Conditions Definition and 978 Threads

I am trying to calculate the ##\beta## functions of the massless pseudoscalar Yukawa theory, following Peskin & Schroeder, chapter 12.2. The Lagrangian is ##{L}=\frac{1}{2}(\partial_\mu \phi)^2-\frac{\lambda}{4!}\phi^4+\bar{\psi}(i\gamma^\mu \partial_\mu)\psi-ig\bar{\psi}\gamma^5\psi\phi.##...

The FRW cosmology is a solution of the FRW that can be foliated into 3D isotropic and homogeneous slices. This foliation is implemented mathematically first by the use of a not generally covariant coordinate condition https://en.wikipedia.org/wiki/Coordinate_conditions#Synchronous_coordinates ...

ΔG=ΔG°+RTlnQ are for reactions that are not under standard conditions. What does it mean under non-standard conditions for the ΔG? And what is the Q in this case? Is it Qp where it is based on the partial pressure of the gas or Qc which is based on the concentration? Thanks

Hello, I am working on a hydraulic cylinder application that will lift some weight that is not aligned with the axis of the cylinder. Take a look at the picture and imagine that instead of ropes there is a hydraulic cylinder fixed to the beam doing the lifting. The load creates moment since it...

Hello! I'm currently making my way through the book "Quantum Field Theory of Point Particles and Strings" and on page 13 they talk are talking about quantization of the classical versions momentum and position. The first part to quantizing these is turning them into operators. The books goes on...

Homework Statement Write down the geodesic equation. For ##x^0 = c\tau## and ##x^i = constant##, find the condition on the christoffel symbols ##\Gamma^\mu~_{\alpha \beta}##. Show these conditions always work when the metric is of the form ##ds^2 = -c^2dt^2 +g_{ij}dx^idx^j##.Homework...

I am trying to set up the mass matrix for a 1D system which I want to solve using finite elements. So the mass matrix is defined as M = \int{NN^T}dL, where N is the finite element linear basis functions. I use hat functions. Say I have 10 elements, corresponding to 11 nodes running from -5...

I read about the wheeler experiment been done in Australia. But one thing I don't understand. If the particle (but let's use a photon) goes through the two slits (or one) and the screen is removed after it already went through, how is it measured? Does it stop after the measurement? My...

Hi! When we model bloch-waves in a solid we assume that there exist some kind of periodic boundary conditions such that the wave function is periodic. In 1D, ##\psi(x)## repeats itself for every ##L##, ##\psi(x) = \psi(x+L)##, such as here: OK, fine, we get pretty wave solutions if we assume...

Question about conditions for conservative field In common textbooks' discussions about conservative vector field. There is always two assumptions about the region concerned, namely the region is simply connected and open. Usually in textbooks there is not much explanations on why these...

we have that Ht1 (x,y,z) - Ht2 (x,y,z) = Js and for the special case Ht1 (x,y,z) - Ht2 (x,y,z) = 0 where there is no surface current. At a boundary with Js =0, which for simplicity let's asume is at at x = a, then knowing that Ht1 and Ht2 are the magnetic fields to the left and right of the...

Let M = {x1, x2, x3, ...} U {p} be a perfect metric space. Let f be continuous, taking M to M with f(xn) = xn+1 and f(p) = p. I would like to know if this dynamical system is necessarily sensitive to initial conditions.

Homework Statement clear all; close all; totalanswers=zeros(100,4); k= ; flag =0; for i =0:25 a=i; if flag ==1 break; end and so forth for a,b,c,d, etc for a finite set of values all have the break values too. x=[ a,b,c,d]; does some math calculationhere is a...

What are the conditions necesairy to collapse a wave function of a electron, photon or an atom (alpha particle mostly?). Wavelength? Asking because I cannot understand why in this video the wave function does not collapse in this box. Seems like in the outside there should be massive...

Consider the radial differential equation ##\bigg( - \frac{d^2}{dr^2} + \frac{(l+\frac{d-3}{2})(l+\frac{d-1}{2})}{r^2} + V(r) + m^2 \bigg) \phi_l (r) = \lambda\ \phi_l (r)##, which I've obtained by solving the Schrodinger equation in ##d## dimensions using the method of separation of...

Suppose that we want to solve the eigenvalue equation with Dirichlet boundary conditions ## \bigg(-\frac{d^2}{dx^2}+V(x)\bigg) \phi_n = \lambda_n \phi_n,\ \ \ \ \ \ \ \ \ \ \ \ \ \phi_n(0)=0,\ \phi_n(1)=0, ## where ##0 < \lambda_1 < \lambda_2 < ...## are discrete, non-degenerate eigenvalues...

Homework Statement "Solve the wave equation with the following initial conditions and boundary conditions." ∂2Y/∂x2 = 1/v2 * ∂2Y/∂t2 Boundary conditions: ∂Y/∂x(x=0, t)=0 and Y(x=L,t)=0 Initial Conditions: ∂Y/∂t(x, t=0) = 0 Y(x,t=0) = δ(x-L/2) Homework Equations Using separation of...

I have a question I'm a little embarrassed to be asking: what is meant in condensed matter when someone describes a system with "open boundary conditions," say in one-dimension for simplicity? I am comfortable with the statement of fixed (Dirichlet) or free (von Neumann) boundary conditions, as...

Hi all! I am trying to solve a system of partial differential equations in Matlab, with both derivatives in time and space domains. I am using the pdepe function for that. The system is, to be simple, a sort of solar thermal panel, made of three layers: an absorber plate, a fluid layer of...

I know this is the Physics Forums and not the Biology Forums, but I feel that this question is more on the physics side of the spectrum than the biology side. What potential effects could the existence of a hypothetical, unusually warped spacetime, where there were naturally-occurring curves...

I have created such vibrating feeder model on SW but on ANSYS I'm only analyzing the frame. 1)How do I set up boundary conditions, I think I need elastic supports? 2)In modal analysis I have elastic, fixed supports, remote displacement - which should I use and in what directions? 3)Do I perform...

Homework Statement This is not homework but I am trying to solve a problem to see to general a set of numbers for the grassmanian equations to use in something else.[/B] I have five variables a,b,c,d,e. a-b,a-c,a-d,a-e,b-a,b-c,...etc so that none of them are the same so it generates all...

I'm reading griffiths electrodynamics and I am confused about a concept. Mainly because I might be interpreting it in different ways. Why does the equation contain an E with a negative in front? Namely, E_below. Isn't the Electric field pointing away from the surface with the surface charge...

Edit: Sorry about the vague title, it was intended to be complex beam system boundary conditions but somehow it turned out like this. Hello, I am trying to learn complex beam system designs and I sometimes struggle to assign boundary conditions. For example I am trying to design the lifting...

In the derivation of the boundary conditions we apply the integral form of maxwell's equations, but once we take a very small volume we find that some terms disappear like the displacement current as well as the time derivative of the magnetic field. Why do these terms disappear? For reference...

Does anyone here have a copy of Griffith's E&M? On page 128, condition III V=V_0 (y) when x = 0. Do you know why then value V_0(y) does not appear in in equation 3.28, V(x,y) = Ce^(-ky)sin(ky)? The author does not explain this.

I stumbled upon this article: http://www.comsol.com/blogs/exploiting-symmetry-simplify-magnetic-field-modeling/ Since the article does not contain any mathematical formulations, I was wondering how the boundary conditions can be expressed in terms of magnetic vector potential. From what I...

Hello, I need to replicate the conditions of a clutch on a pin on disc tribometer to measure the coefficient of friction. However the tribometer I have access to can't spin faster than 1000 RPM. The clutch will reach speeds from 3000 RPM to 9000 RPM. I calculated the normal force required on...

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 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...

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)...

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...

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...

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...