Constraints Definition and 217 Threads

Homework Statement Consider a theory which is translation and rotation invariant. This implies the stress energy tensor arising from the symmetry is conserved and may be made symmetric. Define the (Schwinger) function by ##S_{\mu \nu \rho \sigma}(x) = \langle T_{\mu \nu}(x)T_{\rho...

Hello, I am going over these slides and I am very confused on a couple parts. First of all on the first slide, I don't understand why a linear function has the form ##f(x) = c^Tx##. How is that equal to ##c_{1}x_{1} + c_{2}x_{2} + \dots + c_{n}x_{n}##. Wouldn't this depend on how you define...

Suppose we have a superfield \Phi(x,\theta,\bar{\theta}) this can be expanded in component fields in the standard way as: \Phi(x,\theta,\bar{\theta})= c(x) + \theta \psi(x) + \bar{\theta} \bar{ζ}(x) + \theta^{2} F(x) + \bar{\theta}^{2} Z(x) + \theta \sigma^{\mu} \bar{\theta} u_{\mu}(x) +...

Homework Statement Just a heads up, this is a problem with parts (a) - (o). I am working on (k). I am working on problem 5 in the attached PDF. I will show my code for the other parts. We were told to use N = 5 while writing the code for debugging and testing, but run N = 500 for the real...

Homework Statement Using Lagrange multipliers, find the max and the min values of f: f(x,y,z) = x^2 +2y^2+3x^2 Constraints: x + y + z =1 x - y + 2z = 2Homework Equations ∇f(x) = λ∇g(x) + μ∇h(x)The Attempt at a Solution Using Lagrange multipliers, I obtained the equations: 2x = λ + μ 4y =...

Hello! I'm trying to model my truss with FEM using only beam elements in ANSYS, but I am experiencing difficulties with the constraints between the members (or coupling of the DOFs). For instance, I want my truss chords to be continuous and my lattice members to be pinned to them. I couple...

Homework Statement Consider the LP: max \, -3x_1-x_2 \,\,s.t. \,\,\,\, 2x_1+x_2 \leq 3 \quad \quad \ -x_1+x_2 \geq 1 \quad \quad \quad \quad \ x_1,x_2 \geq 0Suppose I have solved the above problem for the optimal solution. (I used dual simplex and get (0,1) as the optimal solution.) Now...

Homework Statement A bead C can move freely on a horizontal rod. The bead is connected by blocks B and D by a string as shown in the figure. If the velocity of B is v. Find the velocity of block D. Homework Equations As the string is inextensible the velocity of the string along the...

Homework Statement Homework Equations I have to use these set identities: The Attempt at a Solution Pretty sure this is impossible since it's an inequality.

Hi, I have a optimization problem and I need to find a way to solve it even if only with an approximate solution. Let's suppose we have a finite set of vertical containers each with a distinct liquid chemical inside.(say a handful of vertical pipes). At the top, these containers have an...

I've been struggling with shared constraints problems for a while now. I have a game between two players with a shared constraint. For example, player 1 is trying to maximize f(x,y) by choosing x, and player 2 is trying to maximize g(x,y) by choosing y. The players are competing in a...

My question is the following: In field theory, if I have a constraint \chi(q_a, p_a, \partial_i q_a) that depends on the generalised coordinates q_a, momenta p_a and spatial derivatives only of the q_a \partial_i q_a does this count as a non-holonomic constraint? Or is it only...

Hi MHB, I've come across this problem recently: If a²+b²=2 and (c-3)²+(d-4)²=1, find the maximum value of ad-bc. I haven't solved it and actually, I don't know of any algebraic method I could use to solve it and I am wondering if this problem is doable with the Lagrange Multiplier...

I am currently trying to carry out the construction of the generalised Hamiltonian, constraints and constraint algebra, etc for a particular field theory following the procedure in Dirac's "Lectures on quantum mechanics". My question is the following: I have momentum variables that depend on the...

Hello, Is it possible for a structure to be completely constrained and statically indeterminate, or partially constrained and statically determinate? Or does one come with the other automatically? I am having difficulties determining if a structure is partially constrained or completely...

Hello, I need to find a two-arguments function u(x,y) which satisfies six constraints on its derivatives. x and y are quantities so always positive. 1&2: On the first derivatives: du/dx>0 for all x & du/dy>0 for all y (so u is increasing in x and y) 3&4: On the second derivatives...

Any comments on the recent N. P. Pitjev and E. V. Pitjeva paper: Constraints on Dark Matter in the Solar System arXiv: http://arxiv.org/abs/1306.5534 MIT Technology Review article...

Homework Statement The original printed problems can be found as attachments. The questions ask if a set S is a subset Rn. Give Reasons Question 1.) S is the set of all vectors [x1,x2] such that x12 + x22 < 36Question 2.) S is the set of all vectors [x1,x2,x3] such that: x2= 2x1 x3 = 3x1...

Anyone read the article on this? http://phys.org/news/2013-06-precise-quantum-electrodynamics-constrain-fundamental.html I made an effort to read to arXiv paper, but I'm still working on my understanding of QFT, so I didn't get too much out of it.

Homework Statement A particle of mass M moves on the X-axis as follows: It starts from rest at t = 0 from the point x = 0 and comes to rest at t = 1 at the point x = 1. No other information is available about it smotion at intermediate times (0 < t < 1). If α denotes the instantaneous...

Hello all, I've been puzzled by this problem for some time now and was wondering if anyone here could help me out. Textbooks on GR (specifically when going into gravitational waves) tend not to elucidate this. It's often taken for granted that through the gauge diffeomorphism invariance (or...

Did physicists ever try to put empirical constraints on the properties of the aether? I recall reading a popularization by Isaac Asimov in which he remarked that the aether would have had to have a very low density, and then to explain the high speed of light it would have had to have a...

http://img835.imageshack.us/img835/2079/minimise.jpg Both p(x,y) and q(x,y) are probability density functions, q(x,y) is an already known density function, my job is to minimise C[p,q] with respect to 3 conditions, they are listed in the red numbers, 1, 2, 3. Setting up the lagrange function...

I am attempting to recreate Sutton's work on the 'Acrobot' and have modeled a good solution to the following: http://webdocs.cs.uAlberta.ca/~sutton/book/ebook/node110.html The physics is implemented in exactly the same way, however my particular Java implementation requires some constraint...

Homework Statement Condensed/simplified problem statement \vec{E} = f_{y}(x-ct)\hat{y} + f_{z}(x-ct)\hat{z} \\ \vec{B} = g_{y}(x-ct)\hat{y} + g_{z}(x-ct)\hat{z} \\ All the f and g functions go to zero as their parameters go to ±∞. Show that gy = fz and gz = -fy Homework Equations \nabla...

I have no idea what constraints are, nor do I understand why they are important. I get where the constraints in these two examples come from, but not why they're significant. These seem to be relationships between variables, and not much of a "constraint" in the sense I know the word...

Homework Statement passengers cannot have a normal force equal to 0 or greater than 4 times their weight. What are the heights H1 and H2. Coaster starts at H1 and and ends at H2. H1>H2 and there is a low point between the two hills defined as zero height. The radius of the curve at the...

1. Homework Statement We have a bead sliding with friction on a hoop oriented vertically. First the hoop rotates about its center with rotation axis perpendicular to its plane. Second, the hoop rotates about a vertical axis as well. In both of these cases, are the constraints holonomic or...

I'm trying to write a program in fortran that will create a sequence of numbers (starting with a number that I input) that follow the following constraints: If the number (n) in the sequence is even, then the next number in the sequence will be n/2. If the number (n) in the sequence is odd, then...

Homework Statement What constraints are imposed on the use of the Gibbs equation Tds = dh - vdP Homework Equations Tds = dh - vdP The Attempt at a Solution I seem to be stuck on this question. So far I have come up with the following constraints, but I'm not even sure if they are...

Hello, all. I'm wondering about matrix-variate normal distributions. I know they normally assume an n x p random matrix, X, and associated row and column covariance matrices Omega and Sigma, but I'm wondering how the probability density function changes if X is comprised of a square...

In a recent thread, language was described as an activity where: a set of rules is used to define constrains on the world. For instance the word car limits they type of objects in the world which are likely to be denoted by the word car because one might not normally expect one to call a house...

Hey all, First off, I'd like to mention that I am completely unfamiliar with this ANSYS and have been fighting with this program for last 2 and half weeks. Any feedback and help is greatly appreciated! Please refer to the photos attached for referral. My project currently involves analyzing...

I've tried with Goldstein but no luck, i need to understand how the constraint, especially the second class act on system, i also referred Dirac's lecture, they were quiet good, but if u can suggest some books which can help me learn first and second class constraints with examples and problems...

Homework Statement The larger context is that I'm looking at the scenario of fitting a polynomial to points with Gaussian errors using chi squared minimization. The point of this is to describe the likelihood of measuring a given parameter set from the fit. I'm taking N equally spaced x values...

The no-slip boundary value constraint for Navier-Stokes solutions was explained in my fluid dynamics class as a requirement to match velocities at the interfaces. So, for example, in a shearing flow where there is a moving surface, the fluid velocity at the fluid/surface interface has to...

A company produces three products A1, A2, A3 by mixing three ingredients B1, B2, B3. The selling price for A1, A2 and A3 is $13, 14 and 16 $/kg, respec- tively, and at most 75,80 and 90 kg of each can be sold daily. The cost of B1,B2,B3 is 7, 2 and 4 $/kg and the daily supply is at most 40, 95...

That’s an issue for me. I don’t know how should I visualize constraints in constrained optimization problems in R^{3}. This is a problem cause I cannot see how it works the multiplier solution in the inequality constraints. That’s not a matter of exercises, that’s really a problem of...

Now that the superluminal neutrino fiasco is winding down, I'm interested in seeing if I can consolidate what I know about tachyons. One of the things I learned from following the OPERA debacle is that you can have tachyons without Lorentz violation, or you can have FTL particles (still called...

Have a look at http://arxiv.org/abs/1202.5039 Degenerate Plebanski Sector and its Spin Foam Quantization Authors: Sergei Alexandrov (Submitted on 22 Feb 2012) Abstract: We show that the degenerate sector of Spin(4) Plebanski formulation of four-dimensional gravity is exactly solvable and...

Hello there, currently I am trying to solve a least squares problem of the following form: min_{M} ||Y - M*X||^2 where M is a 3x3 matrix and Y and X are 3xN matrices. However, the matrix M is of a special form. It is a rank 1 matrix which satisfies M*M = 0_{3x3} and the trace of M is zero...

So far, every nonholonomic constraint I have seen can be expressed as a collection of inequalities involving the coordinates of the system. For example, a small ball rolling down a sphere with radius a has the constraint r^2-a^2\geq 0, where r is the radial coordinate of the ball. Can every...

I'm not quite sure I get the idea of a degree of freedom for a system. First of all: Is there freedom in characterizing the DOF for a system - i.e. will specifying the DOF for a system relative to any coordinate system always be the same? Next let me do an example: If we have 2 particles free...

What are the constraints (is this the right word) for introducing new fundamental force? Can our Standard Model accommodate a fifth one? Or would it mess up the math so badly that the present four fundamental forces is the final limit?

I started to read Analytical Mechanics. It said that if holonomic constraints are defined as: r = r(q1, q2, ... qn, t) (or without time) This equation holds (dot cancellation): ∂r'/∂q_k' = ∂r/∂q_k where ' specified derivatives. And the question was given to check if it works for...

Homework Statement f(x,y,z) = e^(2x-z) W: x+y+z ≤ 1, x,y,z ≥ 0 Homework Equations 0 ≤ x ≤ 1-y-z 0 ≤ y ≤ 1-x-z 0 ≤ z ≤ 1-x-y The Attempt at a Solution I tried dzdydx and dydzdx but they don't work... or am I doing something wrong?

Homework Statement Find max/min of x^2+y^2+z^2 given x^4+y^4+z^4=3Homework Equations Use of gradient vectors related by LaGrange MultiplierThe Attempt at a Solution \begin{gathered} f\left( {x,y,z} \right) = {x^2} + {y^2} + {z^2};g\left( {x,y,z} \right) = {x^4} + {y^4} + {z^4} - 3 = 0 \\...

Hi, I have a fairly simple question, in particular for the Nambu-Goto string, S = - T \int d^2 \sigma \sqrt{-\gamma} where gamma is the induced metric on the worldsheet. The canonical momenta are p_{\mu} = - T\sqrt{-\gamma}\gamma^{a0}\partial_a x_{\mu} From this it is quite straightforward...

THe universe is around 14 billion years matter falling into the singularity appear to take infinite time. So how would two black holes have had the time to complete a merger under those conditions? According to my understanding of GR we should be able to see mergers still in progress as the...

Hello all, I wonder if anybody knows of a way of generating a random normal vector (i.e. a variate from a multivariate normal distribituion) in which one or more of the vector's values are fixed?. For example, I may want to choose a random vector from a four-dimensional multivariate normal...