Mathematical Modeling in Physical Sciences

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Dear Colleagues,

IC-MSQUARE (https://www.icmsquare.net/) is an international scientific conference that has been held continuously for the last 10 years and which focuses on mathematical techniques and their application in a wide range of sciences. This year, taking into account the 2030 Agenda for Sustainable Development agreed upon by the United Nations ensuring the planet’s balanced, sustainable, and inclusive development, we have decided to focus our research efforts on this direction.

The basic sciences have made a significant contribution to the implementation of this program. They provide necessary tools for addressing critical global challenges, such as universal access to food, energy, healthcare, and communication technologies. They enable us to understand the impact of the currently nearly eight billion people on the planet and to act to limit, and sometimes even reduce, ozone depletion, climate change, natural resource depletion, and extinction of species.

In this context, we are organizing a session in IC-MSQUARE that will focus on the abovementioned subjects. Further, this Special Issue will gather research addressing theoretical and applied challenges that concern not only technological development and industry, but our society as a whole. This Special Issue will highlight important developments in the fields of mathematical, statistical, and computational simulation with applications in complex economic and social systems as well as the development of modern machine learning techniques and evolutionary algorithms that can meet the modern challenges facing our planet.

All contributions are welcome, in addition to those of IC-MSQUARE delegates.

Prof. Dr. Dimitrios Vlachos
Dr. George Kastis
Topic Editors

Keywords

Participating Journals

Journal Name	Impact Factor	CiteScore	Launched Year	First Decision (median)	APC
Algorithms algorithms	1.8	4.1	2008	18.9 Days	CHF 1600
Entropy entropy	2.1	4.9	1999	22.3 Days	CHF 2600
Fractal and Fractional fractalfract	3.6	4.6	2017	23.7 Days	CHF 2700
Mathematics mathematics	2.3	4.0	2013	18.3 Days	CHF 2600

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Published Papers (7 papers)

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All Algorithms Entropy Fractal Fract Mathematics

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13 pages, 1634 KiB  

Open AccessArticle

W-Shaped Bright Soliton of the (2 + 1)-Dimension Nonlinear Electrical Transmission Line

by Mustafa Inc, Rubayyi T. Alqahtani and Ravi P. Agarwal

Mathematics 2023, 11(7), 1703; https://doi.org/10.3390/math11071703 - 2 Apr 2023

Cited by 2 | Viewed by 1441

Abstract

In this paper, we investigate solitary wave solutions of the nonlinear electrical transmission line by using the Jacobi elliptic function and the auxiliary equation methods. We obtain Jacobi elliptic function solutions as well as kink, bright, dark, and W-shaped solitons as a result. [...] Read more.

In this paper, we investigate solitary wave solutions of the nonlinear electrical transmission line by using the Jacobi elliptic function and the auxiliary equation methods. We obtain Jacobi elliptic function solutions as well as kink, bright, dark, and W-shaped solitons as a result. For specific values of the Jacobi elliptic modulus, we depict bright, dark, and W-shaped soliton solutions as suitable parameters of the structure. Using the auxiliary equation method gives the combined bright–bright and dark–dark optical solitons in optical fibers. One result emerges from this analysis: the potential parameters and free parameters of the method can be employed to degenerate W-shaped bright and dark solitons. The acquired results are general and can be used for many applications in nonlinear dynamic systems. Full article

(This article belongs to the Topic Mathematical Modeling in Physical Sciences)

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28 pages, 1403 KiB  

Open AccessArticle

Computing the Gromov-Wasserstein Distance between Two Surface Meshes Using Optimal Transport

by Patrice Koehl, Marc Delarue and Henri Orland

Algorithms 2023, 16(3), 131; https://doi.org/10.3390/a16030131 - 28 Feb 2023

Cited by 2 | Viewed by 3338

Abstract

The Gromov-Wasserstein (GW) formalism can be seen as a generalization of the optimal transport (OT) formalism for comparing two distributions associated with different metric spaces. It is a quadratic optimization problem and solving it usually has computational costs that can rise sharply if [...] Read more.

The Gromov-Wasserstein (GW) formalism can be seen as a generalization of the optimal transport (OT) formalism for comparing two distributions associated with different metric spaces. It is a quadratic optimization problem and solving it usually has computational costs that can rise sharply if the problem size exceeds a few hundred points. Recently fast techniques based on entropy regularization have being developed to solve an approximation of the GW problem quickly. There are issues, however, with the numerical convergence of those regularized approximations to the true GW solution. To circumvent those issues, we introduce a novel strategy to solve the discrete GW problem using methods taken from statistical physics. We build a temperature-dependent free energy function that reflects the GW problem’s constraints. To account for possible differences of scales between the two metric spaces, we introduce a scaling factor s in the definition of the energy. From the extremum of the free energy, we derive a mapping between the two probability measures that are being compared, as well as a distance between those measures. This distance is equal to the GW distance when the temperature goes to zero. The optimal scaling factor itself is obtained by minimizing the free energy with respect to s. We illustrate our approach on the problem of comparing shapes defined by unstructured triangulations of their surfaces. We use several synthetic and “real life” datasets. We demonstrate the accuracy and automaticity of our approach in non-rigid registration of shapes. We provide numerical evidence that there is a strong correlation between the GW distances computed from low-resolution, surface-based representations of proteins and the analogous distances computed from atomistic models of the same proteins. Full article

(This article belongs to the Topic Mathematical Modeling in Physical Sciences)

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17 pages, 1599 KiB  

Open AccessArticle

Motion-Compensated PET Image Reconstruction via Separable Parabolic Surrogates

by Nicholas E. Protonotarios, George A. Kastis, Andreas D. Fotopoulos, Andreas G. Tzakos, Dimitrios Vlachos and Nikolaos Dikaios

Mathematics 2023, 11(1), 55; https://doi.org/10.3390/math11010055 - 23 Dec 2022

Cited by 3 | Viewed by 2027

Abstract

The effective resolution of positron emission tomography (PET) can be significantly degraded by patient motion during data acquisition. This is especially true in the thorax due to respiratory motion. This study concentrates on the improvement of motion correction algorithms both in terms of [...] Read more.

The effective resolution of positron emission tomography (PET) can be significantly degraded by patient motion during data acquisition. This is especially true in the thorax due to respiratory motion. This study concentrates on the improvement of motion correction algorithms both in terms of image quality and computational cost. In this paper, we present a novel motion-compensated image reconstruction (MCIR) algorithm based on a parabolic surrogate likelihood function instead of the loglikelihood function of the expectation maximization (EM) algorithm. The theoretical advantage of the parabolic surrogate algorithm lies within the fact that its loglikelihood is upper bounded by the EM loglikelihood, thus it will converge faster than EM. This is of particular importance in PET motion correction, where reconstructions are very computationally demanding. Relaxation parameters were also introduced to converge closer to the maximum likelihood (ML) solution and achieve lower noise levels. Image reconstructions with embedded relaxation parameters actually converged to better solutions than the corresponding ones without relaxation. Motion-compensated parabolic surrogates were indeed shown to accelerate convergence compared to EM, without reaching a limit cycle. Nonetheless, with the incorporation of ordered subsets in the reconstruction setting, the improvement was less evident. Full article

(This article belongs to the Topic Mathematical Modeling in Physical Sciences)

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18 pages, 2228 KiB  

Open AccessArticle

Effect of Variable Thermal Conductivity and Magnetic Field for the Generated Photo-Thermal Waves on Microelongated Semiconductor

by Abdulkafi M. Saeed, Kh. Lotfy and Alaa A. El-Bary

Mathematics 2022, 10(22), 4270; https://doi.org/10.3390/math10224270 - 15 Nov 2022

Cited by 5 | Viewed by 1712

Abstract

A theoretical analysis of the dynamic impacts of a novel model in the microelongated-stimulated semiconductor medium is investigated. The influence of the magnetic field of the optically excited medium is taken into consideration according to the photothermal transport processes. The governing equations were [...] Read more.

A theoretical analysis of the dynamic impacts of a novel model in the microelongated-stimulated semiconductor medium is investigated. The influence of the magnetic field of the optically excited medium is taken into consideration according to the photothermal transport processes. The governing equations were created during the electronic (ED) and thermoelastic (TED) deformation processes. Thermal conductivity of the semiconductor microelongation medium is taken as temperature dependent. The interaction of thermal, microelongate, plasma, and mechanical waves is examined. Dimensionless formulae are used to solve the main equations in two dimensions (2D) using the harmonic wave method. The physical field equations have complete solutions when some conditions are applied to the semiconductor surface. The theoretical microelongated semiconductor model employed in this experiment was confirmed by comparing it to certain earlier studies. The numerical simulation for the principal physical field distributions is graphically displayed when silicon (Si) material is employed. The topic of the discussion was the impact of several factors, such as the magnetic field, thermal memory, and microelongation, on the propagation of waves for major fields. Full article

(This article belongs to the Topic Mathematical Modeling in Physical Sciences)

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42 pages, 5395 KiB  

Open AccessArticle

A Two-Stage Multi-Objective Genetic Algorithm for a Flexible Job Shop Scheduling Problem with Lot Streaming

by Danial Rooyani and Fantahun Defersha

Algorithms 2022, 15(7), 246; https://doi.org/10.3390/a15070246 - 13 Jul 2022

Cited by 6 | Viewed by 4056

Abstract

The work in this paper is motivated by a recently published article in which the authors developed an efficient two-stage genetic algorithm for a comprehensive model of a flexible job-shop scheduling problem (FJSP). In this paper, we extend the application of the algorithm [...] Read more.

The work in this paper is motivated by a recently published article in which the authors developed an efficient two-stage genetic algorithm for a comprehensive model of a flexible job-shop scheduling problem (FJSP). In this paper, we extend the application of the algorithm to solve a lot streaming problem in FJSP while at the same time expanding the model to incorporate multiple objectives. The objective function terms included in our current work are the minimization of the (1) makespan, (2) maximum sublot flowtime, (3) total sublot flow time, (4) maximum job flowtime, (5) total job flow time, (6) maximum sublot finish-time separation, (7) total sublot finish-time separation, (8) maximum machine load, (9) total machine load, and (10) maximum machine load difference. Numerical examples are presented to illustrate the greater need for multi-objective optimization in larger problems, the interaction of the various objective function terms, and their relevance in providing better solution quality. The ability of the two-stage genetic algorithm to jointly optimize all the objective function terms is also investigated. The results show that the algorithm can generate initial solutions that are highly improved in all of the objective function terms. It also outperforms the regular genetic algorithm in convergence speed and final solution quality in solving the multi-objective FJSP lot streaming. We also demonstrate that high-performance parallel computation can further improve the performance of the two-stage genetic algorithm. Nevertheless, the sequential two-stage genetic algorithm with a single CPU outperforms the parallel regular genetic algorithm that uses many CPUs, asserting the superiority of the two-stage genetic algorithm in solving the proposed multi-objective FJSP lot streaming. Full article

(This article belongs to the Topic Mathematical Modeling in Physical Sciences)

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11 pages, 1451 KiB  

Open AccessArticle

Permeability Prediction of Saturated Geomaterials with Revised Pore–Solid Fractal Model and Critical Path Analysis

by Lei Kou, Wuxue Li and Jujie Wu

Fractal Fract. 2022, 6(7), 351; https://doi.org/10.3390/fractalfract6070351 - 23 Jun 2022

Cited by 4 | Viewed by 2027

Abstract

The revised pore–solid fractal (PSF) model is presented by using the largest inscribed circle-based geometries of squares or cubes to replace the original pore or solid subregions as the new pore or solid phase in porous media. The revised PSF model changes the [...] Read more.

The revised pore–solid fractal (PSF) model is presented by using the largest inscribed circle-based geometries of squares or cubes to replace the original pore or solid subregions as the new pore or solid phase in porous media. The revised PSF model changes the discrete lacunar pore and solid phases in the original PSF model to integrated. Permeability is an intrinsic property of geomaterials and has broad applications in exploring fluid flow and species transport. Based on the revised PSF model and critical path analysis, a fractal model for predicting the permeability of saturated geomaterials is proposed. The permeability prediction model is verified by comparison with the existing predicted model and the laboratory testing. The results show that the predicted permeabilities match the measured values very well. This work provides a theoretical framework for the revised PSF model and its application in predicting the permeability of geomaterials. Full article

(This article belongs to the Topic Mathematical Modeling in Physical Sciences)

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22 pages, 2685 KiB  

Open AccessArticle

Analysis of Dipolar Sources in the Solution of the Electroencephalographic Inverse Problem

by María Monserrat Morín-Castillo, Jesús Arriaga-Hernández, Bolivia Cuevas-Otahola and José Jacobo Oliveros-Oliveros

Mathematics 2022, 10(11), 1926; https://doi.org/10.3390/math10111926 - 4 Jun 2022

Cited by 5 | Viewed by 2240

Abstract

In this work, we propose a solution to the problem of identification of sources in the brain from measurements of the electrical potential, recorded on the scalp EEG (electroencephalogram), where boundary problems are used to model the skull, brain region, and scalp, solving [...] Read more.

In this work, we propose a solution to the problem of identification of sources in the brain from measurements of the electrical potential, recorded on the scalp EEG (electroencephalogram), where boundary problems are used to model the skull, brain region, and scalp, solving the inverse problem from the EEG measurements, the so-called Electroencephalographic Inverse Problem (EIP), which is ill-posed in the Hadamard sense since the problem has numerical instability. We focus on the identification of volumetric dipolar sources of the EEG by constructing and modeling a simplification to reduce the multilayer conductive medium (two layers or regions ${\Omega }_1$ and ${\Omega }_2$) to a problem of a single layer of a homogeneous medium with a null Neumann condition on the boundary. For this simplification purpose, we consider the Cauchy problem to be solved at each time. We compare the results we obtained solving the multiple layers problem with those obtained by our simplification proposal. In both cases, we solve the direct and inverse problems for two different sources, as synthetic results for dipolar sources resembling epileptic foci, and a similar case with an external stimulus (intense light, skin stimuli, sleep problems, etc). For the inverse problem, we use the Tikhonov regularization method to handle its numerical instability. Additionally, we build an algorithm to solve both models (multiple layers problem and our simplification) in time, showing optimization of the problem when considering 128 divisions in the time interval $[0,1]$ s, solving the inverse problem at each time (interval division) and comparing the recovered source with the initial one in the algorithm. We observed a significant decrease in the computation times when simplifying the numerical calculations, resulting in a decrease up to $50\%$ in the execution times, between the EIP multilayer model and our simplification proposal, to a single layer homogeneous problem of a homogeneous medium, which translates into a numerical efficiency in this type of problem. Full article

(This article belongs to the Topic Mathematical Modeling in Physical Sciences)

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