Unification of kinetic and hydrodynamic approaches in the theory of dense gases and liquids far from equilibrium

Simple item page
dc.citation.epage287
dc.citation.issue2
dc.citation.journalTitleМатематичне моделювання та комп'ютинг
dc.citation.spage272
dc.contributor.affiliationІнститут фізики конденсованих систем НАН України
dc.contributor.affiliationНаціональний університет “Львівська політехніка”
dc.contributor.affiliationInstitute for Condensed Matter Physics of the National Academy of Sciences of Ukraine
dc.contributor.affiliationLviv Polytechnic National University
dc.contributor.authorТокарчук, Михайло Васильович
dc.contributor.authorTokarchuk, M. V.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2025-03-04T10:28:11Z
dc.date.created2023-02-28
dc.date.issued2023-02-28
dc.description.abstractОтримано систему немарківських рівнянь переносу для нерівноважної одночастинкової функції розподілу частинок і нерівноважного середнього значення густини потенціальної енергії взаємодії частинок системи, далеких від стану рівноваги. Отримано вирази для ентропії, статистичної суми нерівноважного стану системи, а також нерівноважні термодинамічні співвідношення. Детально розкрито узагальнену структуру ядер переносу з виділенням короткодіючих і далекодіючих вкладів взаємодій між частинками. Встановлено зв’язок ядер переносу із узагальненими коефіцієнтами дифузії, тертя в просторі координат та імпульсів і потенціальною частиною коефіцієнта теплопровідності.
dc.description.abstractA system of non-Markovian transport equations is obtained for the non-equilibrium one-particle distribution function of particles and the non-equilibrium average value of the density of the potential energy of the interaction of the system particles far from the equilibrium state. Expressions for entropy, the partition function of the non-equilibrium state of the system, as well as non-equilibrium thermodynamic relations were obtained. The generalized structure of transfer kernel is revealed in detail with the selection of short-range and long-range contributions of interactions between particles. The connection of transport kernel with generalized diffusion coefficients, friction in the space of coordinates and momentum and the potential part of the thermal conductivity coefficient is established.
dc.format.extent272-287
dc.format.pages16
dc.identifier.citationTokarchuk M. V. Unification of kinetic and hydrodynamic approaches in the theory of dense gases and liquids far from equilibrium / M. V. Tokarchuk // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 10. — No 2. — P. 272–287.
dc.identifier.citationenTokarchuk M. V. Unification of kinetic and hydrodynamic approaches in the theory of dense gases and liquids far from equilibrium / M. V. Tokarchuk // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 10. — No 2. — P. 272–287.
dc.identifier.doidoi.org/10.23939/mmc2023.02.272
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/63410
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofМатематичне моделювання та комп'ютинг, 2 (10), 2023
dc.relation.ispartofMathematical Modeling and Computing, 2 (10), 2023
dc.relation.references[1] Jhon M. S., Forster D. A kinetic theory of classical simple liquids. Physical Review A. 12 (1), 254–266 (1975).
dc.relation.references[2] Boon J., Yip S. Molecular Hydrodynamics. McGraw-Hill Inc., New-York (1980).
dc.relation.references[3] Zubarev D. N., Morozov V. G. Formulation of boundary conditions for the BBGKY hierarchy with allowance for local conservation laws. Theoretical and Mathematical Physics. 60, 814–820 (1984).
dc.relation.references[4] Karkheck J., Stell G., Xu J. Transport theory for the Lennard–Jones dense fluid. Journal of Chemical Physics. 89 (9), 5829–5833 (1988).
dc.relation.references[5] Zubarev D. N., Morozov V. G., Omelyan I. P., Tokarchuk M. V. Kinetic equations for dense gases and liquids. Theoretical and Mathematical Physics. 87, 412–424 (1991).
dc.relation.references[6] Klimontovich Yu. L. The unified description of kinetic and hydrodynamic processes in gases and plasmas. Physics Letters A. 170 (6), 434–438 (1992).
dc.relation.references[7] Klimontovich Yu. L. On the need for and the possibility of a unified description of kinetic and hydrodynamic processes. Theoretical and Mathematical Physics. 92, 909–921 (1992).
dc.relation.references[8] Zubarev D. N., Morozov V. G., Omelyan I. P., Tokarchuk M. V. Unification of the kinetic and hydrodynamic approaches in the theory of dense gases and liquids. Theoretical and Mathematical Physics. 96, 997–1012 (1993).
dc.relation.references[9] Tokarchuk M. V. On the statistical theory of a nonequilibrium plasma in its electromagnetic self-field. Theoretical and Mathematical Physics. 97, 1126–1136 (1993).
dc.relation.references[10] Zubarev D. N., Morozov V. G., R¨opke G. Statistical Mechanics of Nonequilibrium Processes. Berlin, Akademie. Vol. 1 (1996).
dc.relation.references[11] Tokarchuk M. V., Omelyan I. P., Kobryn A. E. A consistent description of kinetics and hydrodynamics of systems of interacting particles by means of the nonequilibrium statistical operator method. Condensed Matter Physics. 1 (4), 687–751 (1998).
dc.relation.references[12] Markiv B., Tokarchuk M. Consistent description of kinetics and hydrodynamics of dusty plasma. Physics of Plasmas. 21, 023707 (2014).
dc.relation.references[13] Kostrobij P., Viznovych O., Markiv B., Tokarchuk M. Generalized kinetic equations for dense gases and liquids in the Zubarev nonequilibrium statistical operator method and Renyi statistics. Theoretical and Mathematical Physics. 184 (1), 1020–1032 (2015).
dc.relation.references[14] Kostrobij P. P., Markovych B. M., Ryzha I. A., Tokarchuk M. V. Generalized kinetic equation with spatiotemporal nonlocality. Mathematical Modeling and Computing. 6 (2), 289–296 (2019).
dc.relation.references[15] Silva C. A. B., Rodrigues C. G., Ramos J. G., Luzzi R. Higher-order generalized hydrodynamics: Foundations within a nonequilibrium statistical ensemble formalism. Physical Review E. 91 (6), 063011 (2015).
dc.relation.references[16] Ramos J. G., Rodrigues C. G., Silva C. A. B., Luzzi R. Statistical mesoscopic hydro-thermodynamics: the description of kinetics and hydrodynamics of nonequilibrium processes in single liquids. Brazilian Journal of Physics. 49, 277–287 (2019).
dc.relation.references[17] Rodrigues C. G., Ramos J. G., Silva C. A. B., Luzzi R. Nonlinear higher-order hydrodynamics: Fluids under driven flow and shear pressure. Physics of Fluids. 33 (6), 067111 (2021).
dc.relation.references[18] Akcasu A. Z., Duderstadt J. J. Derivation of kinetic equations from the generalized Langevin equation. Physical Review. 188, 479–486 (1969).
dc.relation.references[19] Forster D., Martin P. C. Kinetic theory of a weakly coupled fluid. Physical Review A. 2, 1575–1590 (1970).
dc.relation.references[20] Mazenko G. F. Microscopic method for calculating memory functions in transport theory. Physical Review A. 3, 2121–2137 (1971).
dc.relation.references[21] Mazenko G. F. Properties of the low-density memory function. Physical Review A. 5, 2545–2556 (1972).
dc.relation.references[22] Mazenko G. F., Tomas Y. S., Yip S. Thermal fluctuations in a hard-sphere gas. Physical Review A. 5, 1981–1995 (1972).
dc.relation.references[23] Mazenko G. F. Fully renormalized kinetic theory. I. Self-diffusion. Physical Review A. 7, 209–222 (1973).
dc.relation.references[24] Mazenko G. F. Fully renormalized kinetic theory. II. Velocity autocorrelation. Physical Review A. 7, 222–233 (1973).
dc.relation.references[25] Mazenko G. F. Fully renormalized kinetic theory. III. Density fluctuations. Physical Review A. 9, 360–387 (1974).
dc.relation.references[26] Forster D. Properties of the kinetic memory function in classical fluids. Physical Review A. 9, 943–956 (1974).
dc.relation.references[27] Boley C. D., Desai R. C. Kinetic theory of a dense gas: Triple-collision memory function. Physical Review A. 7, 1700–1709 (1973).
dc.relation.references[28] Furtado P. M., Mazenko G. F., Yip S. Hard-sphere kinetic-theory analysis of classical, simple liquids. Physical Review A. 12, 1653–1661 (1975).
dc.relation.references[29] Sj¨odin S., Sj¨olander A. Kinetic model for classical liquids. Physical Review A. 18, 1723–1735 (1978).
dc.relation.references[30] Mryglod I. M., Omelyan I. P., Tokarchuk M. V. Generalized collective modes for the Lennard–Jones fluid. Molecular Physics. 84, 235–259 (1995).
dc.relation.references[31] Hansen J. S. Where is the hydrodynamic limit? Molecular Simulation. 47 (17), 1391–1401 (2021).
dc.relation.references[32] De Angelis U. The physics of dusty plasmas. Physica Scripta. 45, 465–474 (1992).
dc.relation.references[33] Schram P. P. J. M., Sitenko A. G., Trigger S. A., Zagorodny A. G. Statistical theory of dusty plasmas: Microscopic equations and Bogolyubov–Born–Green–Kirkwwood–Yvon hierarchy. Physical Review E. 63, 016403 (2000).
dc.relation.references[34] Zagorodny A. G., Sitenko A. G., Bystrenko O. V.,Schram P. P. J. M., Trigger S. A. Statistical theory of dusty plasmas: Microscopic description and numerical simulations. Physics of Plasmas. 8 (5), 1893–1902 (2001).
dc.relation.references[35] Tsytovich V. N., De Angelis U. Kinetic theory of dusty plasmas. I. General approach. Physics of Plasmas. 6 (4), 1093–1106 (1999).
dc.relation.references[36] Tsytovich V. N., De Angelis U. Kinetic theory of dusty plasmas. V. The hydrodynamic equations. Physics of Plasmas. 11 (2), 496–506 (2004).
dc.relation.references[37] Bonitz M., Henning C., Block D. Complex plasmas: a laboratory for strong correlations. Reports on Progress in Physics. 73 (6), 066501 (2010).
dc.relation.references[38] Bandyopadhyay P., Sen A. Driven nonlinear structures in flowing dusty plasmas. Reviews of Modern Plasma Physics. 6, 28 (2022).
dc.relation.references[39] Tolias P. On the Klimontovich description of complex (dusty) plasmas. Contributions to Plasma Physics. e202200182 (2023).
dc.relation.references[40] Caprini L., Marconi U. M. B. Active matter at high density: Velocity distribution and kinetic temperature. Journal of Chemical Physics. 153 (18), 184901 (2020).
dc.relation.references[41] Marconi U. M. B., Caprini L., Puglisi A. Hydrodynamics of simple active liquids: the emergence of velocity correlations. New Journal of Physics. 23, 103024 (2021).
dc.relation.references[42] Farage T. F. F., Krinninger P., Brader J. M. Effective interactions in active Brownian suspensions. Physical Review E. 91 (4), 042310 (2015).
dc.relation.references[43] Feliachi O., Besse M., Nardini C., Barr´e J. Fluctuating kinetic theory and fluctuating hydrodynamics of aligning active particles: the dilute limit. Journal of Statistical Mechanics: Theory and Experiment. 2022, 113207 (2022).
dc.relation.references[44] Fodor E., Jack R. L., Cates M. E. Irreversibility and Biased Ensembles in Active Matter: Insights from Stochastic Thermodynamics. Annual Review of Condensed Matter Physics. 13 (1), 215–238 (2022).
dc.relation.references[45] Sprenger A. R., Caprini L., L¨owen H., Wittmann R. Dynamics of active particles with translational and rotational inertia. Preprint arXiv:2301.01865v1 (2023).
dc.relation.references[46] Kuroda Y., Matsuyama H., Kawasaki T., Miyazaki K. Anomalous fluctuations in homogeneous fluid phase of active Brownian particles. Physical Review Research. 5 (1), 013077 (2023).
dc.relation.references[47] Hlushak P., Tokarchuk M. Chain of kinetic equations for the distribution functions of particles in simple liquid taking into account nonlinear hydrodynamic fluctuations. Physica A. 443, 231–245 (2016).
dc.relation.references[48] Yukhnovskii I. R., Hlushak P. A., Tokarchuk M. V. BBGKY chain of kinetic equations, non-equilibrium statistical operator method and collective variable method in the statistical theory of non-equilibrium liquids. Condensed Matter Physics. 19 (4), 43705 (2016).
dc.relation.references[49] Yukhnovskii I. R., Tokarchuk M. V., Hlushak P. A. The method of collective variables in the theory of nonlinear fluctuations with account for kinetic processes. Ukrainian Journal of Physics. 67 (8), 579–591 (2022).
dc.relation.references[50] Zubarev D. N., Morozov V. G., R¨opke G. Statistical Mechanics of Nonequilibrium Processes. Berlin, Akademie. Vol. 2 (1997).
dc.relation.references[51] Tokarchuk M. V. To the kinetic theory of dense gases and liquids. Calculation of quasi-equilibrium particle distribution functions by the method of collective variables. Mathematical Modeling and Computing. 9 (2), 440–458 (2022).
dc.relation.references[52] Kobryn A. E., Omelyan I. P., Tokarchuk M. V. The modified group expansions for construction of solutions to the BBGKY hierarchy. Journal of Statistical Physics. 92, 973–994 (1998).
dc.relation.references[53] Markiv B. B., Omelyan I. P., Tokarchuk M. V. On the problem of a consistent description of kinetic and hydrodynamic processes in dense gases and liquids. Condensed Matter Physics. 13 (2), 23005 (2010).
dc.relation.references[54] Markiv B. B., Omelyan I. P., Tokarchuk M. V. On the problem of a consistent description of kinetic and hydrodynamic processes in dense gases and liquids: Collective excitations spectrum. Condensed Matter Physics. 15 (1), 14001 (2012).
dc.relation.references[55] Markiv B., Omelyan I., Tokarchuk M. Consistent description of kinetics and hydrodynamics of weakly nonequilibrium processes in simple liquids. Journal of Statistical Physics. 155, 843–866 (2014).
dc.relation.referencesen[1] Jhon M. S., Forster D. A kinetic theory of classical simple liquids. Physical Review A. 12 (1), 254–266 (1975).
dc.relation.referencesen[2] Boon J., Yip S. Molecular Hydrodynamics. McGraw-Hill Inc., New-York (1980).
dc.relation.referencesen[3] Zubarev D. N., Morozov V. G. Formulation of boundary conditions for the BBGKY hierarchy with allowance for local conservation laws. Theoretical and Mathematical Physics. 60, 814–820 (1984).
dc.relation.referencesen[4] Karkheck J., Stell G., Xu J. Transport theory for the Lennard–Jones dense fluid. Journal of Chemical Physics. 89 (9), 5829–5833 (1988).
dc.relation.referencesen[5] Zubarev D. N., Morozov V. G., Omelyan I. P., Tokarchuk M. V. Kinetic equations for dense gases and liquids. Theoretical and Mathematical Physics. 87, 412–424 (1991).
dc.relation.referencesen[6] Klimontovich Yu. L. The unified description of kinetic and hydrodynamic processes in gases and plasmas. Physics Letters A. 170 (6), 434–438 (1992).
dc.relation.referencesen[7] Klimontovich Yu. L. On the need for and the possibility of a unified description of kinetic and hydrodynamic processes. Theoretical and Mathematical Physics. 92, 909–921 (1992).
dc.relation.referencesen[8] Zubarev D. N., Morozov V. G., Omelyan I. P., Tokarchuk M. V. Unification of the kinetic and hydrodynamic approaches in the theory of dense gases and liquids. Theoretical and Mathematical Physics. 96, 997–1012 (1993).
dc.relation.referencesen[9] Tokarchuk M. V. On the statistical theory of a nonequilibrium plasma in its electromagnetic self-field. Theoretical and Mathematical Physics. 97, 1126–1136 (1993).
dc.relation.referencesen[10] Zubarev D. N., Morozov V. G., R¨opke G. Statistical Mechanics of Nonequilibrium Processes. Berlin, Akademie. Vol. 1 (1996).
dc.relation.referencesen[11] Tokarchuk M. V., Omelyan I. P., Kobryn A. E. A consistent description of kinetics and hydrodynamics of systems of interacting particles by means of the nonequilibrium statistical operator method. Condensed Matter Physics. 1 (4), 687–751 (1998).
dc.relation.referencesen[12] Markiv B., Tokarchuk M. Consistent description of kinetics and hydrodynamics of dusty plasma. Physics of Plasmas. 21, 023707 (2014).
dc.relation.referencesen[13] Kostrobij P., Viznovych O., Markiv B., Tokarchuk M. Generalized kinetic equations for dense gases and liquids in the Zubarev nonequilibrium statistical operator method and Renyi statistics. Theoretical and Mathematical Physics. 184 (1), 1020–1032 (2015).
dc.relation.referencesen[14] Kostrobij P. P., Markovych B. M., Ryzha I. A., Tokarchuk M. V. Generalized kinetic equation with spatiotemporal nonlocality. Mathematical Modeling and Computing. 6 (2), 289–296 (2019).
dc.relation.referencesen[15] Silva C. A. B., Rodrigues C. G., Ramos J. G., Luzzi R. Higher-order generalized hydrodynamics: Foundations within a nonequilibrium statistical ensemble formalism. Physical Review E. 91 (6), 063011 (2015).
dc.relation.referencesen[16] Ramos J. G., Rodrigues C. G., Silva C. A. B., Luzzi R. Statistical mesoscopic hydro-thermodynamics: the description of kinetics and hydrodynamics of nonequilibrium processes in single liquids. Brazilian Journal of Physics. 49, 277–287 (2019).
dc.relation.referencesen[17] Rodrigues C. G., Ramos J. G., Silva C. A. B., Luzzi R. Nonlinear higher-order hydrodynamics: Fluids under driven flow and shear pressure. Physics of Fluids. 33 (6), 067111 (2021).
dc.relation.referencesen[18] Akcasu A. Z., Duderstadt J. J. Derivation of kinetic equations from the generalized Langevin equation. Physical Review. 188, 479–486 (1969).
dc.relation.referencesen[19] Forster D., Martin P. C. Kinetic theory of a weakly coupled fluid. Physical Review A. 2, 1575–1590 (1970).
dc.relation.referencesen[20] Mazenko G. F. Microscopic method for calculating memory functions in transport theory. Physical Review A. 3, 2121–2137 (1971).
dc.relation.referencesen[21] Mazenko G. F. Properties of the low-density memory function. Physical Review A. 5, 2545–2556 (1972).
dc.relation.referencesen[22] Mazenko G. F., Tomas Y. S., Yip S. Thermal fluctuations in a hard-sphere gas. Physical Review A. 5, 1981–1995 (1972).
dc.relation.referencesen[23] Mazenko G. F. Fully renormalized kinetic theory. I. Self-diffusion. Physical Review A. 7, 209–222 (1973).
dc.relation.referencesen[24] Mazenko G. F. Fully renormalized kinetic theory. II. Velocity autocorrelation. Physical Review A. 7, 222–233 (1973).
dc.relation.referencesen[25] Mazenko G. F. Fully renormalized kinetic theory. III. Density fluctuations. Physical Review A. 9, 360–387 (1974).
dc.relation.referencesen[26] Forster D. Properties of the kinetic memory function in classical fluids. Physical Review A. 9, 943–956 (1974).
dc.relation.referencesen[27] Boley C. D., Desai R. C. Kinetic theory of a dense gas: Triple-collision memory function. Physical Review A. 7, 1700–1709 (1973).
dc.relation.referencesen[28] Furtado P. M., Mazenko G. F., Yip S. Hard-sphere kinetic-theory analysis of classical, simple liquids. Physical Review A. 12, 1653–1661 (1975).
dc.relation.referencesen[29] Sj¨odin S., Sj¨olander A. Kinetic model for classical liquids. Physical Review A. 18, 1723–1735 (1978).
dc.relation.referencesen[30] Mryglod I. M., Omelyan I. P., Tokarchuk M. V. Generalized collective modes for the Lennard–Jones fluid. Molecular Physics. 84, 235–259 (1995).
dc.relation.referencesen[31] Hansen J. S. Where is the hydrodynamic limit? Molecular Simulation. 47 (17), 1391–1401 (2021).
dc.relation.referencesen[32] De Angelis U. The physics of dusty plasmas. Physica Scripta. 45, 465–474 (1992).
dc.relation.referencesen[33] Schram P. P. J. M., Sitenko A. G., Trigger S. A., Zagorodny A. G. Statistical theory of dusty plasmas: Microscopic equations and Bogolyubov–Born–Green–Kirkwwood–Yvon hierarchy. Physical Review E. 63, 016403 (2000).
dc.relation.referencesen[34] Zagorodny A. G., Sitenko A. G., Bystrenko O. V.,Schram P. P. J. M., Trigger S. A. Statistical theory of dusty plasmas: Microscopic description and numerical simulations. Physics of Plasmas. 8 (5), 1893–1902 (2001).
dc.relation.referencesen[35] Tsytovich V. N., De Angelis U. Kinetic theory of dusty plasmas. I. General approach. Physics of Plasmas. 6 (4), 1093–1106 (1999).
dc.relation.referencesen[36] Tsytovich V. N., De Angelis U. Kinetic theory of dusty plasmas. V. The hydrodynamic equations. Physics of Plasmas. 11 (2), 496–506 (2004).
dc.relation.referencesen[37] Bonitz M., Henning C., Block D. Complex plasmas: a laboratory for strong correlations. Reports on Progress in Physics. 73 (6), 066501 (2010).
dc.relation.referencesen[38] Bandyopadhyay P., Sen A. Driven nonlinear structures in flowing dusty plasmas. Reviews of Modern Plasma Physics. 6, 28 (2022).
dc.relation.referencesen[39] Tolias P. On the Klimontovich description of complex (dusty) plasmas. Contributions to Plasma Physics. e202200182 (2023).
dc.relation.referencesen[40] Caprini L., Marconi U. M. B. Active matter at high density: Velocity distribution and kinetic temperature. Journal of Chemical Physics. 153 (18), 184901 (2020).
dc.relation.referencesen[41] Marconi U. M. B., Caprini L., Puglisi A. Hydrodynamics of simple active liquids: the emergence of velocity correlations. New Journal of Physics. 23, 103024 (2021).
dc.relation.referencesen[42] Farage T. F. F., Krinninger P., Brader J. M. Effective interactions in active Brownian suspensions. Physical Review E. 91 (4), 042310 (2015).
dc.relation.referencesen[43] Feliachi O., Besse M., Nardini C., Barr´e J. Fluctuating kinetic theory and fluctuating hydrodynamics of aligning active particles: the dilute limit. Journal of Statistical Mechanics: Theory and Experiment. 2022, 113207 (2022).
dc.relation.referencesen[44] Fodor E., Jack R. L., Cates M. E. Irreversibility and Biased Ensembles in Active Matter: Insights from Stochastic Thermodynamics. Annual Review of Condensed Matter Physics. 13 (1), 215–238 (2022).
dc.relation.referencesen[45] Sprenger A. R., Caprini L., L¨owen H., Wittmann R. Dynamics of active particles with translational and rotational inertia. Preprint arXiv:2301.01865v1 (2023).
dc.relation.referencesen[46] Kuroda Y., Matsuyama H., Kawasaki T., Miyazaki K. Anomalous fluctuations in homogeneous fluid phase of active Brownian particles. Physical Review Research. 5 (1), 013077 (2023).
dc.relation.referencesen[47] Hlushak P., Tokarchuk M. Chain of kinetic equations for the distribution functions of particles in simple liquid taking into account nonlinear hydrodynamic fluctuations. Physica A. 443, 231–245 (2016).
dc.relation.referencesen[48] Yukhnovskii I. R., Hlushak P. A., Tokarchuk M. V. BBGKY chain of kinetic equations, non-equilibrium statistical operator method and collective variable method in the statistical theory of non-equilibrium liquids. Condensed Matter Physics. 19 (4), 43705 (2016).
dc.relation.referencesen[49] Yukhnovskii I. R., Tokarchuk M. V., Hlushak P. A. The method of collective variables in the theory of nonlinear fluctuations with account for kinetic processes. Ukrainian Journal of Physics. 67 (8), 579–591 (2022).
dc.relation.referencesen[50] Zubarev D. N., Morozov V. G., R¨opke G. Statistical Mechanics of Nonequilibrium Processes. Berlin, Akademie. Vol. 2 (1997).
dc.relation.referencesen[51] Tokarchuk M. V. To the kinetic theory of dense gases and liquids. Calculation of quasi-equilibrium particle distribution functions by the method of collective variables. Mathematical Modeling and Computing. 9 (2), 440–458 (2022).
dc.relation.referencesen[52] Kobryn A. E., Omelyan I. P., Tokarchuk M. V. The modified group expansions for construction of solutions to the BBGKY hierarchy. Journal of Statistical Physics. 92, 973–994 (1998).
dc.relation.referencesen[53] Markiv B. B., Omelyan I. P., Tokarchuk M. V. On the problem of a consistent description of kinetic and hydrodynamic processes in dense gases and liquids. Condensed Matter Physics. 13 (2), 23005 (2010).
dc.relation.referencesen[54] Markiv B. B., Omelyan I. P., Tokarchuk M. V. On the problem of a consistent description of kinetic and hydrodynamic processes in dense gases and liquids: Collective excitations spectrum. Condensed Matter Physics. 15 (1), 14001 (2012).
dc.relation.referencesen[55] Markiv B., Omelyan I., Tokarchuk M. Consistent description of kinetics and hydrodynamics of weakly nonequilibrium processes in simple liquids. Journal of Statistical Physics. 155, 843–866 (2014).
dc.rights.holder© Національний університет “Львівська політехніка”, 2023
dc.subjectнемарковські рівняння
dc.subjectметод нерівноважного статистичного оператора
dc.subjectентропія
dc.subjectстатистична сума нерівноважного стану
dc.subjectядра переносу
dc.subjectcancer modeling
dc.subjectimmune response
dc.subjectfractional-order
dc.subjectstability
dc.subjectnumerical solution
dc.titleUnification of kinetic and hydrodynamic approaches in the theory of dense gases and liquids far from equilibrium
dc.title.alternativeОб’єднання кінетичного та гідродинамічного підходів у теорії густих газів і рідин, далеких від рівноваги
dc.typeArticle

Files

Original bundle

Now showing 1 - 2 of 2
Thumbnail Image
Name:
2023v10n2_Tokarchuk_M_V-Unification_of_kinetic_272-287.pdf
Size:
1.74 MB
Format:
Adobe Portable Document Format
Download
Thumbnail Image
Name:
2023v10n2_Tokarchuk_M_V-Unification_of_kinetic_272-287__COVER.png
Size:
469.29 KB
Format:
Portable Network Graphics
Download

License bundle

Now showing 1 - 1 of 1
Thumbnail Image
Name:
license.txt
Size:
1.77 KB
Format:
Plain Text
Description:
Download

Collections

Mathematical Modeling And Computing. – 2023. – Vol. 10, No. 2