# Questions tagged [mathematical-modeling]

Questions related to mathematical modeling of materials systems.

41 questions
Filter by
Sorted by
Tagged with
42 views

### What is special about valley-focused Hamiltonians that make them give quantized/rational (valley) Chern numbers?

I have been thinking about so-called valley Chern numbers $C_v$ and associated topological phenomena. To my knowledge, they are usually applicable when inter-valley scattering is suppressed, leaving ...
119 views

### Derivation on correlation function and response functions in polymer physics

I am reading Introduction to Polymer Physics by Doi and I am having trouble understanding a derivation by him on the concentration fluctuations in polymer solutions. I have outlined his method and ...
61 views

### Derivation of probability density of isolated polymers

(Crossposted on physics SE) I am reading Introduction to Polymer Physics by Doi, and in his proof for the probability distribution for ideal polymers of length $N$ and end-to-end vector $\mathbf{R}$, ...
84 views

### Calculating first and second derivatives of a molecular Hamiltonian?

I'm interested in computing first and second derivatives of molecular Hamiltonians with respect to nuclear coordinates. I've been using Psi4 and PySCF to perform Hartree-Fock calculations, and I was ...
205 views

### Help with translating Hamiltonian into matrix

Eq. 19 in this paper gives the following Hamiltonian: $\sigma_a, \tau_a, \eta_a$ are respectively the spin, sublattice pseudospin and valley pseudospin respectively. Normally, I would have chosen a ...
60 views

### Molecular Structure Vectorization for Computational Quantum Mechanics

What are the different ways that a molecule can be encoded into a vector? My answer to that question would employ machine learning but maybe there are other approaches, perhaps analytical, e.g., graph ...
68 views

### References related to the molecular distance geometry problem (estimating true distances based on noisy distances)

One aspect of the molecular distance geometry problem (MDGP) described in this PDF, can be written as follows: "Given observations of noisy distances between atoms in a molecule, estimate the ...
80 views

### Classes of Graphs used in Chemistry

I am looking for common categories of graphs used in chemistry, for math research I am doing in graph theory. When I write categories, the meaning is not for graphs design or types of design, but for ...
65 views

### Mathematical models for the plastic region in the tensile test

The tensile test of a material consists of subjecting a standardized specimen to an increasing axial tensile stress until it breaks. During its performance in the laboratory, we can plot a stress-...
55 views

### Construct a parity operator at a TRIM point?

I want to calculate the band parity at some TRIM (time-reversal invariant momentum) point in Brillouin zone. Parity was defined as the eigenvalue of the inversion operator. My question is how to ...
65 views

### How to solve general wave equation and dispersion relation using Fourier series?

In this paper (open access), the authors used Fourier series with most general wave equation to find the dispersion relation. I am presenting some main equations as snippets to depict their solution. ...
82 views

### Books and online resources to get me started in the finite element method (FEM)

In a course on the mechanical properties of materials, I have been asked to do a paper on the "Finite Element Method" to improve my current grade. However, most of the resources I find on ...
115 views

### What's the information contained in a character table of a group? [closed]

This question has an answer on the Chemistry Stack Exchange: Understanding group theory easily and quickly. Anyone wishing to add alternative or additional perspectives that aren't already covered in ...
240 views

### How can I implement the Cartesian harmonics?

I'm studying the quantum chemistry calculation and now trying to implement the basic methods. For example, given a water molecule, $M = {(\ce{O}, R_\ce{O}), (\ce{H}, R_\ce{H}), (\ce{H}, R_\ce{H})}$, ...
91 views

### Is it possible to get complex numbers as solutions for a secular determinant in simple Hückel method (SHM)?

Past semester we revisited the Hückel molecular orbital theory at class. One day I was trying to solve some problems with SymPy, a Python module that is a computer algebra system (CAS), and noticed ...
146 views

### Can corundum be considered a covalent network?

I know that I learned in Chemistry class that a bond is defined to be ionic if the electronegativity difference between the atoms is more then 1.7, half the electronegativity difference between the ...
151 views

### Can replacing some of the atoms in a covalent network with that of the element one atomic number higher make it nonstick? [closed]

I originally made the title the question I had that is a more suitable question but then it ended up too long. I had the idea that if you replace some of the atoms in a covalent network with the atom ...
146 views

### Has a form of diamond with certain properties ever been theorized?

The following is what a Penrose tiling looks like: I know the verticies of a dodecahedron can be grouped into 5 groups each of which are the verticies of a tetrahedron. So I thought of the idea that ...
1k views

### Introduction to protein folding for mathematicians

My background is mostly in (applied) math with healthy doses of physics and computer science. Are there any good introductions to protein folding and its challenges for someone with that kind of ...
141 views

### Why linear response is absent in a non-centrosymmetric system with time reversal symmetry?

In this paper, it is mentioned that a non-centrosymmetric system with time-reversal symmetry doesn't have a linear response. It is actually a consequence of the Onsager reciprocal theorem. But I didn'...
54 views

29 views

### What is the best way to compare an actual value from an expected value on a linear model? [closed]

I'm comparing the cost of dialysis in each country. The x axis is health expenditure per capita. The y axis is cost of dialysis per patient. As you will see, this incredibly produces a near liner ...
328 views

### What are the applications of chemical graph theory?

Graph theory was originally introduced in computer science to study data structure. Chemists also introduced graph theory to study the relation between structure and properties for molecular compounds....
8k views

### Did the 2019 discovery of O(N log(N)) multiplication have a practical outcome?

Some time ago I've read this news article, Mathematicians Discover the Perfect Way to Multiply, reporting a discovery published in 2019, where Harvey and Hoeven found a algorithm able to execute ...
181 views

### How do you calculate the “true” chemical potential in classical density functional theory?

In classical density functional theory, one traditionally calculates the chemical potential by taking the variational derivative, \begin{equation} \mu_{i} = \frac{\delta F}{\delta \rho_{i}}\tag{1} \...
102 views

### Types of Discrete molecular models

It is often assumed in cheminformatics that molecules with similar physical structure tend to have similar chemical properties . Based on this, our group has used discrete graphs as a model for the ...
128 views

### Is there a software that can do derivatives with respect to user defined vibrational modes? [closed]

I'm doing some property calculations that depend on a sum of derivatives of some quantity with respect to normal vibrational modes. I was hoping to find some physical intuition relating the type of ...
72 views

### What mathematics/computation heavy resources are available for understanding materials behaviour?

Since materials modelling is made possible primarily because of the availability of mathematical models, are there any resources that provide a mathematics heavy picture of materials behaviour? I am ...
63 views

### Modelling ion Drift-Diffusion under an external electric potential, convergency in PDE?

Ion drift-diffusion under the effect of an external electric field is a phenomenon with a huge relevancy in light emitting devices, neuromorphic architectures and in general molecular electronics Up ...
78 views

### What are the modelling techniques that can be used for simulating microstructure evolution in materials?

I am aware that the Potts Model can be used to simulate grain growth, and that Phase Field Models have also been very successful. What are the advantages and limitations of these models? What are the ...