so as to not face a transportation and shipping disruption.


text:
\section{Introduction}
If the surface of a spherical liquid drop is briefly deformed, by a puff of air, for example, it vibrates, ringing at several different frequencies. The eigenfrequencies of these shape oscillations were determined by Lord Rayleigh,
\begin{equation}
  \sigma_T = \left(\frac{Tl(l-1)(l+2)}{\rho a^3}\right)^{1/2} \unit{rad \,s^{-1}},
\label{rayleigheq}
\end{equation}
where $T$ is the surface tension, $\rho$ is the density and $a$ is the radius of the spherical drop at rest \cite{rayleigh1879,lamb}.
By measuring $\sigma$, we can determine the surface tension of the liquid. Beaugnon et al. used diamagnetic levitation to measure $\sigma$ of the lowest order ($l=2$) mode of a diamagnetically levitated liquid droplet \cite{beaugnon01} and, recently, we used diamagnetic levitation to investigate dynamics of a spinning water droplet \cite{hill08}. A diamagnetically-levitated droplet is confined within a magnetogravitational potential trap \cite{berry97,simon00}. The trap acts as an additional cohesive force on the drop, perturbing its eigenfrequency spectrum. Beaugnon et al. observed the shift to higher frequency of the lowest-order $l=2$ mode, and determined an expression for the increase in terms of an enhanced effective surface tension \cite{beaugnon01}. However, their result cannot be generalized to the higher order modes. Here, we use diamagnetic levitation to measure the normal mode frequencies of a levitating drop, for $l\ge 2$. We derive an expression for the eigenfrequencies of a liquid droplet confined by the magnetogravitational potential trap and compare it with our measured frequencies. Our analysis points the way to achieving accurate measurements of surface tension using this non-contact technique. We also consider the effect on the eigenfrequencies of the shape of the potential trap and consider analogies with the vibrations of a model `star'.

\begin{figure}
 \includegraphics[width=85mm]{hill_eaves10_fig1_revised.pdf}
 \caption{Bottom: Magnetogravitational potential $U(x,z)$ of a water droplet levitated by the magnetic field $B(x,z)$ of a vertical-bore superconducting solenoid magnet (contours at $\Delta U/g$ = 0.05~mm intervals); $x$ and $z$ are radial and vertical cylindrical coordinates, respectively, with origin at the geometric center of the solenoid. The field at the center of the solenoid is $B_0 = B(0,0) = 16.5\unit{T}$.  The field profile $B(x,z)$, used to construct the plot, was computed by numerical integration of the Biot Savart integral. The stable levitation point at a local minimum in the potential is labeled $L_0$. An unstable levitation point at a saddle-point in the potential is labeled $L_1$. Top: schematic of the experimental set-up. The magnetic field lines are shown in gray. Rays are shown as bold lines.}
\label{f1}
\end{figure}

\section{Experimental details}
\label{experimental_details}
We use a vertical-bore superconducting solenoid magnet with a room-temperature, 50~mm diameter bore to levitate droplets of water with radii $\sim 1 \unit{cm}$.  The droplets levitate approximately 80~mm above the geometric center of the solenoid, where the diamagnetic force, proportional to $B\nabla B$, is equal in magnitude to, and opposite in direction to, the gravitational force on (i.e. the weight of) the droplet \cite{berry97,simon00}. The magnetic field is $B\approx 12\unit{T}$ and the vertical field gradient is $\partial B/\partial z \approx 120\unit{Tm^{-1}}$ at the levitation  point.

\Fig{f1} shows a spatial map of the magnetogravitational potential
\begin{equation}
U(x,z) = gz - \frac{\chi B^2(x,z)}{2\rho \mu_0}
\label{magnetogravitationalpotential}
\end{equation}
of a unit mass of water in the potential trap, where $x$ and $z$ are radial and vertical cylindrical coordinates with origin at the geometric center of the solenoid coil, $\chi= -9\ten{-6}$ and $\rho=1\ten{3} \unit{kgm^{-3}}$ are the SI volume magnetic susceptibility and density of water respectively, and $g=9.8\unit{ms^{-2}}$. The center of the levitating droplet coincides with the position of the stable levitation point $L_0$ at the center of the trap, as shown. (There is a second point of unstable levitation $L_1$, at the saddle point in $U$, as shown in \fig{f1}. However, this point is not useful for these experiments, and so we do not discuss it further here.) The net force on a unit mass of water, $\bm{\Gamma} = -\nabla U$, is zero at the levitation point. The equilibrium shape of a liquid with no surface tension follows the contours of $U$, as demonstrated recently, using liquid H$_2$ close to the critical point \cite{lorin09}. For water droplets with $a\sim 1\unit{cm}$, however, the surface tension dominates the magnetic and gravitational forces on the drop, so that its equilibrium shape is nearly spherical.

The shape of the magnetogravitational potential trap can be altered by adjusting the current in the magnet solenoid coils. A convenient measure of the current is the magnetic field at the geometric center of the solenoid, $B_0 = B(0,0)$. The field $B(x,z)$ is everywhere proportional to $B_0$. To levitate water requires $B_0 \approx 16-17 \unit{T}$ using our magnet. \Fig{f1} shows the $U(x,z$) for $B_0 = 16.5\unit{T}$. The field profile $B(x,z)$ of the magnet, used to construct this plot, was computed by numerical integration of the Biot Savart integral, using a thin-shell approximation for the current density in the solenoid.

We expand the potential $U$ in a multipole expansion about $L_0$:
\begin{equation}
U(r,\theta) = \sum_{j\geq0} c_j(r) P_j(\cos\theta),
\end{equation}
where $r$ and $\theta$ are spherical coordinates with origin at $L_0$; $\theta$ is the polar angle (i.e. $r \sin \theta = x$). Only the derivative of $U$ normal to the droplet's surface (i.e. the radial component of the force) influences the eigenfrequencies of the normal modes,
\begin{equation}
\label{multipolederivative}
\Gamma_r(r,\theta)=-\frac{\partial U(r,\theta)}{\partial r} = \sum_{j\geq0} c_j'(r) P_j(\cos\theta),
\end{equation}
where $c_j'=\partial c_j/\partial r$. By adjusting $B_0$, we reduce the quadrupole component until it is small compared to the spherically-symmetric component ($c_2' \ll c_0'$). The octopole harmonic ($c_3'$), which cannot be reduced this way, remains comparable to $c_0'$. All other harmonics are small compared to $c_0'$. We shall return to discuss these points further in \sct{nonspherical_potential}.

 \fig{f1}, top, shows a schematic diagram of the water droplet levitating in the vertical magnet bore.  The droplet at rest is close to spherical; we measure the ratio of the equatorial (horizontal) diameter to the polar (vertical) diameter to be $1.00\pm0.02$.  An optical fiber directs light from a HeNe laser at the droplet. The drop focuses the light onto the aperture of a second fiber, which transmits the light to a photodiode outside the magnet. The EMF of the photodiode is measured by a storage oscilloscope. A 1~mm-diameter nozzle, directed at the center of the underside of the droplet (see Fig. 1), is connected to a rubber bulb outside the magnet by a tube. When the bulb is struck on a hard surface, the resulting pulse of air from the nozzle excites several shape oscillation modes simultaneously, with amplitude $< 0.05 a$. Since the focal length of the drop depends on its shape, the intensity of the laser light falling on the photodiode oscillates as the drop vibrates. The temperature of the water was brought to $16^{\circ}$C in a water bath before it was injected into the potential trap, to match the ambient temperature in the magnet bore. At this temperature, the density of the liquid is $\rho = 999 \unit{kg m^{-3}}$, its surface tension is $T = 73.3 \unit{mNm^{-1}}$ and its kinematic viscosity is $\nu = 1.11 \ten{-6}\unit{m^2s^{-1}}$ \cite{lemmon}. The liquid was injected into the trap using a glass pipette. The volume of liquid injected was determined to better than $1\%$ uncertainty from the difference in the weight of the pipette before and after injection. The liquid was drawn out of the bore using a paper towel, by capillary action, after the experiment. By measuring the difference in weight between the wet and dry paper, we obtained a second measurement of the droplet volume. Using this simple and accurate technique, we were able to determine that the mass loss through evaporation of the drop, during the measurement period (approximately 30-60 minutes), was always less than $2\%$. Experiments were performed both in air and in dry nitrogen gas (by filling the bore with N$_2$ from a pressurized gas cylinder). The air experiments were performed at $B_0=16.2 \unit{T}$  and the nitrogen experiments at $16.5 \unit{T}$. The reason for the different $B_0$ may be explained by the oxygen content of the air, which, being paramagnetic, buoys up the droplet \cite{catherall05,catherall03} by an additional force $\bm{\Gamma}_{\mathrm{air}} = -\nabla U_{\mathrm{air}}$. Here, $U_{\mathrm{air}}=  \chi_{\mathrm{air}}B^2/(2\mu_0 \rho)$ and $\chi_{\mathrm{air}} = +3.7\ten{-7}$ is the volume magnetic susceptibility of air (S.I. units). The $c_2'$ component of $U + U_{\mathrm{air}}$ is minimized at $B_0=16.2 \unit{T}$. In nitrogen, the buoyancy force is negligible compared to the diamagnetic force, and $c_2'$ is minimized at $16.5 \unit{T}$ as shown in \fig{f1}.

\begin{figure}

\includegraphics[width=87mm]{hill_eaves10_fig2_revised.pdf}
 \caption
 {Bottom: photodiode voltage $\mathcal{E}$ measuring the shape oscillations of an $a=5.8 \unit{mm}$ water droplet. Center: power spectrum of the oscillations of an $a=5.8 \unit{mm}$ water droplet, as a function of oscillation frequency $f=\omega/2\pi$. Top: measured frequencies $f$ of the oscillation modes of water droplets with radii between $a=4.5\unit{mm}$ and $14\unit{mm}$, up to $l=16$. The broken lines show the Rayleigh frequency spectrum for a water drop, according to \eqn{rayleigheq}. The \emph{measured} frequencies (crosses) are slightly higher, by $\sim 1 \unit{Hz}$, due to the effect of the magnetogravitational potential trap.}
 \label{f2}
\end{figure}
\section{Results}
\Fig{f2}, bottom, shows the oscillations in the photodiode EMF $\mathcal{E}(t)$ developed by the light refracted through an $a=6\unit{mm}$ droplet; they decay exponentially with a time constant $\tau \sim 0.1-10\unit{s}$, dependent on $a$ and $l$, due to the viscosity of the water, i.e. $\mathcal{E}(t) = \sum_l \mathcal{E}_l \exp(i\omega_l t - t/\tau_l)$. The power spectrum of these oscillations is shown in \Fig{f2}, center. Several peaks are evident in this spectrum, corresponding to the $l=2$ to 7 Rayleigh modes of the drop. Peak 1 is due to a small oscillation of the droplet's center of mass of about $L_0$ (amplitude $\sim 1\unit{mm}$). The frequency of this peak is independent of $a$.
The upper panel of \fig{f2} shows the measured peak positions for different drops with radii between $a=4.5\unit{mm}$ and 14~mm; the broken lines show the Rayleigh frequency spectrum for a water drop, according to \eqn{rayleigheq}. Note that the measured frequencies are slightly \emph{higher}, by $\sim 1\unit{Hz}$, due to the effect of the magnetogravitational potential trap. We shall calculate this frequency shift in the following sections of the paper. Although small, it is important to be able to account for this shift, if the technique is to be used to obtain accurate measurements of surface tension, for example.

An estimate of the effect of viscosity on the frequency of oscillation can be obtained by calculating the ratio of the magnitude of viscous stresses to surface tension forces, $f\nu\rho/(TD^{-1}) = \ensuremath{\operatorname{Oh}}[2l(l-1)(l+2)]^{1/2}/\pi$, where $D = 2a$, $f=2\pi\omega$ and $\ensuremath{\operatorname{Oh}}$ is the Ohnesorge number \cite{lefebvre}. This ratio is much smaller than unity for the droplet sizes used in these experiments. This indicates that we can neglect the influence of viscosity on the oscillation frequencies as a small effect. For example, we expect the viscosity of the water to marginally lower the frequency $\omega$ of the $l=2$ mode of an $a=5\unit{mm}$ droplet by $(5\pm 1)\ten{-4}\%$, but this is a small reduction compared to the frequency increase resulting from the trapping potential. (We obtained these estimates by solving numerically the Chandrasekhar equation for the eigenfrequencies of a viscous drop \cite{chandra59, tang74}). The $\ensuremath{\operatorname{Oh}}$ number indicates that viscosity has a significant effect on the frequency of modes $l<20$ only for water drops smaller than $a \sim 10\unit{\mu m}$. The shape of the peaks in the power spectrum agrees well with the Lorentzian shape expected for an exponentially decaying oscillation, with half-width (HWHM) $\Delta \omega =1/\tau \approx \nu a^{-2}(l-1)(2l+1)$ given by the Chandrasekhar equation  \cite{chandra59, tang74}. (Since the power spectrum is the square of the magnitude of the Fourier transform of the oscillations, we compare the shape of the peak with the \emph{square} of the Lorentzian function).

\section{Spherical potential approximation}
We now consider the effect of a spherically-symmetric magnetogravitational potential well on the eigenfrequencies of the drop. We shall discuss the effects of additional harmonics in \sct{nonspherical_potential}. Our derivation follows Lamb's derivation of the Rayleigh frequencies \cite{lamb} closely, with the addition of the force $\Gamma_r$ on the droplet's surface due to the gradient of the magnetogravitational potential at the surface. We write the shape of the $l$th mode of a drop oscillating with frequency $\omega$, for oscillations with small amplitude $\epsilon$, as
\begin{equation}
r= R(\theta, t) = a + \zeta = a + \epsilon P_l(\cos\theta)\sin \omega t
\end{equation}
where $P_l$ is a Legendre polynomial of degree $l\ge1$ ($l=1$ corresponds to an oscillation of the droplet's center of mass in the potential trap).

The pressure equation at the surface of the droplet (to first order) is \cite{lamb}
\begin{equation}
   \left.\frac{\partial \phi}{\partial t}\right|_{r=a} = U(R) + \frac{p(R)}{\rho}+ F(t),
\label{pressureeqn}
\end{equation}
where $F(t)$ is an arbitrary function of $t$ only and $\phi$ is the velocity potential \cite{lamb}
\begin{equation}
   \phi(r,\theta) = -\frac{r^l}{la^{l-1}}\omega \epsilon P_l(\cos\theta)\cos \omega t.
\label{e3}
\end{equation}
The pressure difference across the surface resulting from the surface tension is \cite{lamb}
\begin{equation}
p(R) = T\left(\frac{2}{a} + \frac{\zeta(l-1)(l+2)}{a^2} \right).
\label{lambpressure}
\end{equation}
The magnetogravitational potential $U$ at the surface of the drop is (to first order)
\begin{subequations}
\begin{align}
U(R(\theta,t)) &= U(a) - \Gamma_r(a,\theta)(R-a)\label{potlexp2} \\
               &= U(a) - \epsilon \Gamma_r(a,\theta)P_l(\cos\theta) \sin(\omega t)\label{potlexp},
\end{align}
\end{subequations}
where $\Gamma_r(a,\theta) = -c_0'(a)$ for a spherically symmetric well (see \eqn{multipolederivative}). Inserting Eqns.~\ref{potlexp}, \ref{lambpressure} and \ref{e3} into \eqn{pressureeqn}, we obtain
\begin{equation}
\omega^2 = \sigma_T^2 + \sigma_0^2,
\label{measuredspherical}
\end{equation}
where
\begin{equation}
\label{sigma_gmag}
\sigma_0^2 = \frac{c_0'(a)l}{a}
\end{equation}
is the oscillation frequency (squared) of a hypothetical drop with $T=0$, held together by the magnetogravitational trap alone. The fact that the square of the \emph{measured} frequency $\omega^2$ is a simple sum of the square of the Rayleigh frequency $\sigma_T^2$ and $\sigma_0^2$ is due to the fact that
$l$ remains a good eigennumber for oscillations in a \emph{spherically-symmetric} potential well. In \sct{nonspherical_potential}, we will consider the effect of a non-spherical magnetogravitational well. In a non-spherical well, $l$ is not a good eigennumber in general, but for small deviations from spherical, we can use perturbation theory to obtain corrections to \eqn{measuredspherical}.

We can obtain an experimental measurement of $c_0'$ by examining the difference between the measured frequencies $\omega$ of any two of the modes $l,n\ge2$:
\begin{equation}
h_l\sigma_{0,n}^2-h_n\sigma_{0,l}^2 = h_l\omega_n^2 - h_n\omega_l^2,
\end{equation}
where $h_l=l(l-1)(l+2)$. Dividing by $(nh_l - lh_n)/a$, we obtain an experimental measurement of $c_0'(r)$ from the oscillations of a drop that has radius $a=r$ at rest:
\begin{equation}
\label{gmagmeasure}
c_0'(r) = r\frac{h_l\omega_n^2 - h_n\omega_l^2}
                 {nh_l-lh_n}.
\end{equation}
By using two measured frequencies, $\omega_l$ and $\omega_n$, rather than a single frequency, we obtain a measurement of $c_0'$ independent of the surface tension.
\begin{figure}
\includegraphics[width=82mm]{hill_eaves10_fig3_revised.pdf}
 \caption
 {
    Left panel: Gradient of the magnetogravitational potential trap $c_0'$ obtained from the measured frequencies of two modes, $l=2$ and $l>2$, of a drop with radius $a=r$ at rest. Error bars show the standard error. Filled circles: data obtained in nitrogen atmosphere. Open squares: data obtained in air atmosphere. Dotted line: $c_0'$ computed from the solenoid geometry. Right panel: dependence of the experimentally-obtained $c_0'$ on the mode number with $l>2$ (see text).
 }
 \label{f3}
\end{figure}
\Fig{f3} (left panel) shows the values of $c_0'$ that we obtain from the above `two-frequency' method using the lowest order mode $n=2$ and a second mode $l>2$. We use the $n=2$ mode since the corresponding peak in the power spectrum is always clearly resolved. We plot the mean of the values obtained for each mode $l>2$. Error bars (standard error) indicate the variation in the measured $c_0'$ obtained from different modes $l$. Filled circles and open squares show data obtained from a drop in a nitrogen atmosphere at $B_0=16.5\unit{T}$, and in air at $B_0=16.2\unit{T}$, respectively. The broken line on \fig{f3} shows the value of $c_0'(r)$ computed from the potential $U$ shown in \fig{f1} (i.e. from the geometry of the solenoid and the current $B_0$). This line is in reasonably good agreement with the experimentally measured values of $c_0'$, although the data points fall at slightly higher values. As an additional check of our method, we plot the dependence of the measured $c_0'$ on $l$ (right hand panel). If the trap-induced frequency enhancement that we measure experimentally is accurately given by \eqn{sigma_gmag}, then the $c_0'$ values that we determine by this method should exhibit no dependence on $l$. Although there is some scatter in the data due to experimental error, there is no clear dependence on $l$.

\section{Non-spherical potential}
\label{nonspherical_potential}
In the previous section, we assumed that the potential well was spherically symmetric around $L_0$. However, whilst we have chosen the field $B_0$ to minimize the quadrupole component of the trap, the octopole component remains significant, as can be seen clearly in \Fig{f1}. Thus it initially appears surprising that we can treat the well \emph{as if} it were spherical, in order to calculate its effect on the vibrations of the droplet's shape. (Had we determined an unphysical dependence of our measured $c_0'$ on $l$ in the previous section, it would also have followed that the spherical-well approximation was inadequate.) We now consider the effect on the eigenfrequencies of the drop of additional harmonic components $c_j'$ of the potential trap, and consider why, if the trap has a significant octopole component, the spherical well approximation is so effective at reproducing the measured frequencies of the droplet.

\begin{figure}
\includegraphics[width=82mm]{hill_eaves10_fig4_revised.pdf}
 \caption
 {
     Values of the $j=0$ (spherically-symmetric) and $j=2,3$ (quadrupole and octopole) coefficients $c_j'$ in a multipole expansion of the potential well gradient, \eqn{multipolederivative}, at $B_0 = 16.5 \unit{T}$ (in nitrogen atmosphere). Note, $c_1' = 0$ (see text). The values were determined from the magnetogravitational potential (\eqn{magnetogravitationalpotential}) shown in \fig{f1}. The $c_0'$ line is the same as that shown by the dotted line on \fig{f3}.
 }
 \label{figcoj}
\end{figure}

\begin{figure}
\includegraphics[width=82mm]{hill_eaves10_fig5_revised2.pdf}
 \caption
 {
   The three spheres show the computed magnitude of the vector $\bm{\Gamma}=-\nabla U$ on the surface of three droplets, radius $a=5.0\unit{mm}$, $7.5\unit{mm}$ and $10.0\unit{mm}$ at $B_0 = 16.5 \unit{T}$ (in nitrogen atmosphere); the length and direction of the radiating lines show the direction and magnitude of the (inward pointing) $\bm{\Gamma}$ at the surface; $\bm{\Gamma}$ was determined from the magnetogravitational potential (\eqn{magnetogravitationalpotential}) shown in \fig{f1}. The variation in $|\bm{\Gamma}|$ over the surface of the droplet is due to the octopole component of the potential trap.
 }
 \label{figspheres}
\end{figure}

We first discuss how close to spherical it is possible to make the potential trap; that is, how small the coefficients $c_j'$, $j>0$ can be made. Lorin and Mailfert have considered the relationship between the coil geometry (the distribution of the current density) and the shape of the potential trap \cite{lorin08}. Although we cannot alter the coil geometry, we can alter the coefficients $c_j'$ by adjusting the current flowing in the solenoid. The magnitude of the quadrupole component of the radial force $|c_2'|$ is smallest (for our magnet) at $B_0=16.2\unit{T}$ in air, and at $B_0=16.5\unit{T}$ in nitrogen gas; at this field, $|c_2'| \ll |c_0'|$ and only weakly dependent on $r$. Increasing $B_0$ beyond this value gives a positive $c_2'$, increasing with $r$. Decreasing $B_0$ below this value gives a negative $c_2'$, becoming more negative with increasing $r$. The gradient of the octopole component $c_3'$, however, is of the same order as $c_0'$ and increases as $r^2$. This component is a feature of the magnetogravitational potential trap generated by a solenoid. It can be reduced slightly, by increasing $B_0$, but only at the expense of significantly increasing $|c_2'|$. Note that the dipole component of the trap $c_1$ is necessarily zero (hence $c_1'=0$ too), since the net vertical force on the droplet $F_z$ must be zero for levitation. Since $F_z$ is proportional to the difference between the mean surface potentials of its upper and lower hemispheres, i.e. $F_z \propto \int_0^1 |w| U(a,w) dw - \int_{-1}^0 |w| U(a,w) dw \propto \sum_j c_j \int_{-1}^1 w P_j(w) dw \propto c_1$, it follows that $c_1=0$, where $w=\cos\theta(=P_1)$. The harmonic components $j>3$, are small compared to both $c_0'$ and $c_3'$, in our system. \Fig{figcoj} shows the values of the $j=0$ and $j=2,3$ (quadrupole and octopole) coefficients $c_j'$ at $B_0 = 16.5 \unit{T}$ (for nitrogen atmosphere) computed from the solenoid geometry. The spheres in \fig{figspheres} show the computed magnitude of $\bm{\Gamma} = -\nabla U$ at the surface of three droplets, radius $a=5.0\unit{mm}$, $7.5\unit{mm}$ and $10.0\unit{mm}$. Radiating lines indicate the direction and magnitude of $\bm{\Gamma}$, which is directed toward the interior of the droplet. The variation in $|\bm{\Gamma}|$ over the surface of the droplet is due to the octopole component of the potential trap.

We now consider the effect on the droplet's eigenfrequencies of adding a harmonic component $c_j'$, $j\ge2$ to the potential trap. The analysis proceeds as above, however, we must now include higher order harmonics in the eigenfunction of the shape oscillation
\begin{equation}
r= R(\theta, t) = a + \epsilon \sin \omega t \sum_{l\geq1} b_{l}P_l(\cos\theta),
\label{shapegeneral}
\end{equation}
since $l$ is not, in general, a good eigennumber in a non-spherical potential. In principle, we should decompose the shape into spherical harmonics $Y_l^m$, since the degeneracy in $m$ is also lifted in a non-spherical potential (see \fig{eigenvalues}). However, our method of inducing shape oscillations in the droplet tends to excite only the axisymmetric shapes (i.e. with $m=0$), since the air jet is aligned along the solenoid axis. For this reason, we derive here the frequencies of the $m=0$ oscillations only (\eqn{shapegeneral}), which are sufficient to interpret the experimental results. We summarize the treatment of the general case $|m|\le l$ in the Appendix.

The velocity potential is
\begin{equation}
   \phi(r,\theta) = -\epsilon\omega\cos \omega t \sum_{l\geq1}b_{l}r^ll^{-1}a^{-l+1} P_l(\cos\theta).
\label{phigeneral}
\end{equation}
The magnetogravitational potential $U$ at the surface of the drop is (see \eqn{potlexp2})
\begin{equation}
   U(R) = U(a) - \epsilon \Gamma_r(a,\theta) \sin(\omega t)\sum_{l\ge1} b_l P_l(\cos\theta)
\label{potlexp3},
\end{equation}
where $-\Gamma_r(a,\theta) = c_0'(a) + c_j'(a)P_j(\cos\theta)$ in this case (see \eqn{multipolederivative}).
Inserting \eqn{potlexp3}, \eqn{shapegeneral} and \eqn{phigeneral} into \eqn{pressureeqn}, and equating the time-varying terms, we obtain
\begin{equation}
a\omega^2 \sum_{l\geq1}\frac{b_lP_l}{l} = \sum_{l\geq1}\left[(c_0'(a)+c_j'(a)P_j) +\frac{T}{\rho a^2}(l-1)(l+2)\right]b_lP_l.
\end{equation}
The product $P_lP_j$ appearing on the RHS of this equation can be expanded as a sum of Legendre polynomials \cite{adams1878}, which, for our purposes, is most conveniently written $P_lP_j=\sum_{p=|j-l|}^{j+l} Q(l,j,[j+l-p]/2)P_{p}$, in which \cite{adams1878}
\begin{equation}
  Q(l,j,s)=\frac{A(l-s)A(s)A(j-s)}{A(j+l-s)}\left(\frac{2j+2l-4s+1}{2j+2l-2s+1}\right)
\end{equation}
for integer $s$ and we define $Q(l,j,s)=0$ for half-integer $s$; $A(n) = 1\times3\times5\times\ldots\times(2n-1)/n!$. Equating the coefficients of $P_l$, we obtain
\begin{align}
\omega^2b_l &=  \frac{c_0'(a)l}{a}b_l + \frac{T}{\rho a^3}l(l-1)(l+2)b_l\nonumber \\
&  + \frac{c_j'(a)l}{a}\sum_{p=|j-l|}^{j+l} b_{p}Q(p,j,[j+p-l]/2).
\label{eigenvalueproblem}
\end{align}
This equation has the form of an eigenvalue problem $\omega^2b_l = H_{l\lambda}b_\lambda = (H^{(0)}_{l\lambda} + V_{l\lambda})b_\lambda$ (using the summation convention, $l\geq1$), where $H^{(0)}$, representing the first two terms on the RHS of \eqn{eigenvalueproblem} is a diagonal matrix and $V$, representing the third term on the RHS is not, in general, diagonal. Treating $V$ as a perturbation, the first order correction $(\sigma_j^2)^{(1)} =b_l^{(0)}V_{l\lambda}b_\lambda^{(0)}$ due to a harmonic component $j$ can be computed analytically to obtain the eigenfrequencies $\omega^2 = \sigma_T^2 + \sigma_0^2 + (\sigma_j^2)^{(1)} + \ldots$. For a quadrupole harmonic $j=2$ we obtain
\begin{equation}
  (\sigma_j^2)^{(1)}=\frac{c_2'(a)}{a}\frac{l^2(l+1)}{(2l+3)(2l-1)}.
  \label{firstorderquadrupole}
\end{equation}
For an octopole harmonic $j=3$, and all odd $j$, $(\sigma_j^2)^{(1)}=0$. This explains why our spherical-well approximation works so well in predicting the eigenfrequency spectrum of the droplet: we have minimized $c_2'$ by careful adjustment of $B_0$ and we expect, from the above analysis, that the effect of the octopole harmonic $c_3'$ (which is comparable to the spherically symmetric component $c_0'$) on the measured eigenfrequencies in our experiment, to be minimal. \Fig{eigenvalues} shows the eigenfrequencies determined by using a computer to solve the eigenvalue problem numerically (i.e. beyond first order). The eigenfrequencies of an $a=7.5 \unit{mm}$ droplet, for various $c_2'$ and $c_3'$, are shown (thick lines), along with the first-order result \eqn{firstorderquadrupole} for comparison (thin lines). In addition, we plot the eigenfrequencies of modes with $m\neq0$ (broken lines); the calculation of the frequency of these modes is outlined in the Appendix. The lower plot of \fig{eigenvalues} shows that the effect of the octopole harmonic $c_3'$ on the measured eigenfrequencies is minimal for all $m$ for $|c_3'|\lesssim 1$. For a quadrupole harmonic $c_2'$, the eigenfrequencies depend strongly on $m$, as shown in the upper plot of \fig{eigenvalues}. However, since we have reduced $|c_2'|$ to smaller than $\approx 0.05$ as described above, and since our method of exciting the oscillations tends to excite only the $m=0$ modes, this does not alter our explanation of why the spherical-well approximation works so effectively.

\begin{figure}
\includegraphics[width=87mm]{hill_eaves10_fig6_revised2.pdf}
 \caption{Top: Effect on the eigenfrequencies of an $a = 7.5 \unit{mm}$ water droplet of adding a quadrupole harmonic $c_2'$ to the shape of the magnetogravitational potential well ($c_0' = 0.36\unit{ms^{-2}}$, all other $c_j' = 0$). The thick black lines show the eigenfrequencies (squared) of the $m=0$ modes (i.e. the eigenvalues $\omega^2$ of \eqn{eigenvalueproblem}) corresponding to $l=1-5$; the eigenvalues of \eqn{eigenvalueproblem} were computed using MATLAB. (Note that we have plotted $\omega^2-\sigma_T^2$ for clarity). The thin lines show the first-order approximation, \eqn{firstorderquadrupole}, departing from the numerically-computed frequencies at $|c_2'|\gtrsim 1$. Long-dash,  medium-dash, short-dash, dot-dash and dotted lines show the frequencies of the $|m|=1-5$ modes, respectively (the treatment of the $m\neq0$ modes is summarized in the Appendix). Bottom: Effect on the eigenfrequencies of an $a = 7.5\unit{mm}$ water droplet of adding a harmonic $c_3'$ to the shape of the well ($c_0' = 0.36\unit{ms^{-2}}$, all other $c_j' = 0$).
 }
 \label{eigenvalues}
\end{figure}

\section{Discussion and Conclusion}
Although the forces at the droplet's surface are dominated by the surface tension, we can clearly observe the influence of the magnetogravitational potential trap on the eigenfrequencies. We have demonstrated that the effect of the trap on the eigenfrequencies closely approximates that of a spherically-symmetric potential well. Although the potential well has a significant octopole component in additional to the spherically-symmetric component, we have calculated that the effect of the octopole component on the eigenfrequencies is small and verified this experimentally. The small difference between the values of $c_0'$ calculated from the solenoid geometry and the measurement of $c_0'$ from the measured droplet oscillations, may be due to a small error in the calculated value: the calculation of the field profile $B(x,z)$, performed by numerical integration of the Biot-Savart equation, is based on a thin-shell approximation of the current density in the solenoid coils. We note that the discrepancy cannot be explained by the octopole component of the trap, since this only marginally reduces the eigenfrequencies (\fig{eigenvalues}), which would only \emph{reduce} the measured value of $c_0'$ slightly. Experiments have shown that nonlinear effects become significant for oscillation amplitudes greater than approximately $0.1a$ \cite{becker91}. In our experiments, however, the oscillation amplitude is smaller than this, and we do not observe these non-linear effects.

We have shown how to minimize the quadrupole harmonic of the potential trap, by adjusting the solenoid current. This allowed us to use the relatively simple formula \eqn{sigma_gmag} to calculate the effect of the trap on the eigenfrequencies. This opens up the possibility of using diamagnetic levitation to accurately determine the surface tension of diamagnetic liquids (for example, water, and many water-based and organic solutions): subtracting the contribution of the trap to the eigenfrequencies reveals the Rayleigh-frequency spectrum, from which the surface tension can be obtained directly.
A contactless measurement technique has many advantages, for example, the ability to measure highly reactive liquids and to achieve significant supercooling of the liquid, as demonstrated in experiments on electromagnetically levitated liquid metals \cite{egry95}. Acoustic levitation and the oscillating drop method can be used to measure surface properties of small drops (radius $<2\unit{mm}$) of water and organic liquids (e.g. \cite{trinh88, tian97}). Suspension of small drops in air-flow is also possible \cite{perez99}. However, since the equilibrium droplet shape is distorted significantly from spherical in both of these techniques, it is necessary to make accurate measurements of the equilibrium shape in order to correct for the distortion, which introduces additional significant experimental uncertainty \cite{trinh86,trinh88,tian97,perez99}. Drops can be bounced on a solid surface or a vibrating liquid bath, the drop and surface being separated by a thin layer of air \cite{couder05,gilet07}. In this case, the eigenfrequency spectrum deviates from the Rayleigh spectrum due to the periodic forcing by the oscillating surface \cite{dorbolo08,courty06}. An expression, similar to Rayleigh's, for the eigenfrequencies of vibrating drops in continuous point-contact with a surface, has been determined \cite{courty06} but there remains some uncertainty over the spectrum of bouncing drops \cite{courty06}. Although free-fall can be used to obtain the Rayleigh frequencies directly (for example, in a drop-tower \cite{matsumoto02}), we have shown how diamagnetic levitation could offer an alternative, accurate method of measuring these frequencies; the levitated droplets are near-spherical at rest and the eigenfrequency spectrum is very close to Rayleigh's, as shown in \fig{f2}. The relatively small shift to higher frequency due to the potential trap can be obtained using a simple spherical-well approximation, \eqn{sigma_gmag}. Diamagnetic levitation can levitate cm-size drops (up to $\approx 3$ cm-diameter in our magnet) \cite{beaugnon01,hill08,liu10} enabling the droplet volume to be measured easily and precisely. Currently, there is interest in the temperature dependence of the surface tension of supercooled water \cite{lu06}. The lowest-temperature achieved so far, which used a contact technique, is 245~K \cite{floriano90}; nucleation sites on the container walls trigger freezing before colder temperatures can be reached. We propose that diamagnetic levitation and the oscillating drop technique could be used to obtain measurements of surface tension at temperatures less than 245~K.

It is interesting to consider an analogue between the oscillations of the levitating droplet and that of an object in a gravitational field. We can consider the magnetogravitational force on a unit mass of water, $\bm{\Gamma} = -\nabla U$,
as being an effective gravitational field acting on the liquid. Reid has obtained an expression for the eigenfrequencies of a gravitating body composed of a solid spherical core, radius $R_1$ and density $\rho_1$ covered by an inviscid liquid `mantle' of radius $R_2$, density $\rho_2$ \cite{reid59} (see also Ref. \cite{dolginov84}):
\begin{equation}
\label{reid}
\sigma^2 = \frac{4}{3}\pi G \bar{\rho}l(l+1)\frac{1-\eta^{2l+1}}{1+l(1+\eta^{2l+1})}\left(1-\frac{3}{2l+1}\frac{\rho_2}{\bar{\rho}}\right),
\end{equation}
where $\eta=R_1/R_2$, $\bar{\rho}=\eta^3\rho_1+(1-\eta^3)\rho_2$ is the mean density and $G$ is the gravitational constant. Interestingly, Reid's expression becomes equivalent to \eqn{sigma_gmag} if we let $\rho_2\rightarrow 0$ and $R_1\rightarrow 0$, since this allows the surface effective gravity $\Gamma(a)$ to be equated with a fictitious point mass $m=(4/3)\pi a^3 \bar{\rho} = \Gamma(a)a^2/G \sim 1\ten{8}\unit{kg}$ (approximately the mass of 1~mm$^3$ of nuclear-density material). In this sense, we can view our magnetically-levitated droplet as a `toy model' of an incompressible gravitating body (possessing surface tension), composed of a small-diameter, massive core (the fictitious mass), and a low density outer region (the water). Note that this result differs from that of a \emph{uniform-density} self-gravitating body, $\sigma_G = [(8/3) \pi G \rho
l(l-1)/(2l+1)]^{1/2}$ \cite{kelvin1863}. Bastrukov has recently obtained a similar spectrum for a self-gravitating liquid droplet with radially-varying density distribution $\rho(r<a) \propto 1/r$, having a singular density at the center \cite{bastrukov09}.

By adjusting the current in the magnet (i.e. $B_0$) we can change the quadrupole ($c_2'$) component of the trap. Although we have sought to minimize this component in this paper, it would be interesting to investigate the effect of this quadrupole component on the oscillation frequencies experimentally and compare it with the result we derive above. Unlike the odd harmonics, the even order harmonics have a significant effect on the eigenfrequencies to first order. Using the analogy with a model `star', adding a quadrupole component to the effective gravity $\bm{\Gamma}$ is equivalent to deforming the shape of the core mass from spherical to oblate, perhaps due to rotation, for example.

This project is supported by a Basic Technology Grant from EPSRC, UK; Grant Nos. GR/S83005/01 and EP/G037647/1.

\section{Appendix}
We consider the effect of a trap component $c_j'$ on an arbitrary shape oscillation
\begin{equation}
r= R(\theta, \Phi, t) = a + \epsilon \sin \omega t \sum_{l\geq1} \sum_{m=-l}^{l}b_{l}^m Y_l^m(\theta,\Phi).
\label{shapegeneralA}
\end{equation}
The corresponding velocity potential is
\begin{equation}
   \phi(r,\theta,\Phi) = -\epsilon\omega\cos \omega t \sum_{l\geq1} \sum_{m=-l}^{l} b_{l}^m r^ll^{-1}a^{-l+1} Y_l^m(\theta,\Phi).
\label{phigeneralA}
\end{equation}
Inserting \eqn{shapegeneralA} and \eqn{phigeneralA} into \eqn{pressureeqn}, and equating the time-varying terms, we obtain
\begin{equation}
a\omega^2 \sum_{l\geq1}\sum_{m=-l}^{l}\frac{b_l^m Y_l^m}{l} = \sum_{l\geq1}\sum_{m=-l}^{l}\left[(c_0'+c_j'P_j) +\frac{T}{\rho a^2}(l-1)(l+2)\right]b_l^m Y_l^m.
\end{equation}
The product $Y_l^m P_j = N_l^m e^{im\Phi}P_l^m P_j^0$ can be expanded as $N_l^m e^{im\Phi}\sum_{p=|j-l|}^{j+l} Q(0,j;m,l;p)P_p^m$, where the $Q$ in this case are Gaunt coefficients, as defined in Ref. \cite{cruzan62}, $P_l^m$ are associated Legendre functions and $N_l^m$ are the corresponding normalization factors. Equating the coefficients of $Y_l^m$, we obtain $2l+1$ eigenvalue problems, i.e. one for each $m$, similar to \eqn{eigenvalueproblem}.

redpajama_set_name: RedPajamaArXiv


text:
This Pro-Anorexia Sweater Being Sold On Amazon Is Problematic On So Many Levels
By Claire Warner
This post has been updated with inclusion of a statement from the National Eating Disorders Association.
Do you have an utter lack of empathy and $30 burning a hole in your pocket? Then the "Anorexia Styling Hoodie" sold on Amazon is the sweatshirt for you. No longer do you have to pretend to be a decent person. Wear this hoodie, and people will understand on sight that you prefer making lame, tasteless "jokes" to sympathizing with another person's mental health struggles. Now that is a fashion statement — although it's one not worth making. (Bustle has reached out to Amazon regarding the hoodie, and the company is declining to comment at this time.)
Allow me to explain. Recently, a vendor called AruturoButch began selling the aforementioned hoodie on Amazon. Sold for $26 to $30 depending on size, the simple black sweatshirt is emblazoned with a definition for anorexia you won't find in any psychology textbook. "Anorexia: Like bulimia, except with self-control," it reads in cheery pink font.
Here are some fun facts. According to the National Eating Disorders Association, an estimated 30 million Americans suffer from an eating disorder at some point in their lives. Anorexia nervosa, an eating disorder characterized by extremely low body weight and an intense fear of weight gain, has the highest mortality rate among eating disorders. In a 2005 study following anorexia patients over the course of years, suicide was the most common cause of death among those who died during that time.
Meanwhile, according to the National Eating Disorder Association, the binge-and-purge cycle of bulimia can cause ulcers, inflammation, tooth decay, and electrolyte imbalances leading to heart failure. To put it simply, eating disorders can seriously harm or even kill people — they're not a laughing matter.
"Jokes about eating disorders are dangerous and cliché," said Claire Mysko, CEO of the National Eating Disorders Association, in a statement. "This hoodie propagates the myth that eating disorders are trivial and mere issues of willpower or self-control. Stereotypes like this result in increased stigma and are barriers that prevent people from seeking help. Anorexia is not a 'lifestyle choice,' it is a mental health disorder with socio-biological influences. We ask that Amazon stand with those affected by these deadly illnesses and remove the sweatshirt from their store."
So is the sweatshirt the work of a troll? Someone who suffers from an eating disorder of their own and lost perspective? Judging from the seller's other wares, which include a T-shirt proclaiming the belief in "bros before hoes [sic]," it might just be someone with a fundamental misunderstanding of the meaning of humor. No matter their reason for creating the hoodie, one thing is clear: People are not happy with its existence.
Speaking to the BBC, psychotherapist Dr. Susie Orbach said the hoodie could "make people feel really awful" when they're "already anguished enough." At its core, the problem with the sweatshirt is that it implies that anorexia is somehow "better" than bulimia — that people who live with it are made of sterner stuff than people with other disorders. Not only does this affirm anorexia, but it could also make people with bulimia feel they aren't sick enough. In a society that already pressures people to attain physical perfection, that kind of message can prove literally dangerous.
Online, people have begun calling for Amazon to remove the sweatshirt from sale.
The item's reviews are currently (and understandably) abysmal. Almost all give the sweatshirt one star, focusing on its insensitive message. "This is in poor taste. Anorexia is a serious disorder that should not be trivialised on tasteless merchandise like this," wrote one reviewer.
Another said she had personal experience with an eating disorder, and she found the sight of the hoodie infuriating:
"Are you kidding me? Anorexia isn't a joke, and it's certainly not something to smugly celebrate over BULIMIA. People DIE from this disease. I have this disease. It's taken me a lifetime to learn how to live with it and fight it and get over it. Remove this immediately, you're just inviting more girls to go down the horrible spiral that is eating disorder. How. Dare. You."
However, some have defended the sweatshirt, pointing out that nobody who finds it offensive will be forced to buy it.
Amazon has come under fire for its sellers' wares before. In 2013, it removed a T-shirt with the slogan "Keep Calm and Rape a Lot," albeit after several hours of public backlash.
As of Tuesday afternoon, the anorexia hoodie is still in stock online, and the longer it remains available, the more lives it might affect. Maybe someone should make a hoodie defining the word "humor" for the seller.


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"Travel, in the younger sort, is a part of education; in the elder, a part of experience," -Sir Francis Bacon. I estimate myself to be straddling those two worlds. In late December/ early January, I hopped a plane to Dublin alone and spent a few weeks traveling up to Northern Ireland and then making my way down the west coast. The purpose of this trip was an ambiguous cocktail of pleasure and business. I have long considered applying for a Fulbright Scholarship to spend a year in Ireland devising a piece about Irish history, dance and language. My solo journey allowed me to make more connections than I ever could have anticipated and I find myself in an excellent position to begin the daunting task of completing a Fulbright application.
Did you know I also photograph and travel write? It's true. Check out my newest endeavor down this route here: Off The Beaten Sidewalk.


text:
Matt Fanta Joins Wilbur-Ellis to Lead Nutrition Division, as Andrew Loder Retires
Wilbur-Ellis
October 22, 2021 | News, Nutrition, Press Releases
SAN FRANCISCO – October 22, 2021 – Wilbur-Ellis announced today that Matt Fanta has been named President of its Nutrition division, with the retirement of Andrew Loder.
Wilbur-Ellis President and CEO John Buckley said, "Matt is an experienced leader, having spent over 25 years at Land O'Lakes, with the last 10 years in a variety of senior roles. I'm very pleased that Matt is joining Wilbur-Ellis as we continue to grow and develop the animal nutrition business. With his outstanding leadership skills and extensive background in agriculture, I'm excited about what's to come in the Nutrition division."
Most recently, Fanta was Vice President of Marketing in the Purina Animal Nutrition division at Land O'Lakes. He also served in senior positions in the global dairy ingredients division and the alfalfa seed and technology business, along with leading the Asia-Pacific region. In 2009, Fanta was the recipient of the distinguished Twin Cities 40 Under 40 Award, which recognizes leaders who have accomplished much in their professional lives while giving back to the Minneapolis-St. Paul communities. Fanta holds a Bachelor of Science degree from the University of Wisconsin, River Falls, and an MBA from the University of Minnesota.
"I'm honored to be joining Wilbur-Ellis," Fanta said. "The company and its Nutrition business are well-known for their integrity, industry leadership, and innovation that is squarely focused on creating value for customers. I'm proud to be part of such a sustainable, high-performing organization."
Buckley also wished Andrew Loder well on his retirement, saying: "During his tenure, Andrew strengthened the Nutrition business, enabling it to become the high-performing organization it is today. He oversaw key acquisitions, including Ameri-Pac, Rangen and, most recently, Ametza, to name just a few of his accomplishments. Andrew will be greatly missed at Wilbur-Ellis, but we wish him all the best as he begins this new phase of his life."
About the Wilbur-Ellis Companies
Founded in 1921, the Wilbur-Ellis companies are leading international marketers, distributors and manufacturers of agricultural products, animal nutrients and specialty chemicals and ingredients. By developing strong relationships, making strategic market investments and capitalizing on new opportunities, the Wilbur-Ellis companies have continued to grow the business with sales of over $3 billion. For more information, please visit www.wilburellis.com