Conditions Definition and 1000 Threads

An electric vehicle of mass ##m## moves along the ##0-x## axis according to the law: m\frac{\mathrm{d} v(t)}{\mathrm{d} t} = T(t)-\mu mg-kv(t)^{2} (ma = Thrust - Friction - Drag) It is known that: P(t) = T(t)v(t) (Power = Thrust * Speed) Find the thrust ##T(t)## in such a way that the...

I understand that this has been answered, but I can't follow it. My apologies, physics is a realm I want to understand but it doesn't come naturally and I have no High school physics background just 1st yr Engineering physics. (passed with supps.) A particle is projected vertically upward in a...

For a physical singularity I think it is sufficient that anyone scalar quantity blows up, Why is it not a necessary condition that all blow up? For a curvature singularity am I correct in thinking that it is a sufficient condition to find a coordinate system in which the metric coefficient no...

Homework Statement \[/B] The question I want to ask is how do you relate conditions such as To* and To,1 and To,2, where To,1 and To,2 are the stagnation conditions at the entrance and exit. This is the problem I was doing. Standard atmospheric air is drawn steadily through an isentropic...

Homework Statement A mass-spring system with a natural frequency of 3.6 Hz is started in motion with an initial displacement from equilibrium of 6.1 cm and an initial velocity of 0.7 m/s. What is the value of ϕ? (Question aside: Finding the amplitude of the resulting function?) Homework...

What are the sufficient / necessary conditions for a metric to be stationary / static? - If the metric components are independent of time in some coordinate system , is this sufficient for stationary? - I've read for static if a time-like killing vector is orthogonal to a family of...

I'm trying to solve the following equation (even if I'm not sure if it's well posed) \partial_{x} \, y(x) + a(x)\, y(x) = \delta(x) with ##\quad \lim_{x \rightarrow \pm \infty}y(x) = 0## It would be a classical first order ODE If it were not for the boundary conditions and the Dirac...

Homework Statement What three conditions or ingredients are necessary for polymerization to occur? The Attempt at a Solution I know that carbon is necessary because it is the only element that can form complex molecules readily in nature. But when i try to research this problem it seems there...

Hey! :o A round membrane in space, is over the space $x^2+y^2 \leq a^2$. The maximum coordinate $z$ of a point of the membrane is $b$. We suppose that $(x, y, z)$ is a point of the inclined membrane. Show that the respective point $(r , \theta , z)$ in cylindrical coordinates satisfies...

Homework Statement See the figure below. A thin pipe, open at both ends, with length 0.400 m and 1.0 cm diameter is placed vertically in a cylindrical bucket so that it nearly touches the flat bottom of the bucket, which has an area of 0.100 m2 . The air temperature is 22o C. Water is slowly...

It is said that the metric tensor in GR is generally covariant and obey diffeomorphism invariance.. but the signature, boundary conditions and topology are not. What would be GR like if these 3 obey GC and DI too? Is it possible?

Homework Statement The flat piece is between 2 walls and is pushed eccentrically by force F. what should be the relation between the width x and the height y in order to achieve self locking (that the piece won't go down)? Homework Equations Friction Force: f=μN Balance of moments: F1L1=F2L2...

1 qubit can be expressed as 1/2(I + n.σ). where n = (n_x,n_y,n_z) is a 3D vector, with size <=1. Hence the condition is that the sum of squares of the variables must be 1 or less. In the general expression of multi-qubit systems, we tensor product these individual qubits and also add the...

Hi, Let's say I consider the real numbers and some function real function f, nowhere zero, and positive. My question is, what are the conditions on f for dx/f(x) to be a valid measure on this space? (I have to consider a Hilbert space L^2(R, dx/f(x)) with scalar product a.b = \int a^*(x)...

Hello, Mathematica is very new to me. Please help. n=1,2,3...,10 and stepsize between n(2)-n(1)=0.1 It is periodic. I mean n(11)=n(1). i have a initial function which depends on n and i want to solve this equation by NDsolve like that u[n, t = 0] == 1/(2*n + 1) Do [ u[n, 0], {n, 0, 10...

I have this question on outer measure from Richard Bass' book, supposed to be an introductory but I am lost: Prove that ##\mu^*## is an outer measure, given a measure space ##(X, \mathcal A, \mu)## and define ##\mu^*(A) = \inf \{\mu(B) \mid A \subset B, B \in \mathcal A\}## for all subsets...

Hello, I am taking an introductory class on non relativistic classical field theory and right now we are doing the more mathematical aspect of things right now. The types of differential equations in the function ##f(\vec{r},t)## that are considered in this course are linear in the following...

Is there a physical explanation for why when given a differential equation with spatial derivative of spatial order 2m the maximum order of the essential (displacement) boundary condition is m, and the maximum order of the natural (force) boundary condition is 2m-1 for example, the equaiton...

Hi, I've been doing some work on the finite element method. I have been able to calculate the stiffness matrix and load vector and apply both homogeneous and inhomogeneous Dirichlet conditions but am stuck on calculating the Neumann conditions. I have the definition of it as...

The question asks to solve for delta S surroundings at 298K when 2.49 moles of H2S (g) react. reaction: 2H2S (g) + 3O2 (g)= 2H2O (g) + 2SO2 (g) My problem is that I don't know how to calculate delta S surroundings. So to solve the problem I'm making the assumption that -Delta S surroundings =...

I recently solved a differential equation with the solution: f(x) = Aexp(ikx) + Bexp(-ikx) with the periodic boundary condition f(x+L)=f(x). This condition leads to: Aexp(ikx)exp(ikL) + Bexp(-ikx)exp(-ikL) = Aexp(ikx) + Bexp(-ikx) (1) Now the way I figured out the constants A and B was that...

Homework Statement Given the following circuit: [/B] Where R=C=L=1, with Vs(t) = sin(wt) and complete response Vo(t)=A*sin(wt + π/4). Homework Equations Determine the init. cond. of the capacitor voltage Vc and Inductor current Ic at t = 0. Also, find A and w.[/B]The Attempt at a Solution...

I am working on a PDE problem like this: Consider the wave equation with homogeneous Neumann-Dirichlet boundary conditions: ##\begin{align} u_{tt} &= c^2U_{xx}, &&0<x<\mathscr l, t > 0\\ u_x(0, t) &=u(\mathscr l, t) = 0, &&t > 0\\ u(x, 0) &=f(x), &&0<x< \mathscr l\\ u_t(x, 0) &=g(x), &&0<x<...

If I am trying to derive the energy eigenvalues and quantum numbers for the hydrogen atom (basic hydrogen-1), I obviously need to solve the hydrogen Schrodinger equation and account for some boundary conditions. However, no website ever gives me the boundary conditions. What would be the...

Hello guys, actually I'am working on a model to describe the creep-behaviour of a concrete specimen. This model is based on a 'generalized maxwell-chain'. I attached a picture, where you can see it: The acting load is the tension \sigma, while E_0 and E_1 are the stiffnesses of the...

1. Homework Statement Establish the condition required to make the current through Ze in Figure 1 zero (i.e. For the voltage Vx to equal Vy). Homework EquationsThe Attempt at a Solution I'm not sure if I'm on the right line here, hopefully someone can point me in the right direction if it's...

when a function doesn't satisfy dirichlet condition, why do we not care and go ahead finding the Fourier transform anyway? What is the use? Eg: unit impulse, dirac delta function, etc. don't statisfy the dirichlet conditions but its like dirichlet conditions arent really conditions?

In my university lecture notes, maxwell's equations in matter are written in the following format: \oint \vec E d \vec L = 0 \oint \vec D \vec dS = \int_V P_f (\vec r)dV \oint_S \vec B d \vec S = 0 \oint_L \vec H \vec dL = \int_S P_f \vec J_f d\vec S I am new to electromagnetism...

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...