2d Definition and 1000 Threads

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 ##...

I have completed a 2D finite difference code in MATLAB that has a domain of (0,1)x(0,1) and has Dirichlet Boundary Conditions of value zero along the boundary. I get convergence rates of 2 for second order and 4 for fourth order. My issue now is that I'm now wanting to change the domain to a...

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...

Hi All, I needed some help or guidance starting my MSc reading, as there is tonnes of literature out there and it's difficult to understand what is necessary. I am beginning to look at applying screening models to a 2D system, such as the Thomas-Fermi continuum screening model, to a 2D system...

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...

I wasn't sure where to post this, I hope this was the right section. I've been struggling quite a bit with implementing an autocorrelation code into my current project. The autocorrelation as it is now, is increasing exponentially from 1 at the start of my MC run, and hitting 2 halfway through...

I've made a fluid flow simulator, for anyone interested in fluid dynamics. The simulator models some basic flows which I learned on a 2nd year fluid dynamics course. It doesn't include viscosity, density or whatever else (hence for example the flow past a sphere in the simulator is a perfect...

Hi all , Could you please help me solve Poisson equation in 2D for heat transfer with Dirichlet and Neumann conditions analytically? Thank you

Homework Statement There are two cliffs separated by 40 meters (horizontal displacement). An arrow is shot from a bow at an angle and a velocity of 90 m/s. The arrow takes 0.75 seconds to arrive at the other cliff. What is the angle at which the arrow was released? Neglect air resistance...

I am quite new here, and was wondering if anybody knows how this 2D integral is evaluated. $$ \int_{-\infty}^\infty \int_{-\infty}^\infty \delta(k_1 x-k_2y)\,dx\,dy$$Any help is greatly appreciated! Thanks!

I'm trying to read this paper. Right now my problem is with equations 3.16 and 3.17. I understand that in equation 3.16 we're putting some boundary conditions on the fields, but I have two problems with these boundary conditions: 1) The fields depend on both ## t_E ## and ## x##, i.e. ##...

Hello, I have a project (model reaction diffusion brusselator 2d) ∂u/∂t=A+u^2v-(B−1)u+D1((∂^2)u/∂(x^2)+(∂^2)u/∂(y^2)) ∂v/∂t=Bu−u^2v+D2((∂^2)v/∂(x^2)+(∂^2)v/∂(y^2)) initial conditions: u(x,y,0) = 0.5 + y, v(x,y,0) = 1 + 5x. boundary conditions: ∂u/∂n = 0, ∂v/∂t = 0 n-external normal to the...

I want to make a 2D plot of points with different x, y coordinates and have colors depending on a separate variable. I have make column vectors for x and y coordinates and another column containing 1 or -1. I would like to represent the points with 1 as red and -1 as blue points. I have codes as...

I am performing a 2D analysis on a steel frame structure that is 8 storeys high using NZS 1170.5:2004 (New Zealand Standard for Earthquake Actions). How much of the original 3D structure's mass should be added to the 2D frame to make the analysis realistic? How should this mass be distributed...

Homework Statement A car moving due south at 20.0 m/s enters a highway cloverleaf. The car will exit the cloverleaf to merge with westbound traffic traveling at 29.0 m/s. The time between entering the cloverleaf and exiting to merge with westbound traffic is 20.7 s. What is the magnitude of...

Homework Statement A reasonable approximation for the two-dimensional incompressible laminar boundary layer on the flat surface in Fig. P4.17 is u ≈ U(2*(y/δ) - 6*(y3/δ4) + y4/δ4) δ = Cx1/2 where C is a constant y ≤ δ Homework EquationsThe Attempt at a Solution Incompressible so...

Homework Statement Why are the Center of Momentum velocities of masses after a 2D elastic collision anti-parallel? (as in the following diagram) Homework Equations CM_Velocity = (∑m_i*v_i)/(∑m_i) The Attempt at a Solution This is not actually a problem I have to do. I am just looking for a...

Homework Statement This is a three step problem (I am not fond of the multi-step problems as I can usually do better without multiple steps. Here is the problem: A uniform ring of mass m = 10 kg and radius r = 195 mm carries an eccentric mass m0 = 18 kg at a radius b = 160 mm and is in an...

Homework Statement Here's the question: http://i.imgur.com/zs130b3.png Homework Equations Just the usual Lorentz transform matrix etc. The Attempt at a Solution http://imgur.com/4Oipfu9 Now, the last line is clearly incorrect, since it tends towards infinite relative speed as v --> c. Of...

If you were to look at a simple 2D or 3D static equilibrium diagram, where a mass is suspended by multiple ropes at different angles, my gut feeling is that there is a fairly simple proportion between the distance between the center of mass and the rope (the distance created opposite of the...

Homework Statement [/B] Determine the moment about point B of each of the three forces acting on the beam. Homework Equations M = F*d⊥ The Attempt at a Solution I went and found the components for each of the forces. Please double check it if I did them right: F1 : Fx = 0 Fy = 375 lb F2: Fx...

Homework Statement Question is on the attachment photo. Homework Equations I tried to create an equation but I didn't know the momentum for each of the people in the scenario because none of them have a given speed.[/B]The Attempt at a Solution I just need the velocity of Superman to solve...

Homework Statement Each one of the force vectors are surrounded with dimensions. But you're not given any angles. How do you solve for the resultant vector like that? Homework Equations Fr = F1 + F2 + F3 The Attempt at a Solution I tried taking the arctan(200/210) on the 435 N vector to...

Hi there, I have 1024,1024 arrays (lots of them) which are really roughly 600,800 (it changes) and then buffered by zeros all the way around something like 000000000000000000 000000000000000000 000xxxxxxxxxxxxx000 000xxxxxxxxxxxxx000 000xxxxxxxxxxxxx000 000000000000000000 000000000000000000 i...

Hi, I am a student in the Netherlands, currently 17 years old and at the end of my 'middelbare school', meaning that next year I'll be a bachelor student at a university. I am doing an extended essay/research thing that is custom you do in your last year, with a friend of mine. We picked the...

I have large 2d matrices from dicom files that i wish to filter with a 3x3 mask. the image arrays are of varying size and are padded with one border of zeros for the edge handling of the mask. i need to iterate over every element in the array and multiply it by the mask. I've done it in SciLab...

Hey everyone, I just started, what is supposed to be a beginners course in MatLab, but I am the only one who has never used MatLab before! I'm stuck on the very first HW assignment (although I did manage to get to problem 6 out of 7) and was hoping someone could explain why I keep getting an...

Hi, I have some questions about the 2D SWE (Shallow Water Equations). I would like to know if an exact (analytical) solution is available in the case of the (linear) surface "gravity" wave. Indeed, my example of interest is given by a square [0,L]2 with initial velocity field u = v = 0 and an...

Hi guys, I have a dicom image from a QC spect acquisition. reading the file in with dicom.read_file and pulling pixel data using numpy.pixel_array gives array of shape [2, 1024, 1024] The 2 represents two images, one from each detector head on the spect scanner and the 1024x1024 are the...

I am trying to find and solve the geodesics equation for polar coordinates. If I start by the definition of Christoffel symbols with the following expressions : $$de_{i}=w_{i}^{j}\,de_{j}=\Gamma_{ik}^{j}du^{k}\,de_{j}$$ with $$u^{k}$$ is the k-th component of polar coordinates ($$1$$ is for...

Homework Statement A 2D elastic collision: Two pucks (masses m1 = 0.5 kg and m2 = 0.3 kg) collide on a frictionless air-hockey table. Puck 1 has an initial velocity of 4 m/s in the positive x direction and a final velocity of 2 m/s in an unknown direction, θ. Puck 2 is initially at rest. Find...

Wikipedia says this: "the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it." Say that there is 1D space "contained" within 2D space and the former can be represented as a line in a 2D Cartesian...

The schematic figure, depicted below, shows a 2D layer (yellow) which is over an insulated layer shown by green (see (a)). A potential gate is below the insulator layer and I want to induce a constant potential in the part of the yellow layer located over the gate (See (b)). In other words, I...

Homework Statement Hi, I've been trying to solve this exercise for the last four hours and I'm totally stuck. The problems goes like this: Given the mechanism in the image, located in the vertical plane, the OB cord is cut when t=0. Find the reactions Rx, Ry and N in {Kgf} for the instants...

Should one be able to take the results of 5D Kaluza-Klein theory and turn it into a theory that works with two less space dimensions? Thanks!

Homework Statement For a gas of N fermions with mass M in 2D in a region of area A in thermal equilibrium at temperature T, we are asked to find ##U/N## in fuction of ##T## and ##a=A/N##. The attempt at a solution I used ##U=\sum(<n_i>\epsilon_i) = \sum(\exp(\beta(\mu-\epsilon_i))\epsilon_i...

Could someone please explain me how can we get equation 5.177? Thank you so much for your help

Are there any theorems that say something formal about the fact that any graph is drawable on a 2D surface, and can be mapped to a 2D array of pixels if the pixels are infinitely small?

Hi, I know how to calculate density of states for both cases, but it is not clearly to me how I can go from 3D case to 2D. I have energy from infinite potential well for 3D $$E=\frac{\hbar \pi^2}{2m}(\frac{n_x^2}{l_x}+\frac{n_y^2}{l_y}+\frac{n_z^2}{l_z})$$ let make one dimension very small...

Does there exist any 2D surface whose metric tensor is, ##\eta_{\mu\nu}= \begin{pmatrix} -1 & 0 \\ 0 & 1 \end{pmatrix}##

I am looking for a 2D fft that takes in a 2D array of heights and does a fft in c on the array. I would like if the code was capable of working with big arrays, such as 8192 x 8192 I have tried the paulbourke and sanfoundry websites. The first was not giving me the output that is expected and...