This website is designed and developed by Tony Scott on an ongoing basis using the WordPress publishing platform, with further expansion planned for the future.
Tony is a freelance web designer and developer – he's also the co-ordinator of WPUK.
Tony's activities on the internet started before Tim Berners-Lee's first web server going online in 1991.
In 1995 he became involved in the joint BECTU and NUJ project Media Unions along with Mike Holderness and Tony Lennon.
In 1997, in conjunction with Tony Lennon, he built bectu.org.uk, one of the first union sites in the UK.
The two Tonys continued to develop the BECTU site and generate content for the following 12 years.
From 1993 to 2007 Tony worked at BBC Television Centre as a Lighting and Vision Controller, and before that as a Lighting and Vision Assistant for five years.
He contributed to all the shows produced for network television, everything from Top of the Pops to Grandstand.
Tony was based at Lime Grove Studios London from 1986 to 1988, then the BBC Current Affairs Production Centre, which included working as part of the camera crews on the early days of breakfast television.
Following graduation Tony joined the BBC in 1981, based at Manchester working in studio and outside broadcast cameras.
Find out more about Tony on his website and LinkedIn profile.


In a Large part of the United States it is against the law to own any wildlife, because of the diseases they carry. Below are listed some of the more common diseases that can be contracted by humans and animals.
Here is a link to the United States Center for Disease Control (CDC) with additional information.
Often the symptoms look like the flu. Once the symptoms develop it is too late and is nearly always fatal. We know rabies is a serious issue. Here is a list of common carries in our area: bats, raccoons, foxes, mice, rats, dogs, cats, and coyotes. If your concerned about an animal that may be rabid and what to do – give us a call!
This is a fungus! It is sometimes found growing in pigeon and bat droppings. If you have either or are concerned about health problems associated with histoplasmosis – give us a call we can help!
Raccoon roundworm is not often found in humans but when it is it can be bad especially if it invades the eye, organs, or brain. Cleanup procedures, and complete information about raccoon roundworm can be found on our species page.
Rodents and Rodent problems in an attic can be worse than you think! Histoplasmosis can be fatal, but can be avoided with proper cleanup. Again we recommend the CDC for complete information on hantavirus. If you do have a rodent problem, that your pest control guy cannot fix (he may just be treating with poison, rather than sealing your home) give us call. We work to eliminate your rodent problem for good.


Thrive Beijing is a lifestyle brand and online platform supporting and inspiring foreign young professionals living in Beijing.
Why We Started Thrive Beijing.
We believe that Beijing is the ultimate city for young professionals to Thrive. We started Thrive Beijing to highlight success stories and to connect foreign young professionals to the resources, people and inspiration they need to get the most out of their Beijing experience. Read More.


Clothing - Respectful & appropriate for a co-ed camp during the summer in Colorado's Rocky Mountain high country. Daytime temperatures can rise to 70°-80°, but at night they can dip into the low to mid 40's. Afternoon mountain rain showers are possible. Bring long underwear, a warm jacket/pants, rain coat/pants, hat & gloves.
Shoes/boots suitable for working, climbing and/or hiking the many back-country trails. Sandals are not the best choice around camp.
Swim suits/River shoes. The river is CHILLY, but many guests enjoy its refreshing waters on a hot summer afternoon. Please do not bring your best swim suits... the mud in the river may discolor them.
Bedding. Mattresses are provided, but guests are asked to bring their own sheets/blankets or sleeping bag and pillow. Riverfront Cabins & WeatherPorts are NOT air conditioned/heated so plan accordingly. Cabins have 4 XL Twin beds (lower bunks) and 4 Twin beds (upper bunks). Weatherports have Twin beds and/or Full beds (each one has a different configuration).
Sunscreen/Sunglasses. It may not feel extremely hot, but it's certainly possible to get sunburned in the mountains!
Flashlights. Electricity is provided by a camp generator which is turned off at 10:30pm. Guests will want to have a flashlight with spare batteries in their cabin.
Life jackets. There is a river running through the middle of the camp. Depending on the time of the year, the river may be flowing quite rapidly. Parents will want to equip their young children with an appropriate life jacket.
Refillable Water Bottle. Hydration is very important, especially at high altitudes. We have plenty of fresh mountain well water so you will want to be sure to carry some with you at all times.
Snacks. Guests are provided three meals per day with some snacks available in the dining hall. Guests are welcome to bring their favorite snacks but we do ask that food not be kept in the sleeping cabins.
Musical Instrument. If God has gifted you with a talent for making music, we would love for you to share it with us at camp. You can't beat music & fellowship around a roaring camp fire!
Compact collapsible chairs for enjoying fellowship around the campfire.
Bible/Notepad/Pen. This is a Christian camp and the perfect setting for guests to "connect" with The Lord through His written word. Guests can "unplug" from the outside world since there is no cell phone reception or WiFi connection but we do have a camp phone and internet for special needs.
A sense of adventure! We encourage our guests to step outside of their comfort zones and explore God's magnificent creation!
At night, cabins are pitch black. We've found that a few glow bracelets placed around the cabin can provide just enough light to comfort little ones who are afraid of the dark.
Our camp is 45 minutes from "civilization" so you can't just "run to WalMart" or dash to the laundromat to do some laundry, so do your best to plan accordingly.
Weapons, drugs, tobacco, alcohol, illicit material or electronic video games.
Church leaders and parents are responsible for their team's/kids' safety and behavior.


DVD is quite an investment, one that needs an insurance policy. This is because the precious DVDs can be scratched, damaged, broken, or just lost. The best bet to avoid this is to back up DVDs to hard drive for archiving, and store all of the originals in a box for keeping them safely. And ripping DVD to MP4 format is a nice choice as it is perfectly compatible with major media players and portable devices.
Video formats have grown in leaps and bounds. MP4 would be one of the most popular video formats in the world. It is a container format, allowing a combination of audio, video, subtitles and still images to be held in the one single file. MP4 file supports multiple audio tracks. It can retain 5.1-channle surround audio that would be nice to switch the soundtrack as required. Secondly, MP4 owns a much smaller file size at the same quality compared with other formats. Simply speaking, it saves space and keeps quality well. Thirdly, MP4 are applied to more and more portable devices such as iPhone, iPad, iPod, Apple TV, Samsung, Huawei, PSP, and so on. Above all, backing up DVD to MP4 is quite a wise choice.
You maybe have tried to download free DVD to MP4 ripper, but always get error during the ripping process, some of them even can't load the DVD at all. What happened? This is down to the copy protection technologies adopted in the DVD movies. Is there a powerful DVD ripper that can rip DVD to MP4 successfully yet free of charge. The answer is YES.
There are many kinds of DVD rippers for Mac in the market, some of them are shareware while others claim free of charge but come with watermarks or anything that distracts users. Is it possible to get a safe and clean software with powerful functions? MacX DVD Ripper Mac Free Edition is a totally free DVD ripper for Mac which specializes in converting DVD to MP4 with customized settings. The conversion can be finished within a simple mouse click or menu selection. It also supports converting DVD to MOV, MPEG, iTunes for free on macOS. The output video quality and the ripping speed are all remarkable.
Users may get error when they rip commercial DVDs which are generally encrypted. The encryption technology will prevent the ripping software from digitizing DVD and the videos converted from DVDs might be out of order. Before you rip copy protected DVD, you need to break down the encryption. But the free DVD to MP4 converter features the ability to remove CSS, Sony ARccOS, UOPs, RCE, APS and Disney new copy protections without a hassle. What's more, it continuously upgrades to support the latest copy protections, thus movie fans would not miss the hot movies published by Paramount, Warner, etc.
Below is the step by step user guide that shows you how to rip DVD movies to MP4 format.
Step 1: Free Download the free DVD to MP4 ripper and launch it. Click to Load the DVD, ISO Image or Video_TS Folder. See how to convert Video_TS to MP4 video.
Step 2: Select the output format. Choose DVD to MP4 as output format. Besides, DVD to MP4, there are also DVD to FLV, DVD to MOV, DVD to MPEG, DVD to iTunes, DVD to Music.
Step 3. Choose the output destination, click to browse and choose where the output video will be placed.
Step 4. Start ripping DVD to MP4 by clicking Start button.
1. You can select the titles you want to convert by setting the start time and end time, or drag the bar under the preview windows.
2. Select audio track and language according to your language and needs.
3. Change profile and settings to adjust the video file size, video reslution, frame rate, etc.
MacX DVD Ripper Mac Free Edition is outstanding, but it could have been so much better. Therefore, here comes MacX DVD Ripper Pro, the advanced edition of this free DVD to MP4 ripper for Mac. The primary advantages of it lie in: 1. Update constantly to unlock copy protections of new movies on DVD.
2. Clone DVD to ISO image at 1:1 ratio, backup DVD full title to MKV, and copy DVD main title to a multi-track MPEG2 file.
3. Rip DVD to any formats for any devices, such as MP4, H264, MOV, FLV, MPEG, AVI, MKV, WMV for the latest iPhone (XS/XS Max), iPad Pro, Huawei, Samsung, PS4, Chromebook, etc.
Note: MacXDVD software calls for ripping DVD under the concept of Fair Use and does not encourage any illegal reproduction or distribution of copyrighted content. Please abide by the local DVD copyright law before doing it.
DVD to DivX: Cannot Rip Protected DVDs to DivX AVI? Fixed Here!


We are very pleased to offer this 2012 Toyota Highlander Limited in Black. This vehicle is in great condition, the front bumper has been protected by a 3M film, has no damage history reported on Carfax, and has had a remote start installed in the vehicle. Coming to us as an American vehicle, 68,659 Miles are on the odometer when we took it in, which converts to 110,495 km's driven. This is a top option on the market with it's high edition loadout, fantastic vehicle condition mechanically and cosmetically, Remote Start, and clean carfax history - inquire today!
This Highlander Limited comes with reconditioning history also documented and available for viewing. Our Porsche Certified Technicians have gone through the entire vehicle to ensure all servicing is up-to-date and the vehicle exceeds mechanical safety and quality standards. Vehicle is fully compliant with all AMVIC Mechanical Fitness Assessment regulations.
Competitive Financing and warranty options available. Ask us how we can get you approved today!


text:
Deconstructing the largest NHS hack ever
By Alex Bennett 2017-05-23T09:45:37.142Z
The UK's public health service was just one of the high profile targets affected by the WannaCry ransomware attack.
(Image credit: Image Credit: Marbury / Shutterstock)
The largest ransomware outbreak in history ripped through the UK's National Health Service. How did it happen and could it happen again?
On May 12 2017, the largest ransomware attack ever struck the NHS, knocking 40 hospitals offline and leaving 24 trusts without access to their computers. In an effort to regain access to these critical machines, NHS engineers continue to work tirelessly, days after the infection.
The Wanna Decryptor ransomware also struck organisations across the world, with Russia, India, Ukraine and Taiwan amongst the worst-affected countries. The situation escalates daily and latest reports link North Korea to the massive ransomware attack.
The UK's public health service was amongst the most high profile targets and the attack has engendered heated debates in the run up to a divisive General Election. As the situation unfolds, what happened and what can be done to prevent the NHS being attacked in the future?
How ransomware infected the NHS
The backstory reads like science-fiction. A secret Microsoft exploit affecting , known as ETERNALBLUE, believed to be developed by the NSA, was leaked by a hacking collective known as the ShadowBrokers (TSB).
On discovery of the ETERNALBLUE exploit, Microsoft released a security patch, but many organisations failed to update their computers accordingly. Plus, Windows XP and other unsupported operating systems did not receive this update.
The ransomware used to attack the NHS, known as Wanna Decryptor or Wannacry, was developed to combine the ETERNALBLUE exploit with a self-replicating virus, spreading the contagious ransomware across connected machines.
It's still unclear how the ransomware infected NHS networks. Most ransomware uses phishing emails to convince users to open and download malicious email attachments. However, recent evidence suggests that phishing emails are not entirely to blame.
The NHS has been denounced for using the outdated Windows XP operating system within its trusts, despite Microsoft discontinuing critical security patches in 2014 – including the patch needed to defend against Wanna Decryptor.
Continued use of the outdated XP operating system was highlighted as one of the factors that enabled the ransomware attack to spread so easily across the NHS. Experts also cited a lack of discipline in patching new versions of windows as a larger contributing factor.
The ETERNALBLUE exploit was well known. NHS Digital issued a patch capable of preventing the Wannacry ransomware through its cyber portal two months prior to the attack. It is understood that if this patch had been applied across every NHS trust, it would have prevented the Wannacry ransomware attack.
However, the real controversy centres on a lack of cyber security investment within the NHS. Phishing could have provided the ransomware with its vector of infection, but a lack of cyber security awareness and investment gave Wannacry free reign inside the NHS.
IT standards, including security, vary hugely across the organisation and some trusts do not have a single person responsible for IT sitting on their board. In 2013, when secretary of state for health Jeremy Hunt was briefed on security risks engendered by a lack of NHS IT standards, "Hunt never grasped the problem."
"Where bits and bytes meet flesh and blood"
NHS staff watched in horror as their computers were locked 'one by one' as the Wannacry ransomware took hold.
The ransomware locked down critical NHS computers, displaying nothing but a message from Wannacry's criminal architects. The ransom message contained detailed instructions on how NHS staff could pay to remove the ransomware, even recommending their victims to check the current value of Bitcoin before paying. Thoughtfully, a dropdown menu for language selection was also included.
Once the ransomware infected the machines, it then travelled across the NHS network, spreading from computer to computer, trust to trust and hospital to hospital. At this point computers which were not updated with Microsoft's ETERNALBLUE security patch were quickly compromised.
The ransomware attack left almost 40 hospitals without proper access to their computers, leading to cancelled appointments, diverted A&E services, doctors unable to work as well as cancellations to time-sensitive and life changing operations.
"Where bits and bytes meet flesh and blood" is a term coined by cyber security experts to signify a cyber attack in which physical harm is caused. Whilst no fatalities were reported as a result of the hack, a shutdown in critical NHS services has the power to devastate some of society's most vulnerable. Without proper security safeguards it is just a matter of time until bits and bytes meet flesh and blood.
As a result of one accidental hero, the ransomware spread is halted for now, but reports suggest the malware is spawning new, more aggressive versions.
Despite causing low financial and operational damage, the Wannacry attack remains a wakeup call, drawing attention to a critical lack of cyber security investment and awareness in the NHS.
Cyber security remains a shared responsibility, the recent WannaCry attack makes this clear. That the NHS was so susceptible to the attack, despite warnings from Microsoft and NHS digital shows that top-level employees either don't understand the risk or simply don't care.
Microsoft is now pointing the finger at governments for stockpiling vulnerabilities, like ETERNALBLUE. Instead of being responsibly disclosed, the exploit was leaked, giving Microsoft no warning and businesses even less.
This isn't the first time a government organisation has lost control of a stockpiled cyber exploit either and vulnerabilities stored by the CIA were recently revealed on WikiLeaks.
"Repeatedly, exploits in the hands of governments have leaked into the public domain and caused widespread damage," wrote Microsoft's Brad Smith. "An equivalent scenario with conventional weapons would be the U.S. military having some of its Tomahawk missiles stolen."
Blocking future ransomware attacks will require an investment in cyber security education, through industry recognised qualifications like GIAC's GCIH certification. Cyber security personnel, new computers and a better standard of networking security are also crucial.
This isn't something that can be fixed quickly, but until the UK's health service vastly improves its cyber security, these attacks will continue. This is not the end of Wanna Decryptor, it's an intermission.
Alex Bennett, Technical Writer, Firebrand Training
Image Credit: Marbury / Shutterstock

redpajama_set_name: RedPajamaCommonCrawl


Funny ways to answer the Phone now live on the website!
If you are looking to be incredibly bored I would highly recommend drag racing muffins.
Rock and Roll to early man means something completely different.
Bringing you insanely, or just insane, clever ideas since 35 b.c.


text:
Q: How rotate image and save it from JSP/Servlet page I was able to successfully use JQueryRotate to rotate my images in a JSP page.
However, the user now wants to have the ability to save the rotated image.
But from what I've gathered so far, it seems that it's not possible to do this client side. So I probably have to re-start from scratch.
Is it possible to do a rotate image with saving capability for images rendered in a JSP/Servlet?  If yes, how?
EDIT: By the way, HTML5 is out of the questions because my requirement is to still support IE9.

A: Well, just to sumarize. Using non-HTML5 browsers - no way to save the modified on the client side picture. In a modern browser - you could try to save a canvas containing the image. Also you could keep track of the css trasformation and, on demand, render trasformed image but this is server side and just will show rotated image, not save it. Other thing you could do is send the transformed image to the server when the user ask for saving operation, rotate/transform the image using image manipulation software/library on the server side and send the new image back to the client. This could work, for example php has some image libraries. BTW, some social sites share images but, I think, all the transformation if any (crop, cut, resize, rotate...) is made on the server, when the user upload the image and it is saved on the server. BTW (2) a time ago in a J2EE application we had to do something like this because of user requirement - save an image rendered in a browser to the client machine. Will try to rescue the idea and if there is something interesting will post it.
EDITED
Here is some code we made a time ago for saving screen captures:
import java.awt.AWTException;
import java.awt.Rectangle;
import java.awt.Robot;
import java.awt.image.BufferedImage;
import java.io.File;
import java.io.IOException;
import java.io.OutputStream;

import javax.imageio.ImageIO;

public class Screenshot {

    public Screenshot() {
    }

    public static void imageCapture(int left, int top, int width, int height, String outFileName, String imgFormat) {
        if (!outFileName.toUpperCase().endsWith(imgFormat)) {
            outFileName += "." + imgFormat;
        }
        try {
            Robot robot = new Robot();
            BufferedImage bi = robot.createScreenCapture(new Rectangle(left, top, width, height));
            ImageIO.write(bi, imgFormat, new File(outFileName));
        }
        catch (AWTException e) {
            e.printStackTrace();
        }
        catch (IOException e) {
            e.printStackTrace();
        }
    }

    public static void imageCapture(int left, int top, int width, int height, OutputStream outStream, String imgFormat) {
        try {
            Robot robot = new Robot();
            BufferedImage bi = robot.createScreenCapture(new Rectangle(left, top, width, height));
            ImageIO.write(bi, imgFormat, outStream);
        }
        catch (AWTException e) {
            e.printStackTrace();
        }
        catch (IOException e) {
            e.printStackTrace();
        }
    }

}

As you see we used java.awt. Set full file path or already prepared OutputStream to the file you want to write and then send back to the browser the image file. This approach has a disadvantage - if you have scroll, the parte out of the window (let say "scrolled out") will no be captured. Well in fact it has many disadvantages but that's all I have and you can make some research. Hope this helps.

redpajama_set_name: RedPajamaStackExchange


text:
The 1998 Conference USA men's soccer tournament was the fourth edition of the Conference USA Men's Soccer Tournament. The tournament decided the Conference USA champion and guaranteed representative into the 1998 NCAA Division I Men's Soccer Championship. The tournament was hosted by the University of South Florida and the final games were played at the USF Soccer Stadium.

Bracket

Awards
Most Valuable Midfielder:
Jeff Houser, USF
Most Valuable Forward:
Kevin Alvero, USF
Most Valuable Defender:
Ryan Schwaigert, Memphis
Most Valuable Goalkeeper:
Skip Miller, USF

References

External links

Conference USA Men's Soccer Tournament
Tournament
Conference USA Men's Soccer Tournament
Conference USA Men's Soccer Tournament

redpajama_set_name: RedPajamaWikipedia


Study Abroad Resources: information on general sites, official documents, countries, cultures, money, languages, health and safety, culture shock, using SU library resources abroad, and returning home.
Shepherd Faculty-led Study Abroad Opportunities - see the Study Abroad homepage for current opportunities and How to Choose a Study Abroad Program: Program Types.
ISEP: International Student Exchange Program: Shepherd works with WVU for ISEP programs.
You MUST consult with the Shepherd Study Abroad Office several weeks before applying.


Book an appointment online for any of our wide array of beauty services including, but not limited to, microblading, microdermabrasion, microneedling, dermaplaning, and brow, body + Brazilian waxing services, in The Maven District in the 9th south corridor of Salt Lake City.
Select your service, pick a day + time and enter your contact info. Easy as 1-2-3!


text:
set -e
set -o pipefail

. ./cmd.sh; . ./path.sh;

#(
#bash filter_data.sh  --cmd "$decode_cmd"  data/shadow.uem eval.uem exp/sgmm5_mmi_b0.1/decode_*shadow.uem_it*
#bash filter_data.sh  --cmd "$decode_cmd"  data/shadow.uem eval.uem exp_bnf/sgmm7_mmi_b0.1/decode_*shadow.uem_it*
#) &
#bash filter_data.sh  --cmd "$decode_cmd"  data/shadow.uem eval.uem exp/tri6*_nnet*/decode_shadow.uem*
#wait

(
bash filter_data.sh  --cmd "$decode_cmd"  data/shadow.uem dev10h.uem exp_bnf/sgmm7_mmi_b0.1/decode_*shadow.uem_it*
#bash filter_data.sh  --cmd "$decode_cmd"  data/shadow.uem dev10h.uem exp/sgmm5_mmi_b0.1/decode_*shadow.uem_it*
) &
bash filter_data.sh  --cmd "$decode_cmd"  data/shadow.uem dev10h.uem exp/tri6*_nnet*/decode_shadow.uem
wait

wait
exit

bash make_release.sh --dryrun false --dir exp/sgmm5_mmi_b0.1  --data data/shadow.uem --master dev10h.uem lang.conf ./release
bash make_release.sh --dryrun false --dir exp/tri6b_nnet  --data data/shadow.uem --master dev10h.uem lang.conf ./release
bash make_release.sh --dryrun false --dir exp_bnf/sgmm7_mmi_b0.1  --data data/shadow.uem --master dev10h.uem lang.conf ./release

bash make_release.sh --dryrun false --dir exp/sgmm5_mmi_b0.1 --extrasys "NEWJHU"  --data data/dev10h.uem --master dev10h.uem lang.conf ./release
bash make_release.sh --dryrun false --dir exp/tri6b_nnet --extrasys "NEWJHU"  --data data/dev10h.uem --master dev10h.uem lang.conf ./release
bash make_release.sh --dryrun false --dir exp_bnf/sgmm7_mmi_b0.1 --extrasys "NEWJHU"  --data data/dev10h.uem --master dev10h.uem lang.conf ./release

redpajama_set_name: RedPajamaGithub


A Bridal Gown Infographic You NEED to Pin Now!
I wanted to share some of my favorite bridal gowns and accessories for 2016 to fit every bride and budget. Shop the look book below by clicking the image. And even farther down is a great infographic that was sent my way that I thought you brides that are shopping for wedding gowns would find helpful. I think it could be helpful for all of you shopping for wedding gowns to become acquainted with the various styles, necklines, train lengths, and more. This is one to pin for sure!
And in case you need more wedding dress inspiration, you can follow me on Pinterest or follow my bridal board here. Also, I wrote how I found my dream wedding dress for WAY less here and my tips for finding your wedding dress here.
Artikel zu schreiben großartig, ich sehr viel mit dieser Sicht überein!
wow,the pictures are so beautiful. I love them.
Thank you for posting the infographic! I came across it on pinterest — so helpful for brides-to-be and consultants.
blogger. I have joined your feed and look ahead to in quest of extra of your wonderful post.


text:
Q: AVX2 VPSHUFB emulation in AVX In AVX there's only 128 bits PSHUFB
VPSHUFB xmm1, xmm2, xmm3/m128

and only AVX2 has the full PSHUFB for the whole 256 bits AVX registers
VPSHUFB ymm1, ymm2, ymm3/m256

How can this instruction be emulated efficiently with AVX intrinsics?
Also in this particular case, the source only has 8 elements (bytes) but those could be moved around within the full 32 bytes of the destination. So it's no problem for running just 2 x PSHUFB.
A problem I'm finding with VPSHUFB is it treats 16 (0x10) as 0, only 128 and up are filled with zero! (highest bit set) Is it possible to do it without adding compares and masking out?

A: As @MaratDukhan has noticed, _mm256_shuffle_epi8 (i.e. VPSHUFB for ymm-s) does not perform full 32-byte shuffle. As for me, it is quite a pity...
That's why in order to emulate it without AVX2 you can simply split each register into two halves, permute each half, then combine together:
//AVX only
__m256i _emu_mm256_shuffle_epi8(__m256i reg, __m256i shuf) {
    __m128i reg0 = _mm256_castsi256_si128(reg);
    __m128i reg1 = _mm256_extractf128_si256(reg, 1);
    __m128i shuf0 = _mm256_castsi256_si128(shuf);
    __m128i shuf1 = _mm256_extractf128_si256(shuf, 1);
    __m128i res0 = _mm_shuffle_epi8(reg0, shuf0);
    __m128i res1 = _mm_shuffle_epi8(reg1, shuf1);
    __m256i res = _mm256_setr_m128i(res0, res1);
    return res;
}

If you really want to fully shuffle the 32-byte register, you can follow approach from this paper. Shuffle each half with each half, then blend results together. Without AVX2 it would be something like that:
//AVX only
__m256i _emu_mm256_shuffle32_epi8(__m256i reg, __m256i shuf) {
    __m128i reg0 = _mm256_castsi256_si128(reg);
    __m128i reg1 = _mm256_extractf128_si256(reg, 1);
    __m128i shuf0 = _mm256_castsi256_si128(shuf);
    __m128i shuf1 = _mm256_extractf128_si256(shuf, 1);
    __m128i res00 = _mm_shuffle_epi8(reg0, shuf0);
    __m128i res01 = _mm_shuffle_epi8(reg0, shuf1);
    __m128i res10 = _mm_shuffle_epi8(reg1, shuf0);
    __m128i res11 = _mm_shuffle_epi8(reg1, shuf1);
    __m128i res0 = _mm_blendv_epi8(res10, res00, _mm_cmplt_epi8(shuf0, _mm_set1_epi8(16)));
    __m128i res1 = _mm_blendv_epi8(res11, res01, _mm_cmplt_epi8(shuf1, _mm_set1_epi8(16)));
    __m256i res = _mm256_setr_m128i(res0, res1);
    return res;
}

If you know for sure that only the lower half of reg is used, then you can remove lines for reg1, res10, res11, and remove comparison and blending. Indeed, it might be more efficient to stick with SSE and use 128-bit registers if you have no AVX2.
The general 32-byte shuffling can be significantly optimized with AVX2:
//Uses AVX2
__m256i _ext_mm256_shuffle32_epi8(__m256i reg, __m256i shuf) {
    __m256i regAll0 = _mm256_permute2x128_si256(reg, reg, 0x00);
    __m256i regAll1 = _mm256_permute2x128_si256(reg, reg, 0x11);
    __m256i resR0 = _mm256_shuffle_epi8(regAll0, shuf);
    __m256i resR1 = _mm256_shuffle_epi8(regAll1, shuf);
    __m256i res = _mm256_blendv_epi8(resR1, resR0, _mm256_cmpgt_epi8(_mm256_set1_epi8(16), shuf));
    return res;
}

Beware: code not tested!


Police banned a solidarity demo with the Palestinians that had been scheduled today noon in front of the Arab League HQ.
A handful of activists who showed up early (11:40am) in front of the Arab League HQ were soon surrounded by thugs, plainclothes State Security officers, who ordered them to leave. The activists had formed a delegation that was to get into the Arab League HQ to present a message to its secretariat, denouncing the League's (as always) weak response to the Israeli attacks.
Mohamed Waked, one of the activists present in the scene, told me the State Security officers intimidated and pushed nine activists inside the HQ, saying they could either get into the League's building swiftly to meet the assistant secretary general, or get into the prisoners' trucks. The police was very nervous, and did not want a crowd that can draw more attention of the people in the square. Waked, who was not part of the delegation, said he was pushed by the officers inside against his will. Others included, Kamal Abu 3eita, Mohamed 3abdel Quddos and Ahmad Rami, MB activist at the pharmacists' syndicate.
The activists were met by Ahmad Bin Hilla, 3amr Moussa's assistant. They protested their treatment by the police, but Bin Hilla said this was an "Egyptian internal affair� that the League did not want to intervene in. The activists presented him with a statement, denouncing the League's weak stand and lack of support for the Palestinians. Bin Hilla replied, giving them the expected we-are-doing-our-best diplomatic crap.
Meanwhile, small scattered groups of activists were trying to assemble in Tahrir, but were intimidated by the police, who threatened them with arrest, and were pushing them across the streets to disperse. The activists, mainly socialists and Nasserists from the Karama faction, were exponentially outnumbered by the police, who kept on shoving them all the way from Tahrir Sq to Tal3at Harb sq. The scene was bizarre, and reminded me of the Labor Day demo, where security intimidation against an exponentially outnumbered activists meant run for-your-life kinda situation. After being cornered in Tal3at Harb, around 20 activists decided to head to the Press Syndicate. They were marching in the street, and sometimes running, followed by at least 300 plainclothes security. Whenever any activist stopped walking, even to light a cigarette, battalions of security agents would start pushing him or her to move. The security also kidnapped Wael 3abass in Qasr el-Nil St, and kept him in custody for few minutes, before the rest of the activists assembled and started screaming and shouting till he was released. The same situation happened few minutes later with another activist from the Karama faction who raised Nasser's poster while walking. The activists decided then if they can't demonstrate or chant, the least they could do is to raise their hands up with V signs to attract attention of the public, as they ran for refuge at the press syndicate.
It was around 1:15pm that the CSF conscripts were moved to surround the syndicate, but did not bar those who wanted to get in. Under Cairo's burning July sun, 30 or 40 at best, activists stood with banners denouncing the US, Israel and Mubarak, waiving Palestinian flags, and chanting. They were joined by Kamal Abu 3eita and Mohamed 3abdel Quddos after they were "released� from the Arab League HQ.


text:
A Nation's Holy Land: Kazakhstan's Large-Scale National Project to Map Its Sacred Geography
Nikolay Tsyrempilov, Ulan Bigozhin, Batyrkhan Zhumabayev
History, Philosophy and Religious Studies Department
Sociology and Anthropology Department
This article focuses on the project Sacred Geography of Kazakhstan, launched in 2017 in Kazakhstan as part of the nationwide program Ruqani Zhangyru (Modernization of Spirituality). The officially stated goal of the project is to cultivate a sense of patriotism in the country's residents related to places and geographic sites that are important for the historical memory of independent Kazakhstan. The authors assume that the real goal of the project is national territorialization, or recoding of the semantics of space, by selecting, codifying, and articulating some symbols and practices, while leveling and "forgetting"others. The analysis, which is based on expert interviews and official documents, shows that this postcolonial process fits into the tendency toward ethnonationalization of Kazakhstan, in which discourse on the civil nation continues to be reproduced at the official level, while real activity is more focused on reinforcing the idea of Kazakhstan as the state of the Kazakh nation. The institutionalization of organizing and recoding the sacred landscape involves a wide variety of groups and actors. These factors may explain the success of the project in comparison to other projects being implemented under the Ruqani Zhangyru program.
Nationalities Papers
https://doi.org/10.1017/nps.2021.22
national territorialization
sacred geography
10.1017/nps.2021.22
Dive into the research topics of 'A Nation's Holy Land: Kazakhstan's Large-Scale National Project to Map Its Sacred Geography'. Together they form a unique fingerprint.
Sacred Geography Arts & Humanities 100%
Holy Land Arts & Humanities 78%
Kazakhstan Social Sciences 72%
geography Earth & Environmental Sciences 63%
land Earth & Environmental Sciences 36%
project Earth & Environmental Sciences 34%
Territorialization Arts & Humanities 21%
institutionalization Earth & Environmental Sciences 19%
Tsyrempilov, N., Bigozhin, U., & Zhumabayev, B. (Accepted/In press). A Nation's Holy Land: Kazakhstan's Large-Scale National Project to Map Its Sacred Geography. Nationalities Papers, 1-18. https://doi.org/10.1017/nps.2021.22
A Nation's Holy Land : Kazakhstan's Large-Scale National Project to Map Its Sacred Geography. / Tsyrempilov, Nikolay; Bigozhin, Ulan; Zhumabayev, Batyrkhan.
In: Nationalities Papers, 2021, p. 1-18.
Tsyrempilov, N, Bigozhin, U & Zhumabayev, B 2021, 'A Nation's Holy Land: Kazakhstan's Large-Scale National Project to Map Its Sacred Geography', Nationalities Papers, pp. 1-18. https://doi.org/10.1017/nps.2021.22
Tsyrempilov N, Bigozhin U, Zhumabayev B. A Nation's Holy Land: Kazakhstan's Large-Scale National Project to Map Its Sacred Geography. Nationalities Papers. 2021;1-18. https://doi.org/10.1017/nps.2021.22
Tsyrempilov, Nikolay ; Bigozhin, Ulan ; Zhumabayev, Batyrkhan. / A Nation's Holy Land : Kazakhstan's Large-Scale National Project to Map Its Sacred Geography. In: Nationalities Papers. 2021 ; pp. 1-18.
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abstract = "This article focuses on the project Sacred Geography of Kazakhstan, launched in 2017 in Kazakhstan as part of the nationwide program Ruqani Zhangyru (Modernization of Spirituality). The officially stated goal of the project is to cultivate a sense of patriotism in the country's residents related to places and geographic sites that are important for the historical memory of independent Kazakhstan. The authors assume that the real goal of the project is national territorialization, or recoding of the semantics of space, by selecting, codifying, and articulating some symbols and practices, while leveling and {"}forgetting{"}others. The analysis, which is based on expert interviews and official documents, shows that this postcolonial process fits into the tendency toward ethnonationalization of Kazakhstan, in which discourse on the civil nation continues to be reproduced at the official level, while real activity is more focused on reinforcing the idea of Kazakhstan as the state of the Kazakh nation. The institutionalization of organizing and recoding the sacred landscape involves a wide variety of groups and actors. These factors may explain the success of the project in comparison to other projects being implemented under the Ruqani Zhangyru program. ",
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T1 - A Nation's Holy Land
T2 - Kazakhstan's Large-Scale National Project to Map Its Sacred Geography
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N1 - Funding Information: Interview, Expert 2. Experts 1 and 3 noted that after work was completed on the foundational principles and documents in 2017, they got the impression that higher authorities had lost interest in the project. In fact, the project's funding in the following years was reduced, but in reality, the reduction was minor. For 2020, the budget was around 800 million tenge (without considering inflation). From 2017 through 2020, the project received a total of approximately 10 million US dollars. It is also worth taking into account that the project was funded not only via the Sacred Kazakhstan Center but also via grants given directly to scholarly projects by the Ministry of Education and Science. Publisher Copyright: © The Author(s), 2021. Published by Cambridge University Press on behalf of Association for the Study of Nationalities.
N2 - This article focuses on the project Sacred Geography of Kazakhstan, launched in 2017 in Kazakhstan as part of the nationwide program Ruqani Zhangyru (Modernization of Spirituality). The officially stated goal of the project is to cultivate a sense of patriotism in the country's residents related to places and geographic sites that are important for the historical memory of independent Kazakhstan. The authors assume that the real goal of the project is national territorialization, or recoding of the semantics of space, by selecting, codifying, and articulating some symbols and practices, while leveling and "forgetting"others. The analysis, which is based on expert interviews and official documents, shows that this postcolonial process fits into the tendency toward ethnonationalization of Kazakhstan, in which discourse on the civil nation continues to be reproduced at the official level, while real activity is more focused on reinforcing the idea of Kazakhstan as the state of the Kazakh nation. The institutionalization of organizing and recoding the sacred landscape involves a wide variety of groups and actors. These factors may explain the success of the project in comparison to other projects being implemented under the Ruqani Zhangyru program.
AB - This article focuses on the project Sacred Geography of Kazakhstan, launched in 2017 in Kazakhstan as part of the nationwide program Ruqani Zhangyru (Modernization of Spirituality). The officially stated goal of the project is to cultivate a sense of patriotism in the country's residents related to places and geographic sites that are important for the historical memory of independent Kazakhstan. The authors assume that the real goal of the project is national territorialization, or recoding of the semantics of space, by selecting, codifying, and articulating some symbols and practices, while leveling and "forgetting"others. The analysis, which is based on expert interviews and official documents, shows that this postcolonial process fits into the tendency toward ethnonationalization of Kazakhstan, in which discourse on the civil nation continues to be reproduced at the official level, while real activity is more focused on reinforcing the idea of Kazakhstan as the state of the Kazakh nation. The institutionalization of organizing and recoding the sacred landscape involves a wide variety of groups and actors. These factors may explain the success of the project in comparison to other projects being implemented under the Ruqani Zhangyru program.
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text:
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3 edition of For the relief of Nguyen Quy An found in the catalog.
For the relief of Nguyen Quy An
United States. Congress. House. Committee on the Judiciary
report (to accompany H.R. 1087) (including cost estimate of the Congressional Bueget Office
by United States. Congress. House. Committee on the Judiciary
Published 1996 by U.S. G.P.O. in [Washington, D.C.? .
Nguyen, Quy An, -- 1943-,
Emigration and immigration law -- United States
Series Report / 104th Congress, 2d session, House of Representatives -- 104-811
For the relief of Nguyen Quy An. Be it enacted by the Senate and House of Representatives of the United States of America in Congress assembled, SECTION 1. WAIVER OF CERTAIN NATURALIZATION REQUIREMENTS FOR NGUYEN QUY AN. Nguyen Quy has 98 books on Goodreads, and is currently reading Product-Led Growth: How to Build a Product That Sells Itself by Wes Bush, War and Peace an.
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View Quy Nguyen's profile on LinkedIn, the world's largest professional community. Quy has 3 jobs listed on their profile. See the complete profile on LinkedIn and discover Quy's connections and jobs at similar : Office Manager at GetLinks. This is the biography page for Quy Lam Nguyen.
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For the relief of Nguyen Quy An by United States. Congress. House. Committee on the Judiciary Download PDF EPUB FB2
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th Congress Report HOUSE OF REPRESENTATIVES 2d Session _____ FOR THE RELIEF OF NGUYEN QUY AN _____ Septem Committed to the Committee of the Whole House and ordered to be printed _____ Mr. Hyde, from the Committee on the Judiciary, submitted the following R E P O R T [To accompany H.R.
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CFPB staff watching Sen. Elizabeth Warren defend their agency's mission on the street below.
This week, Public Citizen joined allies in protest outside the Consumer Financial Protection Bureau (CFPB). These protests aim to draw attention to a controversial move by President Donald Trump to turn the operation of the organization over to his budget chief, Mick Mulvaney, who has called the CFPB a "sick, sad" joke.
Before he left the position last Friday, former CFPB director Richard Cordray appointed Leandra English to become deputy director. Under the rules of succession laid out under the Dodd-Frank Act, which established the office, she was to become acting director.
Senator Elizabeth Warren, who originated the idea of the CFPB, spoke at a press conference outside the building today. Employees pressed against the windows overlooking the sidewalk to watch her defend the agency, which has returned nearly $12 billion to over 30 million consumers ripped off by financial institutions.
You can watch our video coverage of today's rally, as well as Monday's rally, which featured Rep. Jamie Raskin and Public Citizen President Robert Weissman.
Protecting consumers from being ripped off is not a joke, and Trump's attempt to bypass the rule of law belongs on the funny pages, not the front page.


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Event: Tower Grove East Neighborhood Picnic & Meeting!
A number of TGE residents are hosting yard sales on Saturday, May 10. View the map here and spend Saturday exploring our neighborhood and meeting your neighbors! The sale goes from 9:00 a.m. – 2:00 p.m.
Free transportation to the first 41 persons provided by and from the FIVE STAR ENIOR CENTER 2832 Arsenal, buses will leave at 6:45 pm sharp. Others are welcome to join us via. alternate transportation.


text:
Next Article in Internet
Don't Tax the Internet
By Sonia Arrison
March 3, 2006 5:00 AM PT
Some members of Congress want to tax the Internet, and they're trying to do it under the guise of "telecom reform." That's a trick Americans won't like. It's time to send Washington a message, loud and clear: hands off the Internet.
During hearings on a government tax and welfare program called the Universal Service Fund (USF), Senate Commerce Committee Chairman Ted Stevens (R-Alaska) sang its praises. "Without Universal Service, just having a dial tone would average about US$200 per month" for some Alaskan residents, he said.
USF has long been a wealth transfer from cities to rural areas, but now that broadband services are being deployed all over the country, someone should tell Senator Stevens that the rationale for the subsidy is gone. Indeed, according to new numbers from the Pew Internet and American Life Project, adoption in rural areas is now occurring at a faster pace than in more populated regions. This should make it a no-brainer to phase out the telecommunications tax and welfare system, but that's not what some powerful senators want to do.
Wasting Cash
Instead, several senators said they wanted to apply USF to the information highway, essentially taxing the Net. That should make American netizens as nervous as cats in a room full of rocking chairs. If government taxes the Net, it will discourage investment, slow connection speeds and cost consumers extra money. Judging from past experience, that money will be wasted on inefficient and corrupt programs.
Consider that the nation's USF budget has nearly doubled in the last eight years, tripling the "telecom tax" on long-distance calling providers and raising telephone costs for consumers. Given that the fund lacks oversight and is subject to massive waste and abuse, one might be tempted to call it "Universal Scam Fund."
For example, federal auditors recently found that school officials in Southern California squandered more than $2 million in USF E-Rate funds to purchase personal laptop computers for faculty members. And it gets worse.
In 2004, the FCC audited 100 E-Rate recipients and found that one-third were non-compliant with government guidelines and many were suspected of scams such as bid rigging, false reporting and other kickback schemes with tech vendors. Indeed, the system seems so open to abuse that it has been alleged that the Gambino crime family used a Missouri-based E-Rate service provider to defraud the program out of nearly $22 million.
Fixing the System
That's not the kind of program that should continue, let alone be applied to a new and innovative platform like the Internet. Yet even with these problems, many analysts are skeptical that the fund will ever disappear.
It seems that too many people with political friends are dependent on the system. Recently, Federal Communications Commission Chairman Kevin Martin showed signs of supporting what has been called a "numbers-based" approach, in which anyone with a phone number, including Voice Over Internet Protocol (VoIP) would pay into the fund.
If Congress is serious about reforming telecommunications, its members should work towards fixing broken systems rather than applying them to new technologies. This is particularly true when broadband is continuing to roll out across the country, making telephone services free or very low-cost.
America is already ranked a lowly 16th in broadband deployment, and moves to saddle the medium with old and dysfunctional programs will only make it worse. That's not telecom reform, only a sneaky move at new taxes and regulation.
USF is as relevant as a horse and buggy, but carries Lamborghini-style costs. Americans should take a stand and e-mail their representatives telling them not to tax the Net. If Americans take no action, their e-mail service might soon become a lot more expensive.
Sonia Arrison, a TechNewsWorld columnist, is director of Technology Studies at the California-based Pacific Research Institute.
More by Sonia Arrison
Silicon Valley's Secret Sauce
America: It's Time to Snap Out of the Pro-Death Trance
Facebook Shouldn't Wall Off Minors
The Antisocial Social Networking Bill
Road to Curation Nation a Bumpy One
Is Silicon Valley Losing Its Edge?
California Shouldn't Follow NY's Internet Tax Plan
In Uncle Sam, You've Got a Friend… Who Wants Everybody's DNA
Hey You, Get Off of My Cloud!
Cloud Computing Calms Open Source Warfare
More in Internet
Piracy Expert Sees Weaponization of Legit Video Providers on the Rise
Watchdog Finds Flourishing Black Market on Facebook for Fraudulent Ad Accounts
5 Cyber Safety Tips To Survive the Internet, Hackers and Scammers
A Third of US Social Media Users Creating Fake Accounts


A portable toilet company in Natrona County had its water temporarily shut off and faces nearly $50,000 in fines for illegally dumping waste into a sewer system numerous times over the past year, according to the Wardwell Water & Sewer District.
The district's elected board of directors voted unanimously last week to shut off the water supply to Shawn's Johns and its owner Shawn Nash, 3270 Salt Creek Highway, after the third notice of violation and the possible threat to public health.
Kyle Ridgeway, attorney for the Water & Sewer District, said Monday the water was shut off from Wednesday through Friday, and was restored on the condition the water be used only for residential purposes.
If violations persist, the board will order plugging the sewer lines, which would not affect neighbors, but it would be costly.
Nash referred questions to his attorney Andrew Sears of the Casper firm Murane & Boswick. Thursday, Smith declined to comment because of the pending litigation.
Hiring an attorney was the first time Nash responded to multiple opportunities to present his side of the story before the district, which serves Bar Nunn and nearby communities. He also did not appear twice in Natrona County District Court for hearings for a preliminary injunction.
The case began a year ago when district manager Gloria Brainard saw Shawn's Johns improperly disposing human waste from its portable toilets directly into the sewer system, according to a civil complaint filed in Natrona County District Court. "Upon this observation, Ms. Brainard spoke with Mr. Nash and explained to him that this constituted illegal dumping in violation of numerous environmental rules, including, but not limited to, Wardwell's Sewer Use Regulations."
A company such as Nash's must take its waste to the Sam H. Hobbs Regional Wastewater Treatment Plant east of Casper that has the equipment to handle large amounts of human waste.
The effect of each illegal mass dump of the portable toilets on the 8-inch sewer line is the equivalent of a 50-home subdivision emptying all of its bathtubs at once. We're not talking about bathwater here, however.
After learning of the violation last year, the Central Wyoming Regional Water System installed a flow meter installed immediately downstream from Shawn's Johns.
The flow meter, another observation by Brainard and complaints about smells from neighbors revealed more illegal dumping on April 16.
Wardwell then issued a Notice of Violation and Order to Cease and Desist. Wardwell also asked Nash to appear at an informal hearing on May 8. He didn't show up and did not request a hearing to respond to the notice.
He hadn't responded by June 5, so the Wardwell board ordered a $500 administrative fine and a $5,000 civil fine against Nash. Those amounts were half of what the board could have imposed.
The board also asked Ridgeway to pursue an injunction through Natrona County District Court for the violations.
Illegal dumping was detected on May 31 and June 12, which prompted the Wardwell board to issue a second notice of violation.
Nash didn't respond to the second notice or for an opportunity to appear in court to defend himself.
On July 9, District Court Judge Catherine Wilking held a second hearing and upheld a previous preliminary injunction.
After the hearing, Brainard said the Wardwell Water & Sewer District never had such a problem in its history.
Ridgeway said he wasn't qualified to comment on whether such dumping posed an immediate threat to human health, but said the case could warrant a look by the EPA.
On Tuesday, the board held its monthly meeting and had asked Nash to appear at its meeting to discuss the violations.
So board the slammed down the lid.
In addition to the previous $500 and $5,000 fines, the board fined him the maximum $1,000 each for the four administrative violations and fined him the maximum $10,000 for each for the civil violations.
The total $49,500 in fines does not include the additional costs for cleaning out the sewer line, attorney's and other fees.
Besides the money, board members agreed that any further violation will result in plugging the sewer line.
That's far more than the $7,000 to $12,000 a year Nash is probably saving by the illegal dumping, board member Mark Pepper said.
The dumping could cause a major problem if portable toilet waste with its disinfectant in a large volume damaged a lift station between Bar Nunn and the wastewater treatment plant, Pepper said.
Likewise, a large amount the disinfectant put in the toilets could kill the good bacteria that render the bad bacteria harmless at the plant, which would render useless the treatment of waste water, Pepper said.


text:
\section{Introduction}

The genetic information in eukaryotic cells (including cells of animals
and plants) is accessed through DNA unwinding on two different length
scales. On the larger scale the DNA double helix has to unwind from
proteins, on the smaller scale the two strands of the double helix need
to be separated. In the first case a semiflexible polymer (DNA double
helix) is wound almost two turns around a protein cylinder forming
the so-called nucleosome \cite{luger97,schiessel14}, in the second
case two flexible polymers (chains of nucleotides) are twisted around
each other leading to the much stiffer double helix. The unwinding
of the DNA from the nucleosome or the separation of the DNA double
helix is achieved inside a cell in various ways, often involving
molecular motors (chromatin remodellers, polymerases...) that usually
give access through a local opening of the structures. Inside
a test tube unwinding can be induced, typically on a global
scale, through a change in temperature (DNA melting/helix-coil
transition \cite{schiessel14,poland66,kafri02,blossey03}), salt
concentration (salt-induced DNA release \cite{yager87,kunze00})
or through application of an external force (nucleosome unwrapping
\cite{schiessel14,brower-toland02,kulic04,mihardja06,blossey11},
DNA unzipping \cite{kafri02,essevaz97}). Local unwinding can also
occur spontaneously leading to the breathing of nucleosomes
and of DNA (usually called site exposure in nucleosomes
\cite{schiessel14,blossey11,polach95,koopmans09,prinsen10} and
denaturation bubbles in DNA \cite{schiessel14,blossey03,ambj07}). Finally,
during transcription, where the elongating RNA polymerase produces a
RNA transcript, one faces again the situation of a flexible chain, the
transcript, being initially wound around the much stiffer DNA double
helix \cite{belo14}.

To gain insights into the unwinding process it is convenient to start
from simple setups.  In this work we study the unwinding process of
an idealized flexible polymer model that is initially wound around a
stiff rod, in a configuration of minimal entropy, which resembles some
of the features of the DNA or RNA unwinding. This model was introduced
and studied in ref.~\cite{wal13}. Here we extend the results of that
analysis focusing in particular on metric properties. We present a scaling
argument which fully captures the early stages of the dynamics that is
characterized by power-law scaling. Despite the simplicity of the model,
there is a complex dynamical behavior.

It is the entropy gain that drives the polymer from the initial
configuration toward the full random coil configuration. A sketch
of this process is given in Figure~\ref{fig:1}, which shows different
snapshots of the polymer configurations in the course of a simulation.
The polymer is initially fully wound in a helix around the rigid rod.
One end of the polymer is tethered to the rod whereas the other end is
free, hence the relaxation proceeds from the free end.  This process
shares some similarities with the simpler problem of the relaxation from
one end of a completely stretched polymer \cite{brochard95,buguin96}.
Consider a polymer tethered at one end and fully stretched by a strong
flow. When the flow is turned off the polymer relaxes back to its coiled
equilibrium conformation. As one end is tethered the relaxation starts
from a free end, from where the coil grows. The unwinding has a similar
relaxation from the free end which occurs through a rotational motion
instead of a translational recoiling. However, the phenomenology in the
case of unwinding is much richer, as we will show.

This paper is organized as follows. In the section Models and Simulations,
we review the models and the type of Monte Carlo simulations used. In the
section Results and Discussion, we focus first on the early unwinding
dynamics which is characterized by power-laws scaling in time. It is
shown that force balance equations and scaling arguments yield exponents
in very good agreement with simulations.  Second, we discuss the late
stage of the relaxation process. Here the theory of ref.~\cite{wal13}
predicts a power-law scaling for the longest relaxation time with
logarithmic corrections.  The analysis is extended to other lattice and
off-lattice models and the results confirm the validity of the theory.

\begin{figure}[!htb]
\begin{tabular}{c}
\includegraphics[angle=0,width=0.45\textwidth]{run1_t0.pdf}\\
\includegraphics[angle=0,width=0.45\textwidth]{run1_t70000_text.pdf}\\
\includegraphics[angle=0,width=0.45\textwidth]{run1_t2000000b.pdf}\\
\includegraphics[angle=0,width=0.45\textwidth]{run1_t5000000.pdf}
\end{tabular}
\caption{Snapshots of a SAW with $L=384$ monomers during
unwinding from a rod.  One end (blue) is attached to the rod and
the other end (red) is free. Snapshots are taken at
times $t=0$, $t=7\times 10^4$, $t=2\times 10^6$, and $t=5\times 10^6$
(from top to bottom).
The second configuration is in the early stage of the unwinding, where one can
recognize three different phases: the part close to the
fixed end is still a tightly wound helix,
the middle section shows a loose helix configuration,
and the part close to the free end forms a random coil.  }
\label{fig:1}
\end{figure}

\section{Models and Simulations
\label{sec:sim}

Figure~\ref{fig:1} shows different snapshots of the polymer configurations
during the unwinding from an infinitely long rod. Initially the polymer
is fully wound and in the course of time it unwraps. The polymer has $L$
monomers labeled with indices $1 \leq k \leq L$.  One end ($k=1$) is
fixed to the rod, while the other end ($k=L$) is free.  We have studied
different cases to check the robustness and universality
of the numerical results. For the
ideal chain (the case without excluded volume) we modeled the polymer
in three different ways.  In a first model we considered a random walk
(RW) with unit steps on a face-centered cubic (FCC) lattice.  In the
initial helical configuration, the polymer performs one turn in six
steps along the rod.  An update of the configuration consists of $L$
attempts of so-called corner flips, where the randomly selected monomer is
moved to a neighboring lattice site if the distances to the neighboring
monomers are conserved (this is a lattice realization of Rouse dynamics~\cite{doi86}).
 The new configuration is accepted if the monomer does
not overlap with the rod.

We also considered a random walk on a square lattice (i.e., a bidimensional lattice).
 In this case the
starting configuration consists of a chain with a rescaled segment length
wound around the origin. In the initial configuration on the square
lattice one turn around the origin is performed by $8$ monomers. The
corner flip method is used here as well.

Finally, we used a freely jointed chain (FJC) to model three-dimensional
off-lattice polymers.
Neighboring monomers have a fixed distance $a$ from each other and the rod has a
diameter $1.5\, a$ ensuring that monomers cannot accidentally pass from
one side to the other in the course of unwinding. The initial helical
configuration is such that one turn is performed with $10$ monomers.
Also in this case a time step of the dynamics
consists in $L$ attempts of moves for randomly chosen monomers. When a
monomer is selected, a new configuration is constructed via a rotation
of that monomer around the axis defined by the two neighboring monomers
by an angle randomly selected from $[0, 2\pi]$. The free end is updated
with a new random position preserving the bond length with the second
monomer. The new configuration is accepted if it does not overlap with
the rod.

For the case of a polymer with excluded volume we use only the model of a self-avoiding
walk (SAW) on the FCC lattice. The procedure is the same as for the ideal
chain on the FCC lattice, with the added constraint of excluded volume
between the monomers: one rejects moves violating it.

\begin{figure*}[!ht]
\hbox{
\includegraphics[angle=0,width=0.3575\textwidth]{LATE_STAGE_2dRW_v02.pdf}
\includegraphics[angle=0,width=0.31\textwidth]{LATE_STAGE_3dRW.pdf}
\includegraphics[angle=0,width=0.31\textwidth]{LATE_STAGE_FJC.pdf}
}
\caption{Average squared distance $R_{\rm e\,RW}^2$ of the free
end from the rod versus time (ideal chain) for (a) a 2D polymer on a
square lattice, (b) a 3D polymer on a FCC lattice and (c) a FJC in 3D,
for various chain lengths. For the three models the short time regime
follows the power law $R_{\rm e\,RW}^2\sim t^{0.25}$. This regime ends
at times scaling as $\tau' \sim L^2$, see insets (the values of $\tau'$
for the shortest chains are indicated by vertical arrows).  The plateaus
indicate the completion of relaxation.  The averages
are made at least (for the largest sizes) over (a) $2000$ and (b)
$3000$ configurations. In (c), due to larger computational effort in
continuous space for a local move, the average is performed only over
$150$ configurations, which explains the larger noise.}
\label{fig:2}
\end{figure*}

\section{Results and Discussion

\subsection{Short-Time Dynamics

\label{sec:short}

\subsubsection{Radial Distance

We consider first the ``radial" distance $R_{\rm e}$ which is defined as
the average distance of the free end monomer from the rod. This quantity
is shown in Figure~\ref{fig:2} (RW's) and~\ref{fig:3}
(SAW). Starting from a minimal value for the fully
wrapped configuration at $t=0$ the growth of $R_{\rm e}$ follows a power
law. In the ideal chain cases we find a first, short-time, regime:
\begin{equation}
R^2_{\rm e\,RW}(t)\sim t^{0.25}\,.
\label{R2RW}
\end{equation}
This scaling with time of a spatial length scale is remarkably slow
($|R_{\rm e}| \sim t^{1/8}$) compared to the usual relaxation time scales
encountered in polymer physics. The exponent is robust and is found
in the minimalistic 2D polymer on a square lattice (Figure~\ref{fig:2}(a)),
the RW on a FCC lattice (Figure~\ref{fig:2}(b)) and the freely jointed chain
off-lattice (Figure~\ref{fig:2}(c)).  We performed also simulations for a 3D
excluded volume chain on an FCC lattice, for which we find a power law
with a slightly larger exponent:
\begin{equation}
R^2_{\rm e\,SAW}(t)\sim t^{0.27}\,,
\label{R2SAW}
\end{equation}
as it can be seen in Figure~\ref{fig:3}.

\begin{figure}[!ht]
\centering\includegraphics[angle=0,width=7cm]{LATE_STAGE_SAW.pdf}
\caption{Squared distance $R^2_{\rm e\,SAW}$ of the free end from the
rod versus time for a excluded volume chain on an FCC lattice. The short
time regime follows the power law $R^2_{\rm e\,SAW}\sim t^{0.27}$. The inset
shows the scaling of $\tau'$ with the polymer length. Averages
are made at least over $3000$ configurations (for the largest size).}
\label{fig:3}
\end{figure}

To understand the origin of this exponent we model the unwinding starting
from a two phase picture.  We assume that during the early stage of the dynamics
the polymer starting from the fixed end has $n$ monomers tightly wrapped
around the rod, which are frozen as in their initial $t=0$ configuration,
while $L-n$ monomers are loose (we indicate these as phase 1 and phase 2,
respectively, see Figure~\ref{fig:config}(a)). We assume
that the loose monomers form a homogeneous helix with a constant pace,
but which is loosely wrapped around the rod. Obviously, if the loose helix
would extend until the free end of the polymer, the radial distance $R_{\rm e}$
would not grow in time. The two phase model is the starting point of our
analysis and we will focus on the configuration of the polymer close to
the free end later. We assume that the dynamics is governed by the
following equation:
\begin{equation}
\gamma_2 \frac{dn}{dt} = - \frac{\partial {\cal F}}{\partial n}\,,
\label{eq:domain1}
\end{equation}
which is a balance between frictional and ``entropic'' forces during the
growth of the helical domain.  Here ${\cal F}(n) = f_1 n + f_2
(L- n)$ is the total free energy of the configuration, with $f_1$ and
$f_2$ the free energies per monomer of the two phases (with $f_2 < f_1$
as the loose helix has a higher entropy than the tight helix).
$\gamma_2$ is the friction coefficient. The total
winding angle of the last monomer is equal to $2\pi$ times the number
of times the polymer is wrapped around the rod.  For the two helices
model such a quantity is then given by:
\begin{equation}
\Theta = n \Delta \theta_1 + (L-n) \Delta \theta_2\,,
\label{thetan}
\end{equation}
where $\Delta \theta_1$ and $\Delta \theta_2$ are the densities of winding
for the two phases (with $\Delta \theta_1 > \Delta \theta_2$,
as phase 2 is more loosely wrapped compared to phase 1).  A decrease
in $n$ leads to a decrease in the total winding angle and the whole
loose helix rotates in a corkscrew motion. The friction coefficient is
then proportional to the length of the rotating domain $\gamma_2 \sim
(L- n)$. Using this input and the form of ${\cal F}(n)$ we get from
the integration of eq.~(\ref{eq:domain1}):
\begin{equation}
L-n \sim \sqrt{t}\,.
\label{growth1}
\end{equation}
The angular velocity is given by eq.~(\ref{thetan}):
\begin{equation}
\Omega = \frac{d\Theta}{dt} \sim \frac{dn}{dt} \sim \frac{1}{\sqrt{t}}\,,
\label{omega}
\end{equation}
which decreases in time as there is an increasing friction when
the loose helix grows.

The assumption that phase 2 is a helix of constant
pace and radius is an approximation. However, as we will show,
the numerical data are in good agreement with a square root growth
(eq.~(\ref{growth1})), which is a consequence of that assumption.  Note that
the assumption can be relaxed, allowing phase 2 to have fluctuations;
the only essential requirement is that the friction $\gamma_2$ should
scale linearly with the length of the domain. Our approximation is similar in spirit to the monoblock
approximation where an inhomogeneously stretched polymer is modeled
by a homogeneously stretched one, an approximation that does not change the
scaling of the large scale geometry of the deformed chain~\cite{brochard94,schiessel97}.

\begin{figure}[!t]
\centering\includegraphics[angle=0,width=7cm]{sketches_unwind.pdf}
\caption{(a-b) Configurations of the polymer during unwinding. (a) Two
phase model consists of a tight helix (phase 1), which is the initial
conformation, and a loose helix with constant pace (phase 2). (b) Extension
of the two phase model accounting for the growth of an unwound coil
of length $l$ at the polymer end. (c-d) View of a polymer anchored
to the rod (which is perpendicular to the plane) and rotating with
angular velocity $\Omega$. If $\Omega$ is small the polymer rotates
while maintaining its equilibrium shape (case (c)). For high $\Omega$
the polymer gets partially wrapped around the rod, while a part of
length $l$ maintains its equilibrium shape. Equation~(\ref{length})
gives an estimate of the length $l$.}
\label{fig:config}
\end{figure}

Let us consider now the growth of a coiled domain at the end of the
chain (the stretch AB of length $l$ shown in Figure~\ref{fig:config}(b)).
This domain grows from a polymer rotating with angular velocity
$\Omega$. Let us assume that the friction originating from  the
coiled part is negligible compared to that of the loose helix, so the
calculations leading to eqs.~(\ref{growth1}) and (\ref{omega}) remain
valid. To understand the coil growth we consider a polymer attached to
a rod and rotating with angular velocity $\Omega$. If the polymer is
sufficiently short and $\Omega$ small, its equilibrium conformation is
not perturbed by the rotation and in particular it will have no winding
(Figure~\ref{fig:config}(c)). If the polymer length exceeds a given threshold
value, then part of the polymer close to the attachment point gets wound
while the final part rotates maintaining its equilibrium shape (length
of the part AB in Figure~\ref{fig:config}(d)).  We estimate now the length of
the end coil for a rotating polymer. To understand the calculation it is
useful to consider the analogous problem of a polymer pulled by one end
by a constant force~\cite{brochard93,brochard94,schiessel95,rowg12,sakaue12}.
The polymer maintains its equilibrium conformation if the applied force,
$f$, or the polymer length, $l$, do not exceed the values fixed by
the equation:
\begin{equation}
f R_F \sim k_B T\,,
\label{fRF}
\end{equation}
where $R_F \sim l^\nu$ is the Flory radius,
$k_B$ the Boltzmann's constant and $T$ the temperature. For a polymer
rotating with an angular velocity $\Omega$ the force which distorts its
shape is due to friction. The expression analogous to eq.~(\ref{fRF})
is then given by
\begin{equation}
\gamma v R_F \sim  k_B T\,.
\label{angular_fRF}
\end{equation}
Using $v = \Omega R_F$ and $\gamma \sim l$ for a Rouse polymer we obtain
the following relation for the length of the coiled unwound end of the
rotating polymer:
\begin{equation}
l^{1+2\nu} \sim  \frac{k_B T}{\Omega}.
\label{length}
\end{equation}
Using the law (\ref{omega}) for the angular velocity we finally obtain
for the growth of $l$:
\begin{equation}
l \sim t^{1/(4\nu+2)}\,,
\label{evol_length}
\end{equation}
and, from the equilibrium relation $R_{\rm e}^2 \sim l^{2\nu}$ we find that
the squared distance from the rod grows as:
\begin{equation}
R_{\rm e}^2 \sim t^z\,,
\label{Revst}
\end{equation}
with $z=\nu/(2\nu+1)$. Note that $z=1/4$ for a Gaussian polymer
($\nu=1/2$) and $z\simeq 0.27$ for a self-avoiding polymer ($\nu \simeq
0.59$) which is in excellent agreement with the numerical results
(Figures~\ref{fig:2} and~\ref{fig:3}).

\begin{figure*}[!ht]
\hbox{
\includegraphics[angle=0,width=0.34\textwidth]{FIG03a_new.pdf}
\includegraphics[angle=0,width=0.325\textwidth]{FIG_shape_3dRW.pdf}
\includegraphics[angle=0,width=0.315\textwidth]{FIG_shape_3dSAW.pdf}
}
\caption{Plot of $d^2(s)$ vs. $s$, for different times in the short time regime
and $L=768$. The quantity $d(s)$, defined in eq.~(\ref{def_ds}), is
the planar distance of the last monomer (index $L$) at the free end from
the $(L-s)$-th monomer. For small $s$, one has $d^2(s) \sim s^{2\nu}$,
indicating that the polymer forms a random coiled phase from its free end.
The region where $d^2(s) \sim s^{2\nu}$ holds grows in time.
The cases shown
are (a) 2D RW, (b) RW on the FCC lattice, (c) SAW on the FCC lattice.
The insets show rescalings of the data, see eq.~(\ref{scaling_ansatz}).
}
\label{fig:4}
\end{figure*}

We expect that the above description remains valid until the loose helix
has grown to reach the first monomer. This corresponds to $n=0$,
i.e. when the tight helix has disappeared. According
to eq.~(\ref{growth1}) this happens at a characteristic time $\tau'$
scaling as $\tau' \sim L^2$. We estimated $\tau'$ for polymers of
different lengths from the simulation data of the radial distance
of Figures~\ref{fig:2} and \ref{fig:3}. This is the time at which the growth
law starts deviating from eq.~(\ref{Revst}).  The vertical arrows in Figure~\ref{fig:2}
mark the estimated $\tau'$ for the polymer of shortest length.
The insets of Figures~\ref{fig:2}(a) and (b) show plots of
$\tau'$ vs. $L$ as obtained from the data of the main plots. There is
an excellent agreement with the predicted scaling $\tau' \sim L^2$. An
equally good agreement was found for all the other cases studied. Note
that the scaling $\tau' \sim L^2$ does not depend on the presence of
self-avoidance, as demonstrated by the data in the inset of Figure~\ref{fig:3}.

\begin{figure*}[!t]
\hbox{
\includegraphics[angle=0,height=4.1cm]{theta0-theta_2dRW.pdf}
\includegraphics[angle=0,height=4.1cm]{theta0-theta_3dFCC.pdf}
\includegraphics[angle=0,height=4.2cm]{theta0-theta_3dFJC.pdf}
}
\caption{Scaling of $\Theta_0-\Theta$ vs. time, for different polymer lengths, for the ideal chain models.
The numerics are well fitted by a power law $\sim t^{1/2}$. (Insets) Plots of $(\Theta_0 - \Theta)t^{-1/2}$ vs. $t^{-1/4}$.
The dashed line is the slope predicted from eq.~(\ref{corr_scaling}).
}
\label{short_theta}
\end{figure*}

We consider next the distance $d(s)$ between the free end monomer at
position $L$ and a monomer $L-s$ projected onto a plane perpendicular
to the rod.  In two dimensional models this is equal to the total
distance $d(s) \equiv |\vec{R}_L-\vec{R}_{L-s}|$ where $\vec{R}_i$
is the position of monomer $i$. In three dimensions, for a rod parallel
to the $z$-axis we have:
\begin{equation}
d(s) = \sqrt{\left(x_L-x_{L-s}\right)^2 + \left(y_L-y_{L-s}\right)^2}\,,
\label{def_ds}
\end{equation}
where $x_i$ and $y_i$ are the coordinates of the monomer $i$. In all
cases analyzed (see Figure~\ref{fig:4}) we find for small $s$ a scaling $d^2(s)
\sim s^{2\nu}$ which demonstrates that the end part of the polymer is an
equilibrated coil. The plots show that $d^2(s)$ saturates at a constant
value for sufficiently large value of $s$. This point identifies the end
of the coil and the beginning of the loose helical region. From scaling
arguments we expect:
\begin{equation}
d^2(s) = s^{2\nu} g\left(\frac {s}{t^{1/(4\nu+2)}}\right)\,,
\label{scaling_ansatz}
\end{equation}
where for small values of $x=s/t^{1/(4\nu+2)}$ the function $g(x)$
converges to a constant. For large $x$ we expect $g(x)\sim 1/x^{2\nu}$
as $d^2(s)$ is independent of $s$, as the projected distance from the
end monomer to the monomers in the helical domain cannot increase.
The inset of Figure~\ref{fig:4} shows a scaling plot of $d^2(s) s^{-2\nu}$
vs. $s/t^{1/(4\nu+2)}$ in full agreement with the scaling ansatz
(\ref{scaling_ansatz}). This result supports the prediction that
the coil growths according to eq.~(\ref{evol_length}). Note that the
scaling function has a maximum at the crossover between the two scaling
regimes. The maximum is not very pronounced but indicates that the
polymer, compared to an equilibrated coil, is slightly more stretched
in the vicinity of the rod.

\subsubsection{Dynamics of the Total Winding Angle}

The theory developed in the previous section can be tested also
on the dynamics of the total winding angle. Taking into account the
presence of the coil of length $l$ at the polymer end we need to modify
eq.~(\ref{thetan}) with:
\begin{equation}
\Theta = n \Delta \theta_1 + (L-l-n) \Delta \theta_2\,,
\label{thetan2}
\end{equation}
as the coil, which is of length $l$, does not contribute to the
winding. We define with $\Theta_0 = L \Delta \theta_1$ the initial
total winding angle. Combining eqs.~(\ref{growth1}),
(\ref{evol_length}) and (\ref{thetan2}), we then get:
\begin{eqnarray}
\Theta_0-\Theta &=& (L-n) (\Delta \theta_1 - \Delta \theta_2 )
+ l \Delta \theta_2\,, \nonumber\\
 &=& A t^{1/2} + B t^{1/(4\nu+2)}\,, \nonumber\\
 &=& A t^{1/2} \left( 1 + \frac{B}{A} \frac{1}{t^{\nu/(2\nu+1)}} \right)\,,
\label{corr_scaling}
\end{eqnarray}
with $A$ and $B$ being some positive constants. The prediction is that
$\Theta_0 - \Theta$ scales as $\sim \sqrt{t}$, with a slowly
decaying correction term originating from the
equilibrated end coil. The correction is predicted to scale as $\sim
t^{-1/4}$ for a RW and $\sim t^{-0.27}$ for a SAW.  In order to test
the validity of eq.~(\ref{corr_scaling}) we plot in Figure~\ref{short_theta}
the quantity $\Theta_0-\Theta$ as a function of $t$ in a log-log scale
for three ideal-chain  models in two and three dimensions, and the same
for SAW's in Figure~\ref{short_theta_SAW}.  In all cases the data approach for
sufficiently long times the expected $\sim \sqrt{t}$ law.

\begin{figure}[!bt]
\hbox{
\includegraphics[angle=0,width=7.8cm]{theta0-theta_3dSAWFCC.pdf}
}
\caption{Scaling of $\Theta_0-\Theta$ vs. time, for different polymer lengths, for the SAW model.
(Inset) Plot of $(\Theta_0 - \Theta)t^{-1/2}$ vs. $t^{-0.27}$. The dashed line is the slope predicted
from eq.~(\ref{corr_scaling}).
}
\label{short_theta_SAW}
\end{figure}

To investigate the nature of the corrections to the leading scaling
behavior we plot in the insets of Figure~\ref{short_theta} the quantity
$(\Theta_0-\Theta)/\sqrt{t}$ vs. $t^{-\nu/(2\nu+1)}$. The data for short
times and for different polymer lengths follow a straight line in good
agreement with the prediction of eq.~(\ref{corr_scaling}). The slope
of the lines are positive and imply $B > 0$, as expected. Some stronger
nonmonotonic behavior is observed in the 3D off-lattice model which does
not have a counterpart in the other cases studied. The behavior of the
winding angle was also investigated in a previous publication~\cite{wal13}
and estimated to scale in the early time dynamics as $\Theta_0-\Theta\sim
t^{\rho}$ where $\rho\approx 0.43-0.44$. This seemed to match the short
time dynamics rather well, although a closer inspection of the data shows
that eq.~(\ref{corr_scaling}) fits the data better. The analysis of
the local winding, which follows, gives further support of a $\sqrt{t}$
growth of the unwound domain.

\subsubsection{Local winding angle}

Further insight of the polymer dynamics can be obtained from the analysis
of the local winding angle $\theta(k)$, which is the winding angle of the
$k$-th momomer. As the winding angle is counted from the monomer attached
to the rod ($k=1$) one has $\theta(1)=0$, whereas the total winding angle
defined above is $\Theta = \theta(L)$. Figure~\ref{fig:local_winding}
shows the time evolution of $\theta(k)$ vs. $k$ for different times
and for a polymer of length $L=512$ for a planar RW.  At $t=0$ the
configuration is fully wrapped around the rod which corresponds to a
linear increase $\theta(k) = \Delta \theta_1 k$.  As the time evolves
$\theta(k)$ decreases in a more pronounced manner starting from the
free end of the polymer; at short times there is a domain of length $n$
which is still fully wrapped as at time $t=0$, followed by a loose part
of length $L-n$.  The inset of Figure~\ref{fig:local_winding} shows a plot
of $L-n$ vs. $t$. The data are in very good agreement with the square
root growth predicted by eq.~(\ref{growth1}). Differently from the data
for the total winding angle of eq.~(\ref{corr_scaling}), in this case
there are no corrections to scaling expected.

\begin{figure}[!bt]
\includegraphics[angle=0,width=0.45\textwidth]{FIG_theta_n.pdf}
\caption{Time evolution of the local winding angle $\theta(k)$ vs.
monomer index $k$ for the 2D RW of size $L=512$. The dashed tilted line corresponds to the
fully wrapped conformation $\theta(k) =\Delta \theta_1 k$. The
data are obtained for increasing times $t_1=10\,000$, $t_2=20\,000$,
$t_3=40\,000$, $t_4=80\,000$, $t_5=160\,000$ and $t_6=320\,000$.
The vertical dashed-dotted line denotes the boundary between the tight
helix of length $n$ and the loose part of length $L-n$ at the time
$t_1$. Inset: The growth of the loose domain follows the square root
behavior predicted by eq.~(\ref{growth1}).}
\label{fig:local_winding}
\end{figure}

\subsection{Late Stage Relaxation}
\label{sec:late}

\begin{figure*}[!ht]
\hbox{
\includegraphics[angle=0,width=0.3525\textwidth]{eff_exp_2d_SQU.pdf}
\includegraphics[angle=0,width=0.31\textwidth]{eff_exp_3d_FCC.pdf}
\includegraphics[angle=0,width=0.31\textwidth]{eff_exp_3d_FJC.pdf}
}
\caption{Effective exponent defined by eq.~(\ref{eff_exp}) for models without
self-avoidance in two and three dimensions. Asymptotically in $L$
this quantity is expected to converge to $2\nu+1=2$. The solid line is given by
eq.~(\ref{eff_exp}) with a single adjustable parameter, the
scale factor $a$.}
\label{fig:eff_exp}
\end{figure*}

In the previous section we have fully characterized the early time
relaxation dynamics. We found that the first regime in which the typical
polymer configuration looks like in Figure~\ref{fig:config}(b) ends at a time
scaling as $\tau' \sim L^2$. At very long times the dynamics was studied
in ref.~\cite{wal13} using a force balance equation for the total winding
angle $\Theta$. This equation reads:
\begin{equation}
\gamma_\tau \frac{d\Theta}{dt} = - \frac{\partial {\cal F}}{\partial\Theta}\,,
\label{late_stage_eq}
\end{equation}
where ${\cal F}$ is the free energy of a polymer in equilibrium with
a total winding angle $\Theta$ and where $\gamma_\tau\sim L^{1+2\nu}$
is the friction coefficient. The free energy is a function of a scaling
variable $\Theta/(\log L)^\alpha$, where $\alpha$ is an exponent governing
the fluctuations of the winding angle at equilibrium. For RW's it is known
rigorously~\cite{rudnick88} that $\alpha=1$ while numerical simulations
of 3D SAW's yield $\alpha\simeq 0.75$~\cite{walter11}.  For small winding
angles the free energy is quadratic in the scaling variable, so that the
relaxation to equilibrium becomes exponential~\cite{wal13}: $\Theta(t)
\sim e^{-t/\tau}$ where $\tau$ is the longest relaxation time:
\begin{equation}
\tau  \sim L^{2\nu+1}(\log L)^{2\alpha}\,.
\label{taup}
\end{equation}
Since the initial configuration is fully wound with $\Theta_0 \sim
L$, the total unwinding time is given by $\tau^* \sim \tau \log L$
\cite{wal13}.  The data are best analyzed using the definition of
a running exponent, which probes the local slope of the data in a
log-log plot.  From eq.~(\ref{taup}) we get:
\begin{equation}
\delta(L)\equiv\frac{d\log\tau^*}{d\log L} =
1+2\nu+\frac{2\alpha+1}{\log (aL)}\,,
\label{eff_exp}
\end{equation}
where we have included a scale term $a$, in order to account for further
corrections to scaling.  Figure~\ref{fig:eff_exp} shows a plot of the
numerical value of $\delta (L)$ in two and three dimensions obtained
from simulations of RW's. These data extend those of ref.~\cite{wal13}
by including the three dimensional case for both FCC lattice (b) and
off-lattice (c) models. The data are compared with eq.~(\ref{eff_exp})
where there is only a single adjustable parameter $a$ used in the fit. The
agreement is very good confirming the validity of the analytical approach
of force balancing in eq.~(\ref{late_stage_eq}), which describes the
process using the total winding angle as a single reaction coordinate.

\section{Conclusion}

In this paper we have investigated the problem of the unwinding dynamics
of a flexible polymer from a rigid rod. Scaling arguments and force
balance equations allowed us to fully characterize the early stages
of the unwinding and the late stages of the relaxation dynamics. These
arguments are supported by extensive numerical simulations in two and
three dimensions, with and without self-avoidance.  The early dynamics can
be understood by a three phase picture, where the polymer configuration
starting from the fixed end can be described by a tight helix, a looser
helix and a free random coil. The latter two phases grow in time following
two different dynamical laws as predicted by eqs.~(\ref{growth1}) and
(\ref{evol_length}). The analysis of various quantities from numerical
simulations as metric distances or winding angles are all consistent with
the analytical theory. Interestingly, the first growth law (\ref{growth1})
does not contain the exponent $\nu$ and hence is superuniversal, being
the same for random and self-avoiding walks.  In the late stage dynamics
we have extended the results of ref.~\cite{wal13} to different models
and confirmed the scaling form of the longest relaxation time which
involves logarithmic corrections.

The emerging picture is that of a relatively quick loosening of the
polymer, which remains very close to the rod in the early stages of
the dynamics. This is followed by an intermediate regime where the
distance from the rod grows in a faster way and leads to the final
relaxation. Differently from the early and late time behaviors the
intermediate regime does not appear to display a clear cut scaling.
This can be seen, for instance, in the behavior of
$R_{\rm e}^2$ depicted in Figure~\ref{fig:2}. During early dynamics, until a
characteristic time $\tau'$, $R_{\rm e}^2$ follows a power-law scaling. In the
late time dynamics $R_{\rm e}^2$ reaches a plateau. The intermediate time regime
links the two regimes showing no clear evidence of a power
law behavior. A typical snapshot of the intermediate
regime is shown in Figure~\ref{fig:1} (third configuration from the top). Its
characterization remains a challenge for future work.

The two phase model description of polymer dynamics has recently gained
some popularity: as examples we mention here the case of the translocation
of a polymer through a nanopore~\cite{sakaue07,rowg11,sakaue11}, the pulling
of a polymer by a constant force from one end~\cite{rowg12,sakaue12} and
the folding of a DNA hairpin~\cite{fred14}. In these problems
the polymer is subject to some local forcing and set into motion through
the propagation of tension along its backbone. As the tension does not
propagate instantaneously, the polymer is not set into motion at once. To
describe the motion it is usually assumed that one can divide the polymer
into different phases, which leads to some analytical predictions of the
exponents governing the dynamics~\cite{sakaue07,rowg11,sakaue11,fred14}. In
this paper a similar approach was adopted to study a complementary
case, namely that of the relaxation dynamics of an initially stretched
(helically wrapped) polymer. The excellent agreement between simulations
and model results shown in this paper, corroborates the validity of a
two phase model approach in the description of nonequilibrium
polymer dynamics.

\section*{Acknowledgement}
We thank G.T.~Barkema and A.~Revyakin for stimulating discussions. This
work is part of the research program of the Foundation for Fundamental
Research on Matter (FOM), which is financially supported by The
Netherlands Organisation for Scientific Research (NWO). J.-C.W. acknowledges
the support by the Laboratory of Excellence Initiative (Labex) NUMEV,
OD by the Scientific Council of the University of Montpellier 2 and
HPC@LR for offering computational resources.

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