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Questions tagged [lattices]

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7
votes
4answers
315 views

How to generate a triangular grid from a list of points?

I am newbie with mathematica and the other day I saw a function that generates points from an original one defined as: ...
0
votes
1answer
75 views

Point lattice leading to triangle lattice

My main purpose is to eventually generate a triangle lattice from one original point, let's say the origin. So I want to start with the origin and generate 6 points around it, which are the vertices ...
3
votes
1answer
179 views

Hexagonal lattice points with center points in 2D

I am using the follwing coder from here, answered by Michael E2, to create 2d lattice points, without the center ponts of the cells. ...
2
votes
1answer
124 views

Creating 2d-HexagonalLattice and 3d-HexagonalClosePacking lattice with LatticeData function

I found here a solution by s0rce on how one can for example create a 3d FaceCenteredCubic lattice structure: ...
4
votes
2answers
216 views

Generating a grid such that the elements in each row add up to one

I'd like to generate a grid such that each element is a dimension $d$ vector ($\vec v$) of non negative components that add up to one. I could use the approach in this post and then choose among the ...
18
votes
2answers
684 views

How to build a neighbor table for the Hexagonal lattice

I want to consider a collection of vertices arranged in a finite Hexagonal lattice, with say $n_{r}$ rows and $n_{x}$ vertices per row, for a total of $N = n_{x}n_{r}$ vertices. The goal is to ...
-1
votes
1answer
149 views

How to plot a 2D triangular lattice

I wonder if I could plot the Fig1.(a) in Physical Review A 87, 063421 (2013), a triangular lattice in MMA. I undetstand that those atoms and interactions can be added by Adobe AI after obtaining the ...
3
votes
2answers
105 views

Minimise discrete function

Let $f\,\colon\,\Lambda\to\mathbb R$ be a real-valued function, where $\Lambda$ is a finite integer lattice. Say, $\Lambda=\mathbb Z_3^n=\{\vec x\,\mid\, x_i=0,1,2\}$ for some $n\in\mathbb N$. I'd ...
7
votes
3answers
156 views

Creating MeshRegions of various 2D lattices

This is a soft question about the best approach to design a function that creates MeshRegion objects of various 2D lattices, e.g. kagome or hexagonal, all through ...
0
votes
0answers
32 views

LatticeReduce (2D) more than two vector [duplicate]

I wonder how LatticeReduce works when I use more than two vector arguments each one in 2D. I know the Gauss algorithm to reduce two vectors. However, how ...
4
votes
1answer
88 views

Perturb lattice positions for non-overlapping particles

Using the below commands, a simple lattice configuration can be generated: ...
0
votes
1answer
108 views

2D wire rope lattice static analysis. FEM/Lattice solution? [closed]

I am looking for a relatively simple method to statically model a 2D lattice of wire ropes, with multiple fixed nodal connections between the wire ropes , fixed external nodes and multiple point force ...
2
votes
2answers
130 views

Defining a piecewise function with underlying lattice

I'm fairly new to Mathematica, and programming in general, but I'm trying to define an $n$-dimensional piecewise function, $F({\bf x})$. Properties of the function are set by an underlying lattice, ...
1
vote
1answer
189 views

How can I make and visualize a connected lattice structure with weighted bonds?

For a problem in condensed matter I am computing nearest-neighbor correlations (real numbers) between spins on a lattice. A good way to visualize this is by drawing a lattice structure with bonds ...
2
votes
0answers
46 views

Why does LatticeReduce require integral or at least rational inputs?

The function LatticeReduce in Mathematica implements the LLL algorithm. It requires the lattice basis to be described as integral or at least rational numbers. ...
7
votes
2answers
190 views

Non-symmorphic lattice

I would like to implement an algorithm for designing this non-symmorphic lattice This has a Glide reflection axis runs northeast-southwest.
1
vote
0answers
64 views

Why is this lattice data missing?

Is there a reason why LatticeData["FaceCenteredOrthorhombic", "Basis"] returns Missing["NotAvailable"] while ...
1
vote
1answer
65 views

Non-Simple Lattice Paths using PathGraph

I am encoding a lattice walk of steps North, South and East on $\mathbb{Z}^{2}$ between the two extremities of the $x$-axis: ...
3
votes
1answer
152 views

Coppersmith method of small integer solutions to multivariate polynomials

In http://link.springer.com/chapter/10.1007%2F3-540-68339-9_14#page-7 is presented a method for finding small solutions to multivariate polynomials. (Although here he mentions that it "is not rigorous"...
12
votes
3answers
277 views

How to generate grid points on boundary of $[-1,1]^d$ for arbitrary dimension $d$ and specified resolution?

This must be a trivial thing, but I was not able to find a function for it in Mathematica. How do you efficiently create a grid with constant but specific resolution $r$ in all directions on the ...
2
votes
2answers
422 views

generate 3D cubic lattice with different atoms in alternate site [duplicate]

I was wondering how to create a 3D cubic lattice and vizualize with A and B atoms in alternate sites? Regards
0
votes
0answers
108 views

LatticeReduce of a linearly dependent basis

l1 = {{-6327, 0, -2109}, {131, 0, -131}, {-6840, 0, 24929}}; LatticeReduce[l1]] returns {{1,0,0},{0,0,1}}. How do I find ...
0
votes
0answers
65 views

LatticeReduce question

Does LatticeReduce work with arbitrary precision arithmetic? That is, if I give it a linearly independent integer basis, but the integers are 40 decimal digits long ...
8
votes
1answer
195 views

What values of $\delta$ and $\eta$ are being used in LatticeReduce?

The Lenstra–Lenstra–Lovász algorithm has a parameter $\delta$ with $1/4 < \delta < 1$, where roughly speaking the closer $\delta$ is to 1 the longer it takes, but the better basis reduction you ...
7
votes
4answers
1k views

Drawing a trihexagonal tiling

I am trying to draw a trihexagonal tiling of the following form using Mathematica. I attempted to begin by using the result given in this Stack Overflow Q & A. However, I couldn't figure out how ...
8
votes
2answers
303 views

Arbitrary shape GridGraph

There is a function GridGraph that generates a finite square lattice graph. Is there a way to make a generalized solution (e.g. with hexagons, or triangles instead of squares)? To put it in more ...
8
votes
3answers
477 views

NIntegrate of surface area of intersecting spheres yields zero

I have a bunch of spheres (it's actually diamond cubic structure. The 0.6 radius doesn't matter), ...
3
votes
1answer
213 views

How to change the atom size of LatticeData [duplicate]

Using the "Image" property of LatticeData, I can generate representation of lattice structures (like the first basic example did)...
0
votes
1answer
287 views

Mathematica Lattice Reduce Command

I'm going through a very old copy of "Mathematica: A System for Doing Mathematics by Computer" for self practice. I'm on chapter 3, and ran into the LatticeReduce ...
16
votes
2answers
10k views

How to create an hexagonal lattice structure

Given an array of atoms A-B-A-B-A-B in an hexagonal pattern, how can I use Mathematica to create with an hexagonal lattice (infinite) with this array so each atom A is sorrounded only by B atoms and ...
2
votes
0answers
859 views

Triangular lattice with periodic boundary conditions [closed]

I am trying to generate an equilateral triangular lattice with fixed vertices and periodic boundary conditions. I am supposed to assign an index (starting from 0) to each vertex in my lattice and then ...
2
votes
1answer
505 views

Cropping a non-cubic lattice unit cell

I would like to crop the hexagonal close-packed system as a hexagon and not as a cube. I would like to use the following volumetricPlot already given on this ...
2
votes
0answers
158 views

A math function similar to “LatticeReduce” for finding linear independent basis

We would like to ask a math function similar to "LatticeReduce" for finding linear independent basis. The input is a list of vectors $M=\{v_1,v_2,v_3,\dots\}$, with the following property: There is a ...
12
votes
3answers
1k views

1D quasicrystal: points on a line nearest to points on a lattice

I have a simple lattice / line manipulation: ...
2
votes
1answer
709 views

Finding 111 plane of Carbon Diamond

All, I looked at the example on the Mathematica Website with the Carbon Diamond Lattice. Example I am referring to I am wondering is there a way to highlight an individual plane such as the 111 or ...
0
votes
1answer
646 views

Using LatticeData to fill a space with spheres in a face-centered cubic (fcc) lattice packing arrangement

I have a large sphere of radius $R_1$ which I would like to pack with $N$ smaller radius of radius $r_2<R_1$ arranged in a face-centered cubic (fcc) packing arrangement (i.e. Kepler's optimal ...
0
votes
2answers
310 views

Visualizing multi-state lattice from a data set

Is there any way to make Mathematica visualize a multistate square lattice? That is, I have a data set from a simulation that is x coloumns wide and y rows tall (just a simple .dat file), where each ...
8
votes
1answer
437 views

How can I sequentially apply different graph embeddings?

Imagine I have some graph G, and I perform a graph embedding using a command like: ...
5
votes
2answers
5k views

How to generate a 3-d simple cubic lattice of length 4 in each dimension?

LatticeData["SimpleCubic", "Image"] The above line gives me a single cube (2 lattice points in each direction). But I want a lattice with 4 lattice points in ...
13
votes
1answer
810 views

Can a LatticeData image be displayed in a space filled fashion

I'd like a FaceCenteredCubic image as in the in LatticeData docs, but space packed, and cropped on all the boundaries, so that it illustrates the geometry of the calculation that leads to the $\pi/\...