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Mathematics
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Mathematical Problems in Chemical Physics
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Mathematical Problems in Chemical Physics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Difference and Differential Equations".

Deadline for manuscript submissions: 31 December 2024 | Viewed by 3477

Special Issue Editors

Prof. Dr. Vasily Novozhilov

E-Mail Website
Guest Editor
1. Institute of Sustainable Industries and Liveable Cities, Victoria University, Melbourne, VIC 8001, Australia
2. N. N. Semenov Federal Research Centre for Chemical Physics, Russian Academy of Sciences, 119991 Moscow, Russia
Interests: ordinary differential equations; partial differ ential equations; mathematical methods of mechanics and chemical physics; computational fluid dynamics
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Sergey M. Frolov

E-Mail Website
Guest Editor
Semenov Federal Research Center for Chemical Physics of the Russian Academy of Sciences (FRC), Moscow 119991, Russia
Interests: combustion; detonation; multiphase flows; advanced propulsion; waste processing
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Chemical Physics offers the most fundamental view and employs the most fundamental investigation methods for investigation of the processes involving chemical transformations as well of the physical and chemical structure of matter. 

Nowadays, this is an extremely vast research field of immense importance—both theoretical and practical. 

Many problems emerging in this field require application of versatile mathematical apparatus. The present Special Issue aims to publish high-quality papers using mathematical methods to investigate various problems of Chemical Physics. 

Particular topics of interest include, but not limited to :

  • chemical kinetics and catalysis
  • reaction-diffusion systems
  • chemically reacting flows (e.g., involving combustion, shock waves, deflagration, detonation, fires, and explosions)
  • chemistry of condensed matter
  • nanomaterials in chemical physics
  • instabilities, bifurcations, and deterministic chaos in chemically reacting systems
  • purely mathematical investigations in mathematical methods related to chemical physics

An additional driving objective of the Special Issue is to identify mathematical problems that are important for progress but have not yet received the deserved attention from the mathematical community.

Submitted papers must have definite emphasis on the mathematical side of investigation and be of high quality.

While it is expected that majority of papers will involve apparatus of differential, integral, or integro-differential equations, ideas regarding the application of other relevant mathematical methods would be of great interest and most welcome, for example, contributions dealing with mathematical methods for data processing in Chemical Physics.

A number of mathematical methods applied in Chemical Physics are quite specialized. Submitting authors are encouraged to present their results in a format accessible to a wider scientific audience, for example, to investigators with major background in physics or chemistry.

The Editor will consider both theoretical and computational papers contributing to the Special Issue. Along with original Research Articles, high-quality Review papers will also be considered. 

Prof. Dr. Vasily Novozhilov
Prof. Dr. Sergey M. Frolov
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (3 papers)

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Research

28 pages, 3317 KiB  
Article
Mathematical Simulation of the Influence of Acoustic on the Efficiency of PM 2.5 Coagulation
by Vladimir Khmelev, Andrey Shalunov and Roman Golykh
Mathematics 2024, 12(5), 692; https://doi.org/10.3390/math12050692 - 27 Feb 2024
Viewed by 393
Abstract
The particles of micron and submicron sizes (PM 2.5 and less) in gas environments pose a significant danger to humanity due to the emergence of specific and very dangerous diseases of the cardiovascular, respiratory, and immune systems of the human body. Such particles [...] Read more.
The particles of micron and submicron sizes (PM 2.5 and less) in gas environments pose a significant danger to humanity due to the emergence of specific and very dangerous diseases of the cardiovascular, respiratory, and immune systems of the human body. Such particles are the most difficult to detect; therefore, their effects on human health have only been discovered in recent decades. Classical ultrasonic coagulation by sinusoidal action turns out to be ineffective for PM 2.5 due to the peculiarities of the physical mechanisms of hydrodynamic and orthokinetic interaction realized in gaseous media. This article presents a theoretical justification for choosing ways to increase the efficiency of ultrasonic coagulation of PM 2.5 by creating special conditions under which nonlinear disturbances of the velocity and pressure of the gas phase in the ultrasonic field occur. The authors performed simulations of ultrasonic coagulation under nonlinear disturbances of the velocity (vortex) and the pressure (shock waves), which has numerical difficulties due to the instability of existing methods. As a result of the numerical analysis, the possibility of increasing the coagulation rate of particles in the submicron size range up to limit values (13 times due to nonlinear pressure disturbances, and an additional increase of at least 2 times due to aerosol compaction in the vortex field of gas velocity) was shown. Full article
(This article belongs to the Special Issue Mathematical Problems in Chemical Physics)
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14 pages, 814 KiB  
Article
Modeling of the Electronic Structure of Semiconductor Nanoparticles
by Vasily B. Novozhilov, Valeria L. Bodneva, Kairat S. Kurmangaleev, Boris V. Lidskii, Vladimir S. Posvyanskii and Leonid I. Trakhtenberg
Mathematics 2023, 11(9), 2214; https://doi.org/10.3390/math11092214 - 08 May 2023
Cited by 1 | Viewed by 1037
Abstract
This paper deals with the mathematical modeling of the electronic structure of semiconductor particles. Mathematically, the task is reduced to a joint solution of the problem of free energy minimization and the set of chemical kinetic equations describing the processes at the surface [...] Read more.
This paper deals with the mathematical modeling of the electronic structure of semiconductor particles. Mathematically, the task is reduced to a joint solution of the problem of free energy minimization and the set of chemical kinetic equations describing the processes at the surface of a nanoparticle. The numerical modeling of the sensor effect is carried out in two steps. First, the number of charged oxygen atoms on the surface of the nanoparticle NO− is determined. This value is found by solving a system of nonlinear algebraic equations, where the unknowns are the stationary points of this system describing the processes on the surface of a nanoparticle. The specific form of such equations is determined by the type of nanoparticles and the mechanism of chemical reactions on the surface. The second step is to calculate the electron density inside the nanoparticle (nc(r)), which gives the minimum free energy. Mathematically, this second step reduces to solving a boundary value problem for a nonlinear integro-differential equation. The calculation results are compared with experimental data on the sensor effect. Full article
(This article belongs to the Special Issue Mathematical Problems in Chemical Physics)
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25 pages, 7016 KiB  
Article
Soot Formation in Spherical Diffusion Flames
by Sergey M. Frolov, Vladislav S. Ivanov, Fedor S. Frolov, Pavel A. Vlasov, Richard Axelbaum, Phillip H. Irace, Grigoriy Yablonsky and Kendyl Waddell
Mathematics 2023, 11(2), 261; https://doi.org/10.3390/math11020261 - 04 Jan 2023
Cited by 4 | Viewed by 1464
Abstract
In the period from 2019 to 2022, the joint American–Russian space experiment (SE) Flame Design (Adamant) was carried out on the International Space Station (ISS). The purpose of the joint SE was to study the mechanisms of control of soot formation in a [...] Read more.
In the period from 2019 to 2022, the joint American–Russian space experiment (SE) Flame Design (Adamant) was carried out on the International Space Station (ISS). The purpose of the joint SE was to study the mechanisms of control of soot formation in a spherical diffusion flame (SDF) formed around a porous sphere (PS), and the radiative extinction of the SDF under microgravity conditions. The objects of this study were “normal” and “inverse” SDFs of gaseous ethylene in an oxygen atmosphere with nitrogen addition at room temperature and pressures ranging from 0.5 to 2 atm. A normal flame is a flame formed in an oxidizing atmosphere when fuel is supplied through the PS. An inverse flame is a flame formed in a fuel atmosphere when an oxidizer is introduced through the PS. This article presents the results of calculations of soot formation in normal and inverse SDFs. The calculations are based on a one-dimensional non-stationary model of diffusion combustion of gases with detailed kinetics of ethylene oxidation, supplemented by a macrokinetic mechanism of soot formation. The results indicate that soot formation in normal and inverse SDFs is concentrated in the region where the local C/O atomic ratio and local temperature satisfy the conditions 0.32 < C/O < 0.44 and T > 1300–1500 K. Full article
(This article belongs to the Special Issue Mathematical Problems in Chemical Physics)
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