# Questions tagged [lattices]

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40 questions
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: ...
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 ...
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. ...
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: ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
1answer
88 views

### Perturb lattice positions for non-overlapping particles

Using the below commands, a simple lattice configuration can be generated: ...
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 ...
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, ...
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 ...
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. ...
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.
0answers
64 views

### Why is this lattice data missing?

Is there a reason why LatticeData["FaceCenteredOrthorhombic", "Basis"] returns Missing["NotAvailable"] while ...
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: ...
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"...
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 ...
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
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 ...
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 ...
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 ...
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 ...
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 ...
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), ...
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)...
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 ...
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 ...
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 ...
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 ...
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 ...
3answers
1k views

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

I have a simple lattice / line manipulation: ...
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 ...
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 ...
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 ...
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: ...
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 ...
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/\...