Separation Definition and 476 Threads

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...

Homework Statement i can't understand part b ii) , i assume the resolving power of eyes is constant . so when the slit separation increase , the wavelength of the light should be decreased to keep the tetha ( here , tetha = resloving power of eyes in radian )...But the book give different ideas...

1. Two events occur simultaneously in an inertial reference frame, separated by a distance of 3 metres. Within a different inertial frame that is moving with respect to the first, one event occurs 10^-8 seconds later than the other. (a) In the moving frame, what is the spatial distance between...

I'm trying to understand the relationship between the spacetime metric \Delta s^2 = \Delta x^2 - c^2\Delta t^2 and the simple formulas for time dilation and length contraction in special relativity x = \frac{1}{\gamma} \bar{x} and t = \gamma \cdot \bar{t}. Suppose from an inertial reference...

Dear friends, my book (an Italian language translation of Kolmogorov-Fomin's Элементы теории функций и функционального анализа) proves the following separation theorem: let ##A## and ##B## be convex sets of a normed space and let ##A## have a non-empty algebraic interior ##J(A)## such that...

Homework Statement according to my notes, if the single slit is made larger , the slit can can been as point source, where each point can produce its own set of intefrence pattern. whi is it so ? i can't understand Homework Equations The Attempt at a Solution

(2xy-3y)dx-({x}^{2}-x)dy=0 ans. xy(x-3)=C ty

I am curious how legitimate a solution Separation of Variables tends to give. I've been working problems out of Griffith's book on Electromagnetism, and am often uneasy as to the way things are done. I have two specific issues. The first, is that in spherical it is often necessary to remove...

I'm having some difficulty setting up a problem. I'm trying to model the temperature of a thermistor connected to a constant current source. The thermistor's resistance varies with temperature, so with a fixed current, I would expect to see the thermistor's temperature to oscillate with time...

hey I got a questions and appreciate obv any reply. I am regarding to Capitel 12, page 128ff. from Gustafson, Sigal; Mathematical Concepts for Quantum Mechanics. So, let's consider on $L^2(\mathbb R^n)$ \begin{align} H_n= \sum_{j=1}^n \frac{1}{2 m_j} p_j^2 +V(x) \end{align} where...

Hey guys, Can anyone help me out with these questions? The first one has a positive initial value. Separation of variables and integrating gave me: |y+3| = k√[(t^2) + 1)] Ultimately, I got k= √5 and thus y=√5√[(t^2) + 1)] - 3. Also, for the second one, I used a similar process, found...

Homework Statement You measure a uniform electric field of 13.3 x 10^3 N/C between two equipotential surfaces. One surface is at a potential of 1543 V and the other is at 951 V. What is the separation between the two surfaces? Homework Equations Eave = - deltaV/delta x The Attempt at...

Homework Statement Find the equilibrium separation between Diamond and Copper materials. Homework Equations Lennard-Jones force/unit area: p_a(z)=\frac{8w}{3z_0}\left[\left(\frac{z}{z_0}\right)^{-9}-\left(\frac{z}{z_0}\right)^{-3}\right] I need to find z_0 which is the equilibrium...

My professor, in his handout (picture below), says the following about this diagram : I disagree with him partly. For \Delta_{mix} G/nRT<0 mixing is spontaneous and hence there solutions would be miscible. Hence at \beta=2.5 should we not expect the components to be fully miscible. ...

I am attempting to complete a basic question involving molecular separation from Alonso & Finn "Fundamental University Physics" Second Edition, Chapter 2, Question 9. The Problem states "Using the data in table 2-1 and A-1, estimate the average separation in molecules of hydrogen at STP (gas)...

Why is it assumed that the method of separation of variables works when the boundary conditions of some boundary valued problem are homogeneous? What is the reasoning behind it?

Hey! :o I have a question.. (Wasntme) When we have the following boundary value problem: $$u_{xx}+u_{yy}=0, 0<x<a, 0<y<b (1)$$ $$u_x(0,y)=u_x(a,y)=0, 0<y<b$$ $$u(x,0)=x, u_y(x,b)=0, 0<x<a$$using the method of separation of variables, the solution would be of the form $u(x,y)=X(x) \cdot Y(y)$...

Why is separation of Earth and sky so common in different mythologies around the world? EDIT: Sorry about my poor phrasing of the question. My question is actually why people would assume Earth and sky were joined once. Which observation/ reasoning led them to make up such a non-obvious story...

An observer sees two spaceships flying apart with speed .99c. What is the speed of one spaceship as viewed by the other? I considered two spaceships A and B. A is moving with velocity vA in the left direction and B is moving with velocity vB in the right direction. Hence, ##v_{sep} = v_A +...

The number of molecules per cubic metre of air at standard temperature and pressure is about 2.7X10^25 / m^3 . What is the average separation of these molecules? I know the number of molecules is derived from the equation pv=nRT.But what does average separation of molecules mean and how do i...

Can someone please help me solve the following using separation of variables: dy/dx = (xy + 3x -y-3)/(xy -4x+6y-24) so that the solution is written in the form: ((x+6)/(y+3))^7 =

Can someone please help me to calculate the following using separation of variables: dy/dx = x*(1 - y^2)^(1/2) to that the solution is in the form: y =

Hi everyone, I have a square matrix J \in \mathbb{C}^{2n \times 2n} where, $J=\left(\begin{array}{cc}A&B\\\bar{B}&\bar{A}\end{array}\right)$ A \in \mathbb{C}^{n \times n} and its conjugate \bar{A} are diagonal.Assume the submatrices A,B \in \mathbb{C}^{n \times n} are constructed in a way...

I am studying Laplace's equation in my electrodynamics course (using griffiths intro to electrodynamics). I am watching a youtube video stepping through the separation of variables method for solving the PDE. It seems to be a common PDE that comes up repeatedly in physics (Helmholtz eqn, Poisson...

If two galaxies are separated by a large distance such that radiation transmitted from the mid-point between the two galaxies never reaches either galaxy due to the expansion of space, how can the expansion of space at the mid-point ever affect the distance between the two galaxies. i.e. how...

I am having some troubles wrapping my head around the electric potential concept. From what I gather it is a separation of charge? Is this true? On a more formal level electric potential energy is the amount of energy in joules it takes to move a charge against an electric field or the amount...

Problems faced by a republic following Montesquieu separation of powers: -If voter supports party A on issues of military but party B on issues of healthcare, then he has to choose which area is more important to him. -Everything that happens is the fault of president/prime minister. :D (yes, I...

I am trying to calculate the apparent separation between the 2 stars Mizar and Alcor. In the question I am given the total distance from me to the 2 stars which is 83 light years and the angle of separation which is 12 arcminutes. The question is multiple choice: (A) 0.1 ly, (B) 0.3 ly, (C) 1...

Hi All, When solving the Schroedinger equation for the zero potential situation, what is the argument for interpreting the separation constant G as the energy of the system. The dimensional aspect I understand but it seems not to be suficient. I guess I am missing some detail. Best wishes...

I read recently, that by separating two quarks, once a high enough energy has been introduced, new quark pairs will form. This sounds to me like a meson, being turned into two mesons. I don't know how clear I am on this, but I was wondering... Is the same true for Baryons. If we magically...

Homework Statement A fluid which is flowing at 3600 m3/hr, at a pressure of 2.3MPa and a temperature of 75°C is to be separated using a vertical separator vessel. The composition of the fluid is 50% water and 50% oil. 1. Assume perfect separation and a residence time of 20 seconds in the...

"Critiquing" separation of variables method for PDE. I am currently taking a course in PDE's and it has been very "applied" and not so much theory based. I can say its been separate this separate that separate this separate that… Enough! We are always "separating variables" and it always...

Homework Statement utt = uxx -(25/4)cos((5/2)x) ux(0,t) =1 u(pi,t)= pi u(x,0)=x ut(x,0)=0 Homework Equations u(x,t)=v(x) + w(x,t) The Attempt at a Solution This is what I did so far: u(x,t)=v(x) + w(x,t) u(x,0) = v(x) +w(x,0) when t is large: vxx - (25/4)cos((5/2)x) = 0 vx =...

I am doing a small project on Gamma Ray Bursts. I am looking at a data set of around a dozen bursts which are observed at an angular offset from their host galaxies (My theory is that they are in dwarf galaxies orbiting the host galaxy). Say the average separation of these GRBs is 4...

Homework Statement Hey guys, I have this problem which I am having a hard time solving. $$u_{tt} -x^2u_{xx} = 0$$ $$1<x<2 \hspace{4mm} t>0$$ $$u(x,0)=0$$ $$u_t(x,0)=g(x)$$ $$u(1,t)=0=u(2,t)$$ Homework Equations $$u_{tt} -x^2u_{xx} = 0$$ $$1<x<2 \hspace{4mm} t>0$$...

Average Separation of Muon and Proton Homework Statement A muon is a particle with a mass of 206.7 me where me is the electron mass, and with the same charge as an electron. It can be captured in "orbit" by a proton to form a muonic hydrogen atom. a. Find the average separation <r> of...

Hello, Here is a homework problem that I have been working on. I am wondering if for the mass balance of substance A, do I include the terms in the reaction rate that involve species R and B? Also, wouldn't A and B start reacting in the pipe before they even go into the CSTR? (I guess put in...

Solve given differential equation by separation of variables \frac{dy}{dx}=\frac{xy+3x-y-3}{xy-2x+4y-8} So separate x and y terms (xy-2x+4y-8) dy = (xy+3x-y-3) ugh I'm stuck:(

Homework Statement Using the technique involving variable separation, solve the following differential equation and use the initial condition to find the particular solution \frac{dy}{dt} = \frac{1}{y^{2}} y(0) = 1 Homework Equations The Attempt at a Solution To be honest...

Hello everyone. My understanding of a dipole moment is it defines the strength of various dipole interactions, eg the common example of torque in an electric field. My confusion stems from the fact that the magnitude of the dipole moment is proportional to the charge separation. In many...

Solve the DE by using separation of variables \frac{dy}{dx} = e^{3x+2y} Break up e^{3x+2y} = e^{3x}e^{2y} Move x's and y's to their own side of the equation. \frac{1}{e^{2y}} dy = e^{3x} dx Integrate both sides of the equation to get \frac{-e^{2y}}{2x}=\frac{e^{3x}}{3}+C I don't know how to...

Solve the differential equation by separation of variables x \frac{dy}{dx} = 4y becomes \frac{1}{4y} dy = \frac{1}{x} dx Integrate to get \frac{1}{4} \ln{|y|} = \ln{|x|}+C I'm stuck here because I want to raise e to the power of both sides of the expression like e^{ \frac{1}{4} \ln{|y|}} =...

Anyone familiar with separation of nanotubes produced by electric discharge

Homework Statement In the problem, we are to consider two candles, call them C1 and C2, with different heights and different thicknesses. Call the height of C1 H1, and for C2, call it H2. The taller candle burns can burn for 7/2 hours, and the short one, 5 hours. After two hours lapses, the...

Homework Statement dL/dp = L/2, L(0) = 100. Find the solution to the differential equation, subject to the given initial condition. My textbook says the answer is L = 100ep/2, but I don't know how to get that answer (or e for that matter). Homework Equations ? The Attempt at a...

I'm having troubles with PDE. Apply separation of variables, if possible, to found product solutions to the following differential equations. a) x\frac{\partial u}{\partial x}=y\frac{\partial u}{\partial y} I suppose that: u=X(x) \cdot Y(y) Then: xX'Y=yXY' xX'/X=yY'/Y So xX'/X=yY'/Y=c because...

Hey guys, I am working on my PhD thesis formulation and I got to a doubt. I need to do some integral separations, for the mesh attached, of the form: \int_0^L f(x,y) d x = \sum\limits_{i=1}^{imax} \int_{x_{i-1}}^{x_i} f(x,y) \, d x Of course, for the double integration in the...

Homework Statement This was done on a sidewalk. Two boxes were set up a distance apart with one line on each box. We measured the distance of ten points going out from the boxes (ten cement tiles on the sidewalk) and were able to use a meter stick to measure by eye from each ten points the...

Well, the question is not weird, but the circumstances are. I am not a physicist, and I am not studying physics. I am a student at a university, and quite interested in physics, but I am intentionally keeping myself away from taking any more physics classes. I like to be able to imagine...