2d Definition and 1000 Threads

This is a seemingly simple question, though I'm not exactly sure where I'm going wrong (if in fact I am going wrong). To start off: you have a 2D un-normalized Gaussian function centred at the origin and with a sigma of 4. If you integrate it over a circle of radius 4 also centred at the...

Hello my name is Pablo, I'm new in the forum and couldn't find any similar post so i decided to ask. I have the following situation: In reference frame S (asumed stationary) there is a stick (length Lo in frame S) which falls from Yo at a vertical speed of 0.6c relative to S. In S the stick is...

I neet to do a structured triangular mesh 2D of a complex geometry with FORTRAN Can someone help me!

Consider the following random walks in 2D, starting at a point we will call the origin: (a) random walk on a square lattice (step size 1 on the integer lattice for example) (b) random walk on a triangular lattice (step size 1 on the lattice of equilateral triangles of side 1). Thus there are 6...

Homework Statement Consider the following inital states of the symmetric 2D harmonic oscillator ket (phi 1) = 1/sqrt(2) (ket(0)_x ket(1)_y + ket (1)_x ket (0)_y) ket (phi 2) = 1/sqrt(2) (ket(0)_x ket(0)_y + ket (1)_x ket (0)_y) Calculate the <p_x (t)> for each state Homework EquationsThe...

Homework Statement Trajectories around a black hole can be described by ## \frac{d^2u}{d\theta^2} + u = \alpha \epsilon u^2 ##, where ##u = \frac{1}{r}## and ##\theta## is azimuthal angle. (a) By using ##v = \frac{du}{d\theta}##, reduce system to 2D and find fixed points and their stability...

Given the equation for a Gaussian as: ##z = f(x,y) = Ae^{[(x-x0)^2 + (y-y0)^2] /2pi*σ^2 }## , how would I go about converting this into cylindrical coordinates? The mean is non-zero, and this seems to be the biggest hurdle. I believe I read earlier that the answer is ~ ##z = f(r,θ) =...

Homework Statement (a) Find energies of states at ##(\frac{\pi}{a},0)##. (b) Find secular equation Homework EquationsThe Attempt at a Solution Part(a)[/B] In 1D, the secular equation for energy is: E = \epsilon_0 \pm \left| V(x,y) \right| When represented in complex notation, the potential...

Hi people. I just read some articles about physicist starting to gain more and more evidence for the Universe to be a 3D Hologram of a 2D world (or that's how I understood it). And apparently for us living in a "Matrix", like the one in the movie. Now I would like to understand the relation...

In 2 dimensions, is the geodesic deviation equation governed by a single scalar, independent of the direction of the geodesics? That is, if ξ is the separation of two nearby geodesics, do we have d^2 \xi/ds^2 + R\xi = 0 where R is a scalar that is completely independent of the direction of the...

Homework Statement A simple model for liquid crystals confined to 2 dimensions is o assume each molecule can only align in one of 2 perpendicular directions. To construct a landau model its convenient to define order parameter, s : s = 2 ( Np - 0.5Nt ) / Nt Np - number molecules...

Hello, I'm trying to derive the perfectly matched layer for the TM mode Maxwell's equations using a complex coordinate stretching. As seen in http://math.mit.edu/~stevenj/18.369/pml.pdf . But I'm running in a bit of trouble somehow. \partial_t H_x =-\mu^{-1} \partial_y E_z\\ \partial_t H_y...

I am working on simulating the magnus effect of lift on a spinning ball. Right now spinning on the z axis I can calculate the force effect it has on the x and y coordinates. If I am to add spin on the x do I do the exact same calculations effecting the y and z coords and just add them to the z...

Homework Statement There is an infinite 2D mesh of conducting wire. Resistance between any two consecutive junctions is R. What is the equivalent resistance between any two consecutive junctions? Homework EquationsThe Attempt at a Solution Every junction is connected to four points and one of...

:ey all, I'm seeking to write an egomotion program and want to do research into existing algorithms and the math of it, but googling "egomotion algorithms" doesn't seem to turn anything up, is there a more popular name for extrapolating 3d scen from 2d scene? Or can anyone post a link? Any help...

Homework Statement An automotive test track forms a curve in the horizontal xy plane specified by y(x) =γx^3 / 2 where γ = 0.2 m^-1/2 and x ≥ 0 . A car moves along the track, starting at rest at the origin at time t = 0 , and picking up speed in accordance with v = ct , where c = 4.8 m s^-2 ...

I understand that this has been answered, but I can't follow it. My apologies, physics is a realm I want to understand but it doesn't come naturally and I have no High school physics background just 1st yr Engineering physics. (passed with supps.) A particle is projected vertically upward in a...

What does f(x,y) in the 2D CT image account for? If for density, then which material is considered as a reference for that density? If for atomic number, then again which is the reference substance?

Homework Statement A 500 g billiard ball is going at 10 m/s [E] when it impacts 2 other identical billiard balls. Afterwards, you observe 2 of the balls moving at 2 m/s [30 W of S] and 3 m/s[45 N of E] respectively. Calculate the Energy lost in the collision. Homework Equations KE = 1/2mv^2...

1. Homework Statement Homework Equations CFD The Attempt at a Solution I'm a bit confused by this question. So at first what I do for the problem on the left, I find the changes in the velocities in X and and Y on all four sides. I notice that the values on the diagram to the left are...

I have measured the conductivity of a 2D material. I want to use σ=N⋅e⋅μ to find the mobility μ=σ/(N⋅e). https://en.wikipedia.org/wiki/Electron_mobility#Relation_to_conductivity I have measured N using a spectroscopic/imaging technique to get a Surface Density with units [cm^-2]. Mobility...

Homework Statement Find the two-dimensional solution to Laplace's equation inside an isosceles right triangle. The boundary conditions are as is shown in the picture: The length of the bottom and left side of the triangle are both L. Homework Equations Vxx+Vyy=0 V=X(x)Y(y) From the image...

Hello, I juste don't know how this was done it is on the solutionnary of a very long exercise and i am not getting this calculation 1. Homework Statement <1,0| ax+ay++ax+ay+axay++axay|0,1> = <1,0|1,0> Homework Equations 3. The Attempt at a Solution We have that |0,1> = ay+ |0,0> I don't...

Hello, i don't understand how i integrate the star equation at the figure. Fot example \int d x_1 \int d x_2 \frac{d^2G}{d x_1} = \int d x_1 \frac{d^2G}{d x_1} \int d x_2 but \int d x_2 x_2|^\epsilon_{-\epsilon}=0 ...sure this is a error, but i don't understand how i find the answer...

PROBLEM FORMULATION: Considering the region \Omega bounded as a square box within x \in [0,1], y \in [0,1] . We wish to solve the 2D, stationary, advection-diffusion equation, 0 = D\nabla^2 \rho(x,y) + \vec{V} \cdot \nabla \rho(x,y) where D is a scalar constant, and \vec{V} =...

I'm studying a two dimensional lattice with delta functions at the lattice points. When I diagonalized the hamiltonian I noticed that if I kept the dimension of my matrix less than 5 I would get band gaps at all the BZ boundaries. However, if I increased my matrix to a dimension 5 or higher...

Homework Statement The problem is stated here (from brilliant.org) http://i.imgur.com/MkWwnjT.png Homework Equations momentum = mass * velocityThe Attempt at a Solution My attempt at a solution can be found here: http://i.imgur.com/Zsco86W.jpg I get the answer 0.035kg, but that is not an...

Homework Statement A string is sewn in a 2D membrane. What is the amplitude of the reflected wave? All the parameters you need in order to get to the result are known. Homework EquationsThe Attempt at a Solution Ok, so we have a 2D membrane, with a string at ##x=0## along the the ##y## axis...

I've formulated a method for modeling the flight of a rocket projectile. Can anyone read it over and point out any mistakes false assumptions, etc? thanks!

Homework Statement Find stationary state of a circular membrane, on which a coin is put. Homework EquationsThe Attempt at a Solution I am not sure about the second boundary condition, so if any of you has the time, please check the following solution: $$u_{tt}=c^2\nabla ^2u+\rho g$$ Where...

Hi everyone, I am a graduate student in psychology and am working on a research project where I am trying to derive the kinematics of a mouse tracking task. I am currently writing a MATLAB script to do this, and I believe my equations for velocity and acceleration are correct, but I have very...

Homework Statement A 2.0 kg ball moving with a speed of 3.0 m/s hits, elastically, an identical stationary ball as shown. If the first ball moves away with angle 30 ° to the original path, determine a. the speed of the first ball after the collision. b. the speed and direction of the second...

Hi guys! I'm new to the forum, i hope you can help me with this trouble! it really is important =D i have a 2D binary compound AB (made of one of the 100 family of planes of a rocksalt structure) and i am asked to "consider a single s-orbital on each atom (atomic energies Ea,Eb) and nearest...

Homework Statement This is not a homework problem per se, but I have been working on it for a few days, and cannot make the logical connection, so here it is: -- The problem is to show that ##\frac{1}{4\pi} \int_{-\infty}^{\infty} \frac{ e^{-\sqrt{\xi ^2 + \alpha^2 } |y-y'| + i \xi (x-x')...

A skier 58.0kg coasts down a 25.0 degree uniform slope. A kinetic frictional force of 70.0N opposes her motion. At the top of the slope her speed is 3.60 m/s. What is her final speed at a distance 57.0 metres down the slope? Kinetic Energy = 1/2mv^2 V=Vi+at^2 F=ma So far I decomposed the...

Homework Statement Consider the following real scalar field in two dimensions: S = \int d^2 x ( \frac{1}{2} \partial_\mu \phi \partial^\mu \phi - \frac{1}{2} m^2 \phi^2 - g \phi^3) What are the Feynman rules for calculating < \Omega | T(\phi_1 ... \phi_n ) | \Omega > 2. Homework...

plane wave is represented as exp (ik.r) and the cylindrical wave as 1/sqrt(r) *exp(ik.r) and the spherical wave as 1/r*exp(ik.r) Have anyone tried to plot these waves? How to do it? Attempt: in Matlab assuming k=1 >> x=linspace(-1,1,100); >> for(ii=1:100) fp(ii)=exp(i*x(ii)); end >>...

Sorry for the confusing tittle but I could not explain it better. Here is what I am trying to ask: When you have 2 axis(x and y) such as the image below, the sum of the two angles, a and b will always be equal to 90 degrees. a + b = 90degrees However when you add a 3rd axis(x, y and z, making...

In adobe photoshop, is it possible to take and wrap a 2D texture onto a 3D model? And is it also possible to make a 2D object from a photo into a 3D one?

Now plasma represents collective wave-like motions of charged particles. In 3D, their frequency is well known to be almost a constant, ##\omega^{3D}_p \approx \sqrt{4\pi ne^2/m}## with n=charge density, m=particle mass. However, in 2D, one can show that it becomes ##\omega^{2D}_p \sim...

Homework Statement A catapult projects a stone in the normal direction to a playground which slopes at a angle of 10 degrees to the horizontal. The initial speed of the stone is 18 m/s. calculate the range parallel to the playground. Homework Equations the usual ones! The Attempt at a...

Homework Statement A two dimensional solid has two electrons per unit cell and has a Bravais lattice with primitive vectors ##\vec a = \ell \hat x## and ##\vec b = \ell \hat y##. The crystal potential is weak and the solid behaves like a free electron metal. a)In a reciprocal space diagram...

I'm recently new to the field of 2D Fourier Transform Infrared Spectroscopy and am learning its applications. I would like to know its applications in biology. Specifically, is there anything in the 400 nm to 1000 nm range that is important in protein structure, protein dynamics or biology in...

Homework Statement charge e is within 2 dimensions in presence of magnetic field. H = 1/2m (p - e/c A)^2 A = 1/2* B x r p and r have two components Show: H in terms of B along z axis resembles 2D HO (with some extra term) express H in terms of x, y, p_x, L_y Homework Equations L = r x...

I need some information urgently. I am working on crack of a 2-D cantilever beam. One side of the beam is fixed. I am applying a sinusoidal time varying load on other end in Y-direction.Beam length and width are 100cm and 10cm respectively. crack is 05 cm in y-direction. I have attached data and...

Problem statement: Two pucks of radius 0.05 meters collide as shown in attached picture. The mass of puck 1 is 0.1 kg and that of puck 2 is 0.15 kg. The initial velocities are v1i = 1 m/s and v2i= 0.6 m/s. (1) Assuming no friction between the pucks, only normal forces during collision, in...

The spectral radiance of a blackbody has units of W·sr-1·m-2·Hz-1. How do I deal with these units if I want to think about a 2D problem of radiation in Cartesian coordinates? I assume that instead of a sphere of emission (which would result in artificial decrease in intensity with the inverse...

Homework Statement Two balls A and B simultaneously start to roll down without friction along two different chords of a circle as shown in the figure. Find which ball will hit the circle first? (image attached) 2. The attempt at a solution I have divided the velocity of the balls into vector...

It can be easily proved that Bose Einstein condensation can be got in infinite 2D. But what about finite 2D with extreme large "Volume" L^2 ?

http://en.wikipedia.org/wiki/Newton%E2%80%93Cotes_formulas Simpson rule: 1 4 1, and the composite version: 1 4 2 4 2 4 2 4 ...4 1 in a double integral we just compute rows, and next columns, a this gives a matrix: http://mathfaculty.fullerton.edu/mathews/n2003/SimpsonsRule2DMod.html Milne's...