Variation Definition and 574 Threads

Why do we treat a scalar field phi and its derivatives as being independent when trying to find a stationary solution for the action? Doesn't that give too general solutions? Where does the restriction that (d_mu phi) is dependent on phi come back in?

My materials professor told me the restoring force of rubber increases with temperature because of entropy. At normal solid forms because the structure is energetically favorable. He says the unstreched state is entropically favorable. Is this reasonable? I plan to test it this weekend when...

http://www.mste.uiuc.edu/users/exner/ncsa/quad/ There's another way of writing the quadratic formula...but how do I derive the 2nd formula using the 1st one? I've tried for hours and I can't get it. I would really appreciate any help.

Consider a pnp transistor with {v_{EB}=0.7V and {i_{E}=1mA. Let the base be grounded and the emitter be fed by a 2 mA constant current source , and the collector be connected toa -5V supply through a 1-Killoohms resistance. if the temperature increases by 30 degree celsius, find the change in...

how does the speed of sound vary with temperature in an ideal gas? how do we derive this relation?

solve using method of variation of parameters y''-y = 2/(1+e^x) y'' ==> second order

I have been trying to get this for a while and can't figure it out: if a fundamental matrix of the system x' = Ax is X(t) \left(\begin{array}{cc}e^t&0\\0&e^{-t}\end{array}\right) find a particular solution yp(t) of x' = Ax + [e^t, 2]^{transpose} such that yp(0) = 0 So, I got u(t) =...

Please correct me if I am wrong, but it is my understanding of Special Relativity that the faster a particle moves the more force it requires to accellorate - laymans terms: becomes more massive. I had a post earlier where I tried to present this in the framework of an "atomic pop gun". I was...

I am having a lot of difficulty with this problem . I don't have the slightest idea on how to do this problem and my textbook does not explain it. Please help me: Determine whether 1 - y = 2x is a direct variation. If so explain. This problem has me stumpted and very frustrated...

I need to solve this D.E. x^2y''-xy' + y = x^3 i'm supposed to use the variation of parameters technique. in that technique i need to get a coeffecient of 1 in the first postion of y'' and then sove the homogenous D.E. y''-\frac{y'}{x} +\frac{y}{x^2}=0 the above leads to...

URGENT maths - variation assignment HEy got to make a poster and contain at least 3 'real' examples of variation. Direct, inverse, joint, part variation should be featured. for each example show -the type of variation, - an explantion of that particular type of variation, and the...

Please give me some hints on resolving this problem. Thanks! For example there are 3 persons who run 2, 2 and 2 metres. n=3 and the mean of the metres is 2. Standard deviation is 2 (let us pretend so). The formula for Coefficient of Variation is ; Standard deviation/ Expected return. I...

Hello, I'm trying to understand this concept. Jere's the problem I'm doing. I have to find the general solution for: y'' + 36y = -4xsin(6x) So you then solve for your characteristic equation and get lamda = +/- 6 so y1 = e^-6x and y2 = e^6x You get your matrix for w, w1, and w2. w =...

the problem is fin the general solution of the differential eq : y''+y=2sect + 3 (-pi/2 < t < pi/2) using variation of parameters. I just needed a check to make sure my answer was correct. r^2+1 = 0 r= -i r= i y1= cost y2= sint g(t)= 2sect+ 3 y(t) = c1cost + c2sint + Y(t)...

hi i got this equation y= x^2 - 2x + 1 / X^2 -x - 2 how do i sketch this finding all intercepts, and asymptotes with a gfx calculator? Please check if the steps i did below is right what i did i factorised the equation so i got y= (x-1)^2 / (x+1)(x-2) ASYMPTOTES the bottom line...

hi, we have just got to the point in my physics course where Newtons laws are now longer that easy to work with anymore and we are now beginning to reformulate those using variational methods, and I am a little confused on one of the problems. The shortest path between two points on a curved...

mathematically why does the mean change when an x-value is changed in a list, but the variation doesn't. if someone could show me a relevant formula which can satisfy this or any other info i would be very grateful for thnak you

problem: Let f \in BV[a,b] . Then \int_{a}^{b} |f'| \leq T_a^b f where T_a^b f is the total variation of f over [a,b]. there are some lemmas, etc that got me this far: \int_{a}^{b} f' \leq f(b)-f(a) = P_a^b - N_a^b \leq P_a^b + N_a^b = T_a^b f where P is the positive variation & N is the...

as part of a physics practical write up i have to measure the temperature of a light bulb envelopes temperature as the voltage increases. first ... am i right in thinking a type J exposed thermocouple would do the trick for this? if so, i heard something about one end being cold, to...

For a launched projectile, what are the following theoretical relationships/proportionalities: variation of range with speed of projectile, keeping a constant launch angle variation of range with launching angle, keeping the launching speed constant thanks for the help

This experiment which is a variation of the double slit experiment , has actually been conducted. We have (a) the source of electrons, (b) screen 1 ( with the double slit ) and finally (c) screen 2 , where the particles are registered. Near the slits in screen 1 and on the far side from the...

The Standard Model of particle physics provides no explanation for the masses of the basic particles. If the masses were much larger- a possibility for a variation of the model- then a small collection of particles could collapse in a black hole. Of course this universe would be different from...

I have a variation of the Motional EMF in Tiplers Physics Second Edition 28-1. A conducting rod of mass m and length l sliding along conducting rails connected by a resistor with a uniform magnetic field normal to the movement of the rod. The variation is that instead of just a resistor, the...

We escape the problems of particle physics by exploring the higher dimensions of String theory. When we have questions about String theory, we jump to the higher dimensions of M-theory to answer them. And some have purposed to use the higher dimensions of F-theory to answer questions about...