text:
Home Sexes and castes Queen bee
updated on September 28, 2020 September 17, 2020 Sexes and castes
The term queen bee is typically used to refer to an adult, mated female (gyne) that lives in a honey bee colony or hive; she is usually the mother of most, if not all, of the bees in the beehive.
Queens are developed from larvae selected by worker bees and specially fed in order to become sexually mature. There is normally only one adult, mated queen in a hive, in which case the bees will usually follow and fiercely protect her.
The term "queen bee" can be more generally applied to any dominant reproductive female in a colony of a eusocial bee species other than honey bees.
However, as in the Brazilian stingless bee Schwarziana quadripunctata, a single nest may have multiple queens or even dwarf queens, ready to replace a dominant queen in a case of sudden death.
Virgin queen bee
Reproduction cycle
Supersedure
Older queen larvae in queen cell lying on top of wax comb
A queen cup
Queen larvae floating on royal jelly in opened queen cups laid on top of wax comb
During the warm parts of the years, female "worker" bees leave the hive every day to collect nectar and pollen. While male bees serve no architectural or pollinating purpose, their primary function (if they are healthy enough) is to mate with a queen bee.
If they are successful, they fall to the ground and die after copulation. Any fertilized egg has the potential to become a queen.
Diet in the larval stage determines whether the bee will develop into a queen or a worker. Queens are fed only royal jelly, a protein-rich secretion from glands on the heads of young workers.
Worker larva are fed bee bread which is a mixture of nectar and pollen. All bee larvae are fed some royal jelly for the first few days after hatching but only queen larvae are fed the jelly exclusively.
As a result of the difference in diet, the queen will develop into a sexually mature female, unlike the worker bees.
Queens are raised in specially constructed queen cells. The fully constructed queen cells have a peanut-like shape and texture. Queen cells start out as queen cups.
Queen cups are larger than the cells of normal brood comb and are oriented vertically instead of horizontally. Worker bees will only further build up the queen cup once the queen has laid an egg in a queen cup.
In general, the old queen starts laying eggs into queen cups when conditions are right for swarming or supersedure. Swarm cells hang from the bottom of a frame while supersedure queens or emergency queens are generally raised in cells built out from the face of a frame.
As the young queen larva pupates with her head down, the workers cap the queen cell with beeswax. When ready to emerge, the virgin queen will chew a circular cut around the cap of her cell. Often the cap swings open when most of the cut is made, so as to appear like a hinged lid.
During swarming season, the old queen is likely to leave with the prime swarm before the first virgin queen emerges from a queen cell.
Metamorphosis of the queen bee
Egg hatches on day 3
Larva (several moltings) day 3 to day 8 1⁄2
Queen cell capped day 7 1⁄2
Pupa day 8 until emergence
Emergence day 15 1⁄2 – day 17
Nuptial flight(s) day 20 – 24
Egg laying day 23 and up
A virgin queen is a queen bee that has not mated with a drone. Virgins are intermediate in size between workers and mated, laying queens, and are much more active than the latter.
They are hard to spot while inspecting a frame, because they run across the comb, climbing over worker bees if necessary, and may even take flight if sufficiently disturbed.
Virgin queens can often be found clinging to the walls or corners of a hive during inspections.
Virgin queens appear to have little queen pheromone and often do not appear to be recognized as queens by the workers.
A virgin queen in her first few hours after emergence can be placed into the entrance of any queenless hive or nuc and acceptance is usually very good, whereas a mated queen is usually recognized as a stranger and runs a high risk of being killed by the older workers.
When a young virgin queen emerges from a queen cell, she will generally seek out virgin queen rivals and attempt to kill them. Virgin queens will quickly find and kill (by stinging) any other emerged virgin queen (or be dispatched themselves), as well as any unemerged queens.
Queen cells that are opened on the side indicate that a virgin queen was likely killed by a rival virgin queen. When a colony remains in swarm mode after the prime swarm has left, the workers may prevent virgins from fighting and one or several virgins may go with after-swarms.
Other virgins may stay behind with the remnant of the hive. Some virgins have been seen to escape the hive to avoid being killed and seek out another without a queen, such as in the eusocial bee Melipona scutellaris. This can contain multiple virgin queens.
When the after-swarm settles into a new home, the virgins will then resume normal behavior and fight to the death until only one remains. If the prime swarm has a virgin queen and the old queen, the old queen will usually be allowed to live.
The old queen continues laying. Within a couple of weeks she will die a natural death and the former virgin, now mated, will take her place.
Unlike the worker bees, the queen's stinger is not barbed and she is able to sting repeatedly without dying.
Capped queen cell opened to show queen pupa (with darkening eyes).
Piping describes a noise made by virgin and mated queen bees during certain times of the virgin queens' development.
Fully developed virgin queens communicate through vibratory signals: "quacking" from virgin queens in their queen cells and "tooting" from queens free in the colony, collectively known as piping.
A virgin queen may frequently pipe before she emerges from her cell and for a brief time afterwards. Mated queens may briefly pipe after being released in a hive.
Piping is most common when there is more than one queen in a hive. It is postulated that the piping is a form of battle cry announcing to competing queens and the workers their willingness to fight.
It may also be a signal to the worker bees which queen is the most worthwhile to support.
The piping sound is a G♯ (aka A♭). The adult queen pipes for a two-second pulse followed by a series of quarter-second toots.
The queens of African bees produce more vigorous and frequent bouts of piping.
The surviving virgin queen will fly out on a sunny, warm day to a "drone congregation area" where she will mate with 12–15 drones.
If the weather holds, she may return to the drone congregation area for several days until she is fully mated. Mating occurs in flight. The young queen stores up to 6 million sperm from multiple drones in her spermatheca. She will selectively release sperm for the remaining 2–7 years of her life.
The young virgin queen has a limited time to mate. If she is unable to fly for several days because of bad weather and remains unmated, she will become a "drone layer."
Drone-laying queens usually signal the death of the colony, because the workers have no fertilized (female) larvae from which to raise worker bees or a replacement queen.
Though timing can vary, matings usually take place between the sixth and tenth day after the queen emerges. Egg laying usually begins 2 to 3 days after the queen returns to the beehive, but can start earlier than this.
A special, rare case of reproduction is thelytoky: the reproduction of female workers or queens by laying worker bees by parthenogenesis. Thelytoky occurs in the Cape bee, Apis mellifera capensis, and has been found in other strains at very low frequency.
Capped swarm queen cells
As the queen ages her pheromone output diminishes. A queen bee that becomes old, or is diseased or failing, is replaced by the workers in a procedure known as "supersedure".
Supersedure may be forced by a beekeeper, for example by clipping off one of the queen's middle or posterior legs. This makes her unable to properly place her eggs at the bottom of the brood cell; the workers detect this and then rear replacement queens.
When a new queen becomes available, the workers kill the reigning queen by "balling" her, clustering tightly around her.
Death through balling is accomplished by surrounding the queen bee and raising her body temperature, causing her to overheat and die. Balling is often a problem for beekeepers attempting to introduce a replacement queen.
If a queen suddenly dies, the workers will attempt to create an "emergency queen" by selecting several brood cells where a larva has just emerged which are then flooded with royal jelly.
The worker bees then build larger queen cells over the normal-sized worker cells which protrude vertically from the face of the brood comb. Emergency queens are usually smaller and less prolific than normal queens.
Unmarked queen with attendants.
The primary function of a queen bee is to serve as the reproducer. A well-mated and well-fed queen of quality stock can lay about 1,500 eggs per day during the spring build-up—more than her own body weight in eggs every day.
She is continuously surrounded by worker bees who meet her every need, giving her food and disposing of her waste. The attendant workers also collect and then distribute queen mandibular pheromone, a pheromone that inhibits the workers from starting queen cells.
The queen bee is able to control the sex of the eggs she lays. The queen lays a fertilized (female) or unfertilized (male) egg according to the width of the cell.
Drones are raised in cells that are significantly larger than the cells used for workers. The queen fertilizes the egg by selectively releasing sperm from her spermatheca as the egg passes through her oviduct.
white 1 or 6
yellow 2 or 7
red 3 or 8
green 4 or 9
blue 5 or 0
Marked queen
The queen bee's abdomen is longer than the worker bees surrounding her and also longer than a male bee's. Even so, in a hive of 60,000 to 80,000 honey bees, it is often difficult for beekeepers to find the queen with any speed; for this reason, many queens in non-feral colonies are marked with a light daub of paint on their thorax.
The paint usually does not harm the queen and makes her easier to find when necessary.
Although the color is sometimes randomly chosen, professional queen breeders use a color that identifies the year a queen hatched, which helps them to decide whether their queens are too old to maintain a strong hive and need to be replaced.
The mnemonic taught to assist beekeepers in remembering the colour order is Will You Raise Good Bees (white, yellow, red, green, blue).
Sometimes tiny convex disks marked with identification numbers (Opalithplättchen) are used when a beekeeper has many queens born in the same year – a method that can also be used to keep multiple bees in the same hive under observation for research purposes.
Queen rearing is the process by which beekeepers raise queen bees from young fertilized worker bee larvae. The most commonly used method is known as the Doolittle method.
In the Doolittle method, the beekeeper grafts larvae, which are 24 hours or less of age, into a bar of queen cell cups. The queen cell cups are placed inside of a cell-building colony.
A cell-building colony is a strong, well-fed, queenless colony that feeds the larva royal jelly and develops the larvae into queen bees.
After approximately 10 days, the queen cells are transferred from the cell building colony to small mating nuclei colonies, which are placed inside of mating yards.
The queen cells hatch inside of the mating nuclei. After approximately 7–10 days, the virgin queens take their mating flights, mate with 10–20 drone bees, and return to their mating nuclei as mated queen bees.
Queen rearing can be practiced on a small scale by hobbyist or sideline beekeepers raising a small amount of queens for their own use, or can be practiced on a larger, commercial scale by companies that produce queen bees for sale to the public. As of 2017, the cost of a queen honeybee ranges from $25 to $32.
Beekeepers can also utilize alternative methods of queen rearing. Examples are the Jenter kit, walk-away split, Cloake board, and artificial insemination.
Previous Article Honey
Next Article Pheromone
updated on September 28, 2020 September 7, 2020 Bee colonies Sexes and castes
Raising Queen Bees
Queenless Beehives


text:
Special deptt sought to curb cyber crime
Federal Investigation Agency (FIA) Director General Syed Mohib Asad on Saturday said Pakistan needed a special department as a first measure to control cyber crimes. Addressing a seminar "Cyber Security: Challenges and Solutions" arranged by the FIA in collaboration with the Punjab Information Technology (IT) Department, he said website hacking was a major problem. "The devising of a proper system to monitor and investigate cyber crimes requires funds and IT experts," he said. The FIA DG said the government had started blocking porno sites, but such sites were in abundance and increasing day by day. "At present we can only monitor websites effectively, but a comprehensive system will be introduced. We (the FIA) have sent a project proposal to the federal government. A central database and clearing house are prerequisite to control cyber crimes," he added. He said the FIA had monitored communications by a group of smugglers between Karachi, Dubai and Singapore and recently seized their shipment of computers at the Karachi Port. "The computers were smuggled from Canada and their worth is US $3 million," he added. Full Story

redpajama_set_name: RedPajamaCommonCrawl


Shut up about Barclay Perkins: What, no beer!
While beer wasn't officially rationed during WW I, it was in short supply, especially during the later years. Which meant it was effectively rationed by breweries. They would limit the amount supplied to each public house. Pubs often ran out of beer.
The little bye-path inns on the outskirts of London, where prior to the war the casual pedestrian from the metropolis found solace and refreshment, are having a very bad time in these days when beer is hard to buy, and most of the wayfarers are foot-slogging elsewhere in khaki. To-day, in a well-inned area within easy tramp of a bus route terminus, I found a state of things that must bring sorrow to the heart of every lover of the quiet countryside round London. Some my favourite hostelries had put their shutters up for good, and not one of those that remained but had on the door of the parlour bar, where of old the good brown ale used to be found, a pathetic little notice with the legend "No beer." Mine hostess of a favourite inn declared that she had been allowed a scrimpy 18 gallons in month, "and how far do they think that will go, sir," she exclaimed indignantly, "with a sun that would melt you to a greasedrop, and the second hay making season its height?" After a pause she added, "Not that haymaking makes so much difference — it's all being done by German prisoners. Perhaps you Western Daily Press - Tuesday 13 August 1918, page 3.have seen them, sir?" I had, and very lazy and un-British lot of men they seemed to be."
Even in in a quiet pub, 18 gallons would only be enough for a couple of days. For a month, it works out to slightly less than five pints a day. Enough for a boozy lunch for one customer.
Bobbejaan Schoepen: "Café zonder bier"


This is Niloufer Ichaporia King's California-style version of an old Parsi favorite, green peas ma gos ("in meat"). The California touches are to use leeks instead of regular onions and to cook the peas for far less time than is traditional. Prep and Cook Time: about 4 hours. Notes: You can make the stew a day or two ahead and chill it (in fact, this makes removing the fat easier, since it solidifies in the refrigerator), but don't add the peas until you're ready to serve the meal. Fresh peas will taste better, but if you must use frozen, rinse off the ice crystals and add them right at the end. Serve the stew with Quick-cooked Pea Shoots and small roasted potatoes (or quinoa, barley, farro, or polenta).
Trim the meat of as much fat and sinew as possible. Mix ginger and garlic paste together; rub onto meat and let it sit at room temperature at least 30 minutes.
Put leeks in a large bowl of water, swish them around, and let the dirt settle. After a couple of minutes, lift leeks from water and put in a colander to drain.
In a deep, heavy 12-in. pot or a 12-in. frying pan with sides at least 2 in. high, heat oil over medium-high heat. Add chiles. When they start to look blistered, add cumin seeds; stir for a few seconds, then add leeks.
Lower heat to medium and cook, stirring from time to time, until leeks soften, about 10 minutes. Push leek mixture to the side and add meat, tossing it constantly so that it changes color without burning or sticking to the pan. Add splashes of water as necessary to keep things from sticking.
Pour in about 7 cups water (or enough to almost cover the lamb). Add 1 tsp. salt, turmeric (if using), and 2 cups cilantro. Bring to a boil, reduce heat to maintain a simmer, cover, and let meat cook until it's meltingly tender but not in shreds, 1 1/2 to 2 hours. Taste for salt and skim excess fat from gravy (see Notes).
Just before serving, transfer shanks to a plate and bring gravy to a boil. Cook until reduced by half, about 20 minutes. Return shanks to pan, add peas, cover, and cook until warmed through, about 5 minutes. Stir in remaining 1/2 cup cilantro and serve.


text:
package org.jetbrains.plugins.scala.annotator

import org.intellij.lang.annotations.Language
import com.intellij.openapi.roots.{OrderRootType, ModuleRootManager}
import java.io.File
import org.jetbrains.plugins.scala.util.TestUtils
import com.intellij.openapi.vfs.VfsUtil
import com.intellij.openapi.application.ApplicationManager
import org.jetbrains.plugins.scala.lang.psi.api.ScalaFile
import org.jetbrains.plugins.scala.base.{ScalaLightPlatformCodeInsightTestCaseAdapter, ScalaLightCodeInsightFixtureTestAdapter}

/**
 * User: Dmitry Naydanov
 * Date: 7/3/12
 */

class InterpolatedStringsAnnotatorTest extends ScalaLightPlatformCodeInsightTestCaseAdapter {
  private def collectAnnotatorMessages(text: String) = {
    configureFromFileTextAdapter("dummy.scala", text)
    val mock = new AnnotatorHolderMock

    new ScalaAnnotator().annotate(getFileAdapter.asInstanceOf[ScalaFile].getLastChild, mock)
    mock.annotations
  }

  private def emptyMessages(text: String) {
    assert(collectAnnotatorMessages(text).isEmpty)
  }

  private def messageExists(text: String, message: String) {
    assert(collectAnnotatorMessages(text).exists(_.toString == message))
  }

  @Language(value = "Scala")
  private val header =
    """
       class ExtendedContext {
         def a(ints: Int*) = ints.length
         def b(args: Any*) = args.length
         def c(s1: String, s2: String) = s1 + s2
         def d(i1: Int, s1: String) = i1 + s1.length
         def d(i1: Int, i2: Int) = i1 + i2
       }

       implicit def extendStrContext(ctx: StringContext) = new ExtendedContext

       val i1 = 1; val i2 = 2; val s1 = "string1"; val s2 = "string2"; val c1 = 'c'

    """.replace("\r", "")

  def testCorrectInt() {
    emptyMessages(header + "a\"blah blah $i1 $i2 ${1 + 2 + 3} blah\"")
  }

  def testCorrectAny() {
    emptyMessages(header + "b\"blah blah ${1} $s1 ${s2 + c1}blah blah\"")
  }

  def testCorrextStrings() {
    emptyMessages(header + "c\"blah blah $s1 ${s2}\"")
  }

  def testMultiResolve() {
    messageExists(header + "d\"blah $s1 blah $s2 blah\"", "ErrorWithRange((459,460),Value 'd' is not a member of StringContext)")
  }

  def testMultipleResolve() {
    messageExists(header + "c\"blah blah $i1 $i2\"", "Error(i1,Type mismatch, expected: String, actual: Int)")
  }

  def testMultipleResolve2() {
    messageExists(header + "c\"blah $i1 blah $s1 $i2\"", "Error(i2,Too many arguments for method c(String, String))")
  }
}

redpajama_set_name: RedPajamaGithub


Achievement was driving Ekki for many years, as a partner at McKinsey and a CEO in three different companies. In his mid forties he got introduced to a basic triangle: the It (strategies, structure, numbers, the hard stuff), the We (relationships, trust, collaboration),and the I (who are you? why are you doing what your doing?) and he had to recognise that 95% of his professional energy was focused on the It. This mid life reflexion phase led to some significant shifts. Ekki founded sum people, a boutique consultancy, helping executive teams integrating the We- and I-dimensions at the service of a better It; in addition, he created a foundation, Mountain Wisdom, where he invites executives to the mountains to reflect on themselves and their purpose. Ekki's purpose: help executives take their heart to work.


wife, mom, woman, marketer, blogger, and more!
I have been wrestling with the post I would write this week in light of Monday's horrific bombing in Boston. I have been brought to tears by the extreme violence and graphic images shown and described via media news outlets. As I listened to President Obama describe some of the immediate actions taken by those in the Boston area at the time I was once again brought to tears driving home last night.
My heart aches with and for those affected by this tragedy. There are stories of bravery and unsung heroes on-hand and ready to help and not flee. Runners still in the marathon changing course to the nearest hospital to donate blood for the injured. Boston residents opening their homes to dozens of people to get them to safety off the street. Student doctors showing up to help not because they were called to, but because there was a need.
I remember back to September 11, 2001 and how our way of American life was forever altered. It wasn't supposed to happen here. Not to us. We're safe. As we know, we were wrong. I lay in bed last night crying to my husband who tells me these things are happening all over the world and I think, yes, they do, but we don't live all over the world. We live here.
To some extent there is a great disconnect because these 2 specific bombings happened on the East Coast and therefore the West Coast still feels secure, but it's all a façade.
I'm reading Home Front this week, about a mother in the National Guard who gets sent to war in 2005. It talks about the selfless sacrifice of our nation's soldiers who are called and they go. They leave their family and they go. They hear the call and they go. And this week our nation heard the call from a bomb at a race on Patriot's Day in Boston, and they responded.
It brings joy to my sad heart that good does still exist in the world. I believe we are all capable of doing good even if we choose not to act.
My husband mentioned last night how a bombing like this can make people question God. I immediately thought, NO! I remember shortly after 9/11 a poem being read at church. I believe it was titled "Where was God?" I could be wrong.
But what I remember is God was everywhere. He was with the passengers on every flight. He was with the pilots who were overtaken. He was with the people in the TwinTowers as some escaped with their lives and others never came home. He was there comforting the hearts of the victims and their families. He was with the first responders who heard the call and came running. God was very busy that day.
And even now I take comfort in knowing God did not allow this to happen. I could go on and on about the effects of sin in our world, but just knowing that bad things will happen and God will always be there brings comfort to my heart.
I pray peace to those grieving and in pain and I take comfort in knowing in the midst of chaos and destruction the good in all of us can overcome the bad things in the world.


text:
<?php namespace frontend\utilities\materialize;

use yii\base\InvalidConfigException;
use yii\helpers\ArrayHelper;
use yii\helpers\Html;

/**
 * Dropdown renders a Materialize dropdown menu component.
 *
 * For example,
 *
 * ```php
 * echo Dropdown::widget([
 *     'items' => [
 *         ['label' => 'DropdownA', 'url' => '/'],
 *         ['label' => 'DropdownB', 'url' => '#'],
 *     ],
 * ]);
 * ```
 * @see http://materializecss.com/dropdown.html
 * @author webmaxx <webmaxx@webmaxx.name>
 * @since 2.0
 */
class Dropdown extends Widget
{
	/**
	 * @var bool if dropdown is suitable for side nav component.
	 */
	public $sideNav = false;
    /**
     * @var string the tag to use to render the button
     */
    public $buttontagName = 'a';
    /**
     * @var string the button label
     */
    public $buttonLabel = 'Dropdown';
    /**
     * @var boolean whether the label should be HTML-encoded.
     */
    public $buttonEncodeLabel = true;
    /**
     * @var array the HTML attributes of the button.
     * @see \yii\helpers\Html::renderTagAttributes() for details on how attributes are being rendered.
     */
    public $buttonOptions = [];
    /**
     * @var array list of menu items in the dropdown. Each array element can be either an HTML string,
     * or an array representing a single menu with the following structure:
     *
     * - label: string, required, the label of the item link
     * - url: string|array, optional, the url of the item link. This will be processed by [[Url::to()]].
     *   If not set, the item will be treated as a menu header when the item has no sub-menu.
     * - visible: boolean, optional, whether this menu item is visible. Defaults to true.
     * - linkOptions: array, optional, the HTML attributes of the item link.
     * - options: array, optional, the HTML attributes of the item.
     * - items: array, optional, the submenu items. The structure is the same as this property.
     *
     * To insert divider use `<li class="divider"></li>`.
     */
    public $items = [];
    /**
     * @var boolean whether the labels for header items should be HTML-encoded.
     */
    public $encodeLabels = true;

    /**
     * Initializes the widget.
     * If you override this method, make sure you call the parent implementation first.
     */
    public function init()
    {
        parent::init();
	    if (!$this->sideNav)
            Html::addCssClass($this->options, 'dropdown-content');
        Html::addCssClass($this->buttonOptions, 'btn');
        Html::addCssClass($this->buttonOptions, 'dropdown-button');
        $this->buttonOptions['id'] = $this->id . '-btn';
        $this->buttonOptions['data-activates'] = $this->id;
    }

    /**
     * Renders the widget.
     */
    public function run()
    {
        $this->registerClientEvents();
        $this->getView()->registerJs("
$('#{$this->id}-btn').dropdown({
      inDuration: 300,
      outDuration: 225,
      constrain_width: false, // Does not change width of dropdown to that of the activator
      hover: false, // Activate on click
      alignment: 'left', // Aligns dropdown to left or right edge (works with constrain_width)
      gutter: 0, // Spacing from edge
      belowOrigin: false // Displays dropdown below the button
});
        ");
        if ($this->buttonLabel !== null) {
            return Html::tag($this->buttontagName, $this->buttonLabel, $this->buttonOptions) . $this->renderItems($this->items, $this->options);
        } else {
            return $this->renderItems($this->items, $this->options);
        }
    }

    /**
     * Renders menu items.
     * @param array $items the menu items to be rendered
     * @param array $options the container HTML attributes
     * @return string the rendering result.
     * @throws InvalidConfigException if the label option is not specified in one of the items.
     */
    protected function renderItems($items, $options = [])
    {
        $lines = [];
        foreach ($items as $i => $item) {
            if (isset($item['visible']) && !$item['visible']) {
                continue;
            }
            if (is_string($item)) {
                $lines[] = $item;
                continue;
            }
            if (!array_key_exists('label', $item)) {
                throw new InvalidConfigException("The 'label' option is required.");
            }
            $encodeLabel = isset($item['encode']) ? $item['encode'] : $this->encodeLabels;
            $label = $encodeLabel ? Html::encode($item['label']) : $item['label'];
            $itemOptions = ArrayHelper::getValue($item, 'options', []);
            $linkOptions = ArrayHelper::getValue($item, 'linkOptions', []);
            $linkOptions['tabindex'] = '-1';
            $url = array_key_exists('url', $item) ? $item['url'] : null;
            if (empty($item['items'])) {
                if ($url === null) {
                    $content = $label;
                    Html::addCssClass($itemOptions, 'dropdown-header');
                } else {
                    $content = Html::a($label, $url, $linkOptions);
                }
            } else {
                $submenuOptions = $options;
                unset($submenuOptions['id']);
                $content = Html::a($label, $url === null ? '#' : $url, $linkOptions)
                    . $this->renderItems($item['items'], $submenuOptions);
                Html::addCssClass($itemOptions, 'dropdown-submenu');
            }

            $lines[] = Html::tag('li', $content, $itemOptions);
        }

        return Html::tag('ul', implode("\n", $lines), $options);
    }
}


text:
\section{Introduction}
\label{sec:Intro}

Diffusive (Fermi) shock acceleration (DSA) is believed to be the mechanism responsible for the production of non-thermal, high-energy distributions of charged particles in collisionless shocks found in diverse astronomical systems (for reviews, see Refs. \cite{Blandford_Eichler_87, MalkovDrury01, TreumannEtAl09Review}).
Particle acceleration is identified in both non-relativistic and relativistic shocks, examples of the latter including shocks in gamma-ray bursts \citep[GRBs; \emph{e.g.,} ][]{KumarZhang15Review}, pulsar wind nebulae, active galactic nuclei, X-ray binaries \citep[\emph{e.g.,} ][]{RomeroEtAl17}, and type Ibc supernovae (for a review, see Ref. \cite{PelletierEtAl17}).
For recent reviews of DSA in relativistic shocks, see Refs. \cite{BykovEtAl12Review, SironiEtAl15_review}.

Collisionless shocks in general, and their particle acceleration in particular, are mediated by electromagnetic waves, and are still not generally understood from first principles. No present analysis self-consistently calculates the long-term generation of waves and the wave-plasma interactions. The particle distribution $f$ is often evolved by adopting some ansatz for the scattering mechanism (\emph{e.g.,}  isotropic diffusion in velocity angle) and neglecting wave generation and shock modification by the accelerated particles, in the so-called test-particle approximation. This phenomenological approach proved successful in accounting for non-relativistic shock observations. For such shocks, DSA predicts a power-law energy spectrum, $df/dE\propto E^{-p}$, where $p\simeq(r+2)/(r-1)$ is a function of the shock compression ratio $r$ \citep{Krymskii_1977, AxfordEtAl77, Bell_1978, BlandfordOstriker78}. For strong shocks in an ideal gas of adiabatic index $\Gamma=5/3$, this gives $p=2$, in agreement with observations.

Analyses of GRB afterglow observations suggested that the ultra-relativistic shocks involved produce high-energy distributions with $p=2.2\pm0.2$ \citep{Waxman97, BergerEtAl03}.
A similar, $p\simeq 2.2$ spectrum is inferred in other astronomical systems, for example the injection of particles radiating above the UV in the Crab nebula \citep{MarcowithEtAl16}.
Such evidence triggered several studies of test-particle DSA in relativistic shocks, with $p$ calculated for a wide range of $\gamma$, various equations of state, and several scattering mechanisms.

DSA analysis is more complicated when the shock is relativistic, mainly because $f$ becomes anisotropic.
Most studies of the problem have thus used Monte-Carlo simulations and various other numerical techniques \citep[\emph{e.g.,} ][]{EllisonEtAl90, BednarzOstrowski98, Kirk_2000, AchterbergEtAl01, Vietri03, BlasiVietri05}. For isotropic, small-angle scattering in the ultra-relativistic shock limit, where upstream (downstream) fluid velocities normalized to the speed of light $c$ approach $\beta_u\simeq1$ ($\beta_d \simeq 1/3$), spectral indices $p=2.22\pm0.02$ were indeed found \citep{HeavensDrury88, BednarzOstrowski98, Kirk_2000, AchterbergEtAl01}.
An approximate expression for the spectrum \citep{Keshet_2005},
\begin{equation} \label{eq:p_iso_app}
p = (\beta_u + 2\beta_d - 2\beta_u \beta_d^2 + \beta_d^3) / (\beta_u - \beta_d)\mbox{ ,}
\end{equation}
was shown to agree with numerical results for different equations of state and for a wide range of shock parameters; in particular, it yields $p = 20/9\simeq 2.22$ in the ultra-relativistic limit.

However, the spectrum was found to be sensitive to the angular dependence of the diffusion function, especially in the downstream and at certain angles \citep{Keshet06}, and it is unclear if the isotropic small-angle scattering assumption behind Eq.~(\ref{eq:p_iso_app}) and most numerical studies is justified.
Ab-initio particle in cell (PIC) simulations have successfully demonstrated the onset of particle acceleration \citep{spitkovsky_08b, sironi_spitkovsky_09, sironi_spitkovsky_11a} and the tightly coupled process of magnetic structure growth \citep{keshet_09, SironiEtAl13}.
However, computational limitations prevent such simulations from resolving the three-dimensional (3D) structure of the shock with evolved electromagnetic modes and saturated non-thermal particle distributions, so the steady-state diffusion function remains poorly constrained.
Such studies rely mostly on 2D (spatially; with two or three momentum dimensions), and in some cases even on 1D \citep[\emph{e.g.,} ][]{dieckmann_06, OkaEtAl11, RajawatSengupta16} simulations, in order to boost the dynamical range; this is useful for studying those effects which are not inherently 3D.

The Fermi acceleration process itself has been studied in 1D previously, but mainly in the Fermi-Ulam model \citep[\emph{e.g.,} ][]{ZaslavskiiChirikov65,  Dolgopyat08, OliveiraEtAl11}, and in non-relativistic shocks \citep{ZhuEtAl09}, usually with more than one dimension in momentum space.
Here we study DSA for an arbitrary relativistic shock in an effective 1D model; the three-dimensional particle diffusion is thus represented by 1D particle scattering.
This has two main advantages over studies in higher dimensions: (i) the results are analytically tractable; and (ii) there is no need for an unjustified diffusion ansatz.
The results are qualitatively similar to those of higher dimensions, shedding light on the qualitative behavior of the latter, and possibly constraining their ultra-relativistic limit.
In addition, our analysis is directly applicable to one dimensional simulations, and is useful as a rigorous pedagogical exercise and for code verification.

The structure of the paper is as follows.
We begin by introducing the shock jump conditions, which determine the accelerated particle spectrum, and in particular those arising from a 1D J{\"u}ttner-Synge equation of state, in \S\ref{sec:Jump1D}.
The DSA problem in 1D is set up in \S\ref{sec:OneDim}, and solved in the non-relativistic limit in \S\ref{sec:NonRelLimit}.
The spectrum of particles accelerated in an arbitrary relativistic shock is derived in \S\ref{sec:GenericDerivation}, and studied in the ultra-relativistic limit in \S\ref{sec:UltraRel}.
Drifts, known \citep[\emph{e.g.,} ][]{decker_88} to significantly affect the spectrum, are incorporated in \S\ref{sec:Drifts}.
The results are summarized and discussed in \S\ref{sec:Discussion}.

\section{Relativistic shock jump conditions}
\label{sec:Jump1D}

The shock jump conditions depend on the assumed equation of state, which we write for convenience in the form $P=(\Gamma-1)({\epsilon}-\rho c^2)$.
Here, $P$, ${\epsilon}$, and $\rho$ are the proper pressure, energy density, and rest-mass density, respectively, $\Gamma$ is the adiabatic index, and $c$ is the speed of light.
We derive $\Gamma$ and the jump conditions for the standard, J{\"u}ttner-Synge equation of state, below.
But first, we estimate the jump conditions for strong shocks in the non-relativistic and ultra-relativistic limits.

In a non-relativistic gas, $\Gamma\simeq 1+2N_{dof}^{-1}$, where $N_{dof}$ is the number of particle degrees of freedom.
The velocity drop factor at the shock is therefore \citep[\emph{e.g.,} ][]{LandauLifshitz59_FluidMechanics}
\begin{equation}\label{eq:rNonRel}
r\equiv\frac{\beta_u}{\beta_d} \to \frac{\Gamma+1}{\Gamma-1} \simeq 1+N_{dof} \mbox{ ,}
\end{equation}
where we took the strong shock limit. Here and below, we neglect the back-reaction of the accelerated particles on the adiabatic index, working in the test particle approximation.

In an ultra-relativistic gas, $\Gamma\simeq 1+N_{dof}^{-1}$, so here
\begin{equation}\label{eq:rUltraRel}
r\equiv \frac{\beta_u}{\beta_d} \to \frac{{\epsilon}_d+P_u}{{\epsilon}_u+P_d} \simeq \frac{{\epsilon}_d}{P_d}\simeq \frac{1}{\Gamma-1} \simeq N_{dof} \mbox{ ,}
\end{equation}
again taking the strong shock limit.
For a mono-atomic gas, $N_{dof}=N$, where $N$ is the number of spatial dimensions.
In particular, for an ultra-relativistic shock in a mono-atomic gas in 1D, $r\to N_{dof}=N=1$, indicating no compression or velocity drop across the shock in this limit. Hence, while the asymptotic behavior can be studied, this limit cannot be realized as the shock becomes ill defined.

Equation (\ref{eq:rNonRel}) uniquely determines the spectral index $p$ of test particles accelerated by a non-relativistic strong shock.
Similarly, Eq.~(\ref{eq:rUltraRel}) uniquely determines $p$ for test particles accelerated by a strong shock in the ultra-relativistic limit, but only in 2D and in 3D, and only if the angular diffusion function is specified.
As we show below, this is not the case in a mono-atomic 1D gas.
Here, there is no need to specify the diffusion function, but the precise deviation from the $r\to N=1$ limit strongly influences the spectrum.
We must therefore specify the equation of state and derive the corresponding shock jump conditions.

In the J{\"u}ttner-Synge equation of state \citep{Juttner1911, Synge57}, the adiabatic index $\Gamma$ smoothly interpolates between $1+2N_{dof}^{-1}$ in the non-relativistic limit, and $1+N_{dof}^{-1}$ in the ultra-relativistic limit.
The same arguments made in the 3D case indicate that in 1D, the specific enthalpy is given by $w/\rho c^2=K_2({\zeta})/K_1({\zeta})$, where $K_n({\zeta})$ are the modified Bessel functions of the first kind (McDonald functions) of order $n$, ${\zeta}\equiv mc^2/k_BT$ is the dimensionless inverse temperature, $T$ is the temperature, $k_B$ is the Boltzmann constant, and $m$ is the particle mass.
The adiabatic index is then given by
\begin{eqnarray}
\!\!\!\!\!\!\!\!\!\Gamma  = \frac{w-\rho c^2}{w-\rho c^2-P}
= \frac{1}{1-{\zeta}^{-1}\left[\frac{K_2({\zeta})}{K_1({\zeta})}-1\right]^{-1}}
\simeq \begin{cases}
3-\frac{3}{2{\zeta}}+\frac{21}{8{\zeta}^2}+O\left({\zeta}^{-3}\right) & \mbox{for ${\zeta}\gg 1$ ;} \\
2+{\zeta}+{\zeta}^2\ln {\zeta}+O\left({\zeta}^{2}\right) & \mbox{for ${\zeta}\ll1$ ,}
\end{cases}
\end{eqnarray}
in agreement with the non-relativistic and ultra-relativistic limits in Eqs.~(\ref{eq:rNonRel}) and (\ref{eq:rUltraRel}).

The shock jump conditions may be derived in the same method as in the 3D case \citep[\emph{e.g.,} ][]{KirkDuffy99}.
In a strong shock, the downstream adiabatic index becomes $\Gamma_d \simeq 1+{\zeta}_d^{-1}(\gamma_r-1)^{-1}$.
Here, $\gamma_r\equiv(1-\beta_r^2)^{-1/2}$, where $\beta_r=(\beta_u-\beta_d)/(1-\beta_u\beta_d)$ is the normalized relative velocity of the upstream with respect to the downstream.
The Taub adiabat in the strong shock limit can be written as
\begin{equation} \label{eq:Taub1}
\frac{K_2({\zeta}_d)}{K_1({\zeta}_d)} = \frac{\gamma_u}{\gamma_d}= \gamma_r + \frac{1}{{\zeta}_d}
\mbox{ ;}
\end{equation}
\begin{equation} \label{eq:Taub2}
\gamma_u^2 = \frac{w_d^2({\epsilon}_d^2-\rho_d^2c^2)/\rho_d^2c^2}{{\epsilon}_d^2-P_d^2-\rho_d^2c^2} = \frac{(\gamma_r^2-1)(1+{\zeta}_d\gamma_r)^2}{(\gamma_r^2-1){\zeta}_d^2-1} \mbox{ .}
\end{equation}
For a given shock Lorentz factor $\gamma_u$, Eqs.~(\ref{eq:Taub1}--\ref{eq:Taub2}) can be solved simultaneously for $\gamma_r$ and ${\zeta}_d$. Given this $\gamma_r$, one may now relate $\beta_d$ to $\beta_u$.

\section{DSA set up}
\label{sec:OneDim}

Consider an infinite, planar shock front in 3D, located at shock-frame coordinate $z=0$, with flow in the positive z direction. Relativistic particles with energy $E$ much higher than any characteristic energy in the problem are assumed to diffuse in their direction of motion. This direction is parameterized by the fluid frame $\mu\equiv\cos(\theta)$, where $\theta$ is the polar angle measured between the velocity vector and the positive $z$ axis.

Anticipating the reduction of 3D diffusion to 1D scattering, we use the transport, scattering-convection equation in the form \cite[\emph{e.g.,} ][]{Vietri03}
\begin{align} \label{eq:ScatConv}
\gamma c  (\beta+\mu) \frac{\partial f}{\partial z}  = \left(\frac{\partial f}{\partial t}\right)_{\mbox{\footnotesize collisions}}
 = \int R({\unit{n}'\to \unit{n}}) f(\unit{n}')\,d\unit{n}' - \int R({\unit{n}\to \unit{n}'}) f(\unit{n})\,d\unit{n}' \mbox{ ,}
\end{align}
where $R({\unit{n}_1\to \unit{n}_2})$ is the fluid-frame rate of collisions that scatter particles from direction $\unit{n}_1$ to $\unit{n}_2$.
We assume, as is customary, that $R$ is separable in the form $R=R_a(z,E)R_b(\unit{n}_1,\unit{n}_2)$.
Equation (\ref{eq:ScatConv}) holds separately in the upstream and in the downstream; we write the upstream/downstream indices $u/d$ only when necessary.
Consider first a constant $R_a$; the general form is addressed in \S\ref{sec:GenericDerivation}.

In 1D, particles propagate only in one out of two directions: either toward the downstream, $\mu=+1$, which we label as the $+$ direction, or toward the upstream, $\mu=-1$, which we label as the $-$ direction.
Diffusion in the direction of motion thus reduces to scattering between these two directions.
It is customary to invoke a symmetry between the scattering probabilities, $R(-\to+)=R(+\to-)$, as an expression of detailed balance \citep[][and references therein]{BlasiVietri05}.
We refer to the case of symmetric scattering as (pure) diffusion, and designate any asymmetry between $R(-\to+)$ and $R(+\to-)$ as a drift.

In the 1D case, the angular distribution thus becomes simple, and the spectrum of the accelerated particles turns out to be independent of the details of their diffusion or scattering.
The absence of a characteristic energy scale implies that a power-law spectrum emerges, as verified numerically \citep{BednarzOstrowski98, AchterbergEtAl01}.
We may therefore write the distribution function as $f=[f_+(z)+f_-(z)]E^{-p}$.

The spectral index $p$ may be derived by solving Eq.~(\ref{eq:ScatConv}) under the following boundary conditions.
Continuity of the accelerated particles across the shock front requires that $f_{u\pm}(z=0)E_u^{-p} = f_{d\pm}(z=0)E_d^{-p}$, where upstream and downstream quantities are related by a Lorentz boost of velocity $c\beta_r$.
The absence of accelerated particles reaching far upstream requires that $f_u(z \to -\infty) = 0$.
The angular diffusion of such particles as they are carried far downstream implies that they eventually isotropize, $f_{d\pm}(E_d,z\to +\infty) = f_\infty
E_d^{-p}$, where $f_\infty>0$ is a constant.

\section{Non-relativistic limit}
\label{sec:NonRelLimit}

There are simpler ways to derive the spectrum of particles accelerated by the shock in the non-relativistic limit, in the present case in 1D.
Consider for example a relativistic particle after $i$ cycles of crossing the shock back and forth, with Lorentz factor $\gamma_i\gg1$ in the upstream frame, $S_u$.
The particle crosses the shock towards the downstream and is then reflected back to the upstream due to elastic collisions in the downstream frame, $S_d$, with some scatterers comoving with the downstream medium.
The balance between the fractional energy gain $g$ of the particle in such a cycle, and its probability $P_{e}$ to escape downstream, fixes the spectrum, as shown in the 3D case by Ref. \cite{Bell_1978}.

After it crosses the shock into the downstream, in $S_d$ the particle has $\gamma_i'=\gamma_r\gamma_i(1+\beta_r\beta_i)\simeq \gamma_i(1+\beta_r)$, where we used $\beta_r\gamma_r\ll 1$ and $\beta_i\gamma_i\gg1$.
Upon returning to the upstream, the particle has an upstream frame $\gamma_{i+1}=\gamma_r^2\gamma_i(1+2\beta_r\beta_i+\beta_r^2)\simeq \gamma_i(1+2\beta_r)$, so the fractional energy gain is $g\equiv(\gamma_{i+1}/\gamma_i)-1\simeq 2\beta_r$.
As in higher dimensions, the downstream distribution $f_d$ is expected to be approximately homogeneous and isotropic in $S_d$.
The flux of particles crossing towards the downstream is then $f_dc/2$, whereas the flux of particles escaping far downstream is $f_d\beta_dc$. The ratio between these two fluxes gives the escape probability, $P_e\simeq 2\beta_d$.

Combining these estimates now yields the spectral index of the accelerated particles,
\begin{equation} \label{eq:P1DNonRel}
p=1-\frac{\ln (1-P_e)}{\ln (1+g)} \simeq 1+\frac{2\beta_d}{2\beta_r}
\simeq\frac{\beta_u}{\beta_u-\beta_d} \mbox{ .}
\end{equation}
For a non-relativistic, mono-atomic gas in 1D, $\Gamma\simeq 3$, and so $\beta_u\simeq 2\beta_d$, giving the well known, flat, $p\simeq 2$ spectrum also found in higher dimensions.

\section{Arbitrary 1D relativistic shock}
\label{sec:GenericDerivation}

Next, consider an arbitrary relativistic shock.
The two components $f_\pm$ of $f$ are coupled by particle scattering, of fluid-frame rate $R$, according to a 1D version of Eq.~(\ref{eq:ScatConv}),
\begin{align} \label{eq:TwoComp1}
& \gamma c (\beta + 1)\partial_z f_+ = R({-\to+})f_- - R({+\to-})f_+ \, ; \nonumber \\
& \gamma c (\beta - 1)\partial_z f_- = R({+\to-})f_+ - R({-\to+})f_- \mbox{ .}
\end{align}
In the absence of drifts, which are incorporated in \S\ref{sec:Drifts}, the scattering rate is symmetric, $R\equiv R({-\to+})=R({+\to-})$.
The precise value of this rate, and its spatial and energetic dependencies, are inconsequential for the spectral analysis, as we may absorb them in the definition of a new spatial coordinate, $\tau\equiv \int^z R_a \,dz'/(\gamma c)$.
This yields two simple, coupled equations, which may be compactly written as
\begin{equation} \label{eq:TwoComp2}
 (\beta\pm 1)\partial_\tau f_\pm = f_\mp-f_\pm \mbox{ .}
\end{equation}

The general solution to these two coupled equations is
\begin{equation}
f_\pm = C_1 +  \frac{C_2}{1\pm\beta} e^{2\beta\gamma^2\tau}\mbox{ ,}
\end{equation}
valid on each side of the shock with different constants $C_1$ and $C_2$, to be determined by the boundary conditions.

In the far downstream, the finiteness of $f_d$ requires that $C_{d2}=0$; the solution throughout the downstream thus becomes homogeneous and isotropic,  $f_{d+}=f_{d-}=C_{d1}$.
In the far upstream, no accelerated particles are assumed to be present, so the $f_{u\pm}(\tau\to-\infty)=0$ boundary condition implies that $C_{u1}=0$.
The particle anisotropy level in the upstream is thus spatially uniform, and given by
\begin{equation}  \label{eq:UpAnisotropy}
f_{u+}/f_{u-}=(1-\beta_u)/(1+\beta_u) \mbox{ .}
\end{equation}
Hence, the upstream distribution even near the shock is dominated by particles moving toward the upstream, away from the shock.
As one approaches the ultra-relativistic limit, $\beta_u\to1$, the fraction of upstream particles moving toward the downstream becomes exceedingly small. This resembles the behavior of the particle distribution found \citep[\emph{e.g.,}  Ref.][and Lavi et al., in prep.]{Kirk_2000} in higher dimensions.

We may now match the upstream and downstream solutions at the shock, $\tau=0$, taking into account the Lorentz boost between the upstream and downstream frames, such that
\begin{equation}
f_{u\pm}(\tau=0) = \gamma_r^{-p} (1\pm\beta_r)^{-p} f_{d\pm}(\tau=0) \mbox{ .}
\end{equation}
Matching the two components yields two constraints, $C_{u2}/(1\pm\beta_u)=C_{d1}\gamma_r^{-p}(1\pm\beta_r)^{-p}$.
Solving for $p$ finally yields the spectral index,
\begin{equation} \label{eq:GenSpec}
p
= \frac{\ln\left[\gamma_u(1+\beta_u)\right]}{\ln\left[\gamma_r(1+\beta_r)\right]}
= \frac{1}{1-\frac{\ln\left[\gamma_d(1+\beta_d)\right]}{\ln\left[\gamma_u(1+\beta_u)\right]}} \mbox{ .}
\end{equation}
This result is shown in Figure \ref{fig:spec_1D}, where it is compared to the spectra derived in 2D and in 3D under the isotropic diffusion ansatz. Notice that Eq.~(\ref{eq:GenSpec}) reduces to Eq.~(\ref{eq:P1DNonRel}) in the non-relativistic limit.

\begin{figure*}
\centerline{\epsfxsize=20.5cm \hspace{1.8cm}\epsfbox{DifferentDim3.eps}}
\caption{
Energy spectral index $p$ of shock-accelerated particles in 1D (Eq.~(\ref{eq:GenSpec}); thick solid blue curve), 2D (dashed green), and 3D (dot-dashed red), for a strong shock and a J{\"u}ttner-Synge equation of state.
In 2D and in 3D, isotropic diffusion was assumed; the results shown are the analytic approximations of Lavi et al. (in prep.) for 2D, and of Ref. \cite{Keshet_2005} for 3D.
In 1D, the result is sensitive to the equation of state even in the ultra-relativistic limit (where the approximation Eq.~(\ref{eq:BetaDApprox}) for the J{\"u}ttner-Synge equation of state is used; thin purple).
This sensitivity is demonstrated by showing the spectrum also for a different ($\Gamma_d=2+\gamma_u^{-0.4}$) interpolation of the downstream adiabatic index between its non-relativistic and ultra-relativistic limits (dotted black).
}
\label{fig:spec_1D}
\end{figure*}

\section{Ultra-relativistic limit}
\label{sec:UltraRel}

In the ultra-relativistic limit in 1D, the compression ratio $r=\beta_u/\beta_d$ asymptotes to unity. Directly introducing this limit into Eq.~(\ref{eq:GenSpec}) leads to a divergence, and so is insufficient for determining the ultra-relativistic limit of the spectrum, $p(\gamma_u\to\infty$).
Therefore, unlike the 2D and 3D cases, in 1D we must specify the equation of state, and thus also the deviation from the limiting value $r(\gamma_u\to\infty)$, in order to derive the asymptotic spectrum.
This is illustrated in Figure \ref{fig:spec_1D} by showing the spectrum for two 1D equations of state, that have the same limiting $\Gamma$ behavior but approach the asymptotic ultra-relativistic limit differently.

Consider the spectrum for the J{\"u}ttner-Synge equation of state, shown in the figure as solid curves.
Remarkably, after the spectrum hardens gradually down to $p(\gamma_u\simeq 57.6)\simeq 1.77$, it turns around and softens back, until converging logarithmically in the ultra-relativistic limit onto the exact same $p\to 2$ value as in the non-relativistic case.
Such spectral hardening followed by softening is found for other equations of state that interpolate between the non-relativistic and ultra-relativistic limits, as illustrated in the figure by the dotted curve, but the limiting spectrum is in general not flat ($p\neq 2$).

Consider the J{\"u}ttner-Synge equation of state in the ultra-relativistic limit. Downstream of the shock, the high temperature implies that $\zeta\to0$.
Solving Eq.~(\ref{eq:Taub1}) to leading order in $\zeta$ yields $\gamma_r = {\zeta}^{-1}-z\ln {\zeta}+O(z)$, diverging in the ultra-relativistic limit in spite of $r\to 1$.
This implies that $\Gamma_d\simeq 2+(\gamma_r-1)^{-1}$, reproducing the anticipated  $\Gamma_d(\gamma_r\to\infty)=2$ of Eq.~(\ref{eq:rUltraRel}).
Expanding Eq.~(\ref{eq:Taub2}) in the ultra-relativistic limit now yields  $\beta_u=1+{\zeta}^4\ln({\zeta})/4+O({\zeta}^4)$ and $\beta_d=1+{\zeta}^2\ln({\zeta})+O({\zeta}^2)$.
These may be combined to give the approximate velocity jump at the ultra-relativistic shock limit,
\begin{eqnarray}\label{eq:BetaDApprox}
\beta_d & \simeq & 1+i(1-\beta_u)^{1/2}W_{-1}[-16(1-\beta_u)]^{1/2} \nonumber \\
& \simeq & 1-[-(1-\beta_u)\ln(1-\beta_u)]^{1/2} \mbox{ ,}
\end{eqnarray}
where $W_k(\xi)$ is the $k$-branch of the Lambert $W$ (product log) function.
The spectrum Eq.~(\ref{eq:GenSpec}) with the approximation Eq.~(\ref{eq:BetaDApprox}) is shown in Figure \ref{fig:spec_1D} as a thin purple curve.
Using the approximation in the second line of Eq.~(\ref{eq:BetaDApprox}), the spectrum in the ultra-relativistic limit becomes approximately
\begin{equation}\label{eq:pApprox}
p(\beta_u\simeq1)\simeq 2\,\frac{\ln[(1-\beta_u)/2]}{\ln\{-(1-\beta_u)/\ln[16(1-\beta_u)]\}} \mbox{ ,}
\end{equation}
which indeed asymptotes to $p(\beta_u\to1)=2$.

\section{Drifts}
\label{sec:Drifts}

Incorporating drifts into the above analysis can be accomplished by allowing for an asymmetric scattering rate, $R\equiv R({-\to+})\neq R({+\to-})$.
Accordingly generalizing Eq.~(\ref{eq:TwoComp2}) now yields
\begin{align} \label{eq:TwoCompDrift}
& \!\!\! (\beta + 1)\partial_\tau f_+ = f_- - q f_+ \, ; \nonumber \\
& \!\!\! (\beta - 1)\partial_\tau f_- = q f_+ - f_- \mbox{ ,}
\end{align}
where the deviation of $q\equiv R({+\to-})/R({-\to+})$ from unity measures the excess drift in the downstream-to-upstream direction.

We may solve these equations analytically if $q$ can be approximated as constant on each side of the shock.
Here, repeating the above considerations leads to the spectrum
\begin{equation} \label{eq:pWithDrift}
p
= \frac{\ln\left[q_d^{-\frac{1}{2}}\gamma_u(1+\beta_u)\right]}{\ln\left[\gamma_r(1+\beta_r)\right]} \\
= \frac{\ln\left[q_d^{-\frac{1}{2}}\gamma_u(1+\beta_u)\right]}{\ln\left[\frac{\gamma_u(1+\beta_u)}{\gamma_d(1+\beta_d)}\right]} \mbox{ .}
\end{equation}
This result, demonstrated in Figure \ref{fig:specDrift}, is valid only if $q<(1+\beta)/(1-\beta)$ both upstream and downstream, corresponding to a drift which does not strongly push particles toward the upstream.
Otherwise, the upstream boundary condition cannot be satisfied, or the downstream distribution becomes under-determined.
Note that in the ultra-relativistic limit, drifts do not affect the spectrum, \emph{i.e.}  $q_d$ can be taken here to unity in Eq.~(\ref{eq:pWithDrift}).

The spectrum in Eq.~(\ref{eq:pWithDrift}) is a function of $q_d$, but is independent of $q_u$ (formally, this is true only as long as $q_u$ is a constant, as assumed above).
The anisotropy $f_{u+}/f_{u-}$ in the upstream is unaffected by either upstream or downstream drifts, and so is still given by Eq.~(\ref{eq:UpAnisotropy}).
The downstream anisotropy, however, depends linearly on the downstream drift, and is now given by $f_{d+}/f_{d-}=1/q_d$.

Equation (\ref{eq:pWithDrift}) reduces in the non-relativistic, weak drift limit to $p\simeq(\beta_u-\xi/2)/(\beta_u-\beta_d)$, where $\xi\equiv q_d-1$ is the downstream drift parameter, here assumed to be small, $|\xi |\ll 1$.
This result can be obtained directly from the non-relativistic derivation in \S\ref{sec:NonRelLimit} by generalizing the escape probability to $P_e\simeq 2(\beta_d-\xi/2)$, as the drift velocity toward the upstream approaches $\xi c/2$ far downstream.

\begin{figure}[h!]
\centerline{\epsfxsize=8.5cm \epsfbox{RelDrift2.eps}}
\caption{Spectral index of particles accelerated in a strong shock in 1D for a J{\"u}ttner-Synge equation of state, with downstream drift parameter $\xi=0$ (solid blue), $+0.2\beta_d$ (dot-dashed red), and $-0.2\beta_d$ (dashed green).
}
\label{fig:specDrift}
\end{figure}

\section{Summary and discussion}
\label{sec:Discussion}

We derived in Eq.~(\ref{eq:GenSpec}) the spectrum of the high-energy tail of relativistic test-particles, accelerated by an arbitrary relativistic shock in 1D. The spectrum, shown in Figure \ref{fig:spec_1D}, is independent of assumptions on the diffusion function, unlike in the 2D and 3D cases.
It reduces to Eq.~(\ref{eq:P1DNonRel}) in the non-relativistic limit, where it yields the familiar flat, $p(\beta_u\to0)=2$ spectrum.
It remains sensitive to the equation of state even in the ultra-relativistic limit, unlike the results in 2D and in 3D, which appear to converge on values independent of the equation of state under the isotropic diffusion ansatz.

The shock jump conditions for the J{\"u}ttner-Synge equation of state, derived for a strong 1D shock in Eqs.~(\ref{eq:Taub1}) and (\ref{eq:Taub2}), yield a spectrum which initially hardens with increasing shock Lorentz factor $\gamma_u$ to $p(\gamma_u\simeq 57.6)\simeq 1.77$, but softens back for faster shocks.
In the ultra-relativistic limit, where the jump conditions and the spectrum are approximated by Eqs.~(\ref{eq:BetaDApprox}) and (\ref{eq:pApprox}), the spectral index logarithmically asymptotes back to the same flat, $p(\gamma_u\to\infty)=2$ value of the non-relativistic case.

Interestingly, some spectral hardening with increasing $\gamma_u$ in the trans-relativistic range was found for a J{\"u}ttner-Synge equation of state also in 3D \citep[][and Arad et al., in prep.]{Kirk_2000}, and possibly also in 2D (Lavi et al., in prep.).
However, in 2D and in 3D this is a weak, barely noticeable effect.

A strong drift toward the upstream would invalidate our analysis, as it can prevent particles from reaching far downstream, or carry them far upstream.
Weak drifts in the upstream have no effect on the 1D spectrum.
The consequences of weak drifts in the downstream are incorporate in Eq.~(\ref{eq:pWithDrift}), and illustrated in Figure \ref{fig:specDrift}.
In general, a downstream drift towards the upstream (downstream) hardens (softens) the spectrum, because it introduces a downstream anisotropy toward the upstream (downstream) and thus lowers (raises) the escape probability.
This effect gradually diminishes with increasing $\gamma_u$, and vanishes altogether in the ultra-relativistic limit.

Test-particle analyses such as presented here do not include non-linear effects caused by the modification of the shock by the accelerated particles themselves, and ignore the injection problem by assuming a pre-existing population of particles that can freely traverse the shock.
Another subtlety is that in such analyses, the velocities $\beta_u$ and $\beta_d$ in the expressions for the spectrum actually pertain to the scattering modes, \emph{i.e.}  to the frames in which the particles scatter elastically.
A relative motion between the scattering modes and the fluid, as expected for example in the shock precursor, would accordingly modify the results.

Our analysis provides a rigorous framework to study, at least qualitatively, various effects that are not inherently high dimensional, such as the dependence of the particle distribution upon $\gamma_u$, the role of the equation of state, and the effect of drifts.
For example, the anisotropy of the particle distribution near the shock, given by Eq.~(\ref{eq:UpAnisotropy}), provides a 1D analog of the anisotropic distribution found \citep[\emph{e.g.,} ][]{Kirk_2000} in 3D.

The emergence of the flat, $p=2$ spectrum, not only in the non-relativistic case, but also in the ultra-relativistic 1D limit, is intriguing.
A flat spectrum, for which the energy in the accelerated particles diverges logarithmically, may serve as an attractor in the ultra-relativistic limit for any dimension.
Such a spectrum was indeed argued in this limit by assuming a microscopically self-similar plasma distribution \citep{Katz_etal_07}.
Thus, is it possible that in higher dimensions, the diffusion function adjusts itself in order to maintain a flat, $p(\gamma_u\to\infty)=2$ spectrum?

\acknowledgments

I thank Y. Nagar, A. Lavi, O. Arad, E. Waxman, A. Heavens, and Y. Lyubarsky for interesting discussions.
This research has received funding from the GIF (grant I-1362-303.7/2016) and the IAEC-UPBC joint research foundation (grant No. 257), and was supported by the Israel Science Foundation (grant No. 1769/15).

\providecommand{\href}[2]{#2}\begingroup\raggedright

redpajama_set_name: RedPajamaArXiv


Keeping the brand message clear and consistent is important to help increase customer recognition. There should be a strong association between the brand and the logo, which should be a graphical representation of this message. A good logo should build loyalty between the business and its customers, creating confidence in the brand and also should help differentiate your business from your competitors. These symbols however, are totally meaningless until the underlying associations are communicated that allow the consumer to become emotionally attached to the brand.
This encourages the identification and loyalty to the brand and the lifestyle it represents.
Consistent use of the logo on your signage, company stationery and marketing materials will help strengthen your brand and encourage your customers to understand its identity.
He said he wasn't in love with the logo initially and thought it would eventually grow on him, however it has gone on to become one of the most iconic, recognised symbols and brands in the world. Of course the products behind the brand have to remain true to their original specification or the brand would not remain successful in such a competitive field.
You may also like:Ways to Brand Your Business with Impressive LogosCreating a logo is not simply about making a design that visually represents a particular business organization and its values, ideas and goals.
Available to help your enterprise move forward and ecosystem means there is a host of third-party.
Your photos in more than one place offers several productivity tools, including online.
Files on mobile devices, but the JustCloud Windows Apps On Microsoft Store Ericsson Secure Cloud make.
Keep their 15 GB worth of free storage space and 15 GB worth of camera.
What you commonly do with cloud storage to each you can open the Google storage.


Best Answers: Youtube.com, problems with videos.?
Originally Answered: How to keep videos on youtube without copyright infringement problems?
If you know of other vids using the same music, either YouTube will take them down eventually, or someone who's jealous will flag them. If you're willing to take the chance and re-upload your video with the same music, do not write the name of the song or artist in your title, description or tags. Also, avoid irrelevant phrases like "no copyright infringement intended", "I do not own the music" or "I don't take any credit for this song". Not only do the computer servers at YouTube's upload center look out for song titles, artists' names and sentences like those, you're also reaffirming that you've knowingly taken, used, copied or maybe even stolen somebody else's copyrighted material. You should also consider the fact that the music-recording industry is starting to use hidden "watermarks" or "fingerprints" buried within their music, in order to uncover and identify their illicit use. As such, it is possible that no matter how many times you try to upload your video, it may always be rejected because of "copyright infringement". You would thus be better off trying to find a different recording of the music you want to use. If you've noticed that other videos are using the exact same music, those videos were probably uploaded before this new technology really started coming into being. The only possible exception to everything that I've just written above is for you to use music that is shorter than 30 seconds. If you listen carefully to any talk-show on radio or TV, they will never use or play other people's music for longer than 30 seconds when introducing a guest or going into/out of commercials. Can you guess the reason? (Hint: it has to do with "licensing fees" and "royalties".) I hope my info has been helpful to you.
Try to use axara video converter. It can download videos from YouTube, convert it to any formats and for any media devices, can create DVD and burn it to disc. Also it has good video editor.
Originally Answered: How can i get more views on my four Youtube videos without becoming a partner or paying for promoted videos?
If you have your own answer to the question youtube videos on problem solving, then you can write your own version, using the form below for an extended answer.
How do you upload videos onto youtube?
Videos on YouTube not Buffering?
My youtube videos won't play?
What camera should i buy for Youtube Videos?
All youtube videos say error.how do I fix this?
No Volume on Youtube videos?
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You can now throw a glowing King Cobra. The King Cobra has the stability players are looking for in a long lasting Champion Mid-Range. Just enough to be straight under full power brand new, and should get straighter finishing with age, just like a go-to Mid-Range disc should be. The King Cobra is more stable than a DX Cobra.


text:
Publication - Research and analysis
Energy efficiency and condition standards in private rented housing: consultation analysis
This report presents an analysis of responses to the consultation on energy efficiency and condition standards in private rented housing.
Profile of respondents
Linking the standard to the Energy Performance Certificate (EPC)
Setting the level of the minimum standard
Bringing in the standard of EPC E at point of rental and then at backstop date
Meeting the standard when there's a change in tenancy after 1 April 2019
Meeting the standard in all private rented properties by 31 March 2022 (the "backstop date")
Minimum standards assessment
Getting the work done
Skills and consumer protection
What happens if the property doesn't meet the standard?
Raising the standard to an EPC D from 2022
Raising the minimum standard beyond EPC D
Assessing impact
Reviewing the standard
Proposals for changes to the repairing standard
Extending the repairing standard
Timing, costs and enforcement
Annex 1 - Organisations responding to the consultation
This report presents analysis of responses to a consultation on Energy Efficiency and Condition Standards in Private Rented Housing.
The Scottish Government has designated energy efficiency as a National Infrastructure Priority, the cornerstone of which will be Scotland's Energy Efficiency Programme ( SEEP). This programme will improve the energy efficiency of homes and buildings, supporting efforts to reduce climate change emissions and tackle fuel poverty. Minimum energy efficiency standards will play a key role.
The consultation opened on 7 April 2017 and closed on 30 June. The consultation paper (available at https://consult.scotland.gov.uk/better-homes-division/energy-efficiency-programme/) asked a total of 68 questions.
Ruth Whatling


text:
Q: Animation in progrssView I use this code to download files. Download animation in progrssView carried out at the last moment. Instead of being implemented during the entire process. How to solve a problem?
Code in my Xcode project:
- (void)viewDidLoad
{
    _progressView = [[UIProgressView alloc] initWithProgressViewStyle: UIProgressViewStyleDefault];
    _progressView.progressTintColor = [UIColor colorWithRed:0.0/255 green:0.0/255 blue:0.0/255 alpha:0.4];
    [[_progressView layer]setFrame:CGRectMake(60, 150, 100, 25)];
    [[_progressView layer]setBorderColor:[UIColor whiteColor].CGColor];
    _progressView.trackTintColor = [UIColor clearColor];
    [_progressView setProgress:(float)(50/100) animated:YES];

    [[_progressView layer]setCornerRadius:_progressView.frame.size.width / 8];
    [[_progressView layer]setBorderWidth:1];
    [[_progressView layer]setMasksToBounds:TRUE];
    _progressView.clipsToBounds = YES;
    [self.view addSubview:_progressView];

    _session = [NSURLSession sessionWithConfiguration:[NSURLSessionConfiguration defaultSessionConfiguration] delegate:self delegateQueue:[NSOperationQueue mainQueue]];

    [self.progressView setProgress:0 animated:NO];
}

-(IBAction) downloadButton:(id)sender
{
        if(_downloadTask == nil){
            _url =[NSURL URLWithString:@"http://www.freeiconspng.com/uploads/ios-png-6.png"];
            _url1 =[NSURL URLWithString:@"http://www.freeiconspng.com/uploads/ios-png-6.png"];
            _downloadTask = [_session downloadTaskWithURL:_url];
            _downloadTask = [_session downloadTaskWithURL:_url1];
            [_downloadTask resume];

        }
        else
            [_downloadTask resume];
        }
}

- (void)URLSession:(NSURLSession *)session downloadTask:(NSURLSessionDownloadTask *)downloadTask didFinishDownloadingToURL:(NSURL *)location
{

    NSArray *paths = NSSearchPathForDirectoriesInDomains(NSDocumentDirectory, NSUserDomainMask, YES);
    NSString *documentsDirectory = [paths objectAtIndex:0];
    NSString *filePath = [documentsDirectory stringByAppendingPathComponent:@"image1.png"];
    BOOL fileExists = [[NSFileManager defaultManager] fileExistsAtPath:filePath isDirectory:NO];

    NSData *urlData = [NSData dataWithContentsOfURL:_url];
    [urlData writeToFile:filePath atomically:YES];

    NSString *filePath1 = [documentsDirectory stringByAppendingPathComponent:@"image2.png"];
    BOOL fileExists1 = [[NSFileManager defaultManager] fileExistsAtPath:filePath1 isDirectory:NO];

    NSData *urlData1 = [NSData dataWithContentsOfURL:_url1];
    [urlData1 writeToFile:filePath1 atomically:YES];
}

- (void)URLSession:(NSURLSession *)session downloadTask:(NSURLSessionDownloadTask *)downloadTask didWriteData:(int64_t)bytesWritten  totalBytesWritten:(int64_t)totalBytesWritten totalBytesExpectedToWrite:(int64_t)totalBytesExpectedToWrite;{
dispatch_async(dispatch_get_main_queue(), ^{
[self.progressView setProgress:totalBytesWritten/totalBytesExpectedToWrite animated:YES];
});
}

UPD
You mean it?
dispatch_async(dispatch_get_main_queue(), ^{
_session = [NSURLSession sessionWithConfiguration:[NSURLSessionConfiguration defaultSessionConfiguration] delegate:self delegateQueue:[NSOperationQueue mainQueue]];

 });

It doesn't work.
I add label in
- (void)URLSession:(NSURLSession *)session downloadTask:(NSURLSessionDownloadTask *)downloadTask didWriteData:(int64_t)bytesWritten  totalBytesWritten:(int64_t)totalBytesWritten totalBytesExpectedToWrite:(int64_t)totalBytesExpectedToWrite;{
    dispatch_async(dispatch_get_main_queue(), ^{
    [self.progressView setProgress:totalBytesWritten/totalBytesExpectedToWrite animated:YES];
        _label = [[UILabel alloc]initWithFrame:CGRectMake(91, 15, 500, 50)];
        _label.text = [NSString stringWithFormat: @"%lld", totalBytesWritten];
        _label.numberOfLines = 1;
        _label.backgroundColor = [UIColor blackColor];
        _label.textColor = [UIColor whiteColor];
        _label.textAlignment = NSTextAlignmentCenter;
        [self.view addSubview:_label];

        });

}

At download time, the numbers in the label increase. After increase number stopped I see progrssView animation.
My label https://drive.google.com/file/d/0B0EJbcHq3ZALX0JNLU1iTFA1d2M/view

A: The code you've posted looks reasonable. You've implemented the URLSession:downloadTask:didWriteData:totalBytesWritten:totalBytesExpectedToWrite: delegate method, which should get called as the data comes in for the file. You're setting the progress view from a call to dispatch_async(dispatch_get_main_queue()), which you should normally do.
One thing I notice is that you create your NSURLSession configuration using [NSOperationQueue mainQueue], which will cause your NSURLSession delegate methods to be called on an operation queue that runs on the main thread.
Try passing in nil for the operation queue. You're already protecting your UI code by wrapping it in calls to dispatch_async(dispatch_get_main_queue()) like you should, so the delegate methods should be safe from a background serial queue.
I would also suggest logging the values of totalBytesWritten and totalBytesExpectedToWrite within your URLSession:downloadTask:didWriteData:totalBytesWritten:totalBytesExpectedToWrite: method to figure out how many times it's being called and with what values.
EDIT
You show code where you create your NSURLSession from inside a call to dispatch_async:
dispatch_async(dispatch_get_main_queue(), ^{
_session =
  [NSURLSession sessionWithConfiguration:
    [NSURLSessionConfiguration defaultSessionConfiguration]
    delegate:self
    delegateQueue:[NSOperationQueue mainQueue]];
 });

That makes no sense whatsoever. What I meant was this:
_session =
  [NSURLSession sessionWithConfiguration:
      [NSURLSessionConfiguration defaultSessionConfiguration]
    delegate: self
    delegateQueue: nil];

By passing nil for the delegateQueue parameter, your delegate methods will be called from the background.
Also adding a new label every time your delegate method gets called is nuts. Simply use NSLog:
- (void)URLSession:(NSURLSession *)session downloadTask:
    (NSURLSessionDownloadTask *) downloadTask
  didWriteData:(int64_t) bytesWritten
  totalBytesWritten:(int64_t)totalBytesWritten
  totalBytesExpectedToWrite:(int64_t)totalBytesExpectedToWrite;
{
  NSLog(@"In didWriteData, totalBytesWritten = %l, filesize = %l",
    totalBytesWritten,
    totalBytesExpectedToWrite);
  dispatch_async(dispatch_get_main_queue(), ^
  {
    [self.progressView setProgress:totalBytesWritten/totalBytesExpectedToWrite
      animated:YES];
  });
}

redpajama_set_name: RedPajamaStackExchange


A huge number of personal development books and blogs are dedicated to the principle of leverage, also known as efficiency, the 80/20 rule, productivity, etc. But the thing is, many people use a "less is more" strategy far too early in the game.
In this great article "Is less really more?" I found via @andyfossett on Twitter, movement, strength, and conditioning coach Clifton Harski challenges the notion in exercise that less is always more.
1. Efficiency for its own sake is often boring, and fun activities are often inefficient precisely because you are doing them for their own sake, not for some outcome.
2. As Harski puts it, "80% is a B-. Those 20% that people ignore, take you from 'ok' to 'good'. They are not unimportant." In other words, you can squeak by with a highly efficient program, but won't get to good or excellent by simply being ruthlessly efficient.
3. "Less is more" recommendations originate from people already doing more–in particular, lots and lots more than you are likely to be doing unless you are at the professional level in that area.
First more is more, until more is less. When more is less, then less is more. That's the rule, more or less.
If you are doing almost nothing, then first you need to get in the game. This is true whether the area is fitness, nutrition, business, learning in a particular field, etc. In all fields, newbies make rapid progress because in systems, more is more at first.
Newcomers to strength training make linear gains, putting up more weight every week if not every session.
People who go on diets to lose weight find that the first few pounds are the easiest to lose (and the last 10 to 15 the hardest).
More marketing for a business that has never done marketing leads to more customers, often in a linear dollars to customers kind of way.
Someone getting organized and "productive" for the first time can easily become 2-3x more productive just by making a to-do list or working on a Pomodoro schedule.
But inevitably, the law of diminishing returns sets in.
Then what happens is that for the same extra effort, fewer results come.
Strength gains were going up by 5lbs on each lift per session, then 5lbs per week, now nothing for weeks.
The first 30 pounds melted away, now you're always hungry and you're losing weight only at a rate of 1/2 lb every two weeks.
You keep spending money on marketing efforts which used to have a big payoff but now they barely even bring in what they used to.
You've gotten basically organized and productive with to-do lists and priorities, but you keep surfing productivity blogs and organizing files with no real productivity gains from these activities.
When we hit this arena of diminishing returns, some people double-down and waste resources. Other people give up entirely. Whereas the most effective strategy now becomes "more is less"–to focus on the most important elements and become efficient.
When a person or organization in this context focuses on putting energy towards priority tasks, then expending fewer resources ("less") brings about more productivity, as measured by the ratio of inputs to outputs. Therefore less is more in this context.
But critical to this discussion is that less is NOT more until it is, until inputs have been maximized, until you are doing sufficient volume in the gym or really putting yourself out there in your marketing, etc. And even then, you might purposely choose inefficiency for reasons of fun, for artistic expression, or to develop excellence in a chosen area.
He does 700 pushups, 10 sets of pullups, and 10 sets of dips, five days a week. It's hard to argue with his results though, and he looks like he enjoys it. Can a person get fit and muscular on less than that? Absolutely. It's all up to you how what you want to do with your life.


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