What is the exact mechanism of flow of electricity? When a steady current flows through a conductor, the electrons in it move with a certain average ‘drift speed’. One can calculate this drift speed of electrons for a typical copper wire carrying a small current, and it is found to be actually very small, of the order of 1 mm s-1. How is it then that an electric bulb lights up as soon as we turn the switch on? It cannot be that a current starts only when an electron from one terminal of the electric supply physically reaches the other terminal through the bulb, because the physical drift of electrons in the conducting wires is a very slow process.   What is the exact mechanism of the current flow, which takes place with a speed close to the speed of light ?
Do electrons move around a circuit? We could imagine a simple electronic circuit composed by a power source and a resistor.   It is usual find descriptions as "The moving charged particles in an electric current are called charge carriers. In metals, one or more electrons from each atom are loosely bound to the atom, and can move freely about within the metal. These conduction electrons are the charge carriers in metal conductors." (wikipedia ). That made me imagine electrons going from power -, running by the wires, crossing the resistor and returning to power +, where they suffer a new kick to power -. All that at near the speed of light.  In this model, it is easy to define "electrical current intensity" as proportional to the number of electrons per second that cross one specific point of the circuit.  However, looking for the physics of resistivity, I can read the phrase "The actual drift velocity of electrons is very small, in the order of magnitude of a meter per hour." (wikipedia ). This is a complete different point of view, where electrons are more or less fixed around a fixed position (or moving very slowly), an electricity is a wave of "collisions" or "jumps" of electrons, like in a Newton's cradle (or "do the wave" as public in a football match). Obviously, we do not need severals hours from the switch on to the light on.  So, the question is, do electrons move around a circuit ? References to band theory are welcome.  A related question is: if electrons doesn't moves along the circuit, what is "electrical current intensity"?  Note: I known there are similar questions already posted, but answers of the ones I've read are not very detailed (could be I've not found the best ones). Please, be a few patient before "close vote".
I have created a logo with pen tool in Illustrator but between lines (where they intersect with each other) there is a gap where it gets the color of the background.  Something like this:  (Black color is the background color) - As you can see where the paths join each other there is a kinda dotted black line. I Grouped them but still the same. I converted to jpeg just to be sure it is not only shown like that but same effect.   NOTE: I want to export that logo as SVG file type and use it in the WEB. I tried some solutions given like anti-aliasing in preferences or art optimize when saving for optimization. But still I have same problem. I want to get that logo in SVG and put it on the web where it will display clean without those strange gaps.  How can i get rid of this? Constructing a circle through a given point, tangent to a given line, and tangent to a given circle While browsing around about problems similar to , I have found references to constructions of all types of circles. For example, not only is it possible to construct a circle tangent to three given circles, but one can construct a circle through any three points, tangent to any three lines, passing through two given points and tangent to a line or circle, passing through a given point and tangent to two given lines or circles, etc. Pretty much any combination of criteria regarding points, lines, and circles, with repetition.  Can we have one of each? I haven't found any resource saying whether it's possible or not to construct a circle through a given point, tangent to a given line, and tangent to a given circle. Is such a construction possible? Thanks. We have added JSON-LD structured data to our website, so Google knows information about our company (company name, url, logo, address, etc.). We worked from the template on Google's .  One thing I couldn't find an answer to is where exactly should this JSON-LD snippet be included on our website? Right now, I only have it on our home page. I didn't know if it would look bad to search engines to have the Organization markup on every single page. But is there any recommendation?  Should Organization markup about our company be included on every page or only on certain pages? I have been trying around different ranges of summations:  $$ \sum_{(m,n) \in \mathbb{Z}^2} \frac{m^2 - n^2}{(m^2 + n^2)^2} = 0$$  That's not any good.  What about if we restrict to $m, n \in \mathbb{Z}$ as positive integers.    $$ \sum_{m &gt; 0, n &gt; 0} \frac{m^2 - n^2}{(m^2 + n^2)^2} = 0$$  Now here's an anti-symmetry.  I do not like taking out the symmetry, but perhaps I can ask about:   $$ \sum_{m &gt;  n &gt; 0} \frac{m^2 - n^2}{(m^2 + n^2)^2}  = \; ? \tag{$*$} $$  There doesn't seem to be a change of variables that can work.  And we've used symmetry about as much as we can.  This looks related to:  $$  \sum \frac{1}{n^2} = \frac{\pi^2}{6}$$  Perhaps this other series ($*$) also has a special value. Has a double slit experiment ever been done using a track chamber or even contemplated? I tried searches and the question has been posed in other fora, but no experiment came up.   Track chambers (cloud chambers, bubble chambers , time projection chambers, solid state detectors like the vertex detectors at LHC)  give the track of the particle as it ionizes the  medium, and could be carried out in geometry after the particle has passed the double slit. The straight track should be pointing back to the slit it came from and its record could be used as the points on the screen in the classical double slit experiment.  The set up as I see it would be the classical setup for single electron through the double slits but instead of a "screen" one has a detector and detects the track.  It should be a long enough detector to get an accuracy less than the slit difference so it could point back to the slit, as the interslit distance is of the order of 100 microns and detectors are giving order of microns accuracies.  This experiment, if possible,  would resolve the controversy whether the detection of the slit destroys the interference pattern or the  at the slits change the boundary conditions and destroy the interference pattern.  An expert's opinion is necessary whether the experiment is possible, whether the energies of the electrons to show interference with a specific d separation is enough to create an accurate track in a solid state detector. If not a cloud chamber would do , but again the energy of the electron would be important because it would have to pass the barrier air/chamber.  It could succeed if the double slits were within a cloud/ bubble chamber; the beam count was low  (10 to twelve per picture) but it was spread in the vertical direction. If the beam could be focused on the slits , it should be doable. How does the kernel prevent a malicious program from reading all of physical RAM? If I write a program that tries to read memory at every possible address, and I run it on a "full" Unix, it will not be able to access all of the physical RAM.  But how does the operating system prevent it from doing so?  I am more familiar with small CPU architectures where any piece of assembly code can access everything. I don't understand how a program (the kernel) can detect such malicious operations. How to show that the nth power of a $n \times n$ nilpotent matrix equals to zero $A^n=0$ $A$ is a $n\times n$ matrix such that $ A^m = 0 $ for some positive integer $m$.   Show that $A^n = 0$.   My attempt: For $n &gt; m$, it's obvious since matrix multiplication is associative.  For $n &lt; m$, $A^n\times A^{m-n} = 0$; not sure what to do next. Also I know that $\det A = 0$. Is the Moonbeam spell amazing, or are we doing it wrong? The description of the moonbeam spell (PHB pg. 261) says:  When a creature enters the spell's area for the first time on a turn or starts its turn there, it is engulfed in ghostly flames that cause searing pain... On each of your turns after you cast this spell, you can use an action to move the beam 60 feet in any direction.  We read this to mean a creature takes damage from moonbeam when any of the following conditions are met:  It begins its turn inside the moonbeam It enters the moonbeam on its turn The creature finds itself inside the beam on another character's turn, no matter how it got there  The creature will not take damage in the following instances:  A creature moves from one part of the beam to another (obviously it had to take damage, but it won't take more damage) A creature is in the beam after having been inside the beam already on that turn.  Following these assumptions, our druid cast a moonbeam and did damage to two enemies, Bob and Frank. On their turn, they took damage again, killing Bob. Frank left the beam. On the druid's next turn, she moved the beam in a circular motion, not exceeding 60 total feet of movement, and in the process the beam came in contact with a dozen enemies and ended on Frank. All dozen enemies received damage, as they were inside the beam at some point during the turn. On Frank's next turn, he again took damage for the fourth time and died. On each of the druid's turns, she moved the moonbeam around like this until the fight ended (it did not exceed the time limit and she made all concentration checks). Is this a legitimate use of moonbeam? It seems awfully powerful for a level 2 spell. Is $\mathbb{Z} \left[ \frac{1+i \sqrt{7}}{2} \right]$ euclidean? What test can I use to compare slopes from two or more regression models? I host am ExpressionEngine based website on a single Amazon EC2 instance in the US East (Virginia) region. I use Ubuntu.    The website allows members to post their content, and displays it for other members and for users who are not logged in.   Goal: I need to begin serving the same website across the globe, equally fast to Hong Kong, New York, and Los Angeles.   I considered two solutions:  1.Setting up three separate EC2 instances for three regions: Virginia, Oregon, and Singapore. Use Amazon Rot53 Geo Location to direct traffic to instances based on the browser's IP address.   Pro: the website will load fast for the region.   Contra: these will be essentially three separate websites. Unless I am mistaken?   Setting up one instance in a region equally remote from all three locations: (Ireliand), and boost the server to the highest performance available.    Pro: It will be the same website for all regions.   Contra: it will cost a lot to make it fast enough.   My challenges:   a) I do not know a way to sync server settings, database, and content between multiple Ubuntu instances in real time. If a knowledgeable person could explain to me how to do that, I would be most grateful.   b) I am not thoroughly familiar with all Amazon AWS resources. Does AWS has a built-in method that would allow me to achieve my goal of serving a single PHP / MySQL based membership website across the globe equally fast in all three chosen locations? Random test data: How to do it right? Several months ago I started an experiment in test automation. Each test, before it starts, picks up random test data. For instance, when my test requires a user with administration privileges, I draw a random account and then I from a group of admin users for this account I draw a random admin user.  The reason for using random test data was two-fold:    First, when we were using static, i.e., hard-coded test data, sometimes tests started to fail, because test data no longer existed in DB, e.g., a user has been removed from the database (we're having production dump in our test DB, so I guess the user has been deleted in production). When we started to find such users at runtime, the problem disappeared.  Second problem was that it was not really clear why certain test data were used for a certain test. We have inherited tests from the other team and couldn't understand their intentions behind, for instance, using user "xyz@awesome.com". By writing queries to find data, we started to explicitly state what type of test data we want, e.g., that we want a user with administration privileges.   While my approach solved both problems, it introduced also some new issues:   Tests occasionally fail, because they pick up wrong test data. This is because queries are sometimes incorrect. For instance, once a test drawn a random account that had no administrators at all. Good thing about that is that this way I keep learning new things about the system under tests, e.g., that there must be business reasons to have accounts without administrators. Test setup becomes more and more complex, as queries start to grow and thus tests seems now a bit more complex to understand.   I was also hoping to increase coverage and find more bugs by using random test data just like it is done in fuzz testing. Instead, I mostly found bugs in my test and learned how little I know about the system under test. Finally, ROI doesn't seem big. Before the change there was a cost of maintaining static test data (updating test data if they were outdates). Now I have to maintain complex queries when the test takes "wrong" test data and this tends to occur more often than outdating of static test data previously.  I wonder whether using random test data really makes sense and how to do it right? Formula Assistance I am creating a formula variable in a Flow but keep getting this error. Crop net Acres is a Number field. IF(     ISBLANK( [Opportunity].Crop_Net_Acres__c),     0,      ( [Opportunity].Crop_Net_Acres__c) )  Error Message:  netAcresFormula (Formula) - The formula expression is invalid: Syntax error. Missing '='  Any thoughts here? Show that $\sum_{n=0}^\infty r^n e^{i n \theta} = \frac{1- r\cos(\theta)+i r \sin(\theta)}{1+r^2-2r\cos(\theta)}$ How can time dilation be symmetric? Ways of getting three of a kind in a 52 card deck This question has probably been asked before, but just to be clear here, I am NOT asking for the answer, I know the answer.  What i want to know is why my solution is not equivalent to the actual solution.  Three of a kind in a deck means you draw 3 cards of the same rank, and 2 other cards each of different ranks.  So. The solution in my book is the following: (13 C 1)(4 C 3) * (12 C 2)(4 C 1)(4 C 1)  The logic is the following:  1) Choose 1 out of the 13 ranks, then for the 4 cards in the chosen rank, pick 3.  2) Choose a combination of 2 ranks from the remaining 12, then for the 4 cards in each rank, choose 1.  Total combinations: 54912  My solution is the following:  ((13 C 1)(4 C 3)) * ((12 C 1)(4 C 1)) * ((11 C 1)(4 C 1))  1) My logic for the 3 of a kind is the same as the solution.   2) Choose 1 of the remaining 12 ranks, and 1 card from the 4 cards in the rank.  3) Choose 1 of the remaining 11 ranks, and 1 card from the 4 cards in the rank.  Total combinations: 109824  My solution says that the combinations are exactly double of the book's solution.  I'm just very confused as to why this is. If anyone could explain this to me I would be very appreciative, thank you. Merging two incoming broadband lines for faster Internet We have a broadband line coming into our building which delivers around 8-10Mbps, which is okay but not great. Fiber is available in our area (30-100Mbps) but it's not available where we are just yet.   Is there some way we could connect two lines (which we would take from two different providers so we would have redundancy if one failed) and merge them into one signal which we could distribute?  Is there some sort of setup that can do this?  Of course we have the option of a leased line but for 12Mbps symmetrical upload/download we'd be looking at around £500 per month compared to £15 per month for normal or fiber broadband.  I made a small pseudo flow chat of the setup below: I have two NTFS partitions, and I don't want to mount them manually every-time I start Ubuntu.   How can I do this?  Is there a tool or a code to use?   If so, is it safe to automount? specially when they are being used by another OS? If I design a PC for use as an NPC, how much XP should he give when killed? As part of an early quest, my PCs are likely to face off against a wizard.  The problem here is that the stat block for Mage NPCs listed in the Basic Rules has a Challenge Rating of 6, while the PCs are going to be five Level 1s. So, instead of messing with the stat block and risk weakening it too much/too little, I'm choosing to create a Level 1 Wizard PC and use it as an NPC for this quest.  The problem with that is that, as far as I can tell, there aren't any designated rules for assigning either Challenge Ratings or XP values to a PC. So, should I just give the wizard a Challenge Rating equal to his level (and thus have him give 200 xp when killed), or is there a better way to do this?  (This is different from , because he's asking for a way to assign a level to an NPC, while I'm asking for a way to assign an XP value/Challenge Rating to a PC (for use as an NPC). Similar questions, but different.) I am constructing a bibliography of as much of the prior research in a field I am working in. I would like to use BibTeX to print the citation in the pdf, and then I would like to add the details of the paper after the citation. Only then would I like to print the next citation. For example:  [1] Jahan M. Dawlaty and Yunquing Chen. Measurement of the optical absorption of graphene in the terahertz. Applied Physics Letters, 2008. Research Group: Cornell Pump Wavelength: 500 nm. Probe Wavelenth: 7 microns. Relaxation Time: 50 fs. [2] Paul George and Dmitry Vekslar, Measurement of Ultrafast Carrier Dynamics in Graphene. Applied Physics Letters, 2009.  . . . and so on. Does anyone know how this could be done?