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    Multi-region Finite Difference- Interface between materials

    I am writing a multi-region diffusion code. The two regions have different material properties, so the analytical solution shows a discontinuity at the interface between the regions. As can be seen here: The numerical code I am running is (Mathematica): While[converge > .00001...
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    Hermite Polynomial Recurrence Question

    1. Homework Statement I need to find an expression for: y^{2}H(y) I know how to find: yH(y) with: yH(y)=\frac{1}{2}H_{n+1}(y)+nH_{n-1}(y) I looked through the miscellaneous relations but nothing stuck out to me. Can someone give me some guidance on how to go about finding a...
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    Historic Question of the Sun

    The history of our understanding of the sun is a very rich area. Ancients believed the sun was a god while we now know the sun is an enormous body of fusion. What I would like to discuss is how the scientists thought the sun worked after the development of the basics of thermodynamics but...
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    Flux and Current

    1. Homework Statement Two monoenergetic neutron beams I1=2*10^10 and I2=1*10^10 intersect at an angle of 30 degrees. Calculate both the flux and current in the region where they intersect. 2. Homework Equations 3. The Attempt at a Solution I lined the first I1 up parallel to...
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    Normalization Question

    1. Homework Statement I am given a trial function and before I use the variational method, I need to normalize the trial function. This is easy usually, but I don't know what to do in this specific case: The trial function is: X[x]=N1(1-x^2)+N2(x-x^3) Domain: -1<x<1 N1 and N2 are the...
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    Finite Difference Approximation, Mathematica code

    1. Homework Statement I have to program a three component decay chain using finite difference approximation. I understand finite difference and have written my code, but I have an error I can not find which is giving me an erroneous answer. The curve is correct, but the magnitude of the...
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    ODE- question about domain

    1. Homework Statement I'm working with a heat equation that requires a Laplace transform. I performed the transform and ended up with a basic ODE with a particular solution. I solved for the particular solution and then realized I was working on an infinite domain in my spacial dimension...
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    Mathematica Mathematica- Rotating a 2D plot into a 3D plot

    I have a plot of radius and temperature. I want to plot it in 3D by rotating it about the origin to produce a 3D plot. I can not figure out how to do this in Mathematica without doing it by hand and then plugging it into the Plot3D function. Any advice would be greatly appreciated. The...
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    Heat Conduction Initial Problem Set Up

    1. Homework Statement I need to set up the mathematical formulation of the following heat conduction scenarios: a) A slab in 0\le x \le L is initially at a temperature f(x). For times t>0 the boundary at x=o is kept insulated and the boundary at x=L dissipates heat by convection into the...
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    Advance Integration By Parts

    1. Homework Statement Integrate the following by parts twice \int_{a}^{b}\frac{d}{dr}(r\frac{dT(r)}{dr})\psi(r)dr and show that it can be written as -\lambda^2\bar{T} , where \bar{T}=\int_{a}^{b}r\psi(r)T(r)dr and the function \psi satisfies the following equation...
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    Graduating with physics undergrad, need some advice

    I am going to graduate soon and am getting my applications ready for graduate school. I know I do not want to continue in pure physics. I want something more "hands on." I also want something in a cutting edge field. I've always liked the idea of nuclear engineering and did well in EM...
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    Proving d'Alembertian Invariant under Lorentz Transformations

    1. Homework Statement Show that (D'Alembertian)^2 is invariant under Lorentz Transformation. 2. Homework Equations The book (E/M Griffiths) describes the D'Alembertian as: \square^2=\nabla^2-\frac{1}{c^2}\frac{\partial^2}{\partial t^2} 3. The Attempt at a Solution I...
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    Beam Divergence

    [SOLVED] Beam Divergence 1. Homework Statement A 1.5mW helium-neon laser beam delivers a spot of light 5mm in diameter across a room 15m wide. The beam radiates from a small circular area of diameter 0.5mm at the output mirror of the laser. Assume that the beam irradiance is constant...
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    Geometric Optics Gradients

    I'm sure many of you guys have seen the videos of a beam of light (namely a laser of some sort) pass through a volume of liquid in which there is a gradient of index of refraction from the bottom of the tank to the top. Think of a sugar solution in which more sugar collects at the bottom and...
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    Acceleration using Power

    I know acceleration can be found by the following basic equation: A=F/M But my question is can you also find acceleration using power or work? Background: I am doing a project in physics right now that involves taking the torque, weight, and drag of the car and calculating the...
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    Projectile motion, WITH ari resistance

    Projectile motion, WITH air resistance... I know you can get range without air resistance with this equation: R=(2(v^2)(cosA*sinA))/G I am wondering (also I need it for a trebuchet project) what the equation would look like with air resistance added into it. I don't need to plot the...
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    Help with a little detail (Thermodynamics)

    I am working on a physics project that has to do with running a gasoline engine on an aqueous fuel mixture. I need some help on one part of my energy balance. The cylinder wall is hot in a running engine, I need to know how much of that heat energy (in kJ)is transfered to the liquid inside of...
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    Gas Expansion, please help.

    I am doing a physics problem in my High School class and I cannot find the answer to this: How much does water expand when changing from a liquid to a solid. Is there a percent? Example, when a gallon of water fully evaporates how much space does the vapor take up? Thanks alot!
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