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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
[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...
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...
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...
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...
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...
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!