2d Definition and 1000 Threads

I have worked out (and then verified against some sources) that ##R^\theta_{\phi\theta\phi} = sin^2(\theta)##. The rest of the components are either zero or the same as ##R^\theta_{\phi\theta\phi} ## some with the sign flipped. I was surprised at this, because it implies that the curvature...

I have a Gaussian function of the form: def f(x,y): a=some number b=... c=... return 3*np.exp(-a*(-0.5 + x)**2+b*(x-0.5)*(y-0.5)-c*(-0.5 + y)**2)This is a Gaussian function symmetric around y=x, and I'd like to rotate it 45 degrees (counter)clockwise. Wikipedia gives an overdetermined...

I know the conventional method for solving this question using the formula for maximum range of a projectile in an inclined plane, but since it is an objective problem, if we consider a non general case where α=0, then clearly we can see that (see attachment) only one option matches which...

Hi everyone! I don't know how to solve the next problem, and if anyone could explain to me step by step how it is solved I would thank you a lot. I know it's not hard, but I'm not seeing how to do it. Thank you in advance!

The question I am trying to solve is what is the velocity vector (direction and magnitude) of an object in 2 d space. We know the distance measured to the car from two different angles. We know the radial velocity of the car on both measurements. The radial velocity is the component of the...

Xcomp: [-(1500kg)(100km/h)(sin(30))+(3500kg)(70km/h)(cos(90))]/5000kg = -15km/h ycomp: [(1500kg)(100km/h)(cos(30))+(350(70km/h)(sin(90))]/5000kg = 74.98km/h

Hi everyone! Both sources I'm currently reading (page 291 of Mathematical Methods of Classical Mechanics by Arnol'd - get it here - and page 202 of Classical Mechanics by Shapiro - here) say that, in the case of the planar harmonic oscillator, using polar or cartesian coordinate systems leads...

Answer is 37.8 g cm^2 new to latex

In the context of forecast for large survey, I have to make cross-correlations between 2D (with angular coordinates of Lagrange transformation for GC photometric and Weak Lensing) and 3D (Fourier transform with radial coordinates for GC spectroscopic). For the moment, only cross-correlation...

I learned about Bessel functions and steady-state temperature distributions in the past. Recently, I was searching online for some example problems on the topic and found the "original question" along with the solution online as a PDF file. While I am unsure will it be appropriate for me to...

Hi all, I'm working on programming a simple 2D method of characteristics program to design the nozzle wall contour for a supersonic rocket nozzle. I'm wondering roughly what sort of difference I should expect from a 2D vs 3D method of characteristics program and where I could find a good...

I am interested, in the context of my work, in the cross correlations between a spectroscopic probe (which gives a 3D distribution of galaxies with redshifts, which is also called spectroscopic Galaxy clustering, GCsp) and a photometric probe (which gives an angular distribution, that is to say...

Hii Friends. I was trying to model an Induction motor in ANSYS Maxwell 2D. The final output of Transient torque (negative torque) looks like shown below. The input passed is a sine wave current with 120 deg phase shift. Any Suggestion will be highly appreciated

Consider a slope with mass, that can move in the horizontal plane without friction. A ball is dropped and hits the slope with restitution coefficient e. How to calculate the final velocities? How can I solve something like this? Note that it's not a simple 2D collision, it has a restriction...

When we try to explain different dimensions we say that higher dimension beings have control over lower dimension beings. If a sphere moves trough a 2D world, the 2D beings will see a dot appear followed by a line which is increasing in size. Thereafter, the line decreases in size and becomes a...

Let's say you have a simple structure with two equal masses connected by a massless rigid baton of length L. Like this: Imagine this structure is totally free in space. It is not hinged in any way. Then forces act on each mass in 2D (x,y). If you have the x and y force vectors acting on each...

Too dim for this kind of combinatorics. Could anyone refer me to/ explain a general way of approaching these without having to think :D. Thanks.

In 2D modules, the 3rd direction isn't shown in model settings. What assumptions are made regarding electrostatics 2D modules? For example, how is a 2D Poisson's equation with point sources solved? Is it based on a 1/r potential or a log potential?

I ultimately want to make a sewing pattern of a ball. If I have an n-hosohedra, how do I figure out the equation of the curves that make up each lune in 2D?

For getting the density of states formula for photons, we simply multiply the density of states for atoms by 2 (due to two spins of photons). I am getting the 2D density of states formula as :- g(p)dp = 2πApdp/h^2 I think this is the formula for normal particles, and so for photons I need to...

Hi! Situation: quasi-free electron in a 2D lattice, considering atomic potential V(r) = exp{-|r|/b} (r is the distance from the atom) I'm trying to compute the first five energy gaps at point (10), firstly I don't understand the meaning of calculated 5 energy gaps at one point and usually we...

I'm trying to compute a 2D Heat diffusion parabolic PDE: $$ \frac{\partial u}{\partial t} = \alpha \{ \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} \} $$ by the ADI method. I am actually trying to go over the example in this youtube video. The video is in another...

Hi, I am trying to find equation of motion and its solutions for a 2D infinite lumped mass spring system as depicted in figure. All the masses are identical, All the springs are identical, and even the horizontal and vertical periodicity is the same n=a. I need to try find dispersive relation...

How do I get the wave dispersion for a 2D continuum unit cell subjected to a periodic boundary which is excited longitudinally? I'll be applying forces in ABAQUS with varying frequencies. I have come across Blochs theorem but I can't find any application of it in continuous systems. Every...

Suppose that I have the coordinates of x and y on a plane. I am writing a piece of software where the user can select a polygon of 3, 4, 5, 6 or 8 sides. All of the polygon points are equidistant from the x, y point. In other words, if you drew a circle where the center was the x, y point, all...

What's the best software to use when designing 2D floor plans for structures?

Hi PF! Do you know what the natural oscillating frequencies are for a 2D circular drop of liquid in an ambient environment (negligible effects)? Prosperetti 1979 predicts the frequencies for both a spherical drop and bubble here at equations 5b and 6b. There must be a simpler circular 2D...

I am unable to find any angle for which the horizontal and vertical components of the linear momentum are conserved. I have added an image of my attempt

I know this topic was raised many times at numerous forums and I read some of these discussions. However, I did not manage to find an answer for the following principal question. I gather one deals with the same set in both cases equipped it with two different structures (it is obvious if one...

Dear experts, How would I find the forces for the truss with both ends pinned? (Fig.1, bottom) I'm trying to determine the forces in all members of some trusses. I've successfully applied the method of sections to a Howe truss (top truss in Fig.1) and I' ve verified it by FEA with MecWay...

import matplotlibimport matplotlib.pyplot as plt import numpy as np from sklearn import datasets, linear_model import pandas as pd # Load CSV and columns df = pd.read_csv("C:\Housing.csv") Y = df['price'] X = df['lotsize'] # Split the data into training/testing sets X_train = X[:-250] X_test =...

It is well known that the 2D free electron gas fermi momentum can be expressed as follows, k_F=\left(2\pi n\right)^{1/2} where n is the electron surface density. Assuming this 2D electron system can be considered as 2-D tight-binding square lattice whose eigenergy can be written as...

Hi, I've been given a homework to do based on 2D Ising model. Ive already read plenty of articles bout 2d ising model but I'm not fairly certain about some things. I got to do a chart similar to the one I attached. Correct me if I am wrong, but on the Y axis, I have to put average of...

Pardon if the answers to my questions are obvious, because as usual I am trying to decipher everything on my own (as the material has not been taught to us quite well; then again it's graduate school). I just need someone to reassure me that I am understanding this correctly. Say for example I...

Hi all, Sorry, in my first message, I posted this question in the Basic Probability section, and so I moved it to this section. I have a surface (for example, a blank paper). In this surface, I have some elements of the set "A" randomly distributed. In this surface, I also have some elements...

Which could be the first step to find the V(t) ?

## \int_{-1}^{1} \int_{-1}^{1} e^{-(x^2 + y^2)} cos(2π (x^2 + y^2)\,dx\,dy ## ## I = \int_{-1}^{1} \int_{-1}^{1}f(x,y) \,dx\,dy \approx \sum_{i=0}^{n}\sum_{j=0}^{n} w_i w_j f(x_i, y_j) ## ## = w_0 w_0 f(x_0, y_0) + w_0 w_1 f(x_0, y_1) + w_1 w_0 f(x_1, y_0) + w_1 w_1 f(x_1, y_1) ## ## w_0 =...

We have a 2D box (billiard table) which have size of Width = 600 and Height = 300. We have two identical ball a radius of 20. Also the balls decelerate with a rate of 5 m/s^2. The problem is to find the position of the ball after 10 second. ( The balls may have collide) from math import...

So ##T+U=\frac{1}{2}m(\dot{x}^{2}+\dot{y}^{2})-mgy=constant##. If I derive this with respect to ##t## $$\dot{x}\ddot{x}+\dot{y}\ddot{y}-g\dot{y}=0$$ Then I use ##\dot{y}=\dot{x}\frac{dy}{dx},\ddot{y}=\ddot{x}\frac{dy}{dx}+\dot{x}^{2}\frac{d^{2}y}{dx^{2}}## to get...

I would like to model the dynamics of a plate. Is it ok to use just the 2d wave equation if the plate will be under tension and fixed at the boundaries? I am a bit confused what the point of the Kirchhoff plate equation is in that case, is it for when the plate is self supporting? Many thanks

I'm tasked with drawing the trajectory of the Moon around the Earth (in 2D), taking into account the fact that the trajectory also undergoes precession, so the elliptical orbit rotates about it's center (I think it should rotate around the Earth-Moon barycenter, but for the first step I...

I have calculated the normalization constant, but I'm struggling with the discontinuities in the derivatives of the wave function. Due to the symmetry, it should suffice to consider the first two cases. The results should be (according to WolframAlpha): \left( \frac{\partial^{2}}{\partial...

Summary: How to explain the focusing properties of a 2D parabolic mirror based on third-order aberration theory? Hello everyone, I am currently studying with full-wave simulations the focusing properties of a 2D parabolic mirror, i.e. the scattered fields resulting from plane wave incidence...

I just tried to find the eigenvalues (for the energy), obtaining E = ±(γħ.√(Bo² + Γo²))/2 and the corresponding eigenvectors for the H matrix. But I don't know what to do to create de state vector χ.

Hi I have a 2d trajectory of a center of mass which I have saved in an array such that r=[[x(t_1),y(t_1)],[x(t_2),y(t_2)],...,[x(t_n),y(t_n)]] where x is x coordinate of the position and y is the y-coordinate of the position. I have tried this: xx = [t[0] for t in r] xy = [t[1] for t in r]...

Since in 2D the riemman curvature tensor has only one independent component, ## R = R_{ab} g^{ab} ## can be reversed to get the riemmann curvature tensor. Write ## R_{ab} = R g_{ab} ## Now ## R g_{ab} = R_{acbd} g^{cd}## Rewrite this as ## R_{acbd} = Rg_{ab} g_{cd} ## My issue is I'm not...

I am trying to understand ergodic theory, i.e. how simple systems reach equilibrium. I consider a classical particle in a 2D (or 3D) box. Funnily, I have never seen this example in books (probably due to lack of knowledge). Instead, in QM, the particle in a box is a prototypical example. My...

Hi, My other post got deleted because it was flagged for spam, but it was just a link to a pdf. So I'm uploading the pdf instead. I am working on a model to predict drag on airfoils in 2D potential flow (e.g. vortex panel methods). Currently, XFOIL uses a semi-empirical wake-momentum-thickness...

My only issue is what this would look like. I can't draw a respective picture.