Chain Definition and 978 Threads

Homework Statement I am facing problem in applying the chain rule. The question which I am trying to solve is, " Find the second derivative of " Homework Equations The Attempt at a Solution So, differentiated it the first time, [BY CHAIN RULE] And now to find the second derivative I...

Homework Statement A polymer chain consist of a large number N>>1 segments of length d each. The temperature of the system is T. The segments can freely rotate relative to each other. A force f is applied at the ends of the chain. Find the mean distance ##\textbf{r}## between the ends...

I request your help in order to know, how can i configure this problem as a continuous markov chain, need to define the main variable, the states, transition rates, and the matrix. I thought that it could be relationed with the independent status of the machines, because if the machine 1 is...

Homework Statement A uniform chain of mass 'm' and length 'l' rests on a rough incline (inclination is angle 'Q') with its part hanging vertically. The chain (inclined) starts moving up the incline (and the vertical part moving down) provided the hanging (vertical) part equals to 'n' times...

Homework Statement a uniform fine chain of length l is suspended with lower end just touching a horizontal table. Find the pressure on the table, when a length x has reached the table.. Homework Equations Pressure = force/area The Attempt at a Solution let mass density, m= mass/l...

Greg Bernhardt submitted a new PF Insights post Demystifying the Chain Rule in Calculus Continue reading the Original PF Insights Post.

How strong a long chain of carbon carbon double bonds will be compared to nano tubes? H>c=c=c=c=c=c=c=c=...=c=c=c=c=c=c=c=c=c=c=c=c<H

Homework Statement I am going through a derivation of the thermal energy equation for a fluid and am stumped on one of the steps. Specifically, the text I am using converts the term: P/ρ*(Dρ/Dt) to: ρ*D/Dt(P/ρ) - DP/Dt where: ρ = density P = pressure D/Dt = material derivative The text...

Homework Statement You are presented with a circumstance in which three children are playing on a frozen pond. The three small children of mass 20.00 kg, 24.00 kg, and 16.00 kg, respectively, hold hands, and are pulled across a smooth frozen pond by a larger boy on skates, who pulls a...

Homework Statement 1D atomic chain with one atom in the primitive cell and the lattice constant a. The system in described within the tight binding model and contains N-->∞ primitive cells indexed by the integer n. The electronic Hamiltonian is $$H_{0} = \sum_{n} (|n \rangle E_{at} \langle n |...

Imagine a car that weights 1000Kg. Its engine pushes it forward with a force of 3kN. So the car is accelerating at 3m/s^2 (imagine there are no friction). After 100 seconds (the speed of car at that moment is 300m/s, very realistic), the car hits a wagon that weighs 1000Kg, that is on rest. And...

Homework Statement So given XXh chain: $$\hat{H} = -J \sum ( S^x_j S^x_{j+1} +S^y_j S^y_{j+1}) + h \sum S^z_j $$ Requred to find $$\langle g| S^z_{j} S^z_{j+n} | g \rangle$$, where g is ground state. 2. The attempt at a solution Using Jordan-Wigner transform firstly I abtain: $$\hat{H} =...

I'm trying to understand why $$\left(\frac{\partial P}{\partial T}\right)_V = -\left(\frac{\partial P}{\partial V}\right)_T \left(\frac{\partial V}{\partial T}\right)_P$$ where does the minus sign come from?

<Moderator's note: Moved from a technical forum and thus no template.> Question: A certain amount of oil on the sea surface can be considered as circular form and the same thickness throughout its surface. At a certain time, the following are noted Data: Oil is supplied to the spot at 5m^3/min...

Homework Statement This is a chain rule problem that I can't seem to get right no matter what I do. It wants me to find the derivative of y=sqrt(x+sqrt(x+sqrt(x))) Homework Equations dy/dx=(dy/du)*(du/dx) d/dx sqrtx=1/(2sqrtx) d/dx x=1 (f(x)+g(x))'=f'(x)+g'(x) The Attempt at a Solution My...

I am reading "Introduction to Real Analysis" (Fourth Edition) by Robert G Bartle and Donald R Sherbert ... I am focused on Chapter 6: Differentiation ... I need help in fully understanding an aspect of the proof of Theorem 6.1.6 ...Theorem 6.1.6 and its proof ... ... reads as follows: In the...

Homework Statement Homework EquationsThe Attempt at a Solution The initial shape of chain is like an inverted "L" with end B just touching the floor . Height of table is "h" . My problem is in identifying the net force on the chain in vertical direction .At any instant of time there are...

Here is an animation I created in R. I built this Markov chain of order 50 by correlating the information in one of the coordinates while randomly varying the rest. Is there an explanation for the clustering and flattening out over increasing dimensions of the vector space? Is it due to the...

I am having difficulty trying to figure the following . What is \frac{\mathrm{d} }{\mathrm{d} x}f(x,y) where x is a function of s and t. Here is my calculation \frac{\mathrm{d} }{\mathrm{d} x}f(x(s,t),y) = \frac{\partial f}{\partial x}\frac{\partial x}{\partial t}+\frac{\partial f}{\partial...

In my quest to understand the Euler-Lagrange equation, I've realized I have to understand the chain rule first. So, here's the issue: We have g(\epsilon) = f(t) + \epsilon h(t). We have to compute \frac{\partial F(g(\epsilon))}{\partial \epsilon}. This is supposed to be equal to \frac{\partial...

Homework Statement Homework Equations I want to check if I think it right! The Attempt at a Solution If N=1: ← or → (2 configurations/ each length is l) N=2: ← or → or ←← or ←→ or →← or →→ ------→----← (6 configurations/ folded polymer's length is l/2 andunfolded polymer's...

An electron can tunnel between potential wells. Its state can be written as: $$ |\psi\rangle=\sum^\infty_{-\infty}a_n|n\rangle $$ Where $|n \rangle$ is the state at which it is in the $n$th potential well, n increases from left to right. $$...

Homework Statement Homework EquationsThe Attempt at a Solution What I know is tension is same in magnitude at all points of the chain along tangential direction due to the symmetry of the system. But how to find it out?[/B]

Homework Statement How to obtain the famous formula of velocity transformation using a chain rule. I know that there is a straightforward way by dividing ##dx## as a function of ##dx`## and ##dt`## on ##dt## which is also a function of them. But I would rather try using the chain rule. Homework...

In the proton chain, a deuteron and proton fuse to make a nucleus of helium 3, releasing 5.493 MeV by E=mc^2. To have the same total momentum before and after fusion, at least two particles must be emitted, right? That way they can "cancel out" some momentum by having roughly opposite...

Homework Statement Consider a 40-foot chain that weighs 4 pounds per foot hanging from a winch 40 feet above ground level. Find the work done by the winch in winding up the entire chain with a 600-pound load attached to it. Homework EquationsThe Attempt at a Solution ##\displaystyle...

Homework Statement To show that ##K=V^uK_u## is conserved along an affinely parameterised geodesic with ##V^u## the tangent vector to some affinely parameterised geodesic and ##K_u## a killing vector field satisfying ##\nabla_a K_b+\nabla_b K_a=0## Homework Equations see above The Attempt at...

Homework Statement Use the top line to get 1) and 2) Homework Equations above The Attempt at a Solution So for 2) split the log up using ##log (AB)=log (A) + log (B) ## and this is simple enough I think I may be doing something stupid with 1) though. I have ##\frac{\partial}{\partial...

Homework Statement http://i.imgur.com/TdPWVgr.pngHomework Equations WD=mgh The Attempt at a Solution mass per length=0.8kg/m mgh= ∫(0,10)(0.8g(10-y))dy=[8gy-0.4y^2g](0,10)=80g-40g=40g However, the answer is 20g whats wrong with my calculation? thanks

Hello. I have devolopped a line amplifier with 3 x MAR-6 MMIC. Normal daisy chain is : antenna followed by a LNA which is followed by my line-amp. If nothing is connected at the input ofLNA, all 3 Mar-6 have normal operating voltage ie 3.5 V and resulting noise is very low (seen with a 100 MHz...

hello. I'm tring to find a compatible sprocket for my chain. I need to know what these abbreviations mean here: http://www.ebay.com/sch/i.html?_odkw=sprocket+40&_sop=15&_osacat=0&_from=R40&_trksid=p2045573.m570.l1313.TR0.TRC0.H0.Xsprocket+40+3%2F4.TRS0&_nkw=sprocket+40+3%2F4&_sacat=0 For...

Homework Statement On a pulley with a very small radius and negligible inertia, that rotates without friction around its fixed horizontal axis, there is a chain of mass m and length l. The chain starts sliding from its equilibrium position. Let x be the distance between the ends of the chain...

Okay this has has been driving me crazy. I would like to know how a conveyor speed can be calculated on the basis of chain pitch, sprocket PCD & no. of teeth and output RPM of gearmotor. So here is a practical example I'm having to solve at the moment: I have to drive a conveyor at a speed of...

Hi, I have a probably very stupid question: Suppose that there is an expression of the form $$\frac{d}{da}ln(f(ax))$$ with domain in the positive reals and real parameter a. Now subtract a fraction ##\alpha## of f(ax) in an interval within the interval ##[ x_1, x_2 ]##, i.e. $$f(ax)...

Homework Statement Question has been attached to topic. Homework Equations Chain rule. The Attempt at a Solution $$\frac {dy}{dt} . \frac{dt}{dx} = \sqrt{t^2+1}.cos(π.t)$$ $$\frac{d^2y}{dt^2}.(\frac{dt}{dx})^2 = 2 $$ $$\frac{d^2y}{dt^2}.(t^2+1).cos^2(π.t)= 2 $$ and for the t=3/4...

Hi. We are using a Pb-210 needle source for our cloud chamber science project. Are we correct that the tracks we are seeing inside the chamber radiating off the needle are: 1) Beta tracks from Pb-210 decaying into Bi-210 (in the .063 MeV range) 2) Beta tracks from Bi-210 decaying into Po-210...

(Sorry for the mistakes first thread using hand held device) Hello, I was working on Harold T. Davis Introduction to Nonlinear Differential and Integral Equations I saw this following equations 1-So equation 4 came as a result of chain rule applies on equation. 3 ? 2- how did equation 5...

Hi, I am studying Matrix chain Multiplication to find out the optimal way of multiplying a series of matrices so that we can reduce the number of multiplications. I have got this example from the book which multiplies the matrices having dimensions given below: A1 30 * 35...

Hello, I am reading about this and I have a question , so let me explain how I understood this and please correct where I am wrong. I will ask about nuclear reactors because obviously in bombs only prompt neutrons matter since there is no need for any control only an exponential increase in...

Given k = ge^(x/y), find ∂k/∂x and ∂k/∂y. The fractional exponent throws me into a loop. Can someone show me step by step how to tackle this problem?

Homework Statement At a lunar base,a uniform chain hangs over the edge of a horizontal platform.A machine does ##1.0J## of work in pulling the rest of the chain onto the platform.The chain has a mass of ##2.0 kg## and a length of ##3.0m##.What length was initally hanging over the...

I understand that when you use the chain rule you multiply the exponent by the number in front and then reduce the power by 1. So the derivative of 2x^3 = 6x^2 I'm confused now however on how you would solve something like e^-3x, the answer turns out to be -3e^-3x Am I missing a rule? Why...

I'm reading a textbook that says: "The directional derivative in direction ##u## is the derivative of the function ##f( \mathbf x + \alpha \mathbf u)## with respect to ##\alpha##, evaluated at ##\alpha=0##. Using the chain rule, we can see that ##\frac {\partial}{\partial \alpha} f( \mathbf x...

We start with: d2y/dx2 And we want to consider x as function of y instead of y as function of x. I understand this equality: dy/dx = 1/ (dx/dy) But for the second order this equality is provided: d2y/dx2 =- d2x/dy2 / (dx/dy)3 Does anybody understand where is it coming from? The cubic...

let df=∂f/∂x dx+∂f/∂y dy and ∂f/∂x=p,∂f/∂y=q So we get df=p dx+q dy d(f−qy)=p dx−y dqand now, define g. g=f−q y dg = p dx - y dq and then I faced problem. ∂g/∂x=p←←←←←←←←←←←←←←← book said like this because we can see g is a function of x and p so that chain rule makes ∂g/∂x=p but I wrote...

Hello, I have been assigned to write a report on a topic of my choice for my Computational Physics class, and I chose to focus on the symplectic integration of Hamiltonian systems, in particular the Lotka-Volterra model. A 3-species model(\gamma eats \beta, \beta eats \alpha) is not, unlike the...

Hello, Here is the question: I can not figure out how we are to apply chain rule to the second order derivative. May somebody clarify that?

I want to evaluate $$ \frac{d}{dt}\int_{0}^{^{\eta(t)}}\rho(p,t)dz $$ where p itself is $$ p=p(z,t) $$ I have the feeling I have to use Leibniz rule and/or chain rule, but I'm not sure how... Thanks.

Hello! (Wave) Suppose that $u(t,x)$ is a solution of the heat equation $u_t-\Delta u=0$ in $(0,+\infty) \times \mathbb{R}^n$. I want to show that $u_k \equiv u(k^2 t, kx)$ is also a solution of the heat equation in $(0,+\infty) \times \mathbb{R}^n, \forall x \in \mathbb{R}^n$. If we have a...

I was thinking if the known methods of integration are enough to integrate any given function. In differentiation, we've evaluated the derivatives of all the basic functions by first principles and then we have the chain rule and product rule to differentiate any possible combination (product or...