Questions tagged [mathematical-modeling]

Questions related to mathematical modeling of materials systems.

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5
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0answers
25 views

Construct a parity operator in TRIM

I want to calculate the band parity at some TRIM in Brillouin zone. Parity was defined as the eigenvalue of the inversion operator. My question is how to construct the matrix representation of the ...
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0answers
61 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. ...
6
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2answers
78 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 ...
5
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0answers
111 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 ...
9
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1answer
209 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, $M = {(\ce{O}, R_\ce{O}), (\ce{H}, R_\ce{H}), (\ce{H}, R_\ce{H})}$, ...
6
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1answer
88 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 ...
3
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1answer
138 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 ...
6
votes
1answer
150 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 ...
12
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1answer
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 ...
20
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3answers
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 ...
12
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1answer
131 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'...
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47 views

Deriving pressure in a pair-wise additive system

I am studying pairwise-additive systems in statistical mechanics. These are systems with particles which only have a 2-body potential defined. When trying to find the pressure of such a system, we do $...
6
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56 views

Deriving relations for a hard sphere phase diagram

In Torquato's Random Heterogeneous Materials, he has written $$\frac{p}{\rho kT} = 1+2^{d-1}\eta g_2 (D^{+})\tag{1}$$ where $g_2(D^+)$ is the contact value from the right-side of the radial ...
8
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1answer
74 views

What software can perform block analysis on time sequence data?

I have a .xyz file for a trajectory and I want to perform block analysis on it, and to find the decorrelation time and to perform analysis on that as well. What ...
10
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0answers
46 views

A viscoelastic material with nonconvex memory kernel?

The title is basically my question. Viscoelastic materials are characterized by a constitutive equation between stress and strain involving a convolution integral. This integral is weighted with a ...
5
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0answers
63 views

Parallel algorithms on unstructured closed graphs [closed]

Some of the work I do in the study of discrete dislocation dynamics (a branch of materials modeling) involves topological changes on a graph: changes in the connectivity of nodes, as well as deletion ...
11
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0answers
99 views

Adiabatic equation related to the Berry phase for lambda with first order terms

Consider the following derivation in David Vanderbilt's book "Berry Phases in Electronic Structure Theory - Electric Polarization, Orbital Magnetization and Topological Insulators" (2018, ...
15
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4answers
312 views

How is group theory used to deduce which of these integrals are equal to 0?

The number of all two-electron integrals: $$ \tag{1} \langle \phi_1 \phi_2|\phi_3\phi_4 \rangle = \int d^3\mathbf r' \int d^3\mathbf r'' \, \phi_1(\mathbf r'') \, \phi_2(\mathbf r') \frac{1}{|\mathbf ...
10
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1answer
85 views

Regarding oscillatory strength theoretical units to experimental ones

The output of Gaussian rotatory and oscillatory strength intensities, plus a gaussian/lorentzian fit, translates to a theoretical CD/UV-vis spectra. In order to try and compare with experimental ...
2
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0answers
105 views

Modeling the fluid dynamics of semen [closed]

Is there a good model for the fluid dynamics of human ejaculation of semen? I'm looking to do some sperm motility research in the near future and would like to tinker with a model from a good paper.
19
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1answer
142 views

Quadrature over three Euler Angles for orientation averaging

Does anybody know about an accurate quadrature rule over three Euler angles $\theta, \phi, \chi$? I am trying to calculate the average value of an arbitrary function $f(\theta, \phi, \chi)$ for a ...
2
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0answers
20 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 ...
16
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6answers
308 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....
68
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7answers
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[1] found a algorithm able to execute ...
24
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1answer
157 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} \...
15
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1answer
98 views

Types of Discrete molecular models

It is often assumed in cheminformatics that molecules with similar physical structure tend to have similar chemical properties [1]. Based on this, our group has used discrete graphs as a model for the ...
15
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0answers
127 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 ...
9
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1answer
70 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 ...
13
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1answer
59 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 ...
13
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1answer
77 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 ...
17
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3answers
224 views

How are continued fractions related to quantum materials?

In my spare time, I have been studying and analysing continued fractions. I was having a conversation with someone on Discord in a Mathematics server and he was telling me that continued fractions ...
8
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0answers
100 views

What are the main mathematical approaches to materials modeling? [closed]

What are the main mathematical approaches to materials modeling? This can include both analytical (closed-form) and numerical techniques.