Questions tagged [mathematical-modeling]

Questions related to mathematical modeling of materials systems.

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0answers
68 views

Optimal Transport-Based Methods for Semen Trajectories [closed]

I'm looking for a good Optimal Transport-based modeling paper for the flight trajectory of semen, as it relates to fertility rates.
7
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1answer
44 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 ...
9
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0answers
36 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
54 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 ...
7
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0answers
43 views

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

The wave function for the adiabatic approach is as follows: \begin{equation} |\psi(t)\rangle=e^{i\phi(\lambda(t))}e^{-i\gamma(t)}|n(t)\rangle \tag{1} \end{equation} where $e^{i\phi(\lambda(t))}$ is ...
14
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4answers
261 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
76 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 ...
3
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0answers
92 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.
18
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0answers
100 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
15 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
270 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....
63
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6answers
7k 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 ...
22
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1answer
112 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}} \end{...
15
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1answer
92 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 ...
9
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1answer
59 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 ...
11
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1answer
43 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
71 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
196 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
98 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.