What is 2d: Definition and 1000 Discussions

I'd like to check if my reasoning is right here and that the numerical factors in the final result are correct. The disks occupy an effective area ##A = (A_{\mathrm{box}}-2r)^2##, excluding the region of width ##r## at the boundary. The area available to the ##n##th disk is then ##A_n = A - 4\pi...

I am trying to implement this equation ##−k∇^2 u = e^{-(x^2+y^2)}## using NDSolve in Mathematica. The idea is to solve for the temperature of a plate 10 x 10 units, with heat inputs as per the RHS. Here is my attempt: NDSolve[{ - Laplacian[u, {x, y}] == Exp[-(x^2 + y^2)], u[x, -5] == 0, u[x...

Hello, I am review some key linear algebra concepts. Let's keep the discussing to 2D. Vectors in the 2D space can be simplistically visualized as arrows with a certain length and direction. Let's draw a single red arrow on the page representing vector ##X##, an entity that is independent of the...

Most of us have probably read Edwin Abbot's "Flatland," which was published in 1884. https://www.gutenberg.org/cache/epub/201/pg201.txt In this novella, sapient and motile polygons & circles inhabit a two-dimensional world. Late in the story, a sapient sphere presents itself to the...

So I tried the following: Getting the velocities for x and y V_xi = 5.2cos(30) = 4.5 V_yi = 5.2sin(30) = 2.6 Then I use v^2 = u^2 +2as to get the final velocities before she leaves the ramp: for V_x the final is the same as the initial since the equation becomes V_xf = V_xi for V_y the final is...

This is not for professional career or something. This is just to practice OOP as I'm learning C++ atm. I found there are not many course for sfml, sdl, allegro, graphics.h,raylib etc unlike unreal engine. So, if you know something which has a good tutorial, please recommend. In OOP way. I want...

Desired output similar to image, but without the objects and with better wave interference: I tried plugging the following into wolfram (I specifically want the values to be adjustable): plot z= H*e^(-m*sqrt((x-a)^2+(y-b)^2))*sin(k*(x-a)+k*(y-b) -w*t) +...

I am looking for books that contain explanations (or to be able to answer) about something like this: 1) Exterior Angle Bisector Theorem The external angle bisector of a triangle divides the opposite side externally in the ratio of the sides containing the angle. This condition occurs usually...

Hi everybody, I don't have M700 grade silicon/electrical steel data to add to Maxwell Electronics 2D Material Library. How/Where can I find this data? Could you help me? Thanks, Oguzhan Gonc

Consider the following heat map: from scipy import special import numpy as np import matplotlib.pyplot as plt u0=200 r0x=25 r0y=25 rmax=2.5 alpha=2 t=0.575 y, x = np.meshgrid(np.linspace(0, 50, 100), np.linspace(0, 50, 100)) r=np.sqrt((x-r0x)**2+(y-r0y)**2)...

Hello! I have some electrons produced from a 3D gaussian source isotropically inside a uniform electric field. The electric field guides them towards a position sensitive detector and I end up with an image like the one below (with more electrons on the edge and fewer as you move towards the...

There is a passage in this book where I don't follow the logic; In this short quotation from 'Quantum Mechanics: The Theoretical Minimum' by Leonard Susskind and Art Friedman \mathcal{A} represents the apparatus that is performing the measurement the apparatus can be oriented (in principle) in...

I have worked through the basics of the FEM method in 2D with rectangular elements and now am trying to learn triangular elements but need a simple enough numerical example. It seems triangular elements are far more complicated and also depend on the global coordinates thus each local stiffness...

Does anyone know a C# class that can return a value (0 - 100 percentage) of How close a perfect gaussian curve an 2D Matrix is? for example, these would all return a 100%:

Hi, Forgive me for the crowded drawing, but please reference the attached screenshot. Let’s say I have 2 plates bolted together by some bolts (red), and on the inside is a pressure w pushing the top plate up, in psi (lb/in^2). In order to get an estimate for the maximum distance between bolts...

I am concerned that this question may instead be a philosophical one although if it it mathematical, any insights would be very appreciated. The question is this; could an object of N dimensions exist entirely in N-1 dimensions? In other words, could an infinitely flat object have 3 degrees of...

So I'm looking at the book "Equilibrium Statistical physics" by Plischke and Bergersen. I'm doing the calculation of the specific heat of the 2D Ising model. I can't seen to quite get out the same expression as in the book - there are a coupe of minus signs that are different. I don't know if I...

I just want to know if there is a consensus on experimental evidence of spin-charge separation in 2d?

I want to solve the 2D heat equation $$\frac{∂^2 {T}}{ ∂x^2} + \frac{∂^2 {T}}{ ∂y^2} = 0$$ The only boundary conditions is I will specify the edge temperatures but there are no heat sources. So I create an average temperature function ##\tilde{T}## and weighting functions ##S_i## over a...

I want to model the advection of debris rock layer with a thickness hd on top of a glacier through ice flow with velocity components u and v. Can anybody explain the physical difference between these 2 equations and which one I should take? Thanks

I wish to set up the node equations for a 2D heated plate with boundary conditions. I understand how to do this in 1D but have not found a suitable example problem worked out in 2D and examples I have seen are very involved and complex. @pasmith showed me you to set up the 1D problem as follows...

Hello there, for the above problem the wavefunctions can be shown to be: $$\psi_{n,l}=\left[ \frac {b}{2\pi l_b^2} \frac{n!}{2^l(n+l)!}\right]^{\frac12} \exp{(-il\theta - \frac {r^2\sqrt{b}}{4l_b^2})} \left( \frac {r\sqrt{b}}{l_b}\right)^lL_n^l(\frac {r^2b}{4l_b^2})$$ Here ##b = \sqrt{1 +...

Hi, I am a game developer and recently found myself in a situation where I wanted to create an enemy that shoots at you given a set of variables. The game takes place in a top down view so there is no need for gravity acceleration, just 2d linear constant movement. The question to answer is...

this is my work but the answers say 11 m/s^2 so I made an error somewhere. Also if someone could help me with solving the direction for the acceleration, that would be greatly appreciated.

I have also put some notes on what is to be done in the problematic function Note also that this is not homework, but am just preparing for an exam. Thanks in advance! forgot to provide the code here, so here it is: # RPG subsystem: check whether the next player move on a 5x5 tileset is...

Hello all! As seen in the summary, I'm not sure if anyone can understand, but I will try to make this as clear as possible. Working in the 3D Plane: Given that there is a trajectory motion in the 3D Plane, and I have the coordinates of the motion at every 1s interval. This means at t=1s, the...

Ive been reading University physics by roger freedman, I’m on section 3 motion in 2d. I can solve most of the problems ag the end of the chapter, or at least understand the solutions. But there is a small extra section called challenge problems. There’s only 3 but I found them very difficult...

Greetings Good People, As the title suggests, I'm having some trouble getting to a 2D model. The process is to select an aircraft (or wing model), and model it as a 2D, 2DOF wing-tunnel model. The aircraft I selected was a Cessna 172. This had a tapered wing, which after some calculations and...

The method I employed was based on a nested loop. I ran into two issues with this approach 1. The code took way too long to run, easily going for over 7 minutes. 2. In the end, it didn't even completely work, due to the "index exceeding the array length". This confuses me For the relevant...

The classical free surface profile for the solitary wave for irrotational and incompressible fluids for small amplitude and long wavelength is the classical Korteweg-deVries(KdV) equation given by:\frac{\partial\eta}{\partial t}+\frac{\partial \eta}{\partial x}+\eta\frac{\partial\eta}{\partial...

I have to find the center manifold of the following system \begin{align} \dot{x}_1&=x_2 \\ \dot{x}_2&=-\frac{1}{2}x_1^2 \end{align} which has a critical point at ##x_0=\begin{bmatrix}0 & 0\end{bmatrix}##. Its linearization at that point is \begin{align} D\mathbf {f}(\mathbf {x_0}) =...

the image on the right shows the problem. the blue ink is the equation someone else gave me, and I don't understand why the force between box2 and ground goes down... (the red is me) the force f is applied to box2 so that it pushes box2 down, so isn't the spring k2 supposed to push upward?

A question of sign. Is the curvature of Flamm's paraboloid positive or negative? If I've gotten the signs correct, it's a negative curvature. This is the opposite of the positive curvature of a sphere, and it implies that that geodesics drawn on Flamm's parabaloid should diverge. I think...

I want to develop a 2D random field and its change with time with constant velocity. My process: 1. Define a 2D grid [x, y] with n \times n points 2. Define 1D time axis [t] with n_t elements 3. Find the lagrangian distance between the points in space with the velocity in x and y ...

I’m planning to write a 2D Minkowsky spacetime diagram generator tool. At this point, I am looking for help reviewing the specification. I am not looking for help with the implemenation. To be clear, I’ve written a complete specification, but it would be a waste if it was missing features that...

I have a 2D space-time PDE and I want to solve it numerically over the time axis. The time initial field is already known with respect to space, i.e., the spatial distribution is already known at time `t = 0`. I solved the same PDF in Mathematica and got a solution. I tried to solve it...

Good day. We know how simple objects, such as 1D wires behave when a simple harmonic wave travels along a wire, or two wires knotted togethe.We also know what happens if you excite a circular thin disc with a single frequency. Are there some material I can read on, that considers the effect...

I'm watching this minutephysics video on Lorentz transformations (part starting from 2:13 and ending at 4:10). In my spacetime diagram, my worldline will be along the ##ct## axis and the worldline of an observer moving relative to me will be at some angle w.r.t. the ##y## axis. When we switch...

Hello! What is the 2D (acting in spin space) representation of the parity operator. In principle we can make it a diagonal matrix with the right transformation and given that ##P^2=1## the matrix would be diag(1,1) or diag(1,-1). However spin shouldn't change under parity and using that it seems...

Let f be a 2 variables function. 1) ##f(x,y)=g(x)+h(y)\Rightarrow df=g'(x)dx+h'(y)dy\Rightarrow\int df=g(x)+k(y)+h(y)+l(x)=f(x,y),\textrm{ if } k=l=0## 2) ##f(x,y)=xy\Rightarrow df=ydx+xdy\Rightarrow\int df=2xy+k(y)+l(x)\neq f(x,y)## Why in the second case the function cannot be recovered ?

I am having problems writing the initials conditions.

Hi, I was attempting the following question, but got confused on this part: Question: Two radar tracking stations provide independent measurements ##x_1## and ##x_2## of the landing site, ##\mathbf{x} = (x, y) ##, of a returning space probe. Both have Gaussian sensor models, ##p(x_i|X_i ) =...

Hi, I was working on the following problem: Two classes ## C_1 ## and ## C_2 ## have equal priors. The likelihoods of ## x## belonging to each class are given by 2D normal distributions with different means, but the same covariance: p(x|C _1) = N(\mu_x, \Sigma) \text{and} p(x|C_2) =...

Can a simplified 2D model of our universe be an expanding ball? Where the surface of the ball is the 2D universe time is the vector normal of the ball measured in imaginary number i. So light will move at 45 degree to any vector normal. The expanding ball gets bigger because time is causing it...

Well, okay, I should say: what does Newtonian gravitation look like in a ##2+1## dimensional Newtonian universe? Consider a flat Earth, i.e. a region ##\mathcal{E} = \{ (x,y): x^2 + y^2 \leq R \}## with mass density ##\rho##, then for ##r > R## a natural guess for the gravitational field seem...

If we were to use three-dimensional spheres to represent sets, could a 3D Venn diagram be constructed that could not be drawn as a normal 2D Venn diagram without changing the relationships between the sets?

Hi, I have question about finding marginal distributions from 2d marginal pdfs that lead to the probabilities being greater than 1. Question: If we have the joint probability distribution ## f(x, y) = k \text{ for} |x| \leq 0.5 , |y| \leq 0.5 ## and 0 otherwise. I have tried to define a square...

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...