Conditions Definition and 978 Threads

What conditions are necessary if it's to be possible to make a Penrose diagram for a 3+1-dimensional spacetime? It seems that rotational symmetry is not necessary, since people draw Penrose diagrams for Kerr black holes. If you don't have rotational symmetry, how do you know what 2-surface is...

Homework Statement I'm trying to plot the steady state concentration of yA vs. x, yB vs x and yu vs x using centered finite difference method. Homework Equations The Attempt at a Solution τ represents the dimensionless time variable, so steady state would mean that the left hand side of...

Homework Statement Example Question: an electron with mass m is confined in a thin wire, with periodic boundary conditions applied in the x direction and harmonic potentials in the y and z direction. Write an expression for the wave functions in the ground state. Write down all the energy eigen...

As i understand, the purpose of laplaces/poissons equation is to recast the question from a geometrical one to a differential equation. im trying to figure out what are the appropriate boundary conditions for poissons equation: http://www.sciweavers.org/upload/Tex2Img_1418842096/render.png...

Homework Statement Let a slab 0 \le x \le c be subject to surface heat transfer, according to Newtons's law of cooling, at its faces x = 0 and x = c , the furface conductance H being the same on each face. Show that if the medium x\le0 has temperature zero and medium x=c has the...

I am currently reading Zwiebach and intend on reading Becker and Polchonski afterwoods. In chapter 4 he slves a partial differential equation with the Dirichlet and Neumann BC. My question is what the difference is between the two BC.(BC=Boundary conditions). Thanks for any help.

Hi All, This is my first post on these forums. I am not looking for a solution to this problem but more interested in seeing if someone can point me to a resource that can explain the following. Thanks in advance for any help. I'm trying to solve a pde which gives a temperature profile. We...

I have the following 2D Poisson equation (which can also be transformed to Laplace) defined on a triangular region (refer to plot): \begin{equation} \frac{\partial^{2}u}{\partial x^{2}}+\frac{\partial^{2}u}{\partial y^{2}}=C\end{equation} with the following three boundary conditions...

Hi! (Smile) Let $B$ be a nonempty set. Does it stand that $\bigcap \mathcal{P}B=\mathcal{P} \bigcap B$? Is the set $B \times B$ always a function? If not, what condition should $B$ satisfy, so that the relation $B \times B$ is a function? Let $x \in \bigcap \mathcal{P}B$. Then $\forall b \in...

An object has initial speed u and acceleration a. After traveling a distance s, its final speed is v. Which of the following includes the two conditions necessary for the equation, v^2 = u^2 +2as, to apply? I know the answer is a has constant magnitude and a has constant direction, but I am...

Homework Statement I am trying to calculate the transmission and reflection coefficients for rectangular finite potential barrier between (-a, a) for a particle of mass m with energy equal to the height of the barrier (E = V0 > 0). Homework Equations...

Dear experts, I´m trying to model in ANSYS Mechanical (v14.5) the linear buckling behavior of a cylinder made of BEAM4 elements under combined loading (axial compression and bending moment) applied at the ends. How should I set up the boundary conditions of a cylinder to keep rigid the ends...

Hi, I want to know the enthalpy of formation of Ga2O3 and Ga2O at low pressure (ultra high vacuum) and high temperature. Temperature seems easy, but I'm not sure how to get the enthalpy values for low pressures. Does anyone know if there are books with enthalpy - pressure diagrams of these...

Homework Statement y'' + 4y = t2 + 6et; y(0) = 0; y'(0) = 5 Homework Equations The Attempt at a Solution So, getting the general solution, we have r2 + 4 = 0, so r = +/- 2i So the general solution is yc = sin(2t) + cos(2t) I then used the method of undetermined coefficients to figure that...

The following is a list of various quantities (molar enthalpy changes) found in a typical Chemistry course: Atomization Enthalpy Formation Enthalpy Combustion Enthalpy Neutralization Enthalpy Solution Enthalpy Hydration Enthalpy Ionization Energy Electron Affinity Lattice Energy Bond Energy...

Dear friends, I read in Kolmogorov-Fomin's that the following property of measurable real or complex valued functions ##\varphi,f## defined on measure space ##X##, proven in the text for ##\mu(X)<\infty## only, is also valid if ##X=\bigcup_n X_n## is not of finite measure, but it is the union of...

The question is: There is only one integer that can be the to this problem.It is a multiple of five,three,seven.No digit occurs ore than once.Can you find the number? The digit in the tens place is a square number.The digit in the hundreds place is a cube.The digit in the hundreds...

Hello! (Wave) I have to solve the recurrence relation $$T(n)=\left\{\begin{matrix} 3T\left (\frac{n}{4} \right)+n & , n>1\\ 1 &, n=1 \end{matrix}\right.$$ and prove by induction that the solution I found is right. I found that the solution of the recurrence relation is $T(n)=O(n)$. I...

Hello! (Smile) When we have a congruence $x^2 \equiv a \pmod {p^n}, n=1,2,3, \dots$ , and we know a solution $\pmod {p^n}$, then we also know a solution $\pmod {p^l}, l<n$. For example, we know that for $n=3$, the congruence $\displaystyle{ x^2 \equiv 2 \pmod { 7^3}}$ has the solution $$x_0...

All, I recently completed a project where transient thermal boundary conditions are rotated around a cylinder for a general number of revolutions. In reality, the cylinder rotated but it was much easier to rotate the thermal conditions around the model in the ANSYS environment. I used 360...

Is anyone aware of how to numerically solve the (1D) SE with periodic boundary conditions?

Homework Statement I have a hollow, grounded, conducting sphere of radius R, inside of which is a point charge q lying distance a from the center, such that a<R. The problem claims, "There are no other charges besides q and what is needed on the sphere to satisfy the boundary condition". I...

For a project in my 3rd year hydraulics course we have to design a water distribution network for a residential area using EPANET and optimizing it using GAWUP (GANEO). I have the entire network set up with all the peak flow demands set for each of the required nodes. Using GANEO I can easily...

Homework Statement I have an infinite plate of which two electrodes are attached at a distance ##2a## and the electric potential between them is ##U##. Now I have to find a function ##\phi (x,y)## that satisfies Laplace's equation ##\nabla ^2 \phi =0## and is equal to ##0## at all possible...

Hi, I am wondering as to how to define the boundary condition for a shape in a unit cell. Just imagine that the shape is the hole for the unit cell. Hence, for a constant thickness on the untextured boundary, thickness is, let's say C, then for the circle, it's C+depth. For example for...

Hello, I was just after an explanation of how people get to this conclusion: Say you are looking at the Helmholtz equation in spherical co-ordinates. You use separation of variables, you solve for the polar and azimuthal components. Now you solve for the radial, you will find that...

Hi there Can anyone tell what is the meaning of boundary conditions for temperature distribution in a flowing viscous fluid in a pipe ? for example I need some one explane for me this: T = T1 at r = R, x<0 T = T0 at x = 0, r<R where T1 is a temperature of well and T0 is a temperature...

Hi everyone, first time post here. Sorry if this isn't the place to ask, but I'm looking to settle disagreement and thought someone here might have the knowledge to set me straight. This is a slightly off color question to start with, and my lack of expertise in any science is not helping the...

Hi all. Say we have a background inflaton field ##\varphi## and that we've integrated the background equation for ##\varphi##, ##H(\eta)##, and ##a(\eta)## up to the number of e-folds of inflation corresponding to ##\epsilon = 1## in the slow-roll parameter. We then wish to solve for the ##k##...

My A level Chemistry textbook defines Lattice Energy as "the enthalpy change when 1 mole of an ionic compound is formed from its gaseous ions under standard conditions"; a definition which I can't fully grasp because of the "standard conditions" part. How can gaseous ions exist under standard...

Hello, I do not know if this is the right place to post this question, but I believe it falls under algebra. Please redirect me if appropriate. Question: How can I show that $$P-QR^3<\frac{R^4}{C}$$ for $$C,P,Q,R > 0?$$ Thanks.

Homework Statement Let ##f## be an entire function such that there exist ##z_0,z_1 \in \mathbb C##, ##\mathbb R##-linearly independent, with ##f(z+z_0)=f(z)## and#f(z+z_1)=f(z)## for all ##z \in \mathbb C##. Show that ##f## is constant. The attempt at a solution From the hypothesis, I know...

Hello! This is my first post to this excellent forum! I would like some help with this exercise: u_{xx} (x,y) + u_{yy} (x,y) = 0, with 0 < x < 2 \pi , 0 < y < 4 \pi u_x (0,y) = 0, \, u_x(2 \pi, y) = 0, \, 0< y < 4 \pi u(x,0) = a \cos(2x), \, u(x, 4 \pi) = a \cos^3(x), \, 0<x<2\pi...

Hİ. How can we sure that the initial conditions , say, for a second-order linear equation must be unique which is also the uniqueness of the solution.

Hi, Can anybody help me withg the following problem: A rectangular plate with points starting from top left corner and going clockwise:: A B C D. Sides CD and DA are simply supported, and a point force F is applied anywhere on the surface. I am looking for the bending stress distribution...

Hi, there Today, a friend came to me and asked the following questions and they made me confused. If the source is strong, the light has to be considered as wave, and the double-slit interference (DSI) can be interpreted, and the conditions for the DSI is (1) same frequencies, (2) parallel...

I was wondering about Earth and it's gravity and I came up with these 2 questions... 1.) What would Earth's gravity be if the Earth stopped spining? 2.) What would Earth's gravity be if the Earth stopped spining and there was no other stars or planets that interfered with there gravity...

Homework Statement Find B and C such that \emptyset \in C B \in C B \subset C The Attempt at a Solution B=\emptyset C=\{B\} It just does not look right. Any feedback?

I usually see that Laplace transform is used a lot in circuit analysis. I am wondering why can we know for sure that the Laplace and its inverse transform always exists in these cases. Thank you.

hi pf! i was reading a sample problem in a text on ode's and came across a boundary condition that didnt really make sense to me. the physical scenario is: a liquid ##L## measured in moles/cubic meter (##mol / m^3##) is injected into a stream of water. ##L## is being injected at a rate...

If I have a grounded conducting material, then I know that $\phi=0$ inside this material, no matter what the electric configuration in the surrounding will be. Now I have a conducting material that is not grounded, then there will be (as long as I am dealing with static problems) no electric...

Homework Statement Part (a): List the boundary conditions Part (b): Show the relation for potential is: Part (c): Find Potential everywhere. Part (d): With a surface charge, where does the Electric field disappear? Homework Equations The Attempt at a Solution Part (a) Boundary conditions...

The Laplace of 1 is: $$\int_{0}^{\infty} 1 \exp(-st) dt = \left[ \frac{\exp(-st)}{-s} \right]_{0}^{\infty} = \frac{\exp(-s \infty) - \exp(-s 0)}{-s} = \frac{0 - 1}{-s} = \frac{1}{s}$$ It's result known, however, for this be true is assumed that s>0, because 0 = exp(-∞) = exp(-s∞). But we...

I don't really understand boundary conditions and I've been trying to research it for ages now but to no real avail. I understand what boundary conditions are, I think. You need them along with the initial conditions of a wire/string in order to describe the shape of motion of the string. I...

Homework Statement Let a,b,c be distinct real numbers satisfying a^3+b^3+6abc = 8c^3 then which of the following may be correct? A) a,c,b are in Arithmetic Progression B) a,c,b are in Harmonic Progression C) a+bω-2cω^2 =0 D) a+bω^2-2cω=0 The Attempt at a Solution I could prove...

Homework Statement A tight string lies along the positive x-axis when unperturbed. Its displacement from the x-axis is denoted by y(x, t). It is attached to a boundary at x = 0. The condition at the boundary is y+\alpha \frac{\partial y}{\partial x} =0 where \alpha is a constant. Write the...

Homework Statement I have been given a complex function I have been given a complex function \widetilde{U}(x,t)=X(x)e(i\omega t) Where X(x) may be complex I have also been told that it obeys the heat equation...

Questions about Green's functions for ODEs, jump conditions I'm having a hard time understanding Green's functions which have been introduced quite early on in the course, and which I think hasn't been well motivated. I can't find any other resource which explains this at this level (have only...

Homework Statement "The lift gradient of a wing under actual flight conditions is 0.1179 per degree. Calculate the lift-drag ratio of the wing with an angle of attak of 3 degrees?" Given is: altitude=5000 m velocity=225 m/s wing area S=149 m2 wing span b=34.5 m span efficiency factor e1=0.82...

Homework Statement Hello, I have to demonstrate that multiplying a differential equation: -d/dx[a(x)*d/dx{u(x)}]=f(x), 0<x<1 subject to u(0)=0 and u(1)=0. by some function v(x) and integrating over an interval [0,1], I get a new equation that can be used in an optimisation problem, that...