Conditions Definition and 978 Threads

Is there any way to mathematically derive functions that satisfy a given set of initial conditions? I know this sounds very general, but say for: f(1)-f(0)=0 and f'(1)=1 I've resolved myself to guessing and checking. I've found a function for the opposite: e*t-exp(t) -- ([e*1 -...

This problem has been bothering me for a while now, hope you can help me. Let's say that the initial velocity of an object, with mass of m is 0 and the initial position is s0 and the force acting on the object is defined as F(s), how do i find the s(t), where t is time. If it's any help, then...

Hi guys! I'm to find the solution to \frac{\partial u}{\partial t} = \frac{\partial^2 u}{\partial x^2} Subject to an initial condition u(x,0) = u_0(x) = a \exp(- \frac{x^2}{2c^2}) And Neumann boundary conditions \frac{\partial u}{\partial x} (-1,t) = \frac{\partial...

Homework Statement Given w'' - w = f(x) w'(0) = 1 w'(1) = 0 Homework Equations Find the Green's Function The Attempt at a Solution The solution to the homogeneous equation is known as: w(x) = A*exp(-x) + B*exp(x) For G's function we have: u(x) = A1*exp(-x) +...

Homework Statement A sphere is enclosed in a bell jar half filled with water. The sphere floats. Air is pumped out to create a vacuum above the water inside the bell jar. Will the sphere float in the same way, float better or will it sink? Homework Equations - The Attempt at a...

Hi I'm new to MATLAB and I'm trying to write a code that executes the same process under two separate conditions> condition 1: that scalar value dE is less than or equal to zero. condition 2: that scalar value r is less than or equal to scalar value w. I'd like to same series of...

Hello all: I'm a newbie, trying to write/use code for solving a 2D advection-diffusion problem. I'm not sure how many boundary conditions I should have for the property that is being transported. In my problem, I have diffusion switched off (advection only). The property being...

Not actually a homework question, this is a question from a past exam paper (second year EM and optics): Homework Statement Use a Gaussian surface and Amperian loop to derive the electrostatic boundary conditions for a polarization field P at an interface between media 1 and 2 with...

Hi. I'm trying to solve the heat equation with the initial boundary conditions: u(0,t)=f_1(t) u(x_1,t)=f_2(t) u(x,0)=f(x) 0<x<x_1 t>0 And the heat equation: \frac{\partial u}{\partial t}-k\frac{\partial^2 u}{\partial x^2}=0 So when I make separation of variables I get: \nu=X(x)T(t)...

Using the Ion Electron Method (acidic conditions) I need to solve: MnO4- + C2O42- -> Mn2+ + CO2 So I tried doing: MnO4- -> Mn2+ And: C2O42- -> CO2 + 2H2O Then I balanced the oxygen atoms with H2O MnO4- -> Mn2+ + 4H2O And: C2O42- -> CO2 + 2H2O Then I added the...

The questions arises because I want to use the solution of one PDE as initial condition to solve another. Then using NDSolve, the first solution is given by InterpolatingFunction. I tried, it takes the whole afternoon, almost kills my computer but still not giving any result. Another computer...

Homework Statement I have found the general solution to a second order pde to be U(x,t) = f(3x + t) + g(-x + t) where f and g are arbitrary functions I have initial conditions U(x,0) = sin(x) Du/dt (x,0) = cos (2x) The Attempt at a Solution I have found that U(x,0) = f(3x) +...

Homework Statement I have a PDE for which i have found the general solution to be u(x,y) = f1(3x + t) + f2(-x + t) where f1 and f2 are arbitrary functions. I have initial conditions u(x,0) = sin (x) and partial derivative du/dt (x,0) = cos (2x)Homework Equations u(x,y) = f1(3x + t) + f2(-x +...

i know that it is possible to have multiple conditions in a for loop. but is it separated by a comma or would it be separated by && like in an if statement? Thanks

Homework Statement here's the problem: Let A and B be n x n matrix with coefficient in K (any field), let Mn(K) be the set of all n x n matrix with coefficient in K . T is a linear map defined like this T : Mn(K)---> Mn(K) T(Y) = AYB what are the necessary conditions for T to be a...

According to the usual way of applying determinism in physics:- If we know all the intitial conditions of a closed system at time t0, we can fully specify the the system at a time t1>t0. This seems natural and obvious within classical physics, but is it really true? I have never heard of a...

Homework Statement See figure attached for problem statement, as well the solution. Homework Equations The Attempt at a Solution I'm confused as to how he is writing these equations from the boundary conditions. What I understand as the boundary condition for D is, \hat{n}...

I have two different scenarios for heat transfer I need some help with understanding. 1.) Given two different materials in perfect contact with each other with no thermal resistance at the interface, what are the interface conditions at the interface? Considering two heat equations with...

Homework Statement No problem, I just have a confusion about a certain concept. Homework Equations The Attempt at a Solution I'm confused as to how they draw the result, \oint_{C} \vec{E} \cdot \vec{dl} = E_{1t}\Delta l - E_{2t}\Delta l = 0 You don't really need to do the...

I'm just wondering if someone can point me in the right direction here.. or maybe I'm just crazy lol. I'm a big coffee drinker. When I go out, I usually grab a coffee and walk around with it in hand. (mall's, convenience stores, book stores, subways and buses etc...) and as expected there is...

1. Will wave functions collapse in a photon double-slit experiment after we place a detector at one of its slits and detect one photon? 2. Will wave functions collapse in a photon double-slit experiment after we detect a photon on the screen? 3. Will wave functions collapse in an electron...

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...

Let us consider Laplace's equation in the spherical coordinates [with azimuthal symmetry]. It's solution is given by: psi[r,theta]=summation over n [from zero to infinity] [An r^n+ Bn r^{- (n+1)}]Pn[Cos(theta)] ----------- (1) An and Bn are arbitrary constants and Pn stands for the Legendre...

Under what special conditions can a wavefunction that depends on a series of coordinates be written as a product of wavefunctions that only depend on one coordinate each? What can you say about the energy in this case? (This is a study/end of the chapter question (P.Chem))... I'm thinking it's...

How many functions satisfy this set of conditions? 1) f(x.y) = f(x) + f(y). 2) f(a)=1. I was trying to define a logarithmic function abstractly as a map from R+ to R satisfying those 2 conditions that this question came to my mind. It's obvious that there are infinitely many functions...

Homework Statement The problem is to find sufficient and preferably also necessary conditions on random variable X such that its characteristic function g(x) satisfies the limit property: \lim_{t\to0}\frac{1-g(\lambda t)}{1-g(t)}=\lambda^2 I may assume X is symmetric around 0, so the...

For fixed-fixed BC's, i have to arrest x and y displ. For simply supported case, i have to arrest y displ. Then my doubt is, while applying force at the end of the column, how the displacement will happen for fixed-fixed column.

Is it possible to impose boundary conditions on the other 2d lattices like a rhombic lattice? a hexagonal lattice? an oblique lattice? How does one typically index such lattices?

I read that if you are in a spaceship orbiting Earth in a circular motion, the astronout feels weightless (meaning the normal force to the astronout is equal to zero). But according to Newton laws equations you get: and then if we assume N=0 (which is really what's happening according to my...

Homework Statement sin(y)\frac{ \partial u}{ \partial x} + \frac{ \partial u}{ \partial y} = (xcos(y)-sin^2(y))u where ln(u(x,\frac{\pi}{2})) = x^2 + x - \frac{\pi}{2} for -1 \leq x \leq 3 determine the characteristic curves in the xy plane and draw 3 of them determine the general...

Homework Statement Consider a boundary between two dielectric media with dielectric constants \epsilon1 and \epsilon2 respectively. The boundary carries a surface charge density \sigma. Use appropriate integral forms of Maxwell equations and an illustrative sketch to derive continuity...

Homework Statement What are the conditions so that the matrix \hat{p} describes the density operator of a pure state? Homework Equations http://img846.imageshack.us/img846/2835/densitymatrix.png p=\sum p_{j}|\psi_{j}><\psi_{j} The Attempt at a Solution I know that tr(\rho)=1 for...

Say you have a free particle, non relativistic, and you want to calculate the density of states (number of states with energy E-E+dE). In doing that, textbooks apply periodic boundary conditions (PBC) in a box of length L, and they get L to infinity, and in this way the states become countable...

Homework Statement I'm trying to derive Equation (1) from the paper: http://idv.sinica.edu.tw/jwang/EP101/Paul-Trap/Winter%2091%20ajp%20demo%20trapping%20dust.pdf We are working with a cylindrically symmetric geometry along the z-axis. r^2 = x^2 + y^2 We have electrodes described by...

1. How many ways are there to rearrange the letters of INVESTIGATION given that the first letter is a V and the last letter is not a T? I get the first part, first letter being V cuts the # of combinations from 13! to 12!, but how do I handle the part about the last letter not being T? Most...

Hello everyone :) I'm reading the book QFT - L. H. Ryder, and I don't understand clearly what are the generating functional Z[J] and vacuum-to-vacuum boundary conditions? Help me, please >"<

As far as I know, the classic paper applying the Hawking singularity theorem to our universe is this one: Hawking and Ellis, "The Cosmic Black-Body Radiation and the Existence of Singularities in Our Universe," Astrophysical Journal, vol. 152, p. 25, 1968...

Setting is like this: I have 52cards of 4 shapes. that's 13 each. I take one card out and put it in a hat. now with 51card I draw 3 consecutive cards. It happens to be that I picked 3 diamonds. Now I want to find the probability of the card in the hat be a diamond. My friend said it...

Homework Statement (Kleppner & Kolenkow - Introduction to Mechanics - 2.17) The first attached image shows a box on an incline which is accelerated at a rate a meters per second squared. \mu is the coefficient of friction between the box and incline surface. The questions are in the image...

Hello everyone and greetings from my internship! It's weekend and I'm struggling with my numerical solution of a 1+1 wave equation. Now, since I'm eventually going to simulate a black hole ( :D ) I need a one-side open grid - using advection equation as my boundary condition on the end of my...

Hey folks, I have an orbit in the circular restricted three body problem with initial conditions [x(0), 0, z(0), 0, y'(0), 0] I'm following this paper http://adsabs.harvard.edu/full/1984CeMec..32...53H on how to correct these initial conditions given the state transition matrix at a...

I am trying to set up for an experiment, and I need to know the time dependence of the temperature of the front surface of an assembly of plates. The assembly has a heater on one side and is exposed to a gaseous environment (of constant known pressure and temperature) on the other. I am...

I wasn’t sure where to put this, I decided that really it could only go here in general discussion. Although the discussion involves matters of the human genome and the growing knowledge of it, the issue is not biological, it’s social. In any case… So, there was a program broadcast here in...

It has come up a few times in recent threads here that the energy conditions on the stress-energy tensor (weak, null, dominant, etc) traditionally used to prove global results (e.g. the singularity theorem, the positive energy theorem, geodesic motion theorems*) are problematic: they allow more...

Hey folks I'm looking into halo orbits and I have a question about how to find the initial conditions from the third order approximation solution... A good run through of the third order solution calculation is found in this paper...

Homework Statement MnO_4^{-} + 8H^{+} + 5e^{-} \rightleftharpoons Mn^{2+} + 4H_2O 1. Explain why the presence of an acid is necessary for aqueous permanganate ions to function as an oxidizing agent. 2. Give two reasons for the aqueous permanganate ions acting as an oxidizing agent in acidic...

Hello, I was wondering under what conditions does free fall need to comply to in order to take effect? I am pretty certain that for an object to be in free fall it needs to be void of any friction, but what about air resistance? Or is air resistance a form of friction? Thank you in advance.

Homework Statement The normal vector of each of the following planes is determined from the coefficients of the x-, y-, z- terms. pi1: a1x+b1y + c1z + d1=0 pi2: a2x+b2y+c2z+d2=0 pi3: a3x+b3y+c3z+d3=0 Define the extended vector for each plan as follows: e1= [a1, b1, c1, d1] e2= [a2, b2, c2...

Please teach me this: The parameters(mass,interaction constant) in classical Lagrangian can be freely changed in classical framwork,but how about in quantum framework?Then why we can freely arrange the renormalization conditions,because I think that we do not know whether the parameters can...

Could you please check if these are the Dirichlet conditions? 1. f(x) is periodic. 2. f(x) has a finite number of maxima and minima over one period. 3. f(x) is single valued, except at a finite number of discontinuities over one period. 4. \int^{-L/2}_{+L/2} \left|f(x)\right| dx is finite...