I was wondering about the microscopic reason why for example when I open the window in the winter the colder air from outside is more likely to be distributed on the floor (of course only in the first time when the air in the room have not yet thermally equilibrated everywhere). On a macroscopic scale I know that the difference in the density together with Archimedes principle leads to the right reasoning.
The usual explanation for warm fluids rising past cooler ones is that the warmer fluid has a lower density.  I'm trying to understand what this looks like at a molecular scale.  The density seems to be a large-scale phenomenon, and I don't understand how it can affect whether a particular molecule rises or falls.  Consider a cylinder of fluid that is being heated at the bottom.  The molecules at the bottom have a higher average energy.  How does this result in the tendency of the warmer molecules at the bottom to move upwards past the cooler ones?
Update values in one table based on contents of another Software Name: Oracle SQL Developer Version 17.2.0.188  I have three tables: orders, order_details, and products.  I wanted to run a query to update units_in_stock in the products table based on quantity in order_details, where the associated orders row has been marked as shipped, and has a shipping date.  Here's what I tried:  UPDATE Products SET (Products.Unit_In_Stock = Products.Unit_In_Stock - Order_Details.Quantity) INNER JOIN (     Orders INNER JOIN Order_Details ON Orders.Order_ID = Order_Details.Order_ID     ) ON Products.Product_ID = Order_Details.Product_ID WHERE (         ((Orders.Shipped_Date) IS NOT NULL)         AND ((Orders.This_Order_Was_Shipped) = "YES")         );   When I run this, I get:  Error at Command Line : 1 Column : 45   Line 1, Column 45 is the equal sign in the very first statement that said  Products.Unit_In_Stock = Products.Unit_In_Stock - Order_Details.Quantity   Can you help me get this working? How does Latex compilers integrate packages into its existing core functions? I have heard that there are some Pokémon that are region specific.  Could someone please clarify which Pokémon are region specific and in which regions that they can be found in? $\max(\{n: n+5 | n^5 + 5\})$ What is the maximum value of $n$ if $n + 5$ divides $n^5 + 5$, $n$ being a natural number? I tried to solve by binomial theorem but it failed. How to format a USB flash drive? In Windows there is a straightforward "Format" option in a flash drive's right-click pop-up menu. Where's that in Ubuntu? I have not been able to watch CBS all access for some time now. Error 2004. I have not found another browser for ubuntu that will play all access either. However firefox for windows plays it fine? Is there a fix in the works for ubuntu firefox? How to show (or hide) a hidden file I wanted to add classpath to my JDK. While searching a way to do it I noticed everyone open .profile file using terminal. But when I want to open and edit it with a text editor I couldn't see that file in Home folder.  Can someone tell me why is this. And also if possible how can I access .profile in home folder the GUI way. Euler's equations of rigid body motion from least action principle I would like to derive Euler's equations of rigid body motion from least action principle.   Suppose we are in free space so we have no gravity so Lagrangian is equal to kinetic energy.   $$ L = T = \int_M \rho(x)(x\cdot \Omega_B)^2 d^3x $$  where $\rho$ is density, $\Omega_B$ is angular velocity bivector in reference body frame and $M$ is the rigid body.  The action principle says(if I haven't messed up something) that   $$ 0 = \frac{d}{ds}\bigg|_{s=0}\int_0^T \int_M \rho(x)[x\cdot (\Omega_B(t)+s \delta \Omega(t))]^2 d^3x $$  for every $\delta \Omega$ with zero ends i.e. $\delta \Omega(0)=\delta \Omega(T) = 0$. I should get these equations:  $$ I(\Omega_B) - \Omega \times I(\Omega_B)=0 $$  where  $$ I(\Omega) = \int_M \rho(x) (x\wedge (x\cdot \Omega)) d^3x. $$  But I can't see where I would get the time derivative of $\Omega_B$ from the action principle. Can someone tell me what I'm doing wrong? I guess there is some trouble with that $\delta \Omega$ can't be completely arbitrary. Writing test code for wrapper class I don't understand philosophy very well, and so I am wondering whether you can "prove" anything in philosophy. It always seems you can go a layer down, and find another question, almost endlessly until you get to the question of "why/how/are we here?"  Can you prove, absolutely, and 100% that something is true, in the field of philosophy? How to mount and unmount hard drives under Windows (the unix way) I am using \if condition in a custom command in my LaTeX document. I would like to know where I can find some good explanation about \if command. I followed a  but it's just an example; there are not any explanation. Proof of this result related to Fibonacci numbers: $\begin{pmatrix}1&1\\1&0\end{pmatrix}^n=\begin{pmatrix}F_{n+1}&F_n\\F_n&F_{n-1}\end{pmatrix}$? $$\begin{pmatrix}1&amp;1\\1&amp;0\end{pmatrix}^n=\begin{pmatrix}F_{n+1}&amp;F_n\\F_n&amp;F_{n-1}\end{pmatrix}$$  Somebody has any idea how to go about proving this result? I know a proof by mathematical induction, but that, in my opinion, will be a verification of this result only. I tried to find through the net, but in vain, if someone has some link or pointer to its proof, please provide, I'll appreciate that.  Thanks a lot! Why don't I hear any sound after calling the Beep function in Windows 7? Focal length of an ellipse and related results listing files with pattern with starting and ending I was working on a userscript today, which had a goal of displaying chat pings immediately at the main site. This would allow me to respond more quicker-like to chat pings.  However, I was met by this fearsome warrior:     Can we please set some decent header things? I want to be able to do this really bad. Refreshing Formula Fields Dynamically (without save) I have an "invoice" custom object which has a couple of summarising formula fields in. I also have a complicated and dynamic visualforce page for building the invoice objects.  As the user is completing this form, different areas are dynamically updated to show "latest" values. This is all fine where I am copying data about or performing bespoke lookups and maths, but - in what is really the simplest case - a formula field, I can find no way to get the value to update, without performing some weird cyclic save + reload of the whole object.  This is inappropriate for a couple of reasons (the object should not be saved until the invoice is complete + accepted) and the other option I have found online is to spoof the value by duplicating my formula field maths into the custom controller and re-executing them there - also unacceptable from a code/logic location/duplication perspective.  Is there anyway to "force" an object/page to recalculate it's formula fields, either through standard or extended controllers? I've a Skype interview for PhD application (it will make me miss  today.) I've been asked, in advance, to prepare a short presentation and then there would be some discussion with the panel (I guess.) I expect that they will ask if I have some questions so, I'm wondering what are the best (type of) questions one might consider? In Harry Potter and the Philosopher's Stone, Hermione is in the toilets when Harry and Ron lock in the troll. She lies and says that she went looking for the troll. Why? She could have just said that she was in there because she needed the toilet (she was allowed to be, it's a girls' bathroom) and Harry and Ron came to save her.   Is there a reason she lied?