Conditions Definition and 978 Threads

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...

Hello hello, I cannot for the life of me wrap my head around the idea of a boundary condition. I understand the idea (at least I think I do) of solving a differential equation with given initial conditions. But is solving for a magnetic field or electric field while enforcing...

[Sorry about the long post] I'm doing an essay where I am exploring whether or not elements were, for the most part, formed under conditions of thermodynamic equilibrium. We know that some element clearly aren't (such as Potassium 40 and uranium which decay radioactivly). I've scoured the web...

Homework Statement For a particle moving in a potential V(x), what are plausible forms of V(x) that give: (i) entirely continuous, (ii)entirely quantised (iii) both continuous and quantised energies of the particle? Sketch, with justification, the forms of V(x) for each of...

Hey guys, just need some hints with this doosey Homework Statement We have (x^2 y')' + ax^2y = 0 where a the eigenvalue (a sturm-lioville problem) (sp?) with y'(0)=y(1) = 0 and we get the hint to substitute f = y/x. The Attempt at a Solution Ok so i get the general solution being a sum of...

This is my question... For the alkyl halide tell which mechanism, E1 or E2, will predominate under both stongly basic (with large base) conditions and strongly acidic. Tell if each reaction is expected to proceed relatively quickly, moderately, or slow (based on sterics for E2 and carbocation...

Does anybody know the conditions of a ideal Stefan Boltzmann gas? And the EoS? thanks a lot florian

Hey guys, I was just wondering if anyone knows how to set the initial conditions for ode45() if you know f(1.5) but NOT f(0) Currently I have >> ode45(f, [0 1 1.8 2.1], [1.5 .5]) But this creates the following error: ? Error using ==> funfun/private/odearguments @(T,Y)...

Hello guys. I have a simple question regarding an LC circuit. Imagine a voltage source V_0, a capacitor C and an inductor L, all hooked up in series. I know that the equation governing the behvior of the system is V_0=\frac{1}{C}q(t)+L\ddot{q}(t), and hence q(t)=A\cos \omega t +...

Suppose one knows a probability density p(x) over a space X (where x\in X) and a conditional probability density p(y|x) over a space Y (where y\in Y). This implies the integral \int{p(x)dx} is well defined as well as \int{p(y|x)dy}. Defining a joint probability density p(x,y)\ =\ p(y|x)p(x)...

what is the concentration of blood plasma under normal conditions?? how do you even begin to answer this question HELP!

If I have a finite boundary, say of length L. Is it possible to demonstrate that if I were to allow all possible CONTINUOUS values of a wave to exist (with unit amplitude) then deconstrutive interference destroys all waves except those with wavelength: k=\frac{n\pi}{L} Where n =0,1...

Homework Statement Does anyone know how to solve this PDE for u:R-->R and some initial conditions? u_{xy}=ku where k is a positive constant. Or this one, also for u:R-->R and some initial conditions: u_{tt}=u_{xx}-Ku where K is a positive constant.The Attempt at a Solution I can solve the...

One thing that's always bothered me about Bloch's theorem is the periodic boundary conditions which are imposed on the system. Clearly, when dealing with an actual solid, the more natural choice would be to impose zero at the boundaries. I know that periodic conditions make the math easier, but...

Hi everyone :D This is my problem: Find conditions on \alpha and \beta in the Euler equation x^{2}y'' + \alphaxy' + \betay = 0 such that: a) All solutions approach zero as x \rightarrow 0 b) All solutions are bounded as x \rightarrow 0 c) All solutions approach zero as x \rightarrow\infty I...

I wasn't completely sure where to put this (programming or Diff.E.'s), so if there's a better place, maybe the mentors could move it for me. I'm doing some numerical simulations involving the (2-D) wave equation, and was wondering if anyone could tell me (or give a reference to a paper which...

For non-equilibrium conditions, can temperature be defined? Does this relate to the zeroeth law of thermo? Thanks!

Hello to all! Homework Statement for testing my program i need a heat equation with numerical initial and boundary conditions: Derivative[2, 0][f][x, t] == Derivative[0, 1][f][x, t] f[x, 0] == numerical f[0, t] == numerical, f[numerical, t] == numerical PS. to moders: please, if...

solve the next differential equation: y´´- a*y= \delta (x-d) with the boundary conditions: \left.\frac{\partial y}{\partial x} \right|_ {x=0} = 0 lim _{x\rightarrow\infty} y = 0 I get the homogeneous solution: y_H = C_1 exp (\sqrt{a}x) + C_2 exp (-\sqrt{a}x) and then to...

[SOLVED] Linear algebra; conditions for spaces Homework Statement 1) If I want to write a basis for R^3, what must the conditions for the three vectors? Must they be linearly independant or orthogonal or what? 2) If I want to write a basis for a supspace of R^3, what must the conditions for...

Remembering the derivation for the Boltzmann distribution it seems to me, that it assumes that energy of a system in contact with a reservoir spreads over all degrees of freedom equally likely (sort of "structure-less"). Now I imagine correlated systems have special behaviours and reactions or...

Hi, I'm trying to find an analytical solution of Laplace's equation: \phi_{xx} + \phi_{tt} = 0 with the tricky boundary conditions: 1. \phi(x=0,|t|>\tau)= 0 2. \phi(x\neq0, |t|>>\tau)=0 3. \phi_{x}(x=0, |t|<\tau)=-1 4. \phi_{t}(x, |t|>>\tau)=0 I have the following ansatz(I...

PDE with boundary conditions Full question A function u(x,y) has two independent variables x and y and satisfies the 1st order PDE x \frac{du}{dx} - \frac{y}{2}\frac{du}{dy}= 0 by first looking for a separable solution u(x,y)=X(x)Y(y), find the general solution of the equation. determine...

write all possible equivalent conditions to "A is invertible," where A is an nxn matrix.

what do mean the author by the red underline line? http://img164.imageshack.us/img164/7404/contfv6.jpg Why would 33.22abe false? Thanks.

A missile is fired at a target from the origin O, with the velocity vector, t seconds after it was fired, given by \overrightarrow v (t) = [u\cos \theta ]\overrightarrow i + [u\sin \theta - gt]\overrightarrow j, where u, theta and g are constants. The target is moving with velocity...

I'm trying to understand the proof for this theorem: The function f(x) = u(x,y) + iv(x,y) is differentiable at a point z= x +iy of a region in the complex plane if and only if the partial derivatives U_{x},U_{y},V_{x},V_{y} are continuos and satisfy the Cauchy-Riemann conditions...

Finding the vibrational motion of a rod. A uniform rod of length l is compressed from both ends so that its new length becomes l(1-2 \epsilon). The compression force is then removed and the rod is left to vibrate freely. Find the subsequent vibrational motion of the rod. What are the...

Hello! I'm very interested in solar cell tehnology. I know that the main material used is crystalline silicon. Is it possible to buy all the materials that are necessary and to make the solar cell at home conditions? I hope that this process is not very complicated and laboratory isn't needed...

Hello. I would like to find an analytical solution of the one group point kinetic equations with the external source. I have a critical reactor and I would do the step change in reactivity. I would like to find the solution for n(t). The ONE-GROUP point kinetics equations...

Does anyone know what the necessary conditions are for a nucleus to undergo fission with a thermal neutron? I have found something for the chain reactions, but not very helpful. I want to find out the conditions for ONE nucleus to undergo fission with a thermal neutron.

Homework Statement What is the stationary (steady state) solution to the following reaction diffusion equation: \frac{\partial C}{\partial t}= \nabla^2C - kC Subject to the boundary conditions C(x, y=0) = 1, C(x = 0, y) = C(x = L, y) (IE, periodic boundary conditions along the...

Hi to all community of Physic's help from Florence, looking at born-von karman BC I'm a bit confused. I put this condition when i assume periodicity of wave function where the period is the spatial dimension of my system. I found that BC first in solid state physic, then I've noticed that...

Hi guys, help me. I have a code for integrate the equations of motion of three bodies in a inertial frame, and in cartesian coordinates (x, y, z, vxi, vyi, vzi), i=1,2,3. The question is, how can i use the data of JPL Horizons to obtain positions and velocities in a inertial frame?

Hello, I am interested in the conditions necessary for entangled states to be created. Unfortunately I only have access to introductory QM texts, and they talk about about how entanglement can exists between particles etc, but no mention of the creation of them (and the conditions required...

Hi, Can anyone please tell me how to go about solving this system of coupled ODEs.? 1) (-)(lambda) + vH''' = -2HH' +(H')^2 - G^2 2) vG'' = 2H'G - 2G'H lambda and v are constants. And the boundary conditions given are H(0) = H(d) = 0 H'(0) = omega * ( c1 * H''(0) + c2 * H'''(0) )...

Hi, Do half lifes dissapate quicker when under critical conditions, e.g- high pressure, high temprature etc.? Is there are difference in half life dissipation in real gases and ideal gases? P.S- I know nothing about half lifes. Cheers.

Hi I am new to solid state. I just read about fermi gas in a cube. For some reason the author used periodic boundary conditions? Why didn't they choose finite well potential where the height of the well is related to the work function?

hey all! does anyone know the conditions a well behaved wavefunction (phi) must satisfy for all x? and any physical justifications for them? is it something to do with continuity at boundaries? or to do with the differential of the wavefunction? cheers for any input roc

Homework Statement How to find the conditions on the coefficients of a quadratic equation for the roots to be outside the unit circle eg bx^2 + x - 1 = 0 where b is a constant How do we find the condition(s) that b must satisfy such that the roots of the quadratic lie outside the unit circle...

Homework Statement Can there be a mapping that may not map any elements from one domain to another? The reason is that the mapping has a condition. For example, it will only map elements if the one in the domain are related in some way to the element they are mapped to (i.e congruence via a...

Determine the motion of this mechanical system- *Pic attached* satisfying the initial conditions :- y1(0) = 1 y2(0) = 2 y1'(0) = -2*sqrt(6) y2'(0) = sqrt(6) I need to find equations for y1(t) and y2(t). Please help :D PS ideal springs, point masses cannot collide, y1 and y2 are...

Find the particleur equation for the given initial conditions:- 1/2y'' + y' + 13y = 0 ; y(0) = 5, y'(0) = 0 The only method I know how to solve these doesn't seem to work. Any help is much appreciated.

I need help figuring out the solution to this diff.eq. y(x) = x + (1/2)*∫(from u=-1 to 1)[ ( 1-| x – u | ) y(u) du] , x є [ -1, 1] I have to show that: y``(x) + y(x) = 0 , x є [ -1, 1] subject to: y(1) + y(-1) = 0 y`(1) + y`(-1) = 2 Thanks for any help you can give.

I would really like to know whether initial conditions given to a time evolution PDE has to satisfy the governing equations. For example, if I have to solve numerically an incompressible flow equation do I need to give initial solution for the velocity field which is divergence free so as to...

Homework Statement The drawing shows a wire loop near a current -carrying wire. Under what conditions would current flow through resistor R from Right to left? Homework Equations Lenz's law The Attempt at a Solution 4 answers a) when the current I is increasing b)when the...

Homework Statement The edges of a square sheet of thermally conducting material are at x=0, x=L, y= -L/2 and y=L/2 The temperature of these edges are controlled to be: T = T0 at x = 0 and x = L T = T0 + T1sin(pi*x/L) at y = -L/2 and y = L/2 where T0 and T1 are constants...

2CO (g) + O2 (g) → 2CO2 (g) 2NO (g) → N2(g) + O2 (g) what do i have to do, so i have to say the best temperature is at 25 celcius and at 1 atm, how do i figure this out is their a way, or i have to look it up on the internet

2CO (g) + O2 (g) → 2CO2 (g) 2NO (g) → N2(g) + O2 (g) how can i figure out the best conditions for these reactions

Hey there, could you guide me in the following question: X x Y is a Banach space if and only if X and Y are both Banach Spaces Thank you