text:
Mining millionaire who demanded $37.5MILLION when he slipped on a wet floor at Woolworths is handed less than $250,000
Stanley MacDonald, 77, slipped on a wet floor in Perth's Floreat Forum in 2012
He damaged two spinal discs, injured his knee and bruised his calf in the fall
Mr MacDonald sued for $37.5million and was last month awarded $250,000
By Charlie Moore For Daily Mail Australia
A millionaire mining tycoon has been awarded around $250,000 after falling over in Woolworths.
Stanley MacDonald, 77, sued for $37.5million after he slipped on a wet floor in Perth's Floreat Forum shopping centre in 2012.
He damaged two spinal discs, injured his knee and bruised his calf.
A millionaire mining tycoon has been awarded around $250,000 after falling over in Woolworths (stock image)
Mr MacDonald, who made $100million from the $1billion sale of his mining company to Gina Rinehart in 2011, argued his injuries caused him economic loss.
He said his pain impacted his quality of life and impeded his work duties, reported WA Today.
Mr MacDonald's lawyers compiled 34 lever arch files of evidence, including records of his 'wheelings and dealings' in mining, to prove that he was affected by the injury.
Outrage as it's revealed supermarket giants Coles as... Revealed: How Coles and Woolies will wage war on Aldi by...
Under WA law, damages payments are limited to $200,000 - but a judge ruled the maximum could be exceeded and awarded him slightly less than $250,000.
The case was protracted because Mr MacDonald was 'unable to sit and converse for long periods' with his lawyers,' the District Court of WA heard last month.
This was due to his injures and also a spate of other medical difficulties.
According to court documents, Mr MacDonald needed 15 operations since the start of the case.
Stanley MacDonald, 77, sued for $37.5million after he slipped on a wet floor in Perth's Floreat Forum in 2012 (stock image)
He was treated for depression, anxiety, alcohol abuse, osteoporosis, kidney pain and irritable bowel syndrome.
Mr MacDonald's lawyer described him as 'one of the most highly successful entrepreneurs in the Western Australian resource market.'
The businessman was director of Giralia Resources for 20 years before it was sold to Gina Rinehart's Atlas Iron.
He is an independent non-executive director of Zenith Minerals.
A Woolworths spokesman said: 'The safety of our customers and team members is incredibly important to us.
'We continue to work hard on improving our processes and team training to create the safest possible environment in our stores.'
Elderly mining entrepreneur wins small victory against Woolworths for slip and fall accident
Mining millionaire sues for $37.5m after falling in Woolworths


Hi everybody! We are Carlo and Umberto, students of Computer Science at the University of Bologna. We want to share our experience in developing a software project, named BaMaNews, during the course in Knowledge Management taught by Valentina Presutti. We have used Apache Stanbol, in particular the Topic Engine for the Enhancer component, in order to develop a new way of navigating newspaper websites.
At the end of the post we provide a link to download our installation guide of the Topic Classification Engine.
In the original concept of faceted classification, there was the intention of creating a method of classification that would provide not only a library catalog for books consultation, but also a way to arrange the books on the shelves according to a suitable order that would allow users to locate directly the documents relevant for them.
The facet is a particular aspect under which a topic can be treated. So the contents of a document can be described by a combination of values of these facets. Documents, with faceted classification, are not cataloged in a hierarchy but instead are described in terms of properties that these possess.
The project "BaMaNews" has the purpose to represent the faceted navigation in the context of the fruition of newspaper articles. So, BaMaNews offers an alternative to the usual navigation of newspapers websites (based on "section" or "keywords"). In particular, the main purpose is to allow a news navigation based on research of entities that are present in the articles.
The entities considered were: people, places and organizations (in the system called "Persone", "Luoghi" and "Organizzazioni"). These are the facets of our system. The recognition of these entities has been achieved through the use of Stanbol Apache enhancers.
In addition to the recognition of entities of the documents, we have identified (again with Stanbol Topic engine) the topics addressed by the documents. "Topic" is the fourth facet (in the system called "Topic"). An additional facet is given by the categories under which the newspaper website has categorized the news (in the system called "Categorie").
For the project we address the Guardian website. The analysis made it necessary an indexing step: the system retrieves data using the Guardian API, retrieves the body of the articles and analyzes, selects and saves the entities and topics that compose and describe the articles.
If you want to try BaMaNews, you can find it at this link.
The project "BaMaNews" has been created during the Knowledge Management course given by Valentina Presutti at the University of Bologna. In this course we have learned the principles and components of the Knowledge Management discipline, what is the Semantic Web and in particular which are the technology in support of KM and how to use them.
Apache Stanbol tool has been one of the technologies we have studied, used and finally exploited to create our project. Besides the use of the official release of the tool, we have also installed, configured and tested the Topic Classification Engine that has allowed us to perform a classification of articles according to arguments.
For this step, it has been very useful to us the documentation published by Olivier Grisel. Below we propose a revision of this documentation with description and explanation of the steps to perform.
34931 one to one relationships between entities and articles.
Here is the document with the description of the procedure we have followed in order to build and deploy the Topic Engine.


text:
September 19, 2020 // National
'Together Strong: Life Unites' is theme of March for Life set for Jan. 29
By Kurt Jensen
WASHINGTON (CNS) — The Sept. 10 announcement of the theme for the March for Life — "Together Strong: Life Unites" — made it clear the annual national event, in some form, will proceed next Jan. 29.
But details of how the march, rally and pro-life conference, which together have drawn as many as 100,000 participants in past years, will cope with COVID-19 self-quarantine restrictions in the District of Columbia were not part of the announcement.
Asked on EWTN's "Pro-Life Weekly" program that evening about whether people should start making plans, Jeanne Mancini, president of the March for Life Education and Defense Fund, said: "You know, everybody has to make that decision on their own. You know, considering their own situations, et cetera."
A young woman is seen with her child during the annual March for Life rally in Washington Jan. 24, 2020. Officials with the March for Life organization announced Sept. 10, 2020, the theme for the 2021 national rally and march marking the Roe anniversary will be "Together Strong: Life Unites." The event will take place in some form Jan. 29. (CNS photo/Tyler Orsburn)
She added, "But I certainly would be (making plans), and I obviously will be there this year. I think that standing for life and standing for inherent human dignity of every life from conception to natural death is all the more important this year when there is so much unrest, so much division in our country. We need to show that we are stronger together and that love and life unite us. They make us stronger."
In July, Mancini had said "we will continue to discern throughout this year what steps should be taken," regarding pandemic restrictions.
Social distancing and masks aren't the issue. Washington health authorities require a 14-day self-quarantine for visitors "participating in nonessential travel" from high-risk areas. The quarantine is adjusted every two weeks, and as of Sept. 8, was extended to visitors from 30 states.
That's a particular obstacle for the many high school and college groups who arrive on long-distance bus rides which have, over the decades, become the pulse of the event.
"If D.C. is still requiring a two-week quarantine for out-of-state travelers, I don't see a way for us to attend," said Ed Konieczka, assistant director of university ministry at the University of Mary in Bismarck, North Dakota. "We are taking care of the details that we can, and recognizing which things are out of our control."
The university typically sends around 200 students and staff members to the march, and in 2018, some 20 students flanked President Donald Trump in the Rose Garden at the White House when he addressed the Mall rally on a video link. This past January, Trump addressed the rally in person, becoming the first president to do so.
The alternative to a Washington trip, Konieczka said, will be a rally that day in Bismarck. "We have been approached by the Diocese of Bismarck with a request to coordinate efforts to have the biggest March for Life event ever at our state capital. We have a shared vision for a large event, where any of our students unable to travel to D.C. will join with members of the diocese."
Planners of state marches face the same uncertainty. "Right now with COVID and the restrictions, we are playing it by ear in Chicago," said Denise Zabor, office manager for Illinois Right to Life.
March for Life has taken place in Washington every January since 1974. It's always held on a date near the anniversary of the Supreme Court's 1973 rulings, Roe v. Wade and Doe v. Bolton, which legalized abortion on demand.
"I believe it's the rallying point for all of pro-life America," said Dave Bereit, the founder of 40 Days for Life, who co-hosted the theme announcement with Mancini.
Among those making remarks during the announcement were Carrie Severino, president of Judicial Crisis Network, and U.S. Rep. Chris Smith, R-New Jersey, who chairs the bipartisan Pro-Life Caucus in the House of Representatives.
"One of the most significant decisions a president has to make is who to put on the federal courts," Severino said. She warned of the danger of judges "who think it is their job to invent new constitutional rights.

redpajama_set_name: RedPajamaCommonCrawl


Danielle is originally from Milton, GA. She attended the University of Kentucky where she earned a B.S. in Kinesiology in 2014. She then pursued her Doctorate of Physical Therapy degree at the University of South Florida and graduated in 2018. During her doctorate program, she served as the APTS treasurer. During her clinical rotations, she focused on pediatric neuro development therapy, inpatient intensive care and orthopedics.
After graduation, she moved back to the Atlanta area and started at Peachtree Orthopedics and is working toward her certification in dry needling. During her free time, she enjoys walking her two dogs and spending time with her family.


I spent a grand total of $5.77 at Fred Meyer this weekend on a gallon of clearance organic milk, 2 loaves of clearance Vita-Bee bread, and a pink of sour cream. I thought I was doing great on my goal of spending very little on groceries.
Today I planned to go to Albertson's to use the double coupons and to my local QFC to get their "grand reopening deals" which would only total about $12.00.
Sadly, my coupons were in DH's car - at his office - when I took the girls to appointments near Albertson's. Happily, DH called and needed some paperwork so after naps the girls and I delivered it and picked up my coupon binder. We headed to QFC and I debated if it was worth it to take all four girls shopping right before dinner. I decided yes because we were desperate for cheese and they had Tillamook for $4.99.
The first thing we saw when we came in were pizzas for $2.99 each! I had just been looking at the pizza deals at Pizza Hut and Domino's planning for tomorrow night when we hide in our dark house and watch a movie. At $2.99 we would be paying less than half of the lowest coupon price I found. This was followed by numerous clearance deals I couldn't pass up so I spent way more than I intended but still stayed within my budget of $60/week.
I was keeping a running total in my mind and realized we were up to $35 or so and I had a $5/$50 coupon for the grand re-opening. I never imagined I'd use it but I decided to pick up a case of baby wipes (we are out and have been using wet baby washcloths for a few days!). Then I checked for green salsa because it's a primary ingredient in the Chicken la Viva that my family loves. It was on sale for 3/$5 so I got 3 of those too.
All told, with my $5 off coupon I spent $37.17 on groceries at QFC.
I decided I didn't need to go to Albertson's after all. Nothing in their ad rang my bell and by the time DH got home and we got through dinner it would have taken some guaranteed screamin' deals to get me out of the house a third time today.
Love your comment about hiding out in your dark house on Halloween. That's what we did. Brady even decided we should have a "picnic" dinner on a blanket in the living room. The kids loved it!
Funny! Ed also wanted to have the "picnic" dinner.


text:
Q: Populate select options from database to dynamic select option using jQuery From the database I have selected the names of the members as the select options. With jQuery, I have a dynamic Add button that adds new select field with the append function. But what could be the standard way to pass my select options generated by php in the append?
I have researched for a while but could not get it working. So any suggestions would be really helpful.
This is the page structure. It looks messy but please have a look at it. I have passed the $members as <?php echo $members; ?> in a static select that already is there from the beginning, but for the dynamic ones, I have created a variable var members and tried to pass it in the append but it is not working.
<?php
   require_once 'db_connect.php';

   $members = '';
   $query = "SELECT memberID, memberName FROM members";
   $result = mysqli_query($connect, $query);
   while($row = mysqli_fetch_array($result))
   {
    $members .= '<option value="'.$row["memberID"].'">'.$row["memberName"].'</option>';
   }
   ?>

<form method="post">
   <fieldset>

            Members

1.

                        <select name='members[]'>
                           <option value=''>Select member</option>
                           <?php echo $members; ?>
                        </select>

                        <button class='delete btn btn-warning btn-xs'>Delete</button>

                     <button id='addNew' type="button" href="#">Add another</button>

   </fieldset>
   <input type="submit" name="submitSave" value="Submit">
</form>

Here is a snippet of the form without the php if you need to see the jQuery in action.

    $(document).ready(function() {
       var fixHelperModified = function(e, div) {
             var $originals = div.children();
             var $helper = div.clone();
             $helper.children().each(function(index) {
                $(this).width($originals.eq(index).width())
             });
             return $helper;
          },
          updateIndex = function() {
             $('div.index').each(function(i) {
                $(this).html(i + 1);
             });
          };
       $("#add").sortable({
          helper: fixHelperModified,
          stop: updateIndex
       }).disableSelection();
       $("#addNew").click(function() {
          $('#add').append("

1.

<select name='members[]'><option value=''>Select member</option></select>

<button class='delete btn btn-warning btn-xs'>Delete</button>

");
          updateIndex();
       });
       $("body").on('click', '#add .delete', function() {
          $(this).closest(".rem").remove();
          updateIndex();
       });
    });

<form method="post">
   <fieldset>

            Members

1.

                        <select name='members[]'>
                        <option value=''>Select member</option>
                        <option value='First'>First</option>
                        <option value='Second'>Second</option>
                        </select>

                        <button class='delete btn btn-warning btn-xs'>Delete</button>

                     <button id='addNew' type="button" href="#">Add another</button>

   </fieldset>
   <input type="submit" name="submitSave" value="Submit">
</form>

A: Each option have double quotation marks and u put string inside same marks, if i correct understood it will break your code, try wrap inside single quotation or use var myvar = <?php echo json_encode($myVarValue); ?>;

A: I dont get you want to use jquery to add a select option from the list of already generated options(generated with php) each time a user clicks the add button?

A: If thats what you want? you can just echo the php into a javascript array

Then the jquery add button can just pick each options from the members array

A: I dont understand your many code but if what you want to do is add an option when clicked this is what i think should work
<select name='members' id="members_select">
<option value=''>Select member</option>
</select>
<button id="add">Add Option</button>

redpajama_set_name: RedPajamaStackExchange


text:
Demi Moore 'despondent' about career
Demi Moore is reportedly "despondent" about her acting career. Bang ShowBiz
DEMI Moore is said to be "despondent" about her acting career.
The 49-year-old star - who was hospitalised last week after she suffered a seizure - is reportedly "very, very unhappy" about the path her acting career has taken in the last 18 months and it is thought she has tried to increase her chances of landing a hit movie role by spending time with her 23-year-old daughter Rumer and her friends.
A source close to the actress - who has starred in 'Ghost', 'Indecent Proposal', 'Striptease' and 'Charlie's Angels' - told RadarOnline: "Demi is very, very unhappy with her acting career.
"Demi is despondent because she feels that her career has stalled. It's been a very long time since Demi was the marquee star that would open a movie.
"One of the reasons that Demi is obsessed with being young is that she feels if she is seen out with her daughter and Rumer's friends that might help increase her chances of being offered a role that might go to a younger actress."
The brunette beauty - who split from husband Ashton Kutcher in November amid speculation he had cheated on her - finished filming her latest movie 'LOL' last year, but insiders believe she doesn't have "any future projects lined up".
Following her hospitalisation last week, Demi opted to pull out of starring as feminist Gloria Steinem in 'Lovelace' - a movie about real-life porn actress Linda Lovelace - and she has since been replaced by Sarah Jessica Parker.
It has also been claimed that Demi has refused to enter rehab, despite being urged by daughters Rumer, Scout, 20, and Tallulah to seek help after she suffered a seizure.
Demi Moore won't go to rehab
Demi Moore released from hospital
'Exhausted' Demi rushed to hospital
Demi Moore's 'love-hate relationship'
Demi Moore dating again after split
Demi to 'punish' Ashton in divorce
Demi and Ashton's 'intense rows'
Demi Moore and Ashton Kutcher split
Demi Moore on 'detox' at rehab clinic
Demi's daughter having 'tough' time
Demi Moore 'isn't over Ashton'
Kutcher and Moore's divorce turns nasty over fortune
Demi Moore's 26-year-old boyfriend has dumped her


text:
package com.portalmgr.inventory.service;

import com.portalmgr.inventory.dao.InventoryDao;
import com.portalmgr.inventory.entity.Inventory;
import com.portalmgr.inventory.entity.InventoryVo;
import com.portalmgr.order.dao.OrderDao;
import com.portalmgr.order.entity.Order;
import com.portalmgr.order.entity.OrderDetail;
import com.portalmgr.util.GsonTools;
import org.springframework.stereotype.Service;
import org.springframework.transaction.annotation.Transactional;

import javax.annotation.Resource;
import javax.servlet.http.HttpServletRequest;
import java.util.ArrayList;
import java.util.Date;
import java.util.List;

/**
 * @author duwk
 * @Description
 * @Date 2017-03-02 15:20
 **/
@Service
public class InventoryService {

    @Resource
    public InventoryDao inventoryDao;
    @Resource
    public OrderDao orderDao;
    public List<Inventory> getInventoryList(InventoryVo inventroyVo) {
        return inventoryDao.getInventoryList(inventroyVo);
    }

    public int getInventoryCount(InventoryVo inventroyVo) {
        return inventoryDao.getInventoryCount(inventroyVo);
    }

    public Inventory findInventory(InventoryVo inventroyVo) {
        return inventoryDao.findInventory(inventroyVo);
    }

    @Transactional
    public int  updateInventory(HttpServletRequest request){

        String type = request.getParameter("type");//1是进货 2是售出
        String jsonStr= request.getParameter("jsonStr");
        String userId=request.getParameter("userId");
       // String jsonStr= hh();
        List<Inventory>  inventoryList = (List<Inventory>) GsonTools.getObjects(jsonStr, Inventory.class);

        //   userSessionInfo = (UserSessionInfo) CommonContext.getSessionValue(ClientConstantPool.SESSION_KEY, request);
        //String userId= userSessionInfo.getUserId()+"";
        //String userId="3";
        //第一步 插入订单表
        Order order = new Order();
        order.setCreateUserId(userId);
        order.setType(type);
        order.setOrderSeq(new Date().getTime()+"");
        orderDao.addOrder(order);
        int id = orderDao.getId();
        order.setOrderId(id);
        System.out.println(order.getOrderId());
        OrderDetail orderDetail =null;

        List<OrderDetail> orderDetailList = new ArrayList<OrderDetail>();
        if("1".equals(type)){
            //入库
            for (Inventory in :inventoryList){
                in.setNum(in.getNum() + in.getCnt());
                orderDetail = new OrderDetail();
                orderDetail.setNum(in.getCnt());
                orderDetail.setPrice(in.getPrice());
                orderDetail.setInventoryId(in.getInventoryId());
                orderDetail.setOrderId(order.getOrderId() + "");
                orderDetailList.add(orderDetail);
            }
        }else if("2".equals(type)){
            //出库
            for (Inventory in :inventoryList){
                in.setNum(in.getNum() - in.getCnt());
                orderDetail = new OrderDetail();
                orderDetail.setNum(in.getCnt());
                orderDetail.setPrice(in.getPrice());
                orderDetail.setInventoryId(in.getInventoryId());
                orderDetail.setOrderId(order.getOrderId() + "");
                orderDetailList.add(orderDetail);
            }
        }

        //第二  更新仓库库存量
        if(!inventoryList.isEmpty()){
          inventoryDao.updateInventory(inventoryList);
            //第三 插入订单明细表
            orderDao.addOrderDetail(orderDetailList);
        }

        return id;

    }

    public  String hh(){

        String str="";
        List<Inventory> inventoryList = new ArrayList<Inventory>();
        Inventory inventory= new Inventory();
        inventory.setNum(55);
        inventory.setCnt(5);
        inventory.setPrice(1864);
        inventory.setInventoryId(1 + "");
        inventory.setShape("sds");
        Inventory inventory1= new Inventory();
        inventory1.setNum(43);
        inventory1.setCnt(2);
        inventory1.setPrice(847);
        inventory1.setShape("sds");
        inventory1.setInventoryId(2 + "");
        inventoryList.add(inventory);
        inventoryList.add(inventory1);
        str=GsonTools.getJson(inventoryList);

        return str;
    }

}

redpajama_set_name: RedPajamaGithub


text:
\section{Introduction}
\label{sec:intro}
Recent years have seen a dramatic rise in opportunities for observing
strong-field gravitational dynamics. New observations of dense
black-hole-like objects, at stellar, intermediate, and supermassive scales are
increasingly frequent.  Anticipated gravitational wave observations by
ground-based and space-based detectors are expected to capture
information about these objects at moments of the strongest
gravitational interactions \cite{Gonzalez:2004nv,Danzmann03}.  Interpretation of data from any such
observations will depend on theoretical modeling of the strong-field
interactions of dense black-hole-like objects in the process of
generating gravitational radiation. General Relativity is the standard
model for describing gravitational interactions and wave generation.
However, the predictions of General Relativity for such cases
are not yet fully understood, and will depend on 3-D numerical relativity
computer simulations \cite{Schutz03}.

While numerical relativity has progressed markedly in recent years \cite{Alcubierre04},
significant improvements in the fidelity of models for events such as
binary black hole coalescence will be essential for the full
interpretation of upcoming observations.  There are many facets to the
problem of improving such simulation, including optimally formulating Einstein's
equations
\cite{Friedrich96,Baumgarte99,Kidder01a,Bona:2003fj}, properly handling boundaries, handling black hole
singularities, handling constraint violations, and making judicious
gauge choices \cite{aei:gauge}.  There are also basic numerical issues concerning how
to, with finite resources, perform such high-fidelity 3-D simulations
with strong short-wavelength gravitational features near the sources,
and weak but critical long-wavelength gravitational (radiation)
features emerging in a large domain.  Approaches to this latter class
of issues include, developing higher order accurate finite
differencing methods \cite{Zlochower:2005bj}, spectral methods \cite{Kidder00a}, mesh refinement techniques \cite{CarpetFMR,Imbiriba04,David} and
other forms of numerical patching techniques
\cite{Calabrese:2004gs,Thornburg:2004dv}.

We focus here on resolving a limitation which has arisen in our work on
numerical relativity simulations of binary black hole systems with
mesh refinement techniques, but which may have analogues in other
numerical patching treatments as well.  Mesh refinement techniques divide the computational domain into regions with separate computational grids which can be of higher resolution in some regions than others. Such approaches involve mesh-structure interfaces across which the details of the finite differencing
treatment suddenly change.  Inevitably, these interfaces contribute to computational error, manifesting such effect as ``reflections'' off the interfaces.
Considerable attention is given to implementing
``clean'' interfaces, which generate small error, compared to error generated in the bulk regions.  At minimum, this requires interface-induced error to converge at least as rapidly as the bulk error.  For some classes of black hole evolutions, with non-vanishing shift advection terms, we have typically observed
large error propagating from mesh interfaces.  Understanding and resolving this problem forms the focus of this paper, and we demonstrate a solution, mesh-adapted
differencing (MAD), that works.

\section{Interface Performance}
\label{sec:symptoms}

The pertinent features of our numerical scheme are as follows.
We are solving the 3+1 BSSN formulation of Einstein's equations \cite{Nakamura87,Shibata95,Baumgarte99,Imbiriba04}.  Our gauge condition is numerically determined, typically with some variation of the 1+log slicing and hyperbolic Gamma-driver shift evolution equations \cite{aei:gauge}.  We integrate in time with the iterative Crank-Nicholson method \cite{Teukolsky00}.  All spatial derivatives are computed by second order accurate, centered differencing, save for advection derivatives, for which
we use second order accurate upwinded differencing.

We are particularly interested in simulating gravitational radiation
generated in black hole collisions.  To resolve the black hole
sources adequately, whilst pushing the computational grid boundary
sufficiently far away, we use fixed mesh refinement (FMR), as
implemented by a software package for this purpose called PARAMESH \cite{MacNeice00}.
With this implementation, the resolutions of two adjacent refinement
regions always differ by a factor of two; i.e. the grid-spacing of the
coarser region is double what it is in the finer region.
``Ghostzones'' or ``guardcells'', typically two layers, are required
to provide buffering between refinement levels.  These guardcells are
filled in by interpolation.

Whether the simulation performs adequately in the presence of
refinement interfaces is a question of particular concern to us.  Inevitably,
refinement boundaries are sources of numerical errors, although these reflections
are often satisfactorily convergent and
negligible.  An exception has plagued us in the case of a
non-negligible shift, $\beta^i$, at refinement boundaries.  In this case
we observe a reflection pulse that propagates at a velocity of
$-\beta^i$.

An example can be seen in the case of single
Schwarzschild black hole (in isotropic Schwarzschild coordinates)
centered in a nested-box
arrangement of refinement regions.  The Hamiltonian constraint
provides a measure of the error in the runs and is plotted in
Fig.~\ref{BSSN_conv}.
\begin{figure}
\includegraphics[scale=.36, angle=-90]{BSSN_conv.eps}
\caption{Convergence plot for the Hamiltonian constraint error $H$ at time $t=4M$.  There is a single puncture black hole centered at the origin,
and refinement boundaries at $|x_i|=1M$, $2M$, and $4M$.  The finest grid spacing $h_f$ for each simulation is indicated in the figure, and the higher resolution is multiplied by a
factor of 4. For errors demonstrating second order convergence the curves should superpose.}
\label{BSSN_conv}
\end{figure}
These ``reflected'' error waves, or ``bumps'', notably propagating toward the black hole (at $x=0$) from each interface, are strongest when the
refinement interface is nearest to the black hole (where $\beta^i$ is
largest).  We have also noticed that the reflections seem to originate
coincidently with the passing of an initial gauge pulse through the
interface.  Such gauge pulses are typical in black hole simulations with ``1+log'' type lapse conditions, and propagate in this case at $\sqrt{2}$ times the speed of light asymptotically.
In Fig.~\ref{BSSN_conv} the convergence of the bumps is indicated by comparing
the error in the Hamiltonian constraint at two resolutions, a moderate resolution run of $h_f=M/32$ and run with uniformly doubled resolution, $h_f=M/64$, where $h_f$ refers to the resolution of the finest grid.  The curves have been rescaled so that they should superpose if the errors are second order convergent.
Disturbingly, the figure indicates that these errors not to converge
at reasonable grid resolutions, $M/32$ and .  Whether these reflection
errors would converge manifestly at sufficiently high resolution is
difficult to determine in our black hole applications of limited
achievable grid size.

In any case, the practical effect is that it
is a challenge to effectively control these errors which may dominate the error
around refinement boundaries in the strong field region.
Interestingly, however, we have not observed any adverse effect,
such as poor convergence, imprinted by these bumps on such phenomena as
gravitational radiation measured far from a binary black hole system \cite{David}.
However, other physical quantities of interest, such as the event horizon,
seem likely to be more sensitive to these near-field errors.

\section{Linearized BSSN}
\label{sec:linearizedbssn}

To understand the source of the $\beta$-speed error exhibited in the last section, we begin by considering a linearized BSSN system with 1+log slicing and hyperbolic Gamma-driver shift.
The system of equations is:
\begin{eqnarray}
{\dot a} &=& -2K\\
{\dot B^i} &=& {\dot{\tilde \Gamma^i}}\\
{\dot \beta_1^i} &=& \frac{3}{4} B\\
{\dot \phi} &=& -{1\over 6}(K - \partial_i \beta_1^i)+\beta_0^k\partial_k\phi\\
{\dot K} &=& - \partial_i \partial_i a +\beta_0^k\partial_k K\\
{\dot h}_{ij} &=& -2 {\tilde A}_{ij} + \partial_i \beta_1^j + \partial_j\beta_1^i - {2\over 3}\delta_{ij} \partial_k\beta_1^k +\beta_0^k\partial_k h_{ij}\\
{\dot{\tilde A}}_{ij} &=& \left[ -\partial_i\partial_ja - {1\over 2}\partial_k\partial_kh_{ij}
+ {1\over 2} \partial_i{\tilde\Gamma}^j + {1\over 2} \partial_j{\tilde\Gamma}^i\right. \nonumber \\ && \left.- 2\partial_i
\partial_j\phi \right]^{\rm TF}
  +\beta_0^k\partial_k {\tilde A}_{ij}\\
\dot{\tilde\Gamma}^i &=& -{4\over 3} \partial_i K + \partial_k\partial_k \beta_1^i + {1\over 3} \partial_i \partial_j \beta_1^j  +\beta_0^k\partial_k {\tilde\Gamma}^i
\end{eqnarray}
where $a \equiv \alpha-1$, $\beta_1^i \equiv \beta^i-\beta_0^i$, (with $\beta_0^i$ assumed spatially uniform for simplicity), and $h_{ij} \equiv
{\tilde \gamma_{ij}}-\delta_{ij}$.

For a problem that varies only in one dimension, with no initial transverse components, if we assume plane-wave solutions (generalizable by Fourier analysis), then the above system of equations can be written in the form:
\begin{eqnarray}
\label{ket_evolution}
\partial_t|u\rangle = ik\mathsf{M}|u\rangle
\end{eqnarray}
where
\begin{equation}
|u\rangle = \left( \begin{array}{c} {\hat a} \\ {\hat B} \\ {\hat \beta_1} \\ {\hat \phi} \\ {\hat K} \\ {\hat h} \\ {\hat A} \\ {\hat \Gamma}   \end{array}  \right)e^{i(kx-\omega t)}
\end{equation}
with ${\hat a}$, ${\hat B}$, ${\hat \beta_1}$, ${\hat \phi}$, ${\hat K}$, ${\hat h}$, ${\hat A}$, and ${\hat \Gamma}$ the amplitudes of $a$, $B^x$, $\beta_1^x$, $\phi$, $K$, $h_{xx}$, ${\tilde A}_{xx}$, and ${\tilde \Gamma}^x$ respectively,
and
\begin{equation}
 \mathsf{M}= \left( \begin{array}{c c c c c c c c}
       0         &        0        &         0       &       0       &  \frac{2}{ik} &       0       &       0       &       0       \\
       0         &        0        &   \frac{4ik}{3} &       0       &  \frac{4}{3}  &       0       &       0       &-\beta_0       \\
       0         & \frac{3}{4ik}   &         0       &       0       &       0       &       0       &       0       &       0       \\
       0         &        0        &  -\frac{1}{6}   &  -\beta_0     & -\frac{1}{6ik}&       0       &       0       &       0       \\
       -ik       &        0        &         0       &       0       &  -\beta_0     &       0       &       0       &       0       \\
       0         &        0        &   -\frac{4}{3}  &       0       &        0      &   -\beta_0    & -\frac{2}{ik} &       0       \\
 -\frac{2ik}{3}  &        0        &         0       & -\frac{4ik}{3}&        0      & -\frac{ik}{2} &  -\beta_0     & -\frac{2}{3}  \\
       0         &        0        & \frac{4ik}{3}   &       0       &  \frac{4}{3}  &       0       &       0       &   -\beta_0
\end{array} \right)
\end{equation}

The eigenvalues are
$0$,$-\beta_0$,$-\beta_0+1$,$-\beta_0-1$,$-\frac{1}{2}\beta_0+\frac{1}{2}\sqrt{\beta_0^2+8}$,$-\frac{1}{2}\beta_0-\frac{1}{2}\sqrt{\beta_0^2+8}$,$-\frac{1}{2}\beta_0+\frac{1}{2}\sqrt{\beta_0^2+4}$, and $-\frac{1}{2}\beta_0-\frac{1}{2}\sqrt{\beta_0^2+4}$.
If $|\lambda \rangle$ is the eigenvector associated with eigenvalue $\lambda$, and $\langle \lambda |$ is defined such that $\sum_{\lambda} |\lambda\rangle\langle \lambda| = \mathsf{I}$,
then
\begin{equation}
\label{ket_operator}
\mathsf{M}=\sum_{\lambda} \lambda |\lambda\rangle \langle \lambda|
\end{equation}
By substituting Eq.~(\ref{ket_operator}) into Eq.~(\ref{ket_evolution}) the system of evolution equations can be decomposed into a series of advection terms, each associated with a characteristic
velocity equal to one of the eigenvalues.  Note that, assuming $\beta_0 \ll 1$, the $\beta$-speed mode is much slower than any of the other non-zero-speed modes.  As we are particularly concerned with this mode, it is instructive to write the evolution
equation thus:

\begin{eqnarray}
\label{eqn:linBSSNadvectionResult}
 \partial_t  \left( \begin{array}{c} { a} \\ { B} \\ { \beta_1} \\ { \phi} \\ { K} \\ { h} \\ { A} \\ { \Gamma}   \end{array} \right)&=&-\beta_0 \partial_x  \left( \begin{array}{r} 0 \\ 0 \\ 0  \\ -\frac{3}{8} \\ 0 \\ 1 \\ 0 \\ 0   \end{array} \right) \left( -\frac{8}{3}\phi  -\frac{1}{3ik}\Gamma  \right) \nonumber \\ &&+\sum_{\lambda\neq-\beta_0} \lambda \partial_x|\lambda\rangle \langle \lambda |u\rangle
\end{eqnarray}

This equation indicates that disturbances originating in $\phi$ and ${\tilde \Gamma}^i$ can propagate in $\phi$ and $h_{ij}$ at $\beta$-speed and, further, that this is the only means of
$\beta$-speed propagation allowed by this system.  Thus $\phi$ is uniquely significant in both generating and propagating $\beta$-speed modes.
Note that \eqnref{linBSSNadvectionResult} resembles the $\dot \phi$ evolution equation in the BSSN system.

\section{A model problem}
\label{sec:bumpy}

Motivated by the discussion of the last section,
a simple model for the generation and propagation of the $\beta$-speed
modes is a one-dimensional advection
problem with an additional driving term,
\begin{equation}
\label{eqn:bumpy}
\dot \varphi(x,t)=\beta \partial_x\varphi(x,t)+f(x,t),
\end{equation}
In our numerical simulations, it appears that the reflected ``bumps'' may be
triggered by a rapidly propagating gauge pulse which propagates
outward early in the simulations.  For our model problem, which we will term
``Bumpy'' because of its most salient feature, we will drive
the advection equation with a pulse propagating at speed $v$,
significantly faster than the advection speed $\beta$. We thus let
$f(x,t)=f(x-vt)$ where $v$ is larger than $\beta$ and both are assumed
positive.  This model equation is simple enough
to be solved directly,
\begin{eqnarray}
\varphi(x,t)&=&\integral{0}{t}{f(x+(t-t')\beta,t')}{t'}\nonumber\\
&=&\frac{-1}{v+\beta}(F(x-vt)-F(x+\beta t))\label{eqn:bumpy-solve}
,
\end{eqnarray}
where $\partial_x F(x)=f(x)$.
For definiteness we can take the driving term to be a Gaussian pulse,
$f(x)=\exp(-x^2)$, implying $F(x)=(\sqrt(\pi)/2)\mbox{erf}(x)$.  For a
localized pulse, such as this, the $F(x+\beta t)$ term in the exact
solution will be negligible in the region of interest, near $x=x_0$.

\begin{figure}
\includegraphics[scale=.3, angle=-90]{BUMP_conv.eps}
\caption{Convergence plot for the error in $\varphi$.  There is a refinement boundary at $x=50$. The coarse grid spacing $h$ of each simulation is indicated in the
figure, and the medium and high resolution curves have been multiplied by $4$ and $16$ respectively, as appropriate to demonstrate second order convergence. }
\label{fig:BUMP_conv}
\end{figure}

To test if this model problem is sufficient, we have numerically
evolved \eqnref{bumpy} using a 1-D finite difference code with a
resolution $dx=h$ for $x<x_0$ and $dx=2h$ for $x>x_0$, realizing a
refinement boundary at $x=x_0=50$.  We evolved over the domain $0<x<100$
with periodic boundary conditions, using three-point upwind finite
difference stencil and a mesh refinement scheme
similar to that in our numerical simulations with PARAMESH.
In \figref{BUMP_conv} we show the errors in our evolution variable
$\varphi$ in the vicinity of the refinement interface
for runs with several resolutions, $h=5/64, 5/128$ and $5/256$
.  In each case there clearly a reflection
error bump propagating to the left, away from the refinement interface,
which we find propagates at speed $\beta$.
As before the errors have been rescaled so that
that second order converging error should superpose.
Comparing the two lower resolution run, we do not see good superposition,
and the peaks appear to converge at roughly first order.  The comparative appearance of these errors is similar to that seen for black hole simulations in
Fig.~\ref{BSSN_conv}.
However, running at higher resolutions, which is readily allowed by this 1-D model, we
find that the reflected error is indeed second order convergent, as is suggested by comparing the two higher resolution runs in  \figref{BUMP_conv}.
This convergence is manifest only at relatively high resolution
(high relative to the wavelength -- and higher than can be easily achieved
with respect to a gravitational wavelength in a binary black hole run).
Further experimentation has indicated that these results are not strongly
affected by variations in the
time-integration method or by changing among mesh refinement interfacing
schemes which are consistent with the overall second order finite differencing
accuracy.

\section{A finite difference analysis}
\label{sec:bumpyfd}

In this section we attempt to understand the numerical behavior of the
Bumpy problem \eqnref{bumpy} by constructing here an analytic model
for the numerical error in our simulations.  Noting that the time
discretization, and the details of the interpolation scheme used in applying
refinement conditions seem not to be directly linked to the problematic
error features we see, we model the error with as few assumptions as
possible about these details.  We treat the numerical errors
continuously in time, and we consider the effects of spatial finite
differencing in terms of a continuous field $\varphi(x,t,h)$ representing the
numerical solution at (fine-grid) resolution $dx=h$.  We then expand
$\varphi$ in orders of $h$,
\begin{equation}
\varphi(x,t,h)=\varphi_e(x,t)+h^2\varphi_2(x,t)+{\cal O}(h^3),
\end{equation}
Where $\varphi_e(x,t)$ is understood to be the exact solution
\eqnref{bumpy-solve}.
We consider the effect of our finite differencing scheme by replacing
the spatial derivative appearing in \eqnref{bumpy} with a suitable
finite difference operator $\tDh$. Thus,
\begin{equation}
\label{eqn:bumpyfd-start}
\dot \varphi(x,t,h)=\beta \tDh\varphi(x,t,h)+f(x,t).
\end{equation}
As above, we include a refinement jump in the grid at $x=x_0$,
represented here by
applying a coarser version of the finite difference stencil in the
$x>x_0$ part of the spatial domain.  This will be consistent with any
refinement interface algorithm which applies the same finite
difference stencil in both the coarse and fine regions, and applies a
interpolative guard-cell filling algorithm at the interfaces which
leads to finite differences at the interface which are consistently
second order accurate.  On a uniform grid the second order error term of
a finite first derivative is generally proportional to the third
derivative of the field,
\begin{equation*}
\Dh\varphi(x,t,h)=\partial_x\varphi(x,t,h)+e_2
h^2\partial_{x}^{3}{\varphi(x,t,h)}+{\cal O}(h^3).
\end{equation*}
For the specific upwind differencing operator used in \secref{bumpy}, the stencil of
which is,
\begin{eqnarray}
  D_{h} &=& \frac{1}{h} \left( -\frac{3}{2} + 2E_h - \frac{1}{2}E_{2h} \right)
\end{eqnarray}
where $E$ is the spatial translation operator defined such that $E_hf(x) = f(x+h)$,
the constant error coefficient turns out to be
$e_2=-1/3$.
Including the refinement jump, we have
\begin{eqnarray}
\tDh\varphi&=&\Dh\varphi+\Theta(x-x_0)(D_{2h}-\Dh)\varphi\label{eqn:Dh}\\
&=&\partial_x\varphi+(1+3\Theta(x-x_0))e_2h^2\partial_{x}^{3}{\varphi}+{\cal O}(h^3).\nonumber
\end{eqnarray}
Substituting into \eqnref{bumpyfd-start}, and rearranging, yields
\begin{eqnarray}
h^2\dot\varphi_2(x,t,h)&=&\left[-\dot\varphi_e(x,t)+\beta \partial_x\varphi_e(x,t)+f(x,t)\right]\nonumber\\
&&+h^2\beta \big[\partial_x\varphi_2(x,t,h)+\nonumber\\
&&\qquad e_2(1+3\Theta(x-x_0))\partial_{x}^{3}{\varphi_e(x,t)}\big]\nonumber\\
&&+{\cal O}(h^3).
\end{eqnarray}
Then noting that the first term vanishes, and taking the limit $h\rightarrow0$, we derive
\begin{eqnarray}
\dot\varphi_2(x,t)&=&\beta\partial_x\varphi_2(x,t)+\label{eqn:bumpyfd}\\
&&\qquad\beta e_2(1+3\Theta(x-x_0))\partial_{x}^{3}{\varphi_e(x,t)}\nonumber,
\end{eqnarray}
where we have used the notation $\varphi_2(x,t)=\varphi_2(x,t,0)$.
This is our model for the generation and propagation of finite differencing error in the numerical model problem in \secref{bumpy}.

Since \eqnref{bumpyfd} is of the same form as \eqnref{bumpyfd} we can
solve it the like fashion.
We leave out the negligible $F(x+\beta t)$ in $\varphi_e$,
substituting
\begin{eqnarray*}
f(x,t)&=&\beta e_2(1+3\Theta(x-x_0))\partial_{x}^{3}{\varphi_e(x,t)}\\
&\simeq&-\frac{\beta e_2}{v+\beta}(1+3\Theta(x-x_0))
\partial_{x}^{3}{F(x-vt)}
\end{eqnarray*}
into the first line of \eqnref{bumpy-solve}. Then, performing the
integral with careful attention to the presence of the step function,
we get the solution
\begin{eqnarray}
\varphi_2(x,t)&=&(s(x-vt)-s(x+\beta t))(1+3\Theta(x-x_0))\nonumber\\
&&+3s\big(\frac{-v}\beta(x-x_0+\beta(t-\frac{x_0}v)\big)\nonumber\times\\
&&\qquad (\Theta(x-x_0+\beta t)-\Theta(x-x_0)) \label{eqn:bumpyfd-solve}
\end{eqnarray}
where,
\begin{eqnarray*}
s(x)&=&\frac{\beta e_2}{(v+\beta)^2}\partial_x^{2}F(x)\\
 &=&-\frac{2 \beta e_2 x}{(v+\beta)^2}\exp{(-x^2)}.
\end{eqnarray*}
As in \secref{bumpy}, the $s(x+\beta t)$ is negligible in the relevant region
near the refinement interface. Thus the first term in
\eqnref{bumpyfd-solve} is effectively the differencing error
associated with the upsweep in $\varphi_e$ which propagates across the
grid at speed $v$.  This part grows four times larger in the coarse
$x>x_0$ region.  The second term is quite interesting, as it propagates
in the reverse direction at speed $\beta$.  It has the same $s(x)$
shape as the forward propagating component, but it is reversed, and
contracted by a factor $\beta/v$.  It is timed to originate at the
interface as the first pulse crosses.  The two terms combine make the
full solution continuous at the interface.  Heuristically, one could
say that the second term is caused by the discontinuity in the
differencing error, generated in order to produce a regular solution,
and then, necessarily advecting away as required by the original model
equation \eqnref{bumpy}.  It is contracted because it propagates at a
different speed than the first term, but their time dependences must match
at the interface.

Note that although we concretely consider second order finite
differencing here, the finite differencing order is largely irrelevant
in this analysis.  The calculation can be directly adapted
for the leading order in a higher order finite differencing
by changing a few coefficients.

\begin{figure}
\includegraphics[scale=.3, angle=-90]{BUMP_annu.eps}
\caption{Numerical error in $\varphi$, immediately after a pulse
incident on the refinement interface at $x=50$ has passed through,
generating a pulse of transmitted error and a contracted pulse of
reflected error.  The error is second order convergent and in
agreement with the analytic prediction of the numerical error, as
indicated.}
\label{fig:BUMP_annu}
\end{figure}
We check that this analysis accurately describes the numerical errors in our
Bumpy model evolutions by comparing the predicted error with the numerical
error results.  As Fig.~\ref{fig:BUMP_annu} shows,
the prediction of \eqnref{bumpyfd-solve} agrees to high precision with the
numerical simulation errors realized in high resolution runs.
The figure shows both the rightward propagating wave which travels at velocity
$v$ with the driving pulse, and the shorter-wavelength reflected wave.
The reason for the slow convergence in our Bumpy simulations is now clear.
Because the reflection must propagate at a significantly slower speed than the
pulse which generated it, while their frequencies must match, the reflected
pulse necessarily has a shortened wavelength.  The key ingredients in this
producing this effect are that we are simulating a system with
strongly mismatched propagation speeds, and with the potential for generating
mode-mixing reflections off numerical features such as our refinement
interfaces such.  In such a situation, with resolution
just sufficient to accurately resolve the long-wavelength features in the
solution, the shortened wavelength of the numerical reflections makes
them unresolvable without a significant increase in the resolution
(say by a factor of $v/\beta$).  We thus have reason to expect that such an
effect is indeed the source of the bumpy reflection in our black hole runs.
We will verify this by attempting to eliminating this type of error.

\section{Improving the differencing stencils}
\label{sec:thefix}

Slowly converging errors of the type exposed in \secsref{bumpy}{bumpyfd}
now seem likely to occur under fairly general circumstances.  This
explains our difficulties in many attempts to eliminate these
effects by tweaking the
interface conditions in various ways.  Our analysis suggests that the only
ways to avoid these problems, aside from eliminating the slowly propagating
modes by setting $\beta^i=0$, is to remove the mode-mixing reflections at
interfaces.
The results of the last section clearly show that the reflected error in the
Bumpy system is overwhelmingly due to the discontinuity in the differencing
operator.  More specifically, the reflection is related to the
discontinuity in the second order truncation error.
This observation suggests a solution.

Consider using modified differencing stencils such that the coefficient
of the second order truncation error in the fine grid region is multiplied by a
constant factor $q_0$ while the coefficient of the second order truncation error in
the coarse grid region is multiplied by a constant factor $q_1$.  Then
the previously constant coefficient $e_2$ of the last section becomes:

\begin{eqnarray}
e_2 \to [q_0+(q_1-q_0)\Theta(x-x_0)]e_2
\end{eqnarray}

Repeating the steps of the last section for this new truncation error,
the solution for the second order error in $\varphi$ becomes,
\begin{eqnarray}
\varphi_2(x,t)&=&(s(x-vt)-s(x+\beta t))(q_0+(4q_1-q_0)\Theta(x-x_0))\nonumber\\
&&+(4q_1-q_0)s\big(\frac{-v}\beta(x-x_0+\beta(t-\frac{x_0}v)\big)\nonumber\times\\
&&\qquad(\Theta(x-x_0+\beta t)-\Theta(x-x_0)) \label{eqn:bumpilessfd-solve}
\end{eqnarray}
Thus for the spatially blueshifted, reflected error, we now obtain,
\begin{eqnarray}
\varphi_{ref}=(4q_1-q_0)s(-\frac{v}{\beta}(x-x_0+\beta(t-\frac{x_0}{v})))
\end{eqnarray}

One possibility would be to eliminate the leading order reflection
error simply by choosing $q_0=q_1=0$.  This choice corresponds to
using higher order stencils, say third or fourth order accurate,
throughout the entire grid.
Higher order differencing methods are clearly valuable in numerical
relativity simulations \cite{Zlochower:2005bj}.
However, we will focus here on identifying a minimal way to realize
effective second order convergence in a second order convergent finite
differencing scheme.  Our result should generalize to arbitrary order.

Note that with the choice $q_0=1$ and $q_1=\frac{1}{4}$, the reflected error vanishes.
More generally, of course, any choice of $q_0$ and $q_1$ that makes the truncation error continuous
across the refinement boundary will remove the second order reflection.  In particular, the choice
\begin{eqnarray}
q_n = \left(\frac{h_0}{h_n}\right)^2
\end{eqnarray}
will work in the $n$th refinement region of a grid with an arbitrary number of refinement levels, where $h_0$ is assumed to be the
grid-spacing in the finest region.  We call such a mesh-adapted differencing scheme MAD.

A second order MAD stencil can be obtained simply by linearly combining a second order accurate stencil with
a higher order accurate stencil, as follows:
\begin{eqnarray}
\label{MAD_general}
D_{h_n} = q_nD_{h_n}^{[2]} + (1-q_n)D_{h_n}^{[j]}
\end{eqnarray}
where the superscripted numbers in square brackets represent the order of accuracy of the differencing operator, and $j>2$.  (Of course, this stratagem can be readily generalized for higher order MAD operators as well.)  In the particular case of a second order
upwinded stencil combined with a third order lopsided stencil, the resulting stencil has the form:
\begin{eqnarray}
\label{MAD_upwind}
  D_{h_n} &=& \frac{1}{h_n} \left[ \left( -\frac{1}{3}+\frac{1}{3}q_n \right) E_{-h_n} + \left( -\frac{1}{2}-q_n \right) \right. \nonumber \\ && \left.  + \left( 1+q_n
  \right)E_{h_n} + \left(
-\frac{1}{6}-\frac{1}{3}q_n \right)E_{2h_n} \right]
\end{eqnarray}

\begin{figure}
\includegraphics[scale=.3, angle=-90]{BUMP_MAD.eps}
\caption{Comparison of the error in $\varphi$ reflected from the refinement boundary at $x=50$ in the case of a second order conventional stencil and a second order MAD stencil.}
\label{BUMP_MAD}
\end{figure}
We have implemented this MAD stencil in the numerical simulations of the
Bumpy system. Fig.~\ref{BUMP_MAD} shows the result for a run at a moderate
resolution.  With the MAD stencil
the dominant reflected error is nearly eliminated.

\section{Results for black hole evolutions}
\label{sec:results}

We can demonstrate that our analysis does indeed explain the problematic reflections in our black hole simulations, by verifying that the same remedies applied to fix our Bumpy model problem, i.e. higher order or MAD stenciling, also
fix the problem in our black hole simulations.

As in \cite{Zlochower:2005bj}, we have found that third or higher order accurate differencing
of advection terms is unstable in the vicinity of black hole punctures, if the stencil has any points on
the ``downwind'' side.  If the 3rd or higher order accurate differencing stencil does not have
any points on the downwind side, it requires three or more layers of guardcells to accommodate
points on the upwind side, which is expensive memory-wise.
Thus, although higher order spatial differencing should reduce reflection
from refinement boundaries, it brings with it a new set of problems to solve.

Use of a second order accurate MAD stencil, as in Eq.~(\ref{MAD_upwind}), for advection, avoids the above difficulties.  As we generally
locate the punctures within the finest grid regions, and the MAD stencil automatically reverts to conventional second order
upwinding in this region, the advection derivative does not take any points on the downwind side in
the vicinity of the puncture and we find that stability is maintained.

In our Einstein solver, we have implemented a second order accurate
MAD stencil for advection.  For all non-advection derivatives, the MAD
stencil is constructed from a linear combination of second order
centered and fourth order centered stencils, as in
Eq.~(\ref{MAD_general}).  As a result, reflection from refinement
boundaries has been dramatically reduced in the case of a single
puncture.
\begin{figure}
\includegraphics[scale=.3, angle=-90]{BSSN_MAD.eps}
\caption{Comparison of the Hamiltonian constraint $H$ in the case of second order accurate, conventional differencing stencils
and second order accurate, MAD stencils, as well as a demonstration of convergence in the latter case.   There is a single puncture black hole centered at the origin,
and refinement boundaries at $|x_i|=1M$, $2M$, and $4M$.}
\label{BSSN_MAD}
\end{figure}
Fig.~\ref{BSSN_MAD} compares the Hamiltonian
 constraint error from a run with conventional stencils with the Hamiltonian
 constraint error in runs with MAD stencils, demonstrating clear improvement.
The plot shows that the reflection error for our $h_f=M/32$ case is
much reduced with the MAD stencil.  By comparing with the $h_f=M/64$,
MAD-stencil run, we also see that the remaining bump now converges away at
second order or better.

For simplicity we only show plots from single black hole simulations here,
though we have applied MAD in more interesting binary black hole cases as well.
We find that the improvements generalize naturally to these cases.
In particular we find that errors in the
Weyl scalars near refinement boundaries are reduced by at least an
order of magnitude.

\section{Conclusions}
\label{sec:conclusions}

We have studied a problem which occurs in numerical relativity simulations
with nonvanishing shift with mesh refinement. These involve slow advection
modes across a mesh interface, and produce slowly converging numerical
reflections that propagate at the speed $\beta$ of the advection.
We have successfully modeled the problem analytically.  Our analysis suggests
that the the effect is a general consequence of discontinuous jumps in the
finite differencing stencil in a problem with propagation modes of widely differing speeds.  Our proposed solution, to adjust the finite differencing
stencils to make the leading order differencing error
continuous across mesh interfaces, is shown to be effective in black hole simulations with mesh refinement, but may have wider application in numerical relativity.
In addition to grids of non-uniform refinement, mesh-adapted differencing may also be appropriate for grids with multiple coordinate patches,
where discontinuous differencing error can also be expected.

\begin{acknowledgments}
We are happy to thank J. David Brown for helpful discussion.
We gratefully acknowledge CPU time grants from the Commodity
Cluster Computing Project (NASA-GSFC) and Project Columbia (NASA
Advanced Supercomputing Division, NASA-Ames).  This work was supported
in part by NASA Space Sciences grant ATP02-0043-0056. JvM was also
supported in part by the Research Associateship Programs Office of the
National Research Council.
\end{acknowledgments}

redpajama_set_name: RedPajamaArXiv


On Sale Now! Free Shipping Included! Save 4% on the Blue Force Gear BLFVCAS-200-OA-BK Vickers 2-Point Padded Combat Sling, Black by Blue Force Gear at Freedom from Government. MPN: BLFVCAS-200-OA-BK. Hurry! Limited time offer. Offer valid only while supplies last. Blue Force Gear, Sling, Molded Acetal Adjuster, No Quick Release, Attached with TriGlide instead of Loop Lock, 2-Point Padded Combat Sling, Black.
If you have any questions about this product by Blue Force Gear, contact us by completing and submitting the form below. If you are looking for a specif part number, please include it with your message.


text:
UK composting: From table to farm
University reducing waste in landfills
LEXINGTON, Ky. (LEX 18)-- — This week, the University of Kentucky took another step in their goal towards reducing their waste in landfills.
The university plans to divert 50% of their waste from landfills to being reusable products by 2022. Using a pulping machine in their kitchens on campus, they're now able to compost nearly everything students leave on their plates.
"They bring their food to the front of the line, and it comes on this conveyor belt where our staff pulls the plates off and they throw any trash into the trashcan, and then all the food waste goes into this tunnel right here that is fed into the pulper," said Carolyn Gahn, the UK Dining Services Sustainability Director. "We are able to to take most every type of food and that includes fresh produce, and scraps, to meds, and dairy, and oils."
Gahn told LEX 18 that the pulper takes all the food and makes it into small pieces and then removes the water weight. The pieces then go into their bins, and the bins go all the way to Woodford County to one of UK's research farms.
"So they add it to material that comes from this farm and it's mainly livestock betting, and it's mixed with that and then goes to the composting system where it's turned a number of times to bring in air into the pile, and then bacteria break down those materials those plant materials and manure were into a product that is the final compost product," said Dr. Mark Williams, the UK Organic Farming Unit Director.
The composting happens at UK's wind-rowing system, and in a matter of weeks, waste will be turned into something more valuable.
"What compost does is it's kind of a broken down form of carbon, it's once you put it in the soil it basically locks and carbon or sequesters carbon that would normally be released into the atmosphere," said Williams. "In many ways, this compost is a soil amendment. It increases our soil organic matter which is one of the key measurements of soil quality."
"It's a win-win in many ways it's a win for the overall planetary standpoint. It's a win for a community standpoint and just in the feels that we apply. And it helps us to be better stewards of the land," Williams told LEX 18.
Increasing the soil quality that then helps grow food on UK's research farms. It's a new program that's been in the works since 2014.
"We'll probably divert three to four tons of food waste a week through this process, so 150 to 200 tons of food waste per year, and that in and of itself is awesome, but this food waste composting program really should be situated in kind of the bigger picture of food waste and how it relates to hunger and food insecurity," said Shane Tedder, the UK Campus Sustainability Coordinator. "Beyond the campus, I think this program will really serve as proof of concept. That composting can work, can be cost-effective with landfilling. And then for a student, it's an educational opportunity that they'll take with them when they leave."
The university is hoping that the composting program will allow them to start moving 25% of their waste to the farm for composting or other recycling outlets.


text:
Весе́ле (також Єлесеєнків хутір) —  село в Україні,  Чернігівській області, Бахмацькому районі.

Історія
Виникло у 80-х роках XVII століття. В селі знаходилася поштова станція і шинок. В шинку завжди було весело. Мабуть, звідси і пішла назва села.

До XVIII століття цей хутір називався Єлесеєнків. Коли прокладався старий шлях Київ - Москва (за часів царювання Катерини II) першими поселенцем на території сучасного хутора Веселого був Єлесеєнко. Звідси і назва - Єлесеєнсків хутір, а пізніше - Веселий.

В 1917 році в хуторі було 10 дворів і проживало 59 чоловік. В 1930 році в хуторі було створено артіль "ІІ-га п"ятирічка".

Посилання
 Погода в селі

Села Чернігівської області
Населені пункти Ніжинського району

redpajama_set_name: RedPajamaWikipedia


in Loralai, Buriwal Hotel is the only hotel which is famous in this city. With the help of this page I am successfully find the address which I am noting, I will definitely contact.
Buriwal Hotel - Find the best Hotels in Loralai with an extensive long range. Discover the amazing city Loralai by visiting your choice of Hotels. We updates you with all the famous Hotels in Loralai. Find complete details with reviews, ratings, map & photos of Buriwal Hotel in Loralai. Get Latest Deals & Packages of Buriwal Hotel 2016 with discounted Room Rent, Booking & Packages 2016 offered by Hotel.


This leading digital agency is looking for a Business Development Director / New Business Director, could be based in either Glasgow or London.
The purpose of this role is to assure a sustainable talent pipeline for Ogilvy EMEA. This will include identifying key talent for the future.


text:
Good reads from good tigers
El Tigre in Print
Join El Tigre
Careers in Journalism & Publication
Humans of Valencia
Tiger Tube
Want El Tigre Swag?
Holocaust Art & Writing Contest 2019-2020
Roar: Powered by El Tigre
A Little Bit of Blues Featuring Alex Hahn
May 23, 2018 El Tigre Staff
On May 18, 2018 at 7:00 P.M. at the Valencia High School Auditorium, the combined jazz bands from Kramer Middle School and Valencia High School performed back-to-back with special guest artist Alex Hahn. 2018 marks the 20th anniversary of Valencia High School hosting a Jazz Guest Artist Concert. Previous years have seen artists like Wayne Bergeron, Barbara Morrison, Bijon Watson, and Francisco Torres perform alongside Valencia's own jazz bands. This year, Valencia and Kramer invited saxophone player Alex Hahn to perform with both schools.
Alex Hahn is an award-winning saxophonist and composer based in Los Angeles, California. He graduated from University of North Texas in 2014 with a Bachelor of Music and later on graduated from the University of California with his Master of Music in Jazz Studies. Along with his accolades, Hahn is well-known for performing with other renowned artists like Herbie Hancock, John Clayton, and Michael Buble. He has traveled and performed in countries like Havana, Cuba and St. Petersburg, Russia. Hahn also leads his own group called The Alex Hahn Crossing recently releasing their new album "Emerging" to critical acclaim.
The Kramer Jazz Band under the direction of Mr. Mark Gunderson performed songs such as "The Blues Walk" by Clifford Brown, "Birdland" by Joseph Zawinul, and "I Gots The Sleepy Man Blues" composed by Hahn himself. Valencia's Jazz II and Jazz I performed with Hahn, "There Will Be Another You," "Second Chances," and featured on Hahn's album, Emerging, "Psychedelic Sun."
After the performance, Hahn spoke about his experience working with the bands. He spoke of both bands having "a great amount of fun working with [him]". He says that he always strive towards "pushing boundaries towards a great performance." When Hahn rehearsed with the bands, he worked on "tweaking and improving students' jazz improvisation" as well as tips on being a better performer. Hahn commented that it was "amazing to work with the jazz students who have a significant amount of energy." He recognized that this performance has "great symbolic meaning to [him] considering [he] has done performances like the one at Valencia when [he] was in high school and that they performed music familiar to [him]."
← Click on the Newest Edition of El Tigre
New Head Coach- OCAD →
Follow EL Tigre on WordPress.com
500 N Bradford Ave
714-996-4970 x10502
Class of 2018's Graduation Date
C/O 2018 GraduatesJune 14, 2018


Master planning defines the connections between buildings, social settings and their surrounding elements. It involves the analysis, recommendations, and proposals for a site's population, housing, transportation, and land use. Public input, surveys, existing developments, social and economic conditions, and much more are factored in to the master plan. At ARTEFACT studio, master planning involves the care and consideration of all these factors and much more.
Our world is growing at an ever-increasing pace. Urban renewal and expansion, land development and reclamation can have a significant impact on the built environment. For the team at ARTEFACT studio, master planning plays a vital role in ensuring that new projects not only serve the current needs but also look ahead and anticipating the needs of the future.
In its simplest form, master planning is a study used to define the long-term development of a particular space or built environment. The end result may extend into many forms, such as a report, website, or publicity campaign. Included in the master plan is a concept and guidelines for future development of the area, which take into consideration factors such as the economy, housing, effects on the environment, population, transportation, existing development, and other socio-economic factors.
When is a Master Plan Needed?
Master Planning is required when it comes to big ideas that impact the landscape of a city or a specific space. It is a critical element to the design process because it provides a comprehensive look at the built environment and how best to prepare for growth and development.
A highly-experienced and skilled team of architects, designers, planners, and experts from various disciplines bring their unique skills to the development of the master plan. This collaborative process ensures that the final design adheres to the wishes and needs of the client, and ultimately the success of the project.
Why Start with a Master Plan?
The decision to develop a master plan can be prompted by the desire to serve the client's needs, understand the current situation, gain community interest and support, set a vision for the future, and/or to define a clear implementation strategy.
· Economic regeneration—attract investment or benefit from ownership.
· Social regeneration—improve social conditions (e.g. lower crime rates, increase jobs) a site or neighborhood.
· Environmental improvement—improve, protect or regenerate a site or area.
· Re-brand—change the identity and appearance of the place and to influence its perception in the public sphere.
Master planning is typically conducted in the early stages of a major development project, such as campuses, retail centers, parks and public spaces, airports, and urban restoration or re-development projects. However, master plans can be useful for a full range of projects.
What Considerations Go into Master Planning?
A feasibility study is an objective review of the options available for development. It includes the analysis and recommendations of visioning and scoping exercises from a given site.
The strategic framework sets the scene and establishes the baseline information relating to the physical, social, and economic context of the site and surrounding environment.
Neighborhood character and heritage – The master plan should show the how the project will integrate with the surrounding area. Considerations for topography, waterways, existing landscape and heritage features should be incorporated into the design.
Various Uses – The master plan should show the location of various uses (e.g. housing and/or commercial uses) and their densities, yields, and lot sizes.
Open and public space – The master plan should show the location of both passive and active open spaces including their functions, sizes, and scales.
Biodiversity – The master plan should identify and explain how significant biodiversity values will be incorporated into the site.
Water management and utilities – The master plan must outline decisions and recommendations for the preservation of wetlands, catchment areas, waterfront areas. Guidelines for public use of waterways must also be included.
Transport – The master plan should show the hierarchy of streets, pedestrian and cycle paths, and public transport and freight routes.
Are you Ready to Start Your Master Planning Project?
ARTEFACT studio's goal is to offer a comprehensive master planning approach that allows our clients to make their ideal future a reality. Our process brings key stakeholders together to provide ideas and input to streamline the framework with which to proceed with the project. To learn more about our master planning process we invite you to schedule a call or meeting with us.