Diffusion equation Definition and 108 Threads

Hi, I have read a lot about Diffusion Equation and solving neutron flux problems in different mediums, planes and groups, but I can't grasp this topic. In other words, I don't know why they mention: 1. Infinite/finite medium 2. Homogeneous/non-Homogenous medium 3. One/two or multi-group...

I'm looking for the analytical solution for the 1D convection diffusion equation with a constant heat flux. Boundary conditions: The domain I'm looking at is x from 0 meters to 1 meter. The temperature at x=0 is T=0 degrees Celsius. At x=1, T=100 C. I'm given the equation...

BOUNDARY CONDITION PROBLEM I have came up with matrix for numerical solution for a problem where chemical is introduced to channel domain, concentration equation: δc/δt=D*((δ^2c)/(δx^2))-kc assuming boundary conditions for c(x,t) as : c(0,t)=1, c(a,t)=0. Where a is channel's length...

Homework Statement BOUNDARY CONDITION PROBLEM I have came up with matrix for numerical solution for a problem where chemical is introduced to channel domain, concentration equation: δc/δt=D*((δ^2c)/(δx^2))-kc assuming boundary conditions for c(x,t) as : c(0,t)=1, c(a,t)=0. Where a is...

Show the diffusion equation is invariant to a linear transformation in the temperature field $$ \overline{T} = \alpha T + \beta $$ Since $\overline{T} = \alpha T + \beta$, the partial derivatives are \begin{alignat*}{3} \overline{T}_t & = & \alpha T_t\\ \overline{T}_{xx} & = & \alpha T_{xx}...

Homework Statement The edges of a thin plate are held at the temperature described below. Determine the steady-state temperature distribution in the plate. Assume the large flat surfaces to be insulated. If the plate is lying along the x-y plane, then one corner would be at the origin...

Homework Statement The equation for the probability distribution of the price of a call option is \frac{\partial P}{\partial t} = \frac{1}{2}\sigma^2 S^2 \frac{\partial^2 P}{\partial S^2} + rS\frac{\partial P}{\partial S} - rP with the conditions P(0,t) = 0, P(S,0) = \max(S-K,0), and...

Homework Statement Solve the diffusion equation with the boundary conditions v(0,t)=0 for t > 0 and v(x,0) = c for t=0. The method should be separation of variables. Homework Equations The separation of variables method. The Attempt at a Solution Attempting a solution of the form...

Homework Statement The one-dimensional heat diffusion equation is given by : ∂t(x,t)/∂t = α[∂^2T(x,t) / ∂x^2] where α is positive. Is the following a possible solution? Assume that the constants a and b can take any positive value. T(x,t) = exp(at)cos(bx) Homework Equations...

Homework Statement Mathews and Walker problem 8-2 (page 253): Assume that the neutron density n inside U_{235} obeys the differential equation \nabla ^2 n+\lambda n =\frac{1}{\kappa } \frac{\partial n }{\partial t} (n=0 on surface). a)Find the critical radius R_0 such that the neutron density...

Hi, I'm trying to find an analytical solution (if one exists) to the 1d diffusion equation with variable diffusivity κ(x); \partial_t u(x,t) = \partial_x[\kappa(x) \partial_x u(x,t)] Could someone point me in the right direction to solve this if its possible to do so analytically. I've...

Homework Statement One face of a thick uniform layer is subject to a sinusoidal temperature variation of angular frequency ω. SHow that the damped sinusoidal temperature oscillation propagate into eh layer and give an expression for the decay length of the oscillation amplitude. A cellar...

Homework Statement Implement the non-linear de-noising algorithm of Perona-Malik. Consider a noisy image, u, with pixel values referenced by u(i,j). Non-linear de-noising can be achieved by solving the following non-linear diffusion equation: ∇ · (g(∇u)∇u) = 0 with g(s) = ((K^2)v) /...

Hi all: Now I have a question about the concept of diffusion coefficient in two cases: the diffusion equation (J=DdT/dx) and the random walk (tao^2=6Dt). My quesion is the two D in two equations are the same or different. If they are different, is there any relationship between them? Best Xu

EDIT: The subscripts in this question should all be superscripts! Homework Statement I'm trying to solve a temperature problem involving the diffusion equation, which has led me to the expression: X(x) = Cekx+De-kx Where U(x,y) = X(x)Y(y) and I am ignoring any expressions where...

I have a 1_D diffusion equation dc/dt = D*d^2c/dx^2-Lc where L,D = constants I am trying to solve the equation above by following b.c. by FTCS scheme -D*dc/dx = J0*delta(t); where delta(t)= dirac delta function ----(upper boundary) I have written the code for it but i just...

Hello, Here is my problem: I need to turn my time dependent neutron diffusion equation into dimensionless one.. So, I have a couple of questions: 1. As neutron flux is a : "A measure of the intensity of neutron radiation in neutrons/cm2-sec" per definition, is "neutron" a unit? If yes, then...

Hi, How can I solve the diffusion equation in one dimension: u_t=ku_{xx} ; -\infty < t < \infty , 0<x<\infty With the boundary conditions: u(0,t)= T_0 +Acos(wt) u(x\rightarrow \infty,t) \rightarrow T_0 Thanks!

Hi, I'm new to the entire neutronics field. I've learned about adjoints as a physics student in undergrad and I'm doing nuclear engineering for my graduate studies. I understand how to derive the adjoint operator for the diffusion equation, but I'm a bit confused as to how to calculate the...

Water pressure in a filtration bed is given by the following diffusion equation: \frac{\partial p}{\partial t} = -k

The problem is as follows: \frac{\partial u}{\partial t}=k\frac{\partial^{2}u}{\partial x^{2}}+c\frac{\partial u}{\partial x}, -\infty<x<\infty u(x,0)=f(x) Fourier Transform is defined as: F(\omega)=\frac{1}{2\pi}\int_{-\infty}^{\infty}f(x)e^{i\omega x}dx So, I took the Fourier...

Hallo everyone, I am trying to find the way to solve the vertical diffusion equation for a spicies X in the atmosphere for steady state conditions (dc/dt=0). The equation has the form, dJ/dz -P+S=0 where J =(vs*C(z)) + rho*kz*d/dz(C(z)/rho(z)) is the flux of spicies X at height z...

Homework Statement at t=0, x=0, a schoolboy sets off a stink bomb halfway down a corridor that is long enough to be considered infinite. The dispersion of the particles obey the modified diffusion formula: \frac{\partial \rho (x,t)}{\partial t} - D\frac{\partial^2...

Hey, I want to solve a parabolic PDE with boundry conditions by using FINITE DIFFERENCE METHOD in fortran. (diffusion) See the attachment for the problem The problem is that there is a droplet on a leaf and it is diffusing in the leaf the boundry conditions are dc/dn= 0 at the upper...

Hallo everyone, I have a 1-D diffusion equation with decay as dA/dt = d2A/dx2-L*A with initial condition C(x,0)=C0=exp(-ax) and boundary condition= -Ddc/dx = I0 where L= decay constant A = certain concentration the concentration A is not in equilibrium. We can solve the above...

hi all, i am a new member here. nice to meet you all. i remember seeing a derivation of diffusion equation from the equation of motion \dot{x}=\eta(t) where \eta(t) is white noise. i can't remember where i saw this... could anyone please help me on that? it should be something like...

I've been combing over websites and papers on this, but I can't get a handle on trying to explain or visualize the similarity between them. The wave equation "smears out" over time as does the diffusion equation?

thermal diffusion equation - URGENT Homework Statement Please see attached q Homework Equations The Attempt at a Solution Ok so thermal diffusion equation is DT/Dt = D del squared T apparently this is a steady state problem, so DT/dt = 0, how am i meant to know? any hints on...

Show that S2 = S(x,t)S(y,t) solves St = k (Sxx + Syy) well St = St(x,t)S(y,t) + S(x,t)St(y,t) Sxx = Sxx(x,t)S(y,t) Syy=Syy(y,t)S(x,t) but what do i do from there?

So i have an organic chemical in a bio-film reactor being diffused into a bio-film and also being metabolized at constant rate R by bacteria. the concentration into the reactor Cin = 2mg/L with f-in at 20 m^3/hr the concentration in the reactor is C1 C3 is the concentration in the...

Homework Statement Solve u_{tt} - 4u_{xx} = 0, x \in \mathbb{R}, t > 0 u(x, 0) = e^{-x^2} , x \in \mathbb{R} Homework Equations General solution to the diffusion equation: u(x, t) = \frac{1}{\sqrt{4\pi kt}} \int\limits_{-\infty}^{\infty} e^\frac{{-(x - y)^2}}{4kt} \varphi(y) \, dyThe...

I have the following diffusion equation \frac{\partial^{2}c}{\partial r^{2}} + \frac{2}{r}\frac{\partial c}{\partial r} = \frac{1}{\alpha}\frac{\partial c}{\partial t} where \alpha is the diffusivity. The solution progresses in a finite domain where 0 < r < b, with initial...

Hi Everyone, on page 238 of lamarsh, section 5.5, first paragraph, it says "flux must also be finite". What does it mean?

Homework Statement A the density of a gas \rho obeys the modified diffusion equation \frac{\partial \rho(x,t)}{\partial t}-D\frac{\partial^2 \rho(x,t)}{\partial x^2}=K\delta(x)\delta(t) A) Express \rho in terms of its 2D Fourier transform \widetilde{\rho}(p,\omega) and express the right...

Homework Statement Obtain the solution of the diffusion equation, u(t,x) a) satisfying the boundary conditions: u(t,0)=u1, u(t,l)=u2, u(0,x)=u1+(u2-u1)x/l+a.sin(n\pix/l); b) in the semi-plane x > 0, with u(t,0)=u0+a.sin(\omegat). Homework Equations Wish I knew... The...

Homework Statement http://img42.imageshack.us/img42/1082/clipboard01lx.jpg Homework Equations (see solution) The Attempt at a Solution I literary just spent 5 hours trying to apply those boundary conditions, trying exponentials, sines, cosines, hyperbolic function etc... I...

Homework Statement Solve the equation U{t}=kU{xx}+cU Hint:use an integrating factor Homework Equations The Attempt at a Solution

Technically speaking, this is not a homework problem; it is something extra that I want to explore using data from my biomedical engineering class. We recently finished a lab involving testing the design of a micromixer; now comes the analysis of the data. No where in the lab are we instructed...

Homework Statement u_t = -{{u_{x}}_{x}} u(x,0) = e^{-x^2} Homework Equations The Attempt at a Solution The initial state is a bell curve centred at x=0. The second partial derivative of u at t=0 is {4x^2}{e^{-x^2}}, which is a Gaussian function, which means nothing to me other than its...

I have been asked to solve a diffusion equation with a source term using finite differences method. I need to numerically integrate the following equation either in MATLAB or C++. The equation is dT/dt = d2T/dx2 + S(x) The form of S(x) is some function given by a Gaussian profile...

help w/ diffusion equation on semi-infinite domain 0<x<infinity Woo! First post! And I'm trying out/learning the latex code which is really neato! Okay, so... please help! I'm trying to solve \frac{\partial^{2}T}{\partial x^{2}} + \frac{1}{x}\frac{\partial T}{\partial x} =...

Homework Statement The Attempt at a Solution I'm really at a loss on this question, which is why i have achieved so little on it so far. I think i more or less understand what a Fourier transform does (transpose amplitude vs time to amplitude vs frequency, ie the Fourier transform...

Hi, I have seen the solution to the diffusion equation written as C=(N/sqrt(4PiDt))exp(-x^2/4Dt). Hoever, as I understand it, this is for an instant input of N material. I want to express the concentration of substance at a point x away from the source for an arbitrary input signal. Is there...

the difference between the Heat and Diffusion equation ?! [FONT="Arial"][SIZE="5"]Please: What is the difference between the Heat and Diffusion equation ?! thank you.

Homework Statement Consider a traveling wave u(x,t) =f(x - at) where f is a given function of one variable. (a) If it is a solution of the wave equation, show that the speed must be a = \pm c (unless f is a linear function). (b) If it is a solution of the diffusion equation, find f and show...

i know that idea would seem a bit weird but, let us suppose we have a surface or volume in d- dimension, here d can be any real number (fractional dimension) the question is that we do not know what value 'd' is \frac{\partial \phi}{\partial t} = D\,\Delta \phi D is a diffusion...

Hey all, I'm wondering if someone can help me understand how to apply the boundary conditions to the diffusion equation in one dimension. Diffusion equation is: \frac{\partial u}{\partial t}=D*\frac{(\partial)^{2}u}{\partial x^{2}} The initial condition is: u(x,0)=0 And the boundary...

Ok, I have been given the steady state diffusion equation in 1d spherical polar coordinates as; D.1/(r^2).'partial'd/dr(r^2.'partial'dc/dr)=0 I know that the solution comes in the form c(r) = A+B/r where A and B are some constants. I just don't know how to get from here to there. I...

Homework Statement The solution to the diffusion equation in 1D may be written as follows: n'(x,t) = N/sqrt(4piDt) * exp(-x^2/4DT) where n'(x,t) is the concentration of the particles at position x at time t, N is the total number of particles and D is the diffusion coefficient. a)...

Hi there, I'm looking for an algorithm which describes the numeric solution to solve the diffusion equation (1D or 2D). I've taken a look on some textbook such as Hamilton and Henry ones but I didn't find a simple solution. anybody knows about it? Where can I find what I'm looking for? Thanks.