2d Definition and 1000 Threads

Can this(image) be used as a proof that the direction of gradient gives the direction of steepest ascent(in 2D).Am I understanding it right ?.The function 'f' in the image is a scalar valued function.Please explain.

Homework Statement Homework Equations The Attempt at a Solution I used Pythagorean theorem to find the length of the ramp (25^2+18^2 = √949) and found the angle of elevation using tangent (Tanθ=18/25) but then got stuck on what formula to use.

I was trying to understand the momentum transport between gas molecules in 2d.In the image below, it is stated that half of the molecules move up(positive velocity in y direction) and half negative.But the author didnt explain why he assumed it.

When you do a discrete Fourier transform (DFT) of a one-dimensional signal, I understand that the second half of the result is the complex conjugate of the first half. If you threw out the second half of the result, you're not actually losing any data and you would be able to recreate the entire...

For illustration purposes, I have attached an image of the line with the angle that I want to calculate. I am trying to determine the angle of rotation and the calculation that I am using currently is as below: angle = math.atan2(y,x) I use this formula to calculate the rotation for A and A'...

Not sure this is the right area to post this. Let's say I have particles on a lattice, and they all have some property (ie, color) that is correlated at some known correlation length. I want to simulate this! In 1D I could do something like have color be a random walk in the given dimension...

Homework Statement Hello I am trying to predict vector after collision of 2 ball in biliard. I am using angle-free representation formulas from wikipedia : https://wikimedia.org/api/rest_v1/media/math/render/svg/14d5feb68844edae9e31c9cb4a2197ee922e409cx1 and x2 are positions of balls, m1 and m2...

Hello everyone. I have recently started working with a model whose output are two stochastic process which evolve trough time. Now, I have two 9*500 matrices, being 9 the number of times for which the model offers a value and 500 the number of realizations. I was wondering if someone could...

Hello, this idea of holographic universe is mind boggling to me. If we are 2d and everything we see is actully 2d hologram, like picture on the monitor https://metro.co.uk/2017/01/30/our-entire-universe-is-an-illusion-and-reality-is-actually-a-2d-hologram-say-scientists-6415724/. There is...

Hi there. It is obvious that if you have two differentiable functions ##f(x)## and ##g(x)##, then the product ##h(x)=f(x)g(x)## is also smooth, from the chain rule. But if now these functions are multivariate, and I have that ##h(x,y)=f(x)g(y)##, that is ##f(x,y)=f(x)## for all y, and similarly...

Homework Statement Have to read a paper and somewhere along the line it claims that for any distinct ## \ket{\phi_{0}}## and ##\ket{\phi_{1}}## we can choose a basis s.t. ## \ket{\phi_{0}}= \cos\frac{\theta}{2}\ket{0} + \sin\frac{\theta}{2}\ket{1}, \hspace{0.5cm} \ket{\phi_{1}}=...

The orientation of frequency components in the 2-D Fourier spectrum of an image reflect the orientation of the features they represent in the original image. In techniques such as nonlinear microscopy, they use this idea to determine the preferred (i.e. average) orientation of certain features...

1. The problem statementhttps://www.physicsforums.com/attachments/225935 Homework Equations3. I have rescaled coordinates which are X=(x1+x2)/√2 and Y=√3(x1-x2)/√2 for which the potential term becomes for a 2D harmonic oscillator of coordinates X and Y. But how to express Kinetic terms in terms...

Suppose we have a particle of mass ##m## moving freely in the xy-plane, except for being constrained by hard walls to have ##-L/2 < y < L/2##. Now, the energy eigenstates would be something like ##\psi (x,y) = C \psi_x (x) \psi_y (y) = C e^{-ikx}\cos\left(\frac{n\pi y}{L}\right) ##, where...

Homework Statement How to prove M = 2.016 X D (M = 2D) if the atomic weight of Hydrogen is 1.008 Homework Equations How to prove M = 2.016 X D (M = 2D).if the atomic weight of Hydrogen is 1.008 The Attempt at a Solution As I know, D = the mass of one molecule of gas / the mass of one...

Hello PF, I am new to the science of turbulence and fluids but recently I have been working with my professor on 2D steady state turbulence and I was looking for a way to model and simulate this scenario: I have a flow affected by a spatially varying magnetic field and having a current pass by...

Homework Statement The attached file is all the information on the problem Homework Equations .5mv^2 =.5mv1^2 + .5m2^2 p = mv The Attempt at a Solution I've tried plugging the known values in the equations and and substituting the various equations together and every time I come up with an...

Hi, I am working on Maxwell version 17. I have a simple motor to analysis 2D FEM. However, when I analyze the model, I see this error. "Maxwell2d solver, process solver2d error: Internal Solver Error: 'Transient solver handles only isotropic conductivity!'. (7:07:10 PM Apr 16, 2018)" I am...

Homework Statement I'd like to solve the following integral using the 2D trapezoidal method in fortran 95 $$I=\int^{1.40406704}_{-1.40406704} \int^{x+1.40406704}_{x-1.40406704} exp(x+y) dy dx$$ Homework Equations $$I= \frac{h}{2} \left(f_0+ 2 \sum_{i=1}^{n-1} f_i +f_n \right)+O(h^2) $$ The...

Homework Statement Homework Equations V^2=rgtan The Attempt at a Solution V^2=.24x9.8xtan25

Homework Statement Solve the Laplace equation in 2D by the method of separation of variables. The problem is to determine the potential in a long, square, hollow tube, where four walls have different potential. The boundary conditions are as follows: V(x=0, y) = 0 V(x=L, y) = 0 V(x, y=0) = 0...

Homework Statement I’m studying orthogonal curvilinear coordinates and practice calculating differential operators. However, I’ve run across an exercise where the coordinate system is only in 2D and I’m confused about how to proceed with the calculations. Homework Equations A point in the...

Homework Statement Two balls with mass m and 4m collide at the location x=y=0 and stick. Their initial velocities just before the collision can be represented as v1=(i+j) v and v2=(j-i)v' respectively. Their final velocity vf makes an angle θ with the +x axis. Find v and v' in terms of vf and...

When you curl 1 dimensional thing like a line.. won't it become 2D? I'm trying to imagine how a compactified dimension in superstring theory actually look like in our world. Let's take our 3D world and say the depth got compactifed or curl up to Planck length or a millimeter. What kind of...

Hello, For a project I am working on, I am trying to design a 2D with parallel sinusoidal patterns. Imagine a 2D section of a pipe (two parallel surfaces with distance in between). Each surface is basically a sine function. Peak points meet with each other, as well as troughs. Liquid is...

In trying to explain the concept of curved space, many books use the example of the surface of a sphere, which can be considered as a curved 2D space embedded in a higher dimensional, 3D space. I could derive, starting from ##a^2=x^2+y^2+z^2##, that the metric, or the line element, on the...

I wasn't sure whether to post this in here or in computer programming, since it touches on both. I have a personal project that is based on a 2-dimensional finite-element fluid simulation (which already works just fine) but needs to be able to simulate an elastic membrane stretched across a...

Homework Statement Compute ##\partial_n f## where ##n## is normal to ##f##, and ##f## lies in the ##x-z## plane and is parameterized by $$x(s) = \frac{1}{c} \sin (c s);\\ z(s) = \frac{1}{c} (1-\cos (c s)) $$ Homework Equations ##\partial_n f = \nabla f \cdot \hat n## The Attempt at a Solution...

A question I have faced in exam to calculate ground state energy Given Hamiltonian 1/2m(px2+py2)+1/4mw2(5x^2+5y^2+6xy) ground state energy has to be obtained Its clear that the Hamiltonian is a 2D LHO Hamiltonian but what for the term 3/4(x+y)2

This has been a real famous analogy and I understand it, except the fact that the balloon surface is a 2D structure. How is it possible to depict a 3D universe on a 2D plane ? What happens when we work with stars at multiple planes ?

Hi there, so I'm not sure if this is allowed or not, but usually before I submit my work I try to check it on the internet to get full marks. I do the work as best as I can to try and get the best understanding of the subject possible. I think a) is correct but I think I messed up somewhere in...

Homework Statement Given the equations a) find the solution to the problem (1) in vectorial form, by first writing equation (1) in component form and then solving the two parts separately. These can then be combined to obtain the vector form of the solution. b) solve the results of the...

1. Homework Equations [/B] P = mv The Attempt at a Solution [/B] VCos(30) + 0 = nCos(60) + 2Cos(20) VSin(30) + 0 = nSin(60) + 2Sin(20) where I let n = any speed, I'm not sure if my attempt at the solution is correct.

I am not familiar with tensors and I would like to know if it's possible to understand GR without using them. I imagine we use them to describe four-dimentional space-time, because a regular vector or matrix wouldn't be enough. Is there an analog of Einstein's equations for a 2D space (plane)...

Hi, I have that the Laplacian operator for three dimensions of two orders, \nabla ^2 is: 1/r* d^2/dr^2 (r) + 1/r^2( 1/sin phi d/d phi sin phi d/d phi + 1/sin^2 phi * d^2/d theta^2) Can this operator be used for a radial system, where r and phi are still valid, but theta absent, by setting...

Homework Statement When calculating the Fourier coefficients of the potential of the following lattice (the potential is a sum of deltas at the atom sites): I get the wrong coefficients if I choose the following primitve cell, with primitve vectors a1,a2: And the right coefficients if I...

Hello guys, I programmed a physics simulation where a particle with some initial conditions bounces off the walls of a 2d container. The simulation also includes gravity in the y-coordinates. The aim of the project is to produce a visual animation and further on include more particles and...

Homework Statement Lo,Im stuck on how to retrieve the specific heat capacity from an MC simulation, with the metropolis algorithm. I want my graph to look something like this: https://i.stack.imgur.com/NXeXs.png Homework Equations C_v = ((<E^2>-<E>^2)/T^2 The Attempt at a Solution My code is...

Hi! I am currently trying to derive the Fourier transform of a 2D HgTe Hamiltonian, with k_x PBC and vanishing boundary conditions in the y direction at 0 and L. Here is the Hamiltonian: H = \sum_{k}\tilde{c_k}^{\dagger}[A\sin{k_x}\sigma_x + A\sin{k_y}\sigma_y + (M-4B+2B[\cos{k_x} +...

Homework Statement I have a 2D integral that contains a delta function: ##\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}\exp{-((x_2-x_1)^2)+(a x_2^2+b x_1^2-c x_2+d x_1+e))}\delta(p x_1^2-q x_2^2) dx_1 dx_2##, where ##x_1## and ##x_2## are variables, and a,b,c,d,e,p and q are some real...

Homework Statement Consider a two-dimensional harmonic oscillator, described by the Hamiltonian ##\hat H_0 = \hbar \omega (\hat a_x \hat a_x ^{\dagger} + \hat a_y \hat a_y^{\dagger} + 1)## Calculate ##\hat H_0 \hat L | n_1, n_2 \rangle## and ##\hat L \hat H_0 |n_1, n_2 \rangle##. What does...

Hi. I have this problem in trying to solve this PDE analytically. The PDE is represented by this diagram: Basically this is solving the Laplace equation with those insulated boundaries except it has that point diffusing its value across the plane. I know how to solve the Laplace equation...

Homework Statement A cube of mass M rests tilted against the wall as shown (see below). There is no friction between the wall and the cube, but the friction between the cube and the floor is just sufficient to keep the cube from slipping. When ##0\lt\theta\lt 45^\circ## find the minimum...

So I have this PDE: d2T/dr2 + 1/r dT/dr + d2T/dθ2 = 0. How do I implement dT/dr || [r = 0] = 0? Also, what should I do about 1/r? This is actually the first time I am going to attack FDF in polar/cylindrical coordinates. I can finite-difference the base equation fairly decently; I am just...

The 2D Laplacian in polar coordinates has the form of $$ \frac{1}{r}(ru_r)_r +\frac{1}{r^2}u_{\theta \theta} =0 $$ By separation of variables, we can write the ## \theta## part as $$ \Theta'' (\theta) = \lambda \Theta (\theta)$$ Now, the book said because we need to satisfy the condition ##...

Dear Community, I was trying to reproduce the 2D GrayScott model given either here: http://blogs.mathworks.com/graphics/2015/03/16/how-the-tiger-got-its-stripes/ or here: http://www.joakimlinde.se/java/ReactionDiffusion/index.php?size=0 The reason was to create a nice screen-saver (so I am...

Homework Statement Serving at a speed of 170 km/h a tennis player hits the ball at a height of 2.5 m and an angle θ below the horizontal. The service line is 11.9 m from the net, which is 0.91 m high. What is the angle θ such that the ball just crosses the net? Will the ball land in the service...

I'm trying to put together a function that sums multiple 2D Gaussian functions in one graph (i.e.; multiple Gaussian pyramids). So far from my research, I formed the following function definition: I'm not sure if my research led me to the correct way of forming the function. Is this how...

Hi, I'm a product designer looking for some help. I need to fit squares into the dimensions of a rectangle. There can be any amount of squares just as long as the squares are complete and their dimensions are complete decimals. The dimensions are 16.5cm x 14cm. I don't want the squares to be...

Hi everyone. What are the components of the 2 Translational Killing Vectors in 2-dimensions, in Polar Coordinates? I've solved the Killing equation using Maple, and the solution was ##\xi_r = 0##, ##\xi_{\theta} = r^2##, but I guess that these are the components for the rotation Killing Vector...