Separation Definition and 448 Threads

The temperature distribution u(x, t), at time t > 0, along a homogeneous metal rod can be obtained by solving the 1d heat equation; ut = kuxx (1) where k = 2 is a constant. The length of the rod is 1m and the temperature at either end of the rod is zero for all time, so that the boundary...

I need some help understanding the countability and separation axioms in general topology, and how they give rise to first-countable and second-countable spaces, T1 spaces, Hausdorff spaces, etc. I more or less get the formal definition, but I can't quite grasp the intuition behind them. Any...

Homework Statement Given two two grounded concentric spherical shells with radii a,b (a<b) and a point charge q between them at a<r=R<b find: 1.The surface charge density of the point charge using the delta function, assume the charge is on the z axis 2.By using the separation of variables...

The USN used to shoot ASROC from box launchers. It was a torpedo with a rocket motor on the back. it was ballistic. The rocket fired and then separated mid flight. the torpedo continued on, a chute was deployed to slow and I think stabilize the water entry after which the torpedo went on...

reading a Nature paper tonight, I read that the NV(-) separation is ~ 1.7Angstroms. There was no equation to show how they arrived at this. Any insight into how this was determined? I don't think there is a direct equation, but perhaps using a to r?

Homework Statement Light of wavelength 680 nm falls on two slits and produces an interference pattern in which the fourth order fringe is 38 mm from the central fringe on a screen 2.0 m away. What is the separation of the two slits? Homework Equations d * sin(theta) = m * lambda The Attempt...

Homework Statement Solve ∇2T(x, y) = 0 with boundary conditions T(0, y) = T(L, y) = T0 T(x, L/2) = T(x, -L/2) = T0 + T1sin(πx/L) Homework EquationsThe Attempt at a Solution Set T(x, y) = X(x)Y(y) Then ∇2T(x,y) = (∂2X/∂x2) Y + (∂2Y/∂y2) X = 0 Rearrange to find two separate ODEs: d2X/dx2 =...

Homework Statement m1v1=m1v1'cosa+m1/2v2'cosB 0=m1v1'sina-(m1v2'sinB/2) m1v1^2=m1v1'^2+(m1v2'^2)/4 Homework Equations The solution in my book is v2'=2v1sqrt(3) The Attempt at a Solution I thought to separate v1' at the firts and put it at the second, but I don't know how to change sin and cos then.

Hello everybody, My question is about variable separation applied in the solution of general time-independent Schrodinger equation, expressed with spherical coordinates as: \hat{H} \psi (r,\theta,\phi) = E \psi (r,\theta,\phi) Is it always possible (theoretically) to seek a solution such as...

1. The problem: If the Sun blows up at some instant and four minutes later we on Earth sit down to eat lunch, these two events are separated by a spacelike interval. The explosion of the sun cannot have influenced us at the time we sat down because it takes 8 minutes for light to reach us from...

Hello, I'm doing some online research on fluid flow in waste water treatment. One of the problem I'm trying to find information about is how can visible particulate matter be separated within a liquid. I saw the following picture: What fluid concepts are going here that allow the grit to...

I have noticed that women don't seem to make them self's up so much as 20yrs ago, and they wear things like raggety jeans, i know i am going to get killed for this but i am being honest, some girls look like boys and some boys look like girls, what has happened to gender separation? mod note...

This is probably painfully obvious, but I keeping getting the impression that aqueous ions can be separated spatially via electrostatic force. For example, dissolve some sodium chloride in water, and then put the container in an electric field. Wouldn't the sodium ions migrate to the negative...

Howdy, I am working in a research lab at The Ohio State University. I need to separate positively charged ions that are intramolecularly bound to negative counterions. I was hoping to use use static electricity to do this. Any suggestions on the power supply/control to do this?Lucas

Homework Statement For an eye in which the pupil has a radius of 3.0 mm, what is the smallest angular separation that can be resolved when two violet (λ = 400 nm) objects are placed side by side? Homework Equations theta_r = sin(theta_r) = 1.22(wavelength/d) The Attempt at a Solution theta_r...

Hello, I have a question concerning electrochemical cells or batteries. It is said that when the battery is at open circuit, it has small charge separation on its electrodes thus having a potential difference equal to the emf of the battery. When the battery is connected to a circuit, the emf of...

Homework Statement 1. The distance between the 1st bright fringle and the 21st bright fringe in a Young's double slit arrangement was found to be 2.7 mm. The slit separation was 1 mm and the distance from the slits to the plane of the fringes was 25 cm. What was the wavelength of the light...

Homework Statement The wave equation for ψ(t, x) in 3D is ##\frac{\partial ^2 \psi}{\partial t^2}## - Δ ##\psi =0## Let ϒ(x) satisfy Δϒ = λϒ where λ<0. The x is in bold presumably to indicate it is in 3D, so represents also y and z? Show there is a solution of the form ψ(t, x) = sin(ωt)ϒ(x)...

Homework Statement The wave equation for ψ=ψ(t,x,y) is given by ##\frac{\partial ^2 \phi}{\partial t^2} - \frac{\partial ^2 \phi}{\partial x^2} - \frac{\partial ^2 \phi}{\partial y^2}## Use separation of variables to separate the equation into 3 ODEs for T, X and Y. Use the separation...

I just wanted to check something. The equation ∂2φ / ∂x2 + ∂2φ / ∂y2 = sin(xy) Was given as an example of a separable equation. I can't separate it, and I found online that to use separation of variables the equation should be linear, which this isn't? Is there a way of separating this?

Homework Statement A potential satisfies ##\nabla^2 Φ = 0## in the 2d slab ## -\inf < x < \inf ##, ##-b < y < b ##, with boundary conditions ## Φ(x, +b) = +V_s(x)## on the top and ##Φ(x, b) = -V_s(x)## on the bottom, where[/B] ##V_s (x)= -V_0 for -a<x<0## ##V_s (x)=+V_0 for 0<x<a## (a) what...

Hi all! As a republican (libertarian to be exact) I would only consider voting for 10 out of the 17 candidates (I mean, if I were voting age). The 7 I would never vote for are in that place because of their lack of understanding of the separation of church and state. I just don't understand how...

Homework Statement A square is made up of four plates with a potential of zero on the top and bottom plates at (x,L/2) and (x,-L/2), and a potential of cos(πy/L)+cos(3πy/L). Find the potential and electric fields inside the square. The Attempt at a Solution I start with...

First of all, sorry if this is in the wrong forum, wasn't quite sure which one to post it in given the question. My question is, given two space-time points ##x^{\mu}## and ##y^{\mu}##, if the events that occur at these points are simultaneous, i.e. ##x^{0}=y^{0}##, are the two events...

Hi all, I was just reading about airplane flaps. From I what I understood, they increase lift and drag (at lower speeds) to help land the aircraft. Do flaps also reduce the tendency of flow separation at lower speeds? Let's say we have an airplane wing with no flaps (Case I) and airplane wing...

About how far apart can the slits get, in the double slit experiment, and still show the interference pattern?

Homework Statement Homework EquationsThe Attempt at a Solution I managed to do the first part of the question. But I'm not sure how to find u(x,t) with that initial condition. The solution says; "since ##u(x,0) = \sum_{n=1}^\infty a_{n}\sin{(n\lambda x)}## Then it follows by linearity that...

Please help I am not sure of how to work this out The angular separation between Styx and Nix 28 days after they are in line with each other on the same side of Pluto. Mass of Nix = 5*10^16 Kg Orbital Radius of Nix = 48675 Km Orbital period of Styx = 20 Earth days

I am using the text by Farlow to study elementary methods of solving PDEs, and there is a point in his illustration of separation of variables where I am not seeing something. I am clear on everything that comes after and before this point, but after having returned to a certain step a few times...

1. A very large loop of metal wire with radius 1meter is driven with a linearly increasing current at a rate of 200amps/second . A very small metal wire loop with radius 5centimeter is positioned a small distance away with its center on the same axis (the loops are coaxial). The small loop...

Hey guys, So, I was in my materials lecture today and something the lecturers and the tutors said was slightly confusing. We were talking about the repulsion and attraction force between atoms. This is all good as I can understand how if two atoms will repel each other if they get really close...

But nikkkom, that makes no sense. 1: Vitrification is not cheap; I doubt that even superficially it is significantly cheaper than reprocessing; you know perfectly well that one does not simply dunk spent fuel rods in molten glass and bobsyouruncle. You first have to get the relevant materials...

How do we know that separable solutions of Schrodinger equation (in 3d) form a complete basis? I understand that the SE is a linear PDE and therefore every linear combination of the separable solutions will also be a solution , but how do we know that the converse, i.e 'every solution can be...

Homework Statement Two blocks, each of mass m, are connected on a frictionless horizontal table by a spring of force constant k and equilibrium length L. Find the maximum and minimum separation between the two blocks in terms of their maximum speed, vmax, relative to the table. (The two blocks...

Hello, There this article "http://www.nature.com/nphys/journal/v11/n1/full/nphys3172.html". High-energy experiments have shown that the electron is a point-like particle with spin-1/2 and electric charge -e. In highly correlated condensed matter systems these two properties can decouple in the...

Homework Statement Why is the velocity the same at minimum separation? For example, two positively charged pucks are traveling towards each other. Find the minimum separation. They oppose each other so they should slow down and reach minimum separation when their velocities are 0. It does not...

I've recently taken to understanding capacitors and capacitance. If I understand them correctly they are what store electrical charge or electrical energy. I don't quite understand their purpose though, do they keep the breadboards from overloading with power but keeping little pockets of...

I saw recently a new article about some kind of PEC cell immersed in water which could separate water into hydrogen and oxygen. (It was news because they found a way to protect the cell from immediate corrosion damage) It seemed that somehow the scientists had designed a cell that could put the...

Homework Statement So I'm doing a question from one of my past exams as attached, there are no copy right issues with this document that I know of and have asked my lecturer who wrote the exam and he said I am welcome to upload it. The question is 1)b)iv), my attempt is attached. I end up with...

If $$u=\frac{1}{2} E^2$$ and $$v=\frac{1}{2}B^2$$ and we have that $$\frac{\partial L}{\partial u} \frac{\partial L}{\partial v} = -1$$ The author says: to obtain explicit solution of the above, one must resort to techniques such as separation of variables in particular coordinate systems. For...

My challenge is to provide a low-tech (DIY) way to purify the glycerol produced from soapmaking or biodiesel production. Simple distillation is out because the boiling point for glycerol is above its smoke point. Vacuum distillation and electrolysis do not count as low-tech. :) The input...

Hello everyone, I came across the following when I was reviewing diffraction gratings: "The condition for maximum intensity is the same as that for a double slit. However, angular separation of the maxima is generally much greater because the slit spacing is so small for a diffraction grating."...

Hi all I can't find any guidance on this on the internet, so hopefully someone here can help! Basically, I want to work out the intensity profile produced by a multiple slit experiment, with 4 slits. No problem there, but I need the separation between slits to be unequal! I've found mention of...

Homework Statement The wavelength of the radiation emitted when the outermost electron of Al (Aluminum) falls from the 4s state to the ground state is about 395 nm. Calculate the energy separation (in joules) between these two states in the Al atom. Draw an energy level diagram of the states...

Homework Statement An assembled system consists of cart A of inertia mA, cart B of inertia mB, and a spring of negligible inertia, clamped together so that the fully compressed spring is aligned between the front end of cart B and the back end of cart A. The internal energy of the system...

[SIZE=14px][FONT=Lato]I'm having trouble understanding why 1) Heating a solution more slowly would increase separation in a distillation and why 2) Lowering the pressure above the solution, i.e. with a vacuum, would decrease separation. Distillation depends on you collecting one component...

So I'm currently taking electricity and magnetism and I'm expected to know how to perform a separation of variables on laplace equation in 2 dimensions.I have taken Zero differntial equations courses and I literally have no freaking idea what's going on. The book I use doesn't spend any time...

My friends and I are in our first senior-level physics course at the University of Alabama in Huntsville, Introductory E&M. At the moment, we're working on using separation of variables to calculate electric potentials inside different objects given certain boundary conditions. One, however, is...

Hello everybody. I have a free scalar in two dimensions. I know that its propagator will diverge for lightlike separations, that is t= ±x. I have to find the prefactor for this delta function, and I don't know how to do this. How do I see from, for example, \int \frac{dk}{\sqrt{k^2+m^2}} e^{i k...

Dear all, We all know that chromatography is a separation technique. In paper or TLC,the mixture is differentiated according to their relative affinities with the solvent on the paper or glass plate. How do we really separate the mixture. Kindly, help me how to extract the components...