Diffusion Definition and 476 Threads

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 A p+-n junction with the n-side donor concentration of 1016cm-3. If ni = 1010cm-3, the relative dielectric constant er = 12, Dn = 50cm2/s, Dp = 20cm2/s, tn = 100ns, tp = 50ns. Calculate the hole diffusion current density 2mm from the depletion edge on the n-side under a...

Hi all I have been working on some unique solutions to advection-diffusion type problems. One inverse Laplace transform that I seem to continue to encounter is the following: Inverse Laplace[F(s)] where F(s)=[(1/(((s-α)^2)+β)*exp(-x*sqrt(s/D))] In their classic 1959 text, Carslaw...

Homework Statement Assuming: Organism weight = 25 g Organism length = 30 cm [Na+ (ECF)] = 200 mM [Na+ (water)] = 500 mM ΔX(gill) = 6 μm ΔX(skin) = 25 μm A(gill) = 5.0 cm^2/gm A(skin) = 10 cm^2/gm Dk(gill) = 2 X 10^4 cm^2/s Dk(skin) = 1 X 10^4 cm^2/s Calculate the Na+ rate...

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...

Ok guys, I've got a problem which I'd like to solve in an elegant way, but I don't how to solve it (if it can be solved analytically). I'm considering the decay chain of Uranium. So Uranium decays to Thorium, which decays to Protactinium, and so on. I know how to solve such a linear system...

Hi, I am solving the diffusion equation using explicit finite difference to model the diffusion of an analyte through a membrane. I am interested in the concentration of the analyte on the other side vs time elapsed. On one side of the membrane is an initial concentration, which I am...

Hi, I am trying to do a simple numerical calculation of diffusion equation. ∂t u(x, t) = ∂x^2 u(x, t). I could replicate a seemingly appropriate result (). However, I found the spectrum of the result is quite strange (). Since "∂x^2 u(x, t)" becomes "-k^2 uk" in Fourier space (uk is Fourier...

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...

hi everybody! I'm studing the gas diffusion in two cases: 1. first case: gas diffusion in 3D open space in a spheric simmetrical case ∆C(x,y,z,t)-(1/D)(∂C(x,y,z,t))/∂t=0 where: x,y,z arbitraries gas concentration =0 for big spheric dimensions lim┬(r→∞)⁡〖C(r,t)〗=0 concentration C is...

I am utterly lost on this problem. This is from Applied Partial Differential Equations by Logan, 2nd edition. Unfortunately, I can't show any attempted work because I don't even know where to start! In the example, they are using some sort of method for solving and ODE, and I have no idea...

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) /...

Homework Statement A student working 3.0m away from you in a chemistry lab performs an experiment which creates a bad odor. It takes a while for the smell to get to you (assume air currents are negligible). You are able to move 2.0m further away from the source but the smell catches up with...

Homework Statement A student working 3.0 m away from you in the chemistry lab creates a bad odour. The odour takes a while to get to you (assume that air currents are negligible). You then move 2.0 m further away, but the odour catches up with you in another 60 seconds. What is the diffusion...

Suppose that a tracheae is 1.17 mm long with a cross-sectional area of 1.01 x 10-9m2. The concentration of oxygen in the air outside the insect is 0.659 kg/m3, and the diffusion constant is 1.99 x 10-5 m2/s. If the mass per second of oxygen is diffusing through a trachea is 1.50 x 10-12 kg/s...

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

Any one have online documents showing the complete derivation of the both with the numerical solution ?

Hey everyone, I was just wondering, in a PEM fuel cell the Hydrogen ion diffusion through the membrane is an important step. But don't these ions need to diffuse through the anode as well to reach the membrane? Also, if this is the case and the anode is a metal like Pt, wouldn't the diffusion...

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...

Homework Statement Find out whether particle or heat diffusion determines the width of the SOL, and whether the ions or electrons are the determining factor. (just compare all of those). Give an expression to estimate the thickness of the SOL and evaluate the expression for Te = 10 and 100...

Hello there! I am solving a heat diffusion problem which is described by the differential equation: θΤ/θt=a*(θ^2Τ/ΘΤ^2). I will apply two diffrent temperatures on the ends of a metal rod. Solving the equation i conclude, according to the boundary conditions of course, at the function...

Homework Statement For ordinary 1D diffusion show that the mean value of the square of the position is equal to 2Dt Homework Equations \left\langle {x^2 \left( t \right)} \right\rangle \equiv \int\limits_0^\infty {x^2 p\left( {x,t} \right)dx} \frac{\partial }{{\partial t}}p\left(...

why simple diffusion does not require a semi-permeable membrane?

Homework Statement Porous membranes are used to separate mixtures in industry, because smaller compounds permeate through them more easily than larger ones. KnoGas Pty Ltd are trialling an experimental separation process, using a membrane to sep- arate compounds A and B: compound A...

Hi. I don't know if this is the correct place to ask this, but prefer you to suggest me where I should ask. I'm starting with numerical simulation and I've been playing with the finite differences method to solve the heat equation on 1D, 2D and 3D uniform grids. This was really simple. Now I...

What is Super Diffusion? I just came up with an article talking about "super diffusion", then I searched the net & came upon the wikipedia article on anomalous diffusion which was very short and not descriptive of the physics behind it... I will highly appreciate any enlightenment :)...

Homework Statement I don't know how to approach this problem, any help would be appreciated. i have a pipe 1 meter in length and 4mm in diameter. it containts 2 gases, D2 and He-3. each half of the pipe contains the 2gases and they are both at 400psi. how long does it take the gases to...

Greetings to all, I will like to know how to determine the concentration gradient of a solute that is dissolved in a liquid (a solute in oil). Droplets of this solute solution are made in another continuous phase (water). The oil is partially soluble in wate. As soon as this difussion starts...

Isn't my calculation of diffusion coefficient correct? A certain silicate is diffused at 750 centigrade... The diffused ion had an ingression depth squared of 2.5x10^-5 cm^2 after 7 days of contineous heating. What is the diffusion coefficient of this ion in this particular silicate...

I am confused because I read that a selectively permeable membrane means that it becomes osmosis and that there can't be a selectively permeable membrane for diffusion. Or is osmosis just diffusion across a selectively permeable membrane?

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...

Homework Statement I have a 1D diffusion equation as du/dt = D*d^2u/dx^2-K*u; where D and k = constants the initial condition is u(t=0)=0 B.C. is u(x=0,t=0)= u0*delta(t); (a pulse like input at x=0 and delta(t)= dirac delta function) where u = contaminant in a semi infinite slab...

Hi, below, you will find an extract from a script. One sentence is: "Move these walkers according to the the Gaussian distribution ..." (you can find this on the second image) My question: Why is it obvious from formula (124) (the short time step proppagator) that we have to move the...

I'm trying to find an analytical solution (probably containing a convolution integral) to a 2D diffusion problem in the xy-plane, when the value h(t) at the origin is known for all times t>=0. The diffusion constant is the same everywhere. The last problem solved under the section...

I am studying fluid dynamics by using adimensional analysis to obtain an expression for a dynamic (thermal) boundary layer in a poiseuille flow. The fluid nearest the boundary (y = 0) is said to have adimenional temperature T = 1 and as y tends to infinity, the temperature is T = 0. The final...

I am trying to model the diffusion of fluorophores in a cell with a source in the middle by solving the appropriate differential equation. I can solve the PDE easily enough, however as I haven't done DE's in a while, I need a refresher on how to apply the appropriate boundary conditions for my...

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...

Hello, I have a 1-D steady state (dc/dt=0) differential equation in the atmosphere. It looks like follows, K*C'' + (K'+K/H)*C' + (1/H*K'- (K/H^2)*H'- (L+Si))C + S = 0 where, C = concentration of the contaminant in the atmosphere at different heights z K = vertical diffusion...

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!

So if I have a general reaction diffusion equation and perform a liner stability analysis on it I would only get the domains in which Turing Instability occurs but not which pattern I would get (stripes , spots etc.). So I need to use a nonlinear analysis. One technique people use is a...

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...

I'm having a little trouble understanding the Sherwood number, (Sh, mass transfer Nusselt number), which gives the ratio of convective to diffusive mass transfer. My question is: given a system that has a molecular diffusion coefficient of D, the effective diffusion coefficient is measured to De...

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...

hello everyone,:wink: is this definition correct? drift current is flow due to applied voltage across P-N junction & Diffusion is flow due to different concentration of hole & electron across P-N junction. warning: [i read this definition somewhere, hence not my own work] 1:-- the...

Hi, I had developed some Matlab code to solve the heat equation using central difference. I was having issues with my code because I was running out of memory trying to keep the algorithm stable. I need to reconfigure my code so to use single vectors in the time/space stepping, rather than...

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...