Capillary action and conservation of energy When I dip a paper towel in a cup of water the water gets drawn up due to . How is this reconciled with conservation of energy, as it would seem on the surface that the potential energy of the system has gone up with no work being done?
When water climbs up a piece of paper, where is the energy coming from? Take a glass of water and piece of toilet paper. If you keep the paper vertical, and touch the surface of the water with the tip of the paper, you can see the water being absorbed and climbing up the paper. This climbing up is intriguing me. Where is the energy coming from?  Supposedly, a lot of water molecules are moving up and gaining potential energy. This has to be balanced by something. I can think of a few possibilities, but I can't tell which one it is.   When the water molecules dilute into the paper, they are at a state of lower potential binding energy. Some molecular interaction (van der Waals?) is at lower energy when you have a water+paper solution, compared to a water-only solution. This compensates the gain in gravitational energy. The surface between the paper and the water is at lower pressure than the atmosphere. This causes the water to be pushed into the paper by the atmospheric pressure, up until the point that the column of water above the surface is heavy enough to counterbalance. The potential energy would be a result of work done by the atmosphere. Some water molecules climb up randomly and loose kinetic energy going up, and somehow get "stuck" up there. Something else?
How to use variable in sed command Looking for a function $f$ that is $n$-differentiable, but $f^{(n)}$ is not continuous I am looking for a real valued function of real variable that is $n$-differentiable, but whose $n$th derivative is not continuous.  This is my function:  $f_n(x) = x^{n+1} \cdot \sin{\frac{1}{x}}$, if $x \neq 0$ and 0, if $x=0$. $n\in \{0,1,2,\ldots\}$ For example, if $n=0$, $f_0$ it's continuous and non diferentiable in $0$. When I use the MouseUp event, I can get it to fire with a mouse right-click. But MouseLeftButtonUp won't fire with either click!  &lt;Button MouseLeftButtonUp="btnNewConfig_MouseUp"  Name="btnNewConfig"&gt;     &lt;StackPanel Orientation="Horizontal"&gt;         &lt;Image Source="Icons\new.ico" Height="24" Width="24" Margin="5"/&gt;         &lt;TextBlock VerticalAlignment="Center"&gt;New&lt;/TextBlock&gt;     &lt;/StackPanel&gt; &lt;/Button&gt;   I know this is most likely something simple. Thanks for the help! How to put small numbers outside the pie slices without making a mess I'm new to LaTeX and need some help with my figures. I would like to to put small numbers outside the pie slices without making a mess. Having found this thread , I tried it out, but didn't get all the way through with it. Right now, my pie looks like this:    I used the following code:  \usepackage{tikz,stackengine} \makeatletter  \tikzstyle{chart}= [legend label/.style={font={\scriptsize},anchor=west,align=left}, legend box/.style={rectangle, draw, minimum size=5pt}, axis/.style={black,thin,-&gt;}, axis label/.style={anchor=east,font={\tiny}}]  \tikzstyle{bar chart}=[ chart, bar width/.code={     \pgfmathparse{##1/2}     \global\let\bar@w\pgfmathresult}, bar/.style={thin, draw=black}, bar label/.style={font={\bf\small},anchor=north}, bar value/.style={font={\footnotesize}}, bar width=.75,]  \tikzstyle{pie chart}= [chart, slice/.style={line cap=round, line join=round, thin, draw=black}, pie title/.style={font={}}, slice type/.style 2 args={     ##1/.style={fill=##2},     values of ##1/.style={}}]  \pgfdeclarelayer{background} \pgfdeclarelayer{foreground} \pgfsetlayers{background,main,foreground}  \newcommand{\pye}[3][]{     \begin{scope}[#1]         \pgfmathsetmacro{\curA}{90}         \pgfmathsetmacro{\r}{1}         \def\c{(0,0)}         \node[pie title] at (270:1.3) {#2};         \foreach \v/\s in{#3}{             \pgfmathsetmacro{\deltaA}{\v/100*360}             \pgfmathsetmacro{\nextA}{\curA + \deltaA}             \pgfmathsetmacro{\midA}{(\curA+\nextA)/2}             \path[slice,\s] \c             -- +(\curA:\r)             arc (\curA:\nextA:\r)             -- cycle;             \pgfmathsetmacro{\d}{max((\deltaA * -(.5/50) + 1) , .5)} %%%              %\pgfmathprintnumberto{#3}{\fnum}  %\ifthenelse{\lengthtest{#3 pt &lt; 10pt}} %{\path (O) -- ++ (\midangle:\radius) %node[inner sep=0,align=left,anchor=west,rotate=\midangle](nums#3)    {~~\fnum};} %{\path (O) -- ++(\midangle:\innerpos)  %node {\scalefont{#3}\beforenumber\fnum\afternumber};}           %%%                         \begin{pgfonlayer}{foreground}                 \path \c -- node[pos=\d,pie values,values of \s]{$\v\%$} +    (\midA:\r);             \end{pgfonlayer}             \global\let\curA\nextA}     \end{scope}}  \newcommand{\legend}[2][]{     \begin{scope}[#1]         \path         \foreach \n/\s in {#2}         {++(0,-5pt) node[\s,legend box] {} +(2pt,0) node[legend label]     {\n}};     \end{scope}}      \begin{document}         \begin{center}      \begin{figure}[H]     \centering \begin{tikzpicture} [pie chart, slice type={A}{black!0}, slice type={B}{black!10}, slice type={C}{black!20}, slice type={D}{black!30}, slice type={E}{black!40}, slice type={F}{black!50}, slice type={G}{black!60}, slice type={H}{black!70}, pie values/.style={font={\small}}, scale=2]  \pye{1994}{6.1/A, 2.9/B, 0.2/C, 54.3/D, 25.2/E, 1.4/F, 6.7/G, 3.2/H} \pye[xshift=2.2cm,values of coltello/.style={pos=1.1}]% {2005}{6.8/A, 3.0/B, 0.5/C, 52.3/D, 25.6/E, 1.8/F, 7.1/G, 2.8/H} \pye[xshift=4.4cm,values of caffe/.style={pos=1.1}]% {2015}{7.2/A, 3.1/B, 0.6/C, 50.6/D, 26.5/E, 2.3/F, 7.5/G, 2.2/H}  \legend[shift={(0cm,-1.5cm)}]{{A}/A, {B}/B}  \legend[shift={(1.4cm,-1.5cm)}]{{C}/C, {D}/D}  \legend[shift={(2.8cm,-1.5cm)}]{{E}/E, {F}/F} \legend[shift={(4.2cm,-1.5cm)}]{{G}/G, {H}/H} \end{tikzpicture} \end{figure}  \end{document}   This looks quite the way I want it to, only the small numbers should be placed outside the pies.  Thanks in advance :) Are there rules for disassembling a slain creature, especially dragon? How does friction stop a car? I'm unable to understand how friction causes motion in cars and also is responsible for stopping them. When it starts the impending motion of tyres is in the backward direction that's why friction is in the forward direction and the car starts moving. But when the car engine turns off, the car stops after some time, but the condition of tyres are the same as in the previous case and friction must be in the forward direction. I need to calculate the surface (m2) of external walls of all the buildings in a town. By external walls I mean all the walls of a building or parts of a wall which are not in contact with another building. I have a 2D shapefile of polygons with the cadastral footprint of the buildings, which includes information of the building’s height in the attribute table.  I don’t really know how can I do it… My idea is to convert the 2D file to 3D and use the 3D shapefile to distinguish the external walls from the shared walls (parts of a building that are shared with other buildings) of all buildings, and from there, calculate the total area but I’m not sure whether this can be done with ArcScene.  Anybody knows how could it be done and if there is an automate way to do it? How can I restart a Windows 7 computer without screen or mouse? If moderators can view , can we see comments we've deleted? We can see our deleted answers, but why not our deleted comments? Limit of $n$th root of $n$! I am asked to determine if a series converges or not:  $$\displaystyle\sum\limits_{n=1}^{\infty} \frac{(2^n)n!}{(n^n)}$$  So I'm using the $n$th root test and came up with $\lim_{n \to {\infty}}\frac{2}{n}\times(\sqrt[n]{n!})$ I know that the limit of $\frac{2}{n}$ goes to $0$ when $n$ goes to infinity but what about the $(\sqrt[n]{n!})$? So today I woke up and noticed new item in inventory which was a booster pack containing 3 cards from L4D 2. From what I see on market these booster packs are new (graph only shows up to 19 of June). No matter the game it seems to always contain 3 cards. There are two actions I can do with it: unpack or sell. There is fancy animation when you unpack the booster ;)    I'm not exactly sure why I got it, I have few guesses:   I got new badge, power player - this could give me a booster? Because of new badge I reached level 10 - maybe every couple levels there are gifts? It just dropped randomly for everyone?   Maybe together we could rule out above guesses. It's also interesting from the point of market, to estimate how many boosters are there. With some games they seem to be more valuable than 3 cards separately, but that maybe only initial confusion. Command-line mv exclusion list In node.tpl.php, I have done some changes, like creating an array of paragraphs:      $paragraphs = explode("&lt;p&gt;",render($content));   So, I have a for loop for showing the paragraphs, like:  $number = count($paragraphs); if($page){   print render($paragraphs[0]);   for ($i=1;$i&lt;$number;$i++)       {          print render($paragraphs[$i]);        &lt;a href="#commenting"&gt;Put comment for Paragraph &lt;?php echo $i?&gt;&lt;br&gt;&lt;/a&gt; &lt;?php  } ?&gt;     &lt;a id="commenting"&gt;&lt;?php print render($content['comments']); ?&gt;&lt;/a&gt; &lt;?php }?&gt;   As you can see I want to create a hyperlink under each paragraph, so when user click on it, they can put comment on the paragraph, But right now, when they click on the hyperlink, it will  jump to the end of the page, which has the comment form.  If you check the CommentPress website, in the right column, you can see for example, it is said: 5 Comment on Paragraph 1, and when you click on it, it will show the comments and the comment form under that link, I want to have the same thing, I mean, when users click on the link under each paragraph, the comment form displays under that link instead of jumping to the end of the page. What is JSON and what is it used for? Background I updated my TeX Live installation on my Mac a while ago and got the error LaTeX3 Error: Mismatched LaTeX support files detected. I found a solution at .  As far as I understand it (which isn't very far), there are system formats and local formats, and TeX Live is updating the wrong one.  The fix is to update the formats. Using fmtutil-user --all worked for me.  It spewed out a load of stuff, then output fmtutil [INFO]: log file copied to: /Users/&lt;user&gt;/Library/texlive/2020/texmf-var/web2c/luatex/dvilualatex.log fmtutil [INFO]: /Users/&lt;user&gt;/Library/texlive/2020/texmf-var/web2c/luatex/dvilualatex.fmt installed.  I don't know what this tells me, but my TeX Live preferences has TeX programs set at /Library/TeX/texbin, which seems to be a link to /usr/local/texlive/2020/bin. Problem Every time I update TeX Live, I have to apply the solution again. Question Is there a way to make TeX Live use the correct formats permanently so that I don't have to keep running fmtutil-user --all after every TeX Live update?  Extra information  to  check if you have some local formats around which hide the system formats. (with eg kpsewhich --all --engine=pdftex pdflatex.fmt)  When I did that, it output /Users/&lt;user&gt;/Library/texlive/2020/texmf-var/web2c/pdftex/pdflatex.fmt /usr/local/texlive/2020/texmf-var/web2c/pdftex/pdflatex.fmt  but I don't know what that's telling me. listing files with pattern with starting and ending I want to list all files in a directory that start with 'abc' and end with '.zip'  I'm trying to use ls.  The directory has a lot of zip files starting with abc&lt;date&gt; and xvz&lt;date&gt;. I only want to get the list of the abc&lt;date&gt;.zip Is my proof of convergence for $\sum\limits^{\infty}_{n=1} \frac {2^n} {n^n}$ true? I want to prove that $\sum\limits^{\infty}_{n=1} \frac {2^n} {n^n}$ is convergent.  Therefore I want to use that it will be convergent if $\lim\limits_{n \to \infty}|\frac {2^{n+1}} {n^n}| &lt; 1$ is true.  But I am not sure if all of my steps are legal to do in order to do it. Here is what I came up with:  $$\lim_{n \to \infty}|\frac {2^{n+1}} {n^n}| &lt; 1$$ $$\lim_{n \to \infty}|\frac {\sqrt[n]{2^{n}} \sqrt[n]{2}} {\sqrt[n]{n^n}}| &lt; \sqrt[n]1$$ $$\lim_{n \to \infty} \frac {2 \sqrt[n]2} {n} &lt; 1$$ $$0&lt;1$$  $\Rightarrow$ It is true. I have noticed that I hardly ever use the \negthinspace command  \!.  This is because I don't know how to use it properly (I do use other spacing commands quite a bit, because I can better understand the guidelines of when they might be useful). When might it be considered appropriate to use this spacing command? How do I suppress the "New release '12.10' available" message? A mysterious app named &quot;10102&quot; shows up in my data usage. It bears only the standard Android app icon (the Bugdroid logo with a cube on its torso). From what the graph tells me, it has used 36 megabytes of data in the background and zero on the foreground. I think I haven't uninstalled anything for months. Is it malware? I haven't sideloaded anything and only authorized my laptop as a USB debugger. If it's malware, how do I remove it? I have no idea how to find its package name and 10102 isn't in the list of downloaded apps in settings. I'm running stock &amp; never-been-rooted Android 4.4.4 on Nexus 4.