Sergey Sobolev | Institute of Problems of Chemical Physics, Russian Academy of Science (original) (raw)
Papers by Sergey Sobolev
Physical Review E, 2018
Some analogies between different nonequilibrium heat conduction models, particularly, random walk... more Some analogies between different nonequilibrium heat conduction models, particularly, random walk, discrete variable model, and Boltzmann transport equation with the single relaxation time approximation, have been discussed. We show that under an assumption of a finite value of the heat carriers velocity, these models lead to the hyperbolic heat conduction equation and the modified Fourier law with the relaxation term. Corresponding effective temperature and entropy have been introduced and analyzed. It has been demonstrated that the effective temperature, defined as a geometric mean of the kinetic temperatures of the heat carriers moving in opposite directions, is governed by a non-linear relation and acts as a criterion for thermalization. It is shown that when the heat flux tends to its maximum possible value, the effective temperature, heat capacity and local entropy go to zero even at a nonzero equilibrium temperature. This provides a possible generalization of the third law to nonequilibrium situations. Analogies between the effective temperature and some other definitions of temperature in nonequilibrium state, particularly, for active systems, disordered semiconductors under electric field, and adiabatic gas flow, have been shown and discussed. Illustrative examples of the behavior of the effective temperature and entropy during nonequilibrium heat conduction in a monatomic gas, a nano film, and a strong shockwave have been analyzed.
Exact assessment of thermal spreading resistance is of great importance to the thermal management... more Exact assessment of thermal spreading resistance is of great importance to the thermal management of electronic devices, especially when completely considering the heat conduction process from the nanoscale heat source to the macroscopic scale heat sink. The existing simulation methods are either based on convectional Fourier's law or limited to small system sizes, making it difficult to accurately and efficiently study the cross-scale heat transfer. In this paper, a hybrid phonon Monte Carlo-diffusion method that couples phonon Monte Carlo (MC) method with Fourier's law by dividing the computational domain is adopted to analyze thermal spreading resistance in ballistic-diffusive regime. Compared with phonon MC simulation, the junction temperature of the hybrid method has the same precision, while the time costs could be reduced up to 2 orders of magnitude at most. Furthermore, the simulation results indicate that the heating scheme has a remarkable impact on phonon transport. The thermal resistance of the heat source (HS) scheme can be larger than that of the heat flux (HF) scheme, which is opposite from the prediction of Fourier's law. In the HS scheme, the enhanced phonon-boundary scattering counteracts the broadening of the heat source, leading to a stronger ballistic effect as the heat source thickness decreases. The conclusion is verified by a one-dimensional thermal resistance model. This work has opened up an opportunity for the fast and extensive thermal modeling of crossscale heat transfer in electronic devices and highlighted the influence of heating schemes.
Combustion, Explosion, and Shock Waves, 1989
Combustion, Explosion, and Shock Waves, 1983
In the area of study of combustion-wave propagation in a thin layer of material, this work invest... more In the area of study of combustion-wave propagation in a thin layer of material, this work investigates the flame jet and the influence of its size on the velocity and limits of propagation of the combustion wave. The position of the region of intense chemical reaction, the magnitude of the gasification-product flow, and the structure of the flame jet are determined. It is found that combustion-wave propagation in the opposing direction to the oxidant flow is only possible when the edge of the chemical-reaction precedes the point of maximum gasification rate of the fuel. Combustion-wave propagation in a concurrent flow of oxidant is considered analogously.
Combustion, Explosion, and Shock Waves, 1989
longer time interval (see Fig. i), taking on a degenerate character. Together with ~ the reaction... more longer time interval (see Fig. i), taking on a degenerate character. Together with ~ the reaction propagation rate along the specimen axis u also decreases. At the limit of combustion the value of u has decreased to ~ee times the rate of the adiabatic process.
IEEE Transactions on Electron Devices
To develop efficient thermal management strategies for wide bandgap (WBG) semiconductor devices, ... more To develop efficient thermal management strategies for wide bandgap (WBG) semiconductor devices, it is essential to have a clear understanding of the heat transport process within the device and accurately predict the junction temperature. In this paper, we used the phonon Monte Carlo (MC) method with the phonon dispersion of various typical WBG semiconductors, including GaN, SiC, AlN, and β-Ga2O3, to investigate the thermal spreading resistance in a ballistic-diffusive regime. It was found that when compared with Fourier's law-based predictions, the increase in the thermal resistance caused by ballistic effects was strongly related to different phonon dispersions. Based on the model deduced under the gray-medium approximation and the results of dispersion MC, we obtained a thermal resistance model that can well address the issues of thermal spreading and ballistic effects, and the influences of phonon dispersion. The model can be easily coupled with FEM based thermal analysis and applied to different materials. This paper can provide a clearer understanding of the influences of phonon dispersion on the thermal transport process, and it can be useful for the prediction of junction temperatures and the development of thermal management strategies for WBG semiconductor devices.
A conceptual foundation for the study of local non-equilibrium solute diffusion under rapid solid... more A conceptual foundation for the study of local non-equilibrium solute diffusion under rapid solidifica-tion conditions is proposed. The model takes into account the relaxation to local equilibrium of the solute flux and incorporates two diffusion speeds, VDb, the bulk liquid diffusion speed, and VD~, the interface diffusive speed, as the most important parameters governing the solute concentration in the liquid phase and solute partitioning. The analysis of the model predicts complete solute trapping and the transition to a purely thermally controlled solidification, which occur abruptly when the interface velocity V equals the bulk liquid diffusion speed VDb. The abrupt change in the solidification mechan-ism is described by the velocity dependent effective diffusion coefficient D * = D(l- V2/V&) and the generalized partition coefficient K*. If V> VDb, then D * = 0 and K * = 1. This implies an uudis-turbed diffusion field in the liquid (diffusionless solidification) and complete...
Journal of Experimental and Theoretical Physics, 2017
he main focus of this paper is the process of the formation of communal lands in a selected area ... more he main focus of this paper is the process of the formation of communal lands in a selected area as part of the formation and construction of the postrevolutionary state. In this sense, it seeks to retrieve a signiicant part of the local history, the speeches and examples of peasant leadership of the municipality of Tanlajas, encompassing them in a major historical context. Furthermore, the present contribution aims at combining oral history and the documented history available in the Historic Archives of the National Agrarian Oice of San Luís Potosí with ield evidence, especially by elaborating original cartography on forms of land ownership until 1920 in a gis format, in order to study the processes of the agrarian reform. he use of the gis tools has allowed a novel insight into the interpretation of the maps available in the agrarian records, and it has led to a better present-day geographic localization of the historical forms of land ownership.
Combustion, Explosion, and Shock Waves, 1989
Journal de Physique III, 1993
Materials Science Forum, 1996
Keywords: Non-equilibrium heat conduction Effective temperature Discrete variable model Nonequili... more Keywords: Non-equilibrium heat conduction Effective temperature Discrete variable model Nonequilibrium entropy Third law The effective temperature, which acts as a criterion for thermalization in systems with heat flux, has been introduced on the bases of a relatively simple discrete variable model (DVM). The DVM is inherently nonlocal and can be used to describe multi-length and-time scale heat conduction including low-dimensional and sub-continuum regimes. Under far from equilibrium conditions when the heat flux tends to its maximum possible value, the effective temperature and the corresponding nonequilibrium entropy go to zero, which points to a possible generalization of the third law in nonequilibrium situations.
Keywords: Non-equilibrium heat conduction Effective temperature Discrete variable model Nonequili... more Keywords: Non-equilibrium heat conduction Effective temperature Discrete variable model Nonequilibrium entropy Third law The effective temperature, which acts as a criterion for thermalization in systems with heat flux, has been introduced on the bases of a relatively simple discrete variable model (DVM). The DVM is inherently nonlocal and can be used to describe multi-length and-time scale heat conduction including low-dimensional and sub-continuum regimes. Under far from equilibrium conditions when the heat flux tends to its maximum possible value, the effective temperature and the corresponding nonequilibrium entropy go to zero, which points to a possible generalization of the third law in nonequilibrium situations.
An analytical discrete-variable model has been developed to describe heat conduction in nano-size... more An analytical discrete-variable model has been developed to describe heat conduction in nano-sized systems. The model assumes that the system consists of a homogeneous array of cells with characteristic size h; each cell interacts with the nearest neighbors in discrete time step s and all the cells compute their new state simultaneously. In the continuum limit h ! 0 and s ! 0, the model reduces to classical heat diffusion equation of parabolic type or heat conduction equation of hyperbolic type, depending on the choice of scaling invariant. The model is applied to heat conduction in nano-films with emphasis on the transition from the diffusive to ballistic heat transport, which occurs with decreasing film thickness. This model provides a simple method for predicting in a self consistent manner the effective cross-plane thermal conductivities, the temperature jump at the boundaries, the heat flux across the film, and the temperature gradient within the film as functions of the film thickness. The results are in good agreement with molecular dynamic and Monte Carlo simulations.
Journal of Crystal Growth, 2013
This article appeared in a journal published by Elsevier. The attached copy is furnished to the a... more This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues.
Physical Review E, 2018
Some analogies between different nonequilibrium heat conduction models, particularly, random walk... more Some analogies between different nonequilibrium heat conduction models, particularly, random walk, discrete variable model, and Boltzmann transport equation with the single relaxation time approximation, have been discussed. We show that under an assumption of a finite value of the heat carriers velocity, these models lead to the hyperbolic heat conduction equation and the modified Fourier law with the relaxation term. Corresponding effective temperature and entropy have been introduced and analyzed. It has been demonstrated that the effective temperature, defined as a geometric mean of the kinetic temperatures of the heat carriers moving in opposite directions, is governed by a non-linear relation and acts as a criterion for thermalization. It is shown that when the heat flux tends to its maximum possible value, the effective temperature, heat capacity and local entropy go to zero even at a nonzero equilibrium temperature. This provides a possible generalization of the third law to nonequilibrium situations. Analogies between the effective temperature and some other definitions of temperature in nonequilibrium state, particularly, for active systems, disordered semiconductors under electric field, and adiabatic gas flow, have been shown and discussed. Illustrative examples of the behavior of the effective temperature and entropy during nonequilibrium heat conduction in a monatomic gas, a nano film, and a strong shockwave have been analyzed.
Exact assessment of thermal spreading resistance is of great importance to the thermal management... more Exact assessment of thermal spreading resistance is of great importance to the thermal management of electronic devices, especially when completely considering the heat conduction process from the nanoscale heat source to the macroscopic scale heat sink. The existing simulation methods are either based on convectional Fourier's law or limited to small system sizes, making it difficult to accurately and efficiently study the cross-scale heat transfer. In this paper, a hybrid phonon Monte Carlo-diffusion method that couples phonon Monte Carlo (MC) method with Fourier's law by dividing the computational domain is adopted to analyze thermal spreading resistance in ballistic-diffusive regime. Compared with phonon MC simulation, the junction temperature of the hybrid method has the same precision, while the time costs could be reduced up to 2 orders of magnitude at most. Furthermore, the simulation results indicate that the heating scheme has a remarkable impact on phonon transport. The thermal resistance of the heat source (HS) scheme can be larger than that of the heat flux (HF) scheme, which is opposite from the prediction of Fourier's law. In the HS scheme, the enhanced phonon-boundary scattering counteracts the broadening of the heat source, leading to a stronger ballistic effect as the heat source thickness decreases. The conclusion is verified by a one-dimensional thermal resistance model. This work has opened up an opportunity for the fast and extensive thermal modeling of crossscale heat transfer in electronic devices and highlighted the influence of heating schemes.
Combustion, Explosion, and Shock Waves, 1989
Combustion, Explosion, and Shock Waves, 1983
In the area of study of combustion-wave propagation in a thin layer of material, this work invest... more In the area of study of combustion-wave propagation in a thin layer of material, this work investigates the flame jet and the influence of its size on the velocity and limits of propagation of the combustion wave. The position of the region of intense chemical reaction, the magnitude of the gasification-product flow, and the structure of the flame jet are determined. It is found that combustion-wave propagation in the opposing direction to the oxidant flow is only possible when the edge of the chemical-reaction precedes the point of maximum gasification rate of the fuel. Combustion-wave propagation in a concurrent flow of oxidant is considered analogously.
Combustion, Explosion, and Shock Waves, 1989
longer time interval (see Fig. i), taking on a degenerate character. Together with ~ the reaction... more longer time interval (see Fig. i), taking on a degenerate character. Together with ~ the reaction propagation rate along the specimen axis u also decreases. At the limit of combustion the value of u has decreased to ~ee times the rate of the adiabatic process.
IEEE Transactions on Electron Devices
To develop efficient thermal management strategies for wide bandgap (WBG) semiconductor devices, ... more To develop efficient thermal management strategies for wide bandgap (WBG) semiconductor devices, it is essential to have a clear understanding of the heat transport process within the device and accurately predict the junction temperature. In this paper, we used the phonon Monte Carlo (MC) method with the phonon dispersion of various typical WBG semiconductors, including GaN, SiC, AlN, and β-Ga2O3, to investigate the thermal spreading resistance in a ballistic-diffusive regime. It was found that when compared with Fourier's law-based predictions, the increase in the thermal resistance caused by ballistic effects was strongly related to different phonon dispersions. Based on the model deduced under the gray-medium approximation and the results of dispersion MC, we obtained a thermal resistance model that can well address the issues of thermal spreading and ballistic effects, and the influences of phonon dispersion. The model can be easily coupled with FEM based thermal analysis and applied to different materials. This paper can provide a clearer understanding of the influences of phonon dispersion on the thermal transport process, and it can be useful for the prediction of junction temperatures and the development of thermal management strategies for WBG semiconductor devices.
A conceptual foundation for the study of local non-equilibrium solute diffusion under rapid solid... more A conceptual foundation for the study of local non-equilibrium solute diffusion under rapid solidifica-tion conditions is proposed. The model takes into account the relaxation to local equilibrium of the solute flux and incorporates two diffusion speeds, VDb, the bulk liquid diffusion speed, and VD~, the interface diffusive speed, as the most important parameters governing the solute concentration in the liquid phase and solute partitioning. The analysis of the model predicts complete solute trapping and the transition to a purely thermally controlled solidification, which occur abruptly when the interface velocity V equals the bulk liquid diffusion speed VDb. The abrupt change in the solidification mechan-ism is described by the velocity dependent effective diffusion coefficient D * = D(l- V2/V&) and the generalized partition coefficient K*. If V> VDb, then D * = 0 and K * = 1. This implies an uudis-turbed diffusion field in the liquid (diffusionless solidification) and complete...
Journal of Experimental and Theoretical Physics, 2017
he main focus of this paper is the process of the formation of communal lands in a selected area ... more he main focus of this paper is the process of the formation of communal lands in a selected area as part of the formation and construction of the postrevolutionary state. In this sense, it seeks to retrieve a signiicant part of the local history, the speeches and examples of peasant leadership of the municipality of Tanlajas, encompassing them in a major historical context. Furthermore, the present contribution aims at combining oral history and the documented history available in the Historic Archives of the National Agrarian Oice of San Luís Potosí with ield evidence, especially by elaborating original cartography on forms of land ownership until 1920 in a gis format, in order to study the processes of the agrarian reform. he use of the gis tools has allowed a novel insight into the interpretation of the maps available in the agrarian records, and it has led to a better present-day geographic localization of the historical forms of land ownership.
Combustion, Explosion, and Shock Waves, 1989
Journal de Physique III, 1993
Materials Science Forum, 1996
Keywords: Non-equilibrium heat conduction Effective temperature Discrete variable model Nonequili... more Keywords: Non-equilibrium heat conduction Effective temperature Discrete variable model Nonequilibrium entropy Third law The effective temperature, which acts as a criterion for thermalization in systems with heat flux, has been introduced on the bases of a relatively simple discrete variable model (DVM). The DVM is inherently nonlocal and can be used to describe multi-length and-time scale heat conduction including low-dimensional and sub-continuum regimes. Under far from equilibrium conditions when the heat flux tends to its maximum possible value, the effective temperature and the corresponding nonequilibrium entropy go to zero, which points to a possible generalization of the third law in nonequilibrium situations.
Keywords: Non-equilibrium heat conduction Effective temperature Discrete variable model Nonequili... more Keywords: Non-equilibrium heat conduction Effective temperature Discrete variable model Nonequilibrium entropy Third law The effective temperature, which acts as a criterion for thermalization in systems with heat flux, has been introduced on the bases of a relatively simple discrete variable model (DVM). The DVM is inherently nonlocal and can be used to describe multi-length and-time scale heat conduction including low-dimensional and sub-continuum regimes. Under far from equilibrium conditions when the heat flux tends to its maximum possible value, the effective temperature and the corresponding nonequilibrium entropy go to zero, which points to a possible generalization of the third law in nonequilibrium situations.
An analytical discrete-variable model has been developed to describe heat conduction in nano-size... more An analytical discrete-variable model has been developed to describe heat conduction in nano-sized systems. The model assumes that the system consists of a homogeneous array of cells with characteristic size h; each cell interacts with the nearest neighbors in discrete time step s and all the cells compute their new state simultaneously. In the continuum limit h ! 0 and s ! 0, the model reduces to classical heat diffusion equation of parabolic type or heat conduction equation of hyperbolic type, depending on the choice of scaling invariant. The model is applied to heat conduction in nano-films with emphasis on the transition from the diffusive to ballistic heat transport, which occurs with decreasing film thickness. This model provides a simple method for predicting in a self consistent manner the effective cross-plane thermal conductivities, the temperature jump at the boundaries, the heat flux across the film, and the temperature gradient within the film as functions of the film thickness. The results are in good agreement with molecular dynamic and Monte Carlo simulations.
Journal of Crystal Growth, 2013
This article appeared in a journal published by Elsevier. The attached copy is furnished to the a... more This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues.