Gradient Definition and 723 Threads

Hello, I don't understand the meaning of equation \int\dot{s}_{ij}\frac{\partial v_{j}}{\partial x_{i}} dV where \dot{s} is rate of change of stress, v_{j} is velocity. Can anybody describe the meaning of this equation? Thank you.

It states in course notes: ------------------------------------------- If y = f(x) defines a surface in (n+1) dimensional space then the normal is defined as the (n+1)-dimensional vector: (\frac{\partial f(x)}{\partial x1},(\frac{\partial f(x)}{\partial x2},...,(\frac{\partial f(x)}{\partial...

Homework Statement What is the relationship between electric field strength and the potential gradient? Homework Equations The Attempt at a Solution This is my Calc based Physcis lab question but I am at a total loss. I do not understand what potential gradient is in the...

Hi, I was asked to prove this identity, I found the determinants for both the left and the right side, and now I basically have to prove that (d/dy)(f(dg/dz))=(df/dy)(dg/dz), the d's are actual partials though. Can anyone give me an idea on how to prove this? Thanks.

Homework Statement gradient of the stationary points of y=1-2sinx domain 0<x<2piHomework Equations The Attempt at a Solution dy/dx = -2cosx -2cosx=0...?

Hello everyone! Having a field \bf B = \nabla \times \bf A , how is it possible to get \bf A ? For constant fields, the answer is easy, but is there a general approach to find A ? Some algorithm to do it numerically would help me immensly, too. If anyone knows some book or reference...

I teach marine biology and have been presenting the traditional model of the equilibrium tidal theory (2 humps on rotating earth) as still presented in most basic texts, but have not been able to find the theory or presumed explanation for the apparent generally increasing amplitude in tidal...

Hi, I'm trying to compute the gradient tensor of a vector field and I must say I'm quite confused. In other words I have a vector field which is given in spherical coordinates as: \vec{F}=\begin{bmatrix} 0 \\ \frac{1}{\sin\theta}A \\ -B \end{bmatrix} , with A,B some scalar potentials and I...

We need a MATLAB code for a normalized gradient eq. help! :) Hello, we need help in converting this normalized gradient equation into a MATLAB code. Please see the image. Thanks! :) http://img706.imageshack.us/img706/7998/thesisformula.jpg

Homework Statement There are two parts to this problem. On the curve 2x^2-5 lie two points P and Q. Let the abscissa of P be "x" and the abscissa of Q be "x+h". No numerical coordinates are given. a) State the coordinates of P and Q. b) Using these points find the gradient of...

I'm working on a control theoretical problem and trying to implement the solution in Matlab. Part of the solution requires minimizing a function f(x), for which my predecessor has opted to use a conjugate gradient method. He wrote his own conjugate gradient method, but it's not converging. I've...

I would like to demonstrate an identity with the INDICIAL NOTATION. I have attached my attempt. Please let me know where I made mistakes. Any suggestion? I am trying to understand tensors all by myself because they are the keys in continuum mechanics Thanks

URGENT: Heat transfer - temperature gradient value at a certain point Homework Statement Given a very long cylinder of inner R1 = 0,01 m, outer radius R2 = 0,1 m, that transports water at 150ºC, and surrounded by air at 25ºC, find the temperature gradient value at R = 0,07m. \lambda = 500...

Hello, I just want to confirm with the experts here that I have understood the concept of the gradient correctly. So, a gradient for a function is a vector field that has the partial derivatives of the function. So, for each point in the domain of the function there is a vector associated...

Coulomb gauge fixes gauge by setting div(A)=0. What has it to do with adding a gradient to A and subtract a partial time derivative from V?

In chapter 1 of Sean Carroll's Lecture Notes on General Relativity, p. 12, he writes: In spacetime the simplest example of a dual vector is the gradient of a scalar function, the set of partial derivatives [of the function] with respect to the spacetime coordinates, which we denote by "d"...

Ok hydrogen ion gradient drives ATP synthase. In secondary active transport the preexisting concentration gradient drives the molecules. My question is what do they mean when they say concentration gradient provides energy to do this. Is it the movement of ions like hyrdogen from high to low...

Homework Statement A hiker climbs a mountain whose height is given by z = 1000 - 2x2 - 3y2. When the hiker is at point (1,1,995), she moves on the path of steepest ascent. If she continues to move on this path, show that the projection of this path on the xy-plane is y = x3/2 Homework...

I have to find the gradient of a scalar field, h, at a certain point in a direction given by a vector. I know, \vec{\nabla}h will give me the direction of maximum slope, and its magnitude is the magnitude of the slope, but i don't know where to start in finding the slope in any other...

OK, this is really confusing me. Mostly because i suck at spatial stuff. If the gradient vector at a given point points in the direction in which a function is increasing, then how can it be perpendicular to the tangent plane at that point? If it's perpendicular to the tangent plane...

First of all, I don't have a concrete example for this, but I hope it's not too hard to understand what I'm trying to get at. For a multivariable function of, say, 2 variables x and y, the gradient at a point only depends on the existence of partial x and partial y, right? In other words, if...

Homework Statement show that the pyramids cut off from the first octant by any tangent planes to the surface xyz=1 at points in the first octant must all have the same volume Homework Equations The Attempt at a Solution i don't know how to start this problem. any hints?

I need to compute the normal velocity of an evolving front in two dimensions (x,y). Let's say that I have collected numerous x and y position data as a function of time. If I plot these data on a set of x,y,t coordinate axes and fit a surface through them in a manner analogous to fitting a...

Can anyone help me with the following question? Find the path of the steepest descent along the surface z=x^3 + 3y^2 from the point (1, -2, 13) to (0,0,0) Note: the general solution of the differential equation f ' (t)-kf(t) =0 is f(t) = ce^kt, where c is an arbitary number...

Homework Statement Find the gradient of 3r^2 in spherical coordinates, then do it in Cartesian coordinates Homework Equations \nabla f=\hat r \frac{\partial f}{\partial r} + \hat \theta \frac{1}{r} \frac{\partial f}{\partial \theta}+ \hat \phi \frac{1}{r\sin \theta}\frac{\partial...

Homework Statement Suppose you are climbing a hill whose shape is given by the equation below, where x, y, and z are measured in meters, and you are standing at a point with coordinates (120, 80, 1064). The positive x-axis points east and the positive y-axis points north. z = 1200 - 0.005x2...

This is doing my nut in. I'm looking at causes of errors in a rotating gradiometer. It uses a loop of superconductor formed so that the current in the loop is proportional to the gradient of the magnetic field threading the loop. I think that an error current will arise due to the Lorentz...

Hi, Say I have a sphere of radius r that has a constant surface temperature of T_s. The sphere is surrounded by air at a constant temperature T_amb. I am interested in the temperature gradient surrounding the sphere. From the little I know, I think i have to look at the natural...

There is an equation for the electric field E=V/d. This tells me the change in voltage per distance. Lets say I have a 1-meter wire and a 1-volt battery, so the electric field would be 1V/m. What is the significance of this in the circuit?

Homework Statement I have a derivation for an equation here: https://www.physicsforums.com/showthread.php?t=334692 Basically, I need to invert the gradient operator, so I have: \nabla B = k_z k is known and I want to solve for B numerically. How do I get rid of the gradient...

Homework Statement From Townsend "Modern Approach to Quantum Mechanics", problem 1.1: "Determine the field gradient of a 50-cm long Stern-Gerlach magnet that would produce a 1 mm separation at the detector between spin-up and spin-down silver atoms that are emitted from an oven at T=1500K...

Homework Statement Calculate the gradient of the scalar field f(x,y) = x^{2} - y^{2} . Sketch the gradient for a few point on two straight lines y = x and y = -x on the plane and comment on the properties of the sketch. Homework Equations The Attempt at a Solution So I worked...

Homework Statement Check the gradient theorem for the scalar field T= x^2 + 4xy + 2yz^3 and the paths a) (0,0,0) to (1,0,0) to (1,1,0) to (1,1,1) Homework Equations Equations = none well maybe divergence of a vector field= (df/dx)*x + (df/dy)*y + (df/dz)* z where x,y and z are...

Gradient and velocity Just curious Let's say I have a plane with the equation 4x + 5y + 6z = 45 If I find \nablaF(x,y,z) and then find it's magnitude, I get the direction of steepest descent/ascent in the direction of <\partialF(x,y,z)/\partialx,\partialF(x,y,z)/\partialy...

Okay, I have two points on my graph - (-2,72) and (0,64). Here is the question on my assignment - "Find another two points on your curve which have the same gradient as those in Parts 3 and 4 and find the equations of the tangents to the curve at these points." The problem I have is I don't...

Homework Statement Find the gradient of y with respect to x: y=\frac{3\sqrt{\theta^{2}+1}}{\frac{1}{2}cos(x^{2}+2\theta)} Well, I am at a complete loss where to start with this. The learning package I have in all its examples and text has no similar worded examples or utilises 2...

Hi all, just an very elementary question, arising from the first study of generating harmonic solutions. How to get the gradient twice for 1/r in spherical coordinates?

Can someone remind me why the electric field is defined as the negative gradient times the electric potential, rather than the gradient times the electric potential? Thanks, JL

Hello everyone, I have 2 components of a gradient, for example, the dz/dx and the dz/dy, I want to find the overall gradient it forms, how would I do that? Is it simply by combining the two gradients like this: overall gradient = ((dz/dx)^2 + (dz/dy)^2)^(1/2) I don't need the direction, I...

Hi All, A potassium channel is designed to filter out potassium ions at a maximum rate of 100,000,000 ions s-1 A common concentration (cell's interior) of potassium is 100 mM and 5 mM outside. This means there is 553 water molecules for 1 potassium ion inside (55.3/0.100) and 11,060 water...

Physical interpretation of gradient says that its a vector normal to equipotential (or level) surface \phi(x,y,z) = 0 but what about other surfaces, say the surface which are not equipotential? This is my first question. ok, now as grad \phi is a vector normal to surface it can't be 0...

The equation widely used to calculate the force on a projectile in an electromagnetic launcher, more specifically a railgun, is: F = 0.5 * L' * I^2 where: --> F is the force in Newtons --> L-prime is the inductance gradient of the rails in henries/meter (H/m) --> and I is the current...

Homework Statement Find the gradient vector of: g(r, \theta) = e^{-r} sin \theta Homework Equations The Attempt at a Solution I know how to get gradients for Cartesian - partially derive the equation of the surface wrt each variable. But I have no idea how to do it for...

Homework Statement The temperature in a room is given by T(x,y,z)=2x^2+3y^2 - 4z. A flying bug located at P(1,1,2) in the room desires to fly in such a direction that it will warm as soon as possible. In what direction must the bug fly? Taking the gradient of T: 4x(x hat)+6y(y hat)-4(z...

Homework Statement Lord Kelvin used the heat flow at the surface of the Earth to argue that the Earth was 100 million years old withing a factor of 4 error. a.) Reproduce his logic by deriving the temperature gradient at the surface of the Earth for a planet that is cooling by conduction...

grad(A*B)=(A*grad)B + (B*grad)A + A curl B + B curl A i'm not sure how to read the RHS to begin to work out the index definition.i'm thinking if add and subtract terms this will work out. i think i can see the first two terms, but the last two maybe "A cross nabla" is what they mean acting on...

In physics texts, its customary to write (and even to define the gradient as) the following: dT = (\nabla T) \cdot dl Working in Cartesian coordinates, we can expand this as follows: dT = \frac{\partial T}{\partial x} dx + \frac{\partial T}{\partial y} dy + \frac{\partial T}{\partial...

Homework Statement http://img245.imageshack.us/img245/2353/87006064.th.jpg I need to find the unit vector in the direction of \vec{F} at the point (1, 2, -2). Homework Equations The Attempt at a Solution well first of all I need to find what F is right, which is gradf.. how can I get...

Homework Statement h(sph)=exp(r2sin2(\theta)sin2(\phi)+r2cos2(\theta)) need to find gradient of this function, i have er and etheta... but can someone please tel me why when maple differentiates with respect to phi, why does it say it equals zero? coz i get...

Homework Statement Suppose that the function f: Rn --> R has first-order partial derivatives and that the point x in Rn is a local minimizer for f: Rn --> R, meaning that there is a positive number r such that f(x+h) > f(x) if dist(x,x+h) < r. Prove that Df(x)=0. Homework Equations...