Conditions Definition and 978 Threads

If one could drill a hole to the centre of the earth, presumably the gravitational force on the body would decrease as one passed down this theoretical hole until one could float freely right at the centre where the gravitational force is equal and opposite in all directions with a net effect of...

boundary conditions for pressurized cylinder in fem?

In an Isothermic and reversible condition why is DH=0? (D=delta) I can understand that DU=0 but DH? but why would DH not change? DH should also =0 if it was an adiabtic and irreversible condition? since DH=dq/T -> as long as there is no heat transfer DH=0? Since it's reversible would...

Homework Statement Find the integral of cot^6(x) without using the reduction formula. Homework Equations Potentially any trig identities involving the cotangent The Attempt at a Solution I tried splitting up the cot^6 in various ways such as cot^4*cot^2 and cot^2*cot^2*cot*2 but...

Homework Statement R = { (a+1, b 0) | a, b are real numbers} S = { (a+b, b, c) | a, b, c are real numbers) T = R intersect S I have shown that R and S are subspaces of R^3. Now I have to determine whether T is also a subspace of R^3. The answer provided is that yes, T is also a...

For part of my lab write up on pendulum motion, my professor wanted us to find out why a pendulum was not a simple harmonic oscillator, and under what conditions it was. He also wanted to show this mathematically. So far what I have is that if there is no damping(friction?) and if the the...

Its been argued that inflation needs the initial conditions to be finely tuned: eg: http://en.wikipedia.org/wiki/Inflation_(cosmology)#Fine-tuning_problem does this paper resolve this problem...

What are the conditions for some matrix to be a density matrix ? I know of these conditions: 1.) \rho=\rho^{2} 2.) Tr(\rho)=1 (for pure state) Is this all ?

Homework Statement Solve: \frac{\partial H}{\partial t} = -4\kappa H^{2} With initial condition: H(0) = 1/L^{2} To find: H(t) = \frac{1}{4\kappa t + L^{2}} 2. The attempt at a solution I tried using Taylor series expansion such that: H(t)\approx H(0)+t\frac{\partial...

Can one say a body which has the conditions above mentioned be in thermal equilibrium? How does one apply the definition of temperature equilibrium to this situation? (Physically I think it's possible for a body to be in this situation if some part of it receives heat from the outside and...

Ey guys, this is a problem from my Mech Eng Dynamcis of Machine class I believe i have the solution already since I've spoken to the lecture'r/tutors who run the subject but would like further clarification just incase I've done something completely wrong. This is the problem The...

Hello Everyone, Is there a list online somewhere of which variable values are 0 and why (conceptually), based on initial conditions? Like I know that for a system at constant volume, w=0. I am looking for a list for the other effects like isothermal, adiabatic, what does pressure= if there is...

Homework Statement http://img843.imageshack.us/img843/3515/11193469.png Homework Equations The Attempt at a Solution [PLAIN][PLAIN]http://img801.imageshack.us/img801/4829/scan0001i.jpg An upload of my attempt to solve the problem. Not sure to interpret the results. A = B...

Homework Statement http://img685.imageshack.us/img685/5585/63862334.png Homework Equations -The Attempt at a Solution y_1(0,t)=y_2(0,t) \longrightarrow 1+\frac{B}{A}e^{2i \omega t} = \frac{C}{A} y_1_x(0,t)=y_2_x(0,t) \longrightarrow 1+\frac{B}{A}e^{2i \omega t} =\frac{k_2}{k_1}...

Hello, I am facing a diffusion equation.. \frac{du(x,t)}{dt} = D \frac{d^2u}{dx^2} .. with slightly exotic boundary conditions: u(0,t) = 0 \frac{d^2u(a,t)}{dx^2}+ \alpha \frac{du(a,t)}{dx} = 0 I expected the solution to be relatively easy to find, since separation of variables quickly...

Homework Statement Under what conditions are the following true? a) |\mathbf{a}\cdot \mathbf{b}| =|\mathbf{a}||\mathbf{b}| b) (\mathbf{a} + \mathbf{b}) \cdot (\mathbf{a} - \mathbf{b}) = |\mathbf{a}|^2 - |\mathbf{b}|^2 Homework Equations None. The Attempt at a Solution a) I...

I am sure to those of you who know GR this will be a simplistic question. I can only hope there will be a simplistic and definitive answer :-) Assume a dust cloud of radius=5 and a mass =mc ANother equivalent mass of condenced matter md=mc with a radius=1 What would be the...

Homework Statement Find the voltage across the capacitors in the circuit given under DC conditions.Homework Equations V=IRThe Attempt at a Solution The solution is already given (the picture attached was obtained from the solution manual. I have a difficult time understanding how they arrived...

Homework Statement determine the conditions on a b c and d such that the matrix a b c d will be row equivalent to the given matrix: 1 0 0 1 and 1 0 0 0 Homework Equations The Attempt at a Solution I have no idea what its asking, I mean on no. 1: a = 1 b = 0 c...

Homework Statement d^2T/dx^2 + S^2*T+B=0 Boundary Conditions: dT/dx=0 @ x=0 T=T_2 @ x=L Homework Equations The Attempt at a Solution I think you either have to make some type of substitution or find the roots and do it that way. P.S. This is assignment is a review of diff...

Homework Statement d^2T/dx^2+S/K=0 Boundary Conditions T=Tsub1 @ x=0 and T=Tsub2 @ x=L Homework Equations The Attempt at a Solution d^2T/dx^2 = -(S/K) <--- intergrate to get dT=-(S/K)dx+ C1 <--- intergrate to get T=(-S/K)x+c1+c2 apply both boundary conditions to get...

hi all, I am trying to solve this PDE by separation of variables, it goes like this: \frac{\partial u}{\partial t} = \alpha\frac{\partial ^2 u}{\partial z^2} for 0\leq z\leq infty the initial condition I have is: t=0; u = uo. the boundary condtions: z=0; \frac{\partial...

How to derive boundary conditions for interfaces between ferromagnetic material and air? Please see the attached figure. Any hints will be greatly appreciated!

Hi, these days I have been trying to understand the essentials of the so-called topological insulators (TBI), such as Bi2Te3, which seem very hot in current research. As i understand, these materials should possesses at the same time gapped bulk bands but gapless surface bands, and spin-orbit...

Homework Statement For a particular sample of monatomic gas, the rate of change of pressure with volume under isothermal conditions is -2 x 10^7 Pa m^-3. Calculate the rate of change under adiabatic conditions. Homework Equations isothermal: dP/dV = -2 x 10^7 Q = nRTln(Vf/Vi)...

Hi folks, I was wondering how to code a Maxwell solver for a problem with time-dependent boundary conditions. This is not my homework, but I love programming and would like to implement what I learned in my physics undergrad course to get a better understanding. More precisely, if I have an...

Let me see if I can line out my question a little better to hopefully get some sort of input. I am trying to understand where a type of boundary condition approx. called stiff spring BCs. I have, among a couple of other examples, an example comsol "dialysis" model that uses it. I have been...

Hey! I'm an international student - thinking of pursuing an Aerospace Engg. Bachelors' degree in US. What are the job opportunities in US in this field for international students? I've heard that US companies that offer Aerospace jobs for non-American citizens are quite rare. Is this true...

What are the minimal conditions to have a non-relativistic quantum theory like Schrödinger theory?

Are there general boundary conditions for the wave equation PDE at infinity? If there is, could someone suggest a book/monograph that deals with these boundary conditions? More specifically, if we have the following wave equation: \[ \nabla ^2 p = A\frac{{\partial ^2 p}}{{\partial t^2...

Homework Statement Consider the following cantilevered beam: The beam has a mass of m = 25 kg and is 2.2 meters long. The suspended block has a mass M = 280 kg and the supporting cable makes an angle of 30 degrees with the beam. Determine the force that the wall exerts on the beam at the...

Equations of motion! the conditions pleasezz What are the conditions that enable the equations of motion to be used except from the fact that acceleration must be uniform ?

The total energy of a particle is given by: E_{tot} = 2 \dot{x}^{2} - cos(\frac{1}{2} \pi x) and I'm told that the particle passed through the point x=1 [m] with a velocity of \vec{v}=-\frac{1}{2} \hat{x} [m/sec]. I'm required to find the maximum velocity of the particle during its motion...

The alternating series test contains two conditions for convergence. The first condition is that the nth term (extracting the power of -1) is always positive and monotonically decreasing. The second is that the limit of that nth term goes to 0 as n goes to infinity. I've seen a proof...

Homework Statement I'm getting through a paper and have a few things I can't wrap my head around. 1. In defining the boundary conditions for a membrane (a function of vector 'r'), the author claims that for a small displacement (u) and a boundary movement (f), the boundary condition can be...

I have this, probably quite simple, problem. In the RNS superstring, when varying the action, we obtain in general a term \int d\tau [X'_{\mu}\delta X^{\mu}|_{\sigma=\pi}-X'_{\mu}\delta X^{\mu}|_{\sigma=0} + (\psi_+ \delta \psi_+ - \psi_- \delta \psi_-)|_{\sigma=\pi}-(\psi_+ \delta \psi_+ -...

Hello, what are the conditions that a continuous even function f must satisfy in order to have \int_{-\infty}^{+\infty}f(x)dx < \infty ?

Homework Statement (a) A siren emits a frequency of 900 Hz. Wind is blowing at a steady speed of 15.0 ms-1. The speed of sound in calm air is 343 ms-1. What is the frequency heard by someone approaching at 15.0 ms¹, (i) when the wind blows from the person to the siren, (ii) when the wind...

Hallo Every one, Homework Statement y(x,t)=sin(x)cos(ct)+(1/c)cos(x)sin(ct) Boundary Condition: y(0,t)=y(2pi,t)=(1/c)sin(ct) fot t>0 Initial Condition : y(x,0)=sin(x),( partial y / Partial t ) (x,0) = cos(x) for 0<x<2pi show that y(x,t)=sin(x)cos(ct)+(1/c)cos(x)sin(ct)...

Homework Statement So using the D'Alembert solution, I know the solution of the wave equation is of the form: y(x,t) = f(x-ct) + g(x+ct) I'm told that at t=0 the displacement of an infinitely long string is defined as y(x,t) = sin (pi x/a) in the range -a<= x <= a and y =0...

Hello everybody, I've been puzzling over something (quite simple I assume). Take S^1. Now consider the action of a Z_2 which takes x to -x, where x is a natural coordinate on the cylinder ( -1< x <1). Now we mod out by this action. The new space is an orbifold: smooth except at x=0. It...

Consider an aluminum cylindrical rod 1.0 meter long connecting two heat reservoirs. Both of the reservoirs are maintained at T=300 K. Initially, the cylinder is at 300 K, except for the center point of the cylinder which has been rapidly irradiated to a temperature of 600 K. There is no heat...

1. I have a rod of length 4,cross section 1 and thermal conductivity 1.Nothing is mentioned about the end at the origin x=0, but at the opposite end x=4, the rod is radiating heat energy at twice the difference between the temperature of that end and the air temperature of 23 celcius. Find the...

Homework Statement A hot air balloon has a volume of 2000m^3, and air is always at atmospheric pressure due to large opening. What is the mass of the air if the temp is 120*c. Assume a molecular weight of 28.8g/mol for the air) Homework Equations PV=nrt The Attempt at a Solution...

One of the conditions for oscillation is that the (regenerative) feedback loop must provide a 180 degree phase shift. This is due to the fact that, for a regenerative effect, the signal must undergo n*360 degrees phase shift: 180 from the amplifier and another 180 from the feedback network...

Homework Statement The steady state temperature distribution, T(x,y), in a flat metal sheet obeys the partial differential equation: \frac{\partial^2{T}}{\partial{x}^2}+{\frac{\partial^2{T}}{\partial{y}^2}}=0 Separate the variables and find T everywhere on a square flat plate of sides S with...

Homework Statement Attached question Homework Equations The Attempt at a Solution I tried rearranging S1 for Z then using Maple to plot it, which gave me a cone extending from the point z=1. For S2, would I have to plot it twice? once for <1 and once for =1? I have no...

Hello everybody, This is just a general question I have, and probably the title did a very bad job at explaining it, so here it goes. Is there any material that is available, or even if its still in research (as long as you have some links), that bends/flexes or contracts in certain...

Homework Statement Let n be a nonzero integer and let a be an integer with gcd(a, n) = 1. We have two equivalent conditions which characterize primitive roots: (i) a is primitive modulo n if the order of a is \phi(n). (ii) a is primitive modulo n if for every element b with gcd(b, n) = 1 we...

Homework Statement A surface at z = 0 is held at potential V (x, y) = V0 cos(qx) sin(qy). Find the potential in the region z > 0. Homework Equations Laplace's equation in Cartesian coordinates The Attempt at a Solution I wrote at least a page of my past 2 attempts at a solution...