The Maxwell-Boltzmann velocity distribution arises from non-reactive elastic collisions of particles and is usually discussed in the context of the  (for gases). There are various offhand remarks, for example  (slide 5), that state without reference that particles observe a similar velocity distribution in liquid. Is that true? References?  The main reason I'm curious is that it seems as though the mean free path would be extremely short in liquid vs. gas. I'm actually most curious about the nature of the collisions in liquid vs. gas, i.e., are collisions in liquid still (on average) elastic?  EDIT: The linked post on  is definitely interesting and weighs in on this question, and I appreciate the distinction made between local position fluctuation vs. long range movement. Still, let me frame this question in a few different ways.   Gillespie proposed  which is formulated on the idea that non-reactive elastic collisions serve to 'uniformize' particle position so that the assumption of well-mixedness is always satisfied (see page 409 in the linked version). This is formulated from kinetic theory. A corollary to this is that a non-reactive collision between two molecules that are able to react does not induce local correlation, i.e., two particles able to react with each other that just collided, but didn't react are no more likely to react with each other in the next dt than any other particle pair in the volume. Gillespie's algorithm is commonly used in biology where biochemical species are modeled in the aqueous environment of cells. Is this valid, and if so why? On a microscopic scale, suppose we are interested in two 'A' particles diffusing in one dimension in an aqueous environment. The two A particles collide but don't react. What is their behavior immediately after the collision? Is it a 'reflection' which conserves velocity and might correspond to a Neumann BC? In a gas that approach seems natural, but in liquid the short mean-free path makes me think that diffusive forces would rapidly dissipate any momentum from the A-A collision, which might imply the A particles collide and 'stop'. How should I be thinking about this?   Just to bring it back to the original question, I think both (1) and (2) depend on the statistical velocity behavior of particles in liquid.
I seem to remember from first year physics that we can calculate the RMS speed of a stationary, ideal gas with $v=\sqrt{\frac{3RT}{M}}$. Does a similar equation exist for liquids?
How can I sound proof bathroom walls? I'm trying to figure out the best, least intrusive way of sound proofing the walls of a bathroom. The bathroom shares a wall with my bedroom, and my 3 yea old's bedroom. The main problem is the sound of water running (plus every bump on the counter and everything) echos loud and clear through the wall into my sons room.  I found  and it seems like a good choice. Another option is adding another layer fo drywall with something like  between them. But all the walls and ceilings in the house are textured. So replacing just one or two walls in a room is just not possible.   This is the layout of the two rooms. I've added red box around the wall with the most noise.   Is there anything else I'm missing here that I could do to dampen the noise short of tearing the bathroom apart? What is the reasoning behind limiting "recidivists" to post one question per week? currently restricts recreated accounts to "posting only one question per week..."  I would like to understand why this rate was picked, and not, say, once a day or once a month?  The reason why I ask is that some users limited or banned at Stack Overflow . I expect that learning more about the limitation would help me better understand its impact on Programmers. Player A taps  targeting Player B; its "deals 1 damage to target player" ability is placed on the stack.  Player B gets priority and responds with , targeting Goblin Fireslinger.  Both players pass priority. Snap resolves, and Goblin Fireslinger is returned to its owner's hand.  Does Player B still take 1 damage from Goblin Fireslinger's activated ability?  I know that if the creature had been killed/sent to the graveyard, the ability would still resolve, but I was told recently that because a player's hand is a private zone it couldn't. If anyone could confirm or deny this for me, it would be most appreciated. Changing parameter values according to other parameter choice in Processing script using QGIS 3? Calling PHP functions within HEREDOC strings In PHP, the HEREDOC string declarations are really useful for outputting a block of html.  You can have it parse in variables just by prefixing them with $, but for more complicated syntax (like $var[2][3]), you have to put your expression inside {} braces.  In PHP 5, it is possible to actually make function calls within {} braces inside a HEREDOC string, but you have to go through a bit of work.  The function name itself has to be stored in a variable, and you have to call it like it is a dynamically-named function.  For example:  $fn = 'testfunction'; function testfunction() { return 'ok'; } $string = &lt;&lt;&lt; heredoc plain text and now a function: {$fn()} heredoc;   As you can see, this is a bit more messy than just:  $string = &lt;&lt;&lt; heredoc plain text and now a function: {testfunction()} heredoc;   There are other ways besides the first code example, such as breaking out of the HEREDOC to call the function, or reversing the issue and doing something like:  ?&gt; &lt;!-- directly output html and only breaking into php for the function --&gt; plain text and now a function: &lt;?PHP print testfunction(); ?&gt;   The latter has the disadvantage that the output is directly put into the output stream (unless I'm using output buffering), which might not be what I want.  So, the essence of my question is: is there a more elegant way to approach this?  Edit based on responses: It certainly does seem like some kind of template engine would make my life much easier, but it would require me basically invert my usual PHP style.  Not that that's a bad thing, but it explains my inertia..  I'm up for figuring out ways to make life easier though, so I'm looking into templates now. How to identify unused CSS definitions from multiple CSS files in a project A bunch of CSS files were pulled in and now I'm trying to clean things up a bit. How can I efficiently identify unused CSS definitions in a whole project? Existence of a local geodesic frame Let $(M,g)$ be a Riemannian manifold of dimension $n$ with Riemannian connection $\nabla,$ and let $p \in M.$ Show that there exists a neighborhood $U \subset M$ of $p$ and $n$ (smooth) vector fields $E_1,...,E_n \in \chi (U),$ orthonormal at each point of $U,$ s.t. at $p,$ $\nabla_{E_i}E_j(p)=0.$  What I've found so far;  Let $V$ be a normal neighborhood at $p.$ Let $(W,x(x_1,...,x_n))$ be a local coordinate system at $p$ s.t. $x(W) \subset V.$  Let $\{X_i:=\frac{\partial}{\partial x_i}\}$ be the standard basis of $T_pM.$ By Gram-Schmidt, there exists an orthonormal basis $\{E_i\}$ of $T_pM.$ Consider the orthonormal frame $E_i(t),$ by parallel transporting $\{E_i(0)=E_i\}$ along a  a geodesic $\gamma :I \to M$ starting at $\gamma(0)=p$ and ending in $\gamma(1)=q,$ where $q \in V.$ This gives us an orthonormal frame at each point of $V.$ To satisfy the second condition, let $E_i(t)=\sum_{l}a_{li}X_l$ and  $E_j(t)=\sum_{s}b_{sj}(t)X_s.$ Then   $$\nabla_{E_i}E_j=\sum_{k}(\sum_{l,s} a_{li}(t)b_{sj}(t)\Gamma^k_{ls}+E_i(b_{kj}))X_k,$$  where $\Gamma^k_{is}$ are Christoffel symbols.   To have $\nabla_{E_i}E_j(p)=0,$ we must have $\sum_{l,s}a_{li}(0)b_{sj}(0)\Gamma^k_{ls}+E_i(b_{kj})(p)=0$ for each $k.$      How can I conclude the argument? The following  (links to pdf) in the  has no provided source. The book  by Ash and Gross seems to use a similar style. Where can I find hints for typesetting publication standard articles/books as above in TeX. I looked around a bit but couldnt find much from else from keyword searches.  Particularly, I am looking at the chapter headings, title page design, and the mirror effect. Sorry for the title, as I dont really know what its called. Replace symbols with values without evaluation How to use multiple Effect Strips in Blender Video Sequence Editor? I want my Java code to be typeset in a monospaced font, so I am using the verbatim environment. LaTeX commands are highlighted in Eclipse, but as soon as I use the verbatim environment everything inside and the color of the environment itself becomes gray.  \begin{verbatim}   public class main {  public static void main (string[] args){      for(int i = 0; i &lt; arg.length; i ++){          System.out.println(args[i]);      }    }  };  \end{verbatim}   I'm using the verbatim and alltt packages.  Update 1.  MWE.  \documentclass[xcolor=dvipsnames]{beamer}  \mode&lt;presentation&gt; { \usetheme{CambridgeUS} \setbeamercovered{transparent} }  % Поддержка русского языка \RequirePackage[utf8]{inputenc} \RequirePackage[T2A]{fontenc} \RequirePackage[russian]{babel}  \RequirePackage{amsfonts}  \usepackage{algorithmic} \usepackage{mathptmx} \usepackage[scaled=.90]{helvet} \usepackage{courier} \usepackage{pst-node} \usepackage{pst-tree} \usepackage{auto-pst-pdf} \usepackage{color} \usepackage{colortbl} \usepackage{pstricks} \usepackage{verbatim} \usepackage{alltt} \usepackage{listings} \usepackage{animate} \usepackage{multimedia}  \title{Title}  \author{Name}  \institute{}  \date{\today}  \begin{document}  \begin{frame} \titlepage \end{frame}  \begin{frame} \frametitle{Outline} \tableofcontents \end{frame}  \section{Introduction}  \begin{frame}{Классификация по поколениям}  \begin{itemize}  \item Третьего поколения (высокоуровневые языки) - последовательность высокоуровневых конструкций (циклы, условные выражения, классы, интерфейсы, методы, процедуры, \ldots) \pause  \begin{exampleblock}{Пример}  \begin{centering}  Fortran, C, C++, C\#, Java, Lisp.  \begin{verbatim}  public class main { public statiс void main (string[] args){ for(int i = 0; i &lt; arg.length; i ++){ System.out.println(args[i]); } } };  \end{verbatim}  \end{centering}  \end{exampleblock}\pause  \item Четвертого поколения (для конкретного применения) - последовательность инструкций конкретной предметной области \pause  \begin{exampleblock}{Пример} SQL, Postscript, XML, Mathlab. \end{exampleblock} \pause  \end{itemize}  \end{frame}  \end{document} What is object slicing? Biasing circuit - Voltage follower circuit I am using , which is and Bias controller/sequencer. I am using this for Providing gate voltage and drain voltage to the . In the datasheet, it is mentioned that the module with combination of EVM can be used in two applications. Application Option 1: Fixed negative gate biasing with pulsed drain biasing. Application Option 2: Pulsed negative gate biasing with pulsed drain biasing. I am trying to design both applications on a single board. The second option for future use. For the 1st application option, he has mentioned a few pins as No connection and he has used those NC pins on the 2nd application.  The issue I am facing:- They have used voltage followers for providing a low impedance output path for pin number 3(GCO). I have reverse-engineered the Ckt from the below-attached image, but I am unable to identify the voltage follower they have used. Pin number 2 of the voltage follower has been connected to pin number 2 (NC/GCP) of the Module. There has been no description of this pin number. I am guessing these:-  Pin numbers 1 and 4 are connected together and output is provided through them. Pin number 5 is +Ve supply hence connected to GND(Highest +Ve supply)? Pin number 3 is connected to -8V Pin number 2 is connected to pin number 2 of MABC-001000-DP000L, which I am unable to understand.  I have mailed component manufacturer regarding full schematic, till now I haven't heard from them. Can anybody help me with this? Thanks in Advance. Low-resolution pic of EVM. I don't think it helps in any way.   Layout Image How to deal with hierarchical / nested data in machine learning Lyircs of Free by Natalia Kills:     I'm free      I just spent all my money       but I rocked that like it don't cost a thing   Shouldn't it be "I've just spent all my money"? As far as I remember, our English told us to use Present Prefect in such case because of the just. Bluetooth is on but can't find or be found by any other devices.  Output of sudo service bluetooth status:  ● bluetooth.service - Bluetooth service    Loaded: loaded (/lib/systemd/system/bluetooth.service; enabled; vendor preset: enabled)    Active: active (running) since ხუთ 2015-06-04 22:33:18 GET; 13min ago  Main PID: 26678 (bluetoothd)    CGroup: /system.slice/bluetooth.service            └─26678 /usr/sbin/bluetoothd -n  ივნ 04 22:39:14 Rangoo bluetoothd[26678]: Endpoint registered: sender=:1.63 path=/MediaEndpoint/BlueZ4/HFPAG ივნ 04 22:39:14 Rangoo bluetoothd[26678]: Endpoint registered: sender=:1.63 path=/MediaEndpoint/BlueZ4/HFPHS ივნ 04 22:39:14 Rangoo bluetoothd[26678]: Endpoint registered: sender=:1.63 path=/MediaEndpoint/BlueZ4/A2DPSource ივნ 04 22:39:14 Rangoo bluetoothd[26678]: Endpoint registered: sender=:1.63 path=/MediaEndpoint/BlueZ4/A2DPSink ივნ 04 22:39:14 Rangoo bluetoothd[26678]: bluetoothd[26678]: Endpoint registered: sender=:1.63 path=/MediaEndpoint/BlueZ4/HFPAG ივნ 04 22:39:14 Rangoo bluetoothd[26678]: bluetoothd[26678]: Endpoint registered: sender=:1.63 path=/MediaEndpoint/BlueZ4/HFPHS ივნ 04 22:39:14 Rangoo bluetoothd[26678]: bluetoothd[26678]: Endpoint registered: sender=:1.63 path=/MediaEndpoint/BlueZ4/A2DPSource ივნ 04 22:39:14 Rangoo bluetoothd[26678]: bluetoothd[26678]: Endpoint registered: sender=:1.63 path=/MediaEndpoint/BlueZ4/A2DPSink ივნ 04 22:39:14 Rangoo bluetoothd[26678]: Adapter /org/bluez/26678/hci0 has been enabled ივნ 04 22:39:14 Rangoo bluetoothd[26678]: bluetoothd[26678]: Adapter /org/bluez/26678/hci0 has been enabled   Output of lsusb:  Bus 003 Device 005: ID 0a5c:21d7 Broadcom Corp. BCM43142 Bluetooth 4.0   How can I fix it? What is your favorite method to handle errors in Bash?  The best example of handling errors I have found on the web was written by William Shotts, Jr at .   He suggests using the following function for error handling in Bash:  #!/bin/bash  # A slicker error handling routine  # I put a variable in my scripts named PROGNAME which # holds the name of the program being run.  You can get this # value from the first item on the command line ($0).  # Reference: This was copied from &lt;http://www.linuxcommand.org/wss0150.php&gt;  PROGNAME=$(basename $0)  function error_exit {  #   ---------------------------------------------------------------- #   Function for exit due to fatal program error #       Accepts 1 argument: #           string containing descriptive error message #   ----------------------------------------------------------------       echo "${PROGNAME}: ${1:-"Unknown Error"}" 1&gt;&amp;2     exit 1 }  # Example call of the error_exit function.  Note the inclusion # of the LINENO environment variable.  It contains the current # line number.  echo "Example of error with line number and message" error_exit "$LINENO: An error has occurred."   Do you have a better error handling routine that you use in Bash scripts? Java : How to determine the correct charset encoding of a stream What can I expect from a Skype interview for PhD admissions? Over at , there is overlapping text in the Database Schema under Close-As-Off-Topic-Reason-Types:  that makes it really hard to read.  This is also happening underneath &quot;Pending Flags&quot;, and seemingly with every long line in the schema.  This would be fine if you could increase the width of the list as you can with the height, which would in theory separate the lines, but you can't.  Can we fix this, please?  UPDATE: I have found that  post is almost exactly the same as mine, but steady on with duplicate votes.   comment says that it will be fixed, but that question was asked more than five years ago, and in that time the problem has not been resolved.  UPDATE 2: It seems that  would help.  I changed a little CSS/HTML, and came up with this:  Although mine is a little cruder than it could be.  This is just an example.