Conditions Definition and 978 Threads

If I could be inside the LHC Atlas detector during a proton bean collision what would I see? Would there be a huge flash of light? Would I be killed, if yes how fast? Or would there be nothing to see?

Homework Statement n is given by: ∂2Θ/∂x2=1/α2 ∂Θ/∂t , where Θ(x, t) is the temperature as a function of time and position, and α2 is a constant characteristic for the material through which the heat is flowing. We have a plate of infinite area and thickness d that has a uniform...

In standard, run-of-the-mill, one-dimensional scattering problems (e.g., finite square wells), we calculate transmission and reflection amplitudes by (in part) making sure that our wave function \psi satisfies the following conditions at discontinuities of the potential: (1) It is continuous...

I am trying to solve the following heat equation ODE: d^2T/dr^2+1/r*dT/dr=0 (steady state) or dT/dt=d^2T/dr^2+1/r*dT/dr (transient state) The problem is simple: a ring with r1<r<r2, T(r1)=T1, T(r2)=T2. I have searched the analytical solution for this kind of ODEs in polar coordinate...

Hello all! :smile: I am wondering: Since we derive the equilibrium constant by minimizing the Gibbs free energy, it means that me are taking advantage of the fact that at the minimum, we have (dG)_{T,P,m}=0. Does this mean that in order to determine the products of a reaction using the...

Homework Statement Find the standard matrix for the linear transformation T: R^3-->R^3 satisfying: T([1 2 2]) = [1 0 -1], T([-1 -4 -5]) = [0 1 1], T([1 5 7]) = [0 2 0] All of the vectors are columns not rows, I couldn't type them correctly as columns. The Attempt at a Solution I...

Under what conditions is Faraday’s Law independent of Ampere’s Law? I want to say that this is so only in the static case, however this isn't right (or at least there's more to it). What am I missing?

a steel rod, 40mm in diameter and 1.00m long is pinned at each end calculate the euler bucking load Answer: using PE = pie sqaured 210x10cubed kN/mm x 1.25 x 10power 5mm to the 4 divided by 1000mm sqaured =259.1kN b) indentify three other possible end fixity conditions for the...

vw= Velocity of Wave vm= Velocity of Wave Source fw= Frequency of the Wave fd= Frequency of the Wave relative to Detector as Wave Source is also moving q= Infinity For the wave frequency detected by a detector at rest as the wave source* is moving towards it, there is: fd=( vwfw )/(...

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!

What will be the limiting conditions?

Homework Statement Hi guys, I'm having trouble understanding the finite potential well, in particular the boundary conditions The well under scrutiny has potential V(x)= 0 for |x|<a and V(x)=V_0 for >a Homework Equations \frac{d^2\psi}{dx^2}=-\sqrt{\frac{2mE}{\hbar^2}}\psi=-\alpha^2\psi...

It's just the final part (e) that I don't get, I have the rest but just for completeness I thought I'd put it in (iii) Let f : (0,infinity) -> R be a function which is differentiable at 1 with f '(1) = 1 and satisfies: f(xy) = f(x) + f(y) (*) (a) Use (*) to determine f(1) and show that f(1/x)...

I've seen equations for Fanno flow and Rayleigh flow but I am confused on how to use them properly. Fanno Flow \frac{P}{P^{*}}=\frac{1}{M}\frac{1}{\sqrt{\left(\frac{2}{\gamma+1}}\right)\left(1+\frac{\gamma-1}{2}M^2\right)}...

I have seen lots of simulations using the shallow water equations, and every one I've seen involves having some sort of initial displacement in the water, resulting in a propagation of waves through a medium of either constant or variable depth, as a function of position. However, can you...

The LHC is supposed to create conditions similar to the big bang. Although energy densities, temperatures and other conditions may be similar to those theorized in the big bang and soon thereafter, are the conditions of space and time the same now as then? If time and or space were fundamentally...

Hi! As a part of a mathematical construction I used the rate of change of F(s) with s, i.e. dF/ds. F and s are smooth functions. The problem is that s(u,v,w) is a function of u, v & w and actually I need to find the rate of change of F with respect to u, v & w. The question is: what does...

Hi everyone! I'm trying to find a smooth function that can replace the intersection of a continuous piecewise function made up of two lines of different slopes, one of which starts at the origin. Right now, I'm trying to find a logarithmic function that goes from the origin (or close to it)...

Homework Statement For every set S and every metric d on S, which of the following is a metric on S? A. 4 + d B. ed + 1 C. d - |d| D. d2 E. square root of d Homework Equations none The Attempt at a Solution I've ruled out A. because d(x,x) does not equal 0. I've ruled out C. because it's...

[FONT="Times New Roman"] [SIZE="3"]When a PN juction is in the open circuit condition, my textbooks says the following. "The voltage measured between the terminals is zero. That is the junction Voltage Vo does not appear across between the diode terminals.This is because of the contact...

Homework Statement Consider \frac{\partial u}{\partial t} = k\frac{\partial^2u}{\partial x^2} subject to u(0,t) = A(t),\ u(L,t) = 0,\ u(x,0) = g(x). Assume that u(x,t) has a Fourier sine series. Determine a differential equation for the Fourier coefficients (assume appropriate continuity)...

Homework Statement Base metal zinc (Zn) reacts with concentrated hydrochloric acid (HCl) forming gaseous hydrogen and zinc chloride. STP conditions: pressure p = 101,3 kPa , temperature t = 0C. The equation of state for ideal gas: pV = nRT R = 8,314 J /(mol K) Homework Equations Write...

So, I do not think I did this properly, but if f(-x)=-f(x), then u(-x,0)=-u(x,0), and if g(-x)=-g(x), then ut(-x,0)=-ut(x,0). According to D`Alambert`s formula, u(x,t)=[f(x+t)+f(x-t)]/2 + 0.5∫g(s)ds (from x-t to x+t) so, u(0,t)=[f(t)+f(-t)]/2 + 0.5∫g(s)ds (from -t to t) f is odd, and so is...

Calculus of variations problem. I want to make stationary the integral of (1+yy')^2 dx from 0 to 1. I know what the Euler-Lagrange differential equation turns out to be, but how do I interpret the limits of integration as initial conditions for the diff eq? also, can i use laplace transforms to...

Hi, Assume the following action: \int d^4 x L[\phi,A]+ \int d^4 x A_{\mu} (x) J^{\mu}(x) What are the conditions on the form of action to have space/time translational invariance for a two point function: \left\langle J_{\mu}(x) J_{\nu}(y) \right\rangle = G_{\mu \nu}(x-y)...

Hello I have a question about coupled oscillators and what initial conditions affect what constants of integration. In the book I have, A.P. French Vibrations and Waves, the guesses at solutions are chosen at random and sometimes do include a phase shift, while sometimes they dont. For...

I am sometimes just not sure how to go about solving magnetics problems and applying the right boundary conditions. I was hoping for a little advice. For example in an infinitely long cylinder (along z-axis) with radius a, and a permanent magnetization given by: \vec{M} =...

Homework Statement I'm told these are (1) f(x) is a periodic function; (2) f(x) has only a finite number of finite discontinuities; (3) f(x) has only a finite number of extrem values, and I've got a function 1/(3-x) which I'm asked to give reasons why it doesn't satisfy the...

Homework Statement A sphere under uniform rotation R, in a simple shear flow, given at infinity by ui = G(x2 + c)deltai1 The centre of sphere is fixed at x2 Boundary conditions are ui = EijkRjxk on sphere, and ui = G(x2 + c) at...

Homework Statement Find the solution of the equation v''- 4v'+5v=0,such that v=-1 and v'=1 when x=pi=3.14159Homework Equations ... The Attempt at a Solution I treat it as a polynomial=>r^2+4r+5=0 =>delta=-4=>r1=2+2i and r2=2-2i v=e^[x+2](A*cos[2]+B*i*sin[2]) v=-1=e^[pi+2](A*cos[2]+B*i*sin[2])...

Boundary conditions & time domain electromagnetic waves: does classical model fit? Consider two propagating media: a lossy dielectric medium and a lossless dielectric medium. Thus, the interface that separates them has two tangential components of electric field, one for each medium. One of...

I don't seem to grasp the meaning of boundary conditions for Laplace's equation. Consider the Lagendre expansion of the potential at x due to a unit charge 1/|x-x'|, where x' is the position of the unit point charge. To do the expansion, we need to consider a volume in space where the...

What is the mechanism that results in formic acid quickly converting to CO2. I know this happens under basic conditions so I'm assuming the first step is forming the formate ion.

When solving Schrodinger's eqn for a quantum ring, what would be the boundary conditions? The solution (polar) should be Ψ(Φ) = A exp(ikΦ) + B exp(-ikΦ) And I believe the boundary conditions are Ψ(0) = Ψ(2pi) Ψ(0) = A + B Ψ(2pi) = A exp(ik*2π) + B exp(ik*2π) and I suppose I can...

If a PDE has no boundary conditions specified, how does one go about providing a solution--even if this is a general solution? I'm stuck looking at the separation of variables and other methods which all seem to heavily rely on those boundary conditions and initial conditions. If anyone...

Hi, Sean Carroll talks about energy conditions in ch4 of his GR book. From what I understand we want to impose co-ordinate invariant restrictions so we need to form a scalar from the energy momentum tensor, which is done by just arbitrarily contracting with timelike/null vectors (why not...

Hello, everybody! During the whole of my undergraduate study of physics, this one thing always bothered me. It concerns the interplay of conserved quantities, symmetries, Noether's theorem and initial conditions. For a system of N degrees of freedom, governed by the usual Newton's laws...

Homework Statement Find v(t) across a cap. in a series rlc circuit with no driving force (initial v across cap: 24V) Homework Equations from the values of the components, \alpha > \omega_0, the circuit is overdamped, and the following equation can be used: v(t) =A_1 e^{s_1 t} + A_2...

How do you specify, in mathematical notation, that a condition is true for all cases? For example, I want to say that t=5 for every value of n. Basically like \lim_{n\to\infty}{t=5}, but instead for every value of n, not just as n approaches infinity. Also, how to specify the range of n...

What weather conditions are needed to produce fine snow rather than the big flaky wet snow. .

Short version: How accurate is this paper: http://www.wbabin.net/ajay/sharma17.pdf Long version: Hello! Physics is not my field of study, but here's my situation: I was having a religious debate and we were discussing the origin of the universe. I decided to quote Lawrence Krauss (a physicist)...

Klein–Gordon equation with time dependent boundary conditions. Suppose we look for solutions to the Klein–Gordon equation with the following time dependent boundary conditions, psi(r,theta,phi,t) = 0 zero at infinity psi(on surface of small ball, B_1,t) = C*exp[i*omega*t] psi(on...

Say we consider the time independent Klein–Gordon equation, see: http://en.wikipedia.org/wiki/Klein%E2%80%93Gordon_equation Lets impose the following boundary conditions, the function is zero at infinity and on some small ball of radius R centered on some origin the function is some...

Homework Statement I've been given equations that have derivatives as initial conditions, rather than things like u(0,t)=u(L,t)=0 Things like this: http://img444.imageshack.us/img444/5082/mathu.th.jpg Uploaded with ImageShack.us Homework Equations The Attempt at a...

Homework Statement Consider a discrete-time system, driven by: x[k+1] = Ax[k] for non-zero inital conditions x[0] a) write the closed-form solution of x[k]. If the system is asymptotically stable how should x(k) behave? b) what is condition for asymptotic stability? Homework Equations...

Homework Statement I am trying to solve the Laplacian Equation with mixed boundary conditions on a rectangular square that is 1m x 1m. Homework Equations \nabla2T=0 .....T=500K ....________ ....|@@@@| T=500K...|@@@@|...T=500K ....|@@@@| ....|______.| ....Convection ....dT...

Homework Statement If 18.75 mol of helium gas is at 10.0C and a gauge pressure of 0.035atm, calculate a) the volume of the helium gas under these conditions. b) calculate the temp if the gas is compressed to half the voume at a gauge pressure of 1.00atm. Homework Equations PV=nRT...

I understand \vec J_{free} only exist on boundary surface of perfect conductors. Copper is close enough and have surface current. Also copper is paramagnetic material which implies \mu_{cu} = \mu_0 or very very close. In order to find the exact angle of the of the magnetic field inside the...

Homework Statement Hi Can anyone help on this. The questions is as follows: In a double slits experiment using red light, a fringe pattern is observed on a screen at a fixed distance from the double slits. How would the finge pattern change if: a) The screen is moved closer to the...

In another thread, https://www.physicsforums.com/showpost.php?p=2973770&postcount=45, some questions came up about what the conditions are for a spacetime to admit flat spatial slices, and for a spacetime to have a time-independent "scale factor" (see definition below). These questions...