The Experts below are selected from a list of 10272 Experts worldwide ranked by ideXlab platform
Jürgen Vollmer - One of the best experts on this subject based on the ideXlab platform.
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multibaker map for shear flow and viscous heating
Physical Review E, 2001Co-Authors: Laszlo Matyas, Jürgen VollmerAbstract:A consistent description of shear flow and the accompanying viscous heating as well as the associated Entropy Balance is given in the framework of a deterministic dynamical system. The laminar shear flow is modeled by a Hamiltonian multibaker map which drives velocity and temperature fields. In the appropriate macroscopic limit one recovers the Navier-Stokes and heat conduction equations along with the associated Entropy Balance. This indicates that results of nonequilibrium thermodynamics can be described by means of an abstract, sufficiently chaotic, and mixing dynamics. A thermostating algorithm can also be incorporated into this framework.
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shear flow viscous heating and Entropy Balance from dynamical systems
EPL, 2001Co-Authors: Jürgen Vollmer, L MatyaAbstract:A consistent description of a shear flow, the accompanied viscous heating, and the associated Entropy Balance is given in the framework of a deterministic dynamical system, where a multibaker dynamics drives two fields: the velocity and the temperature distributions. In an appropriate macroscopic limit their transport equations go over into the Navier-Stokes and the heat conduction equation of viscous flows. The inclusion of an artificial heat sink can stabilize steady states with constant temperatures. It mimics a thermostating algorithm used in non-equilibrium molecular-dynamics simulations.
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Multibaker map for thermodynamic cross effects in dynamical systems
Physical Review E, 2000Co-Authors: Laszlo Matyas, Tamás Tél, Jürgen VollmerAbstract:A consistent description of simultaneous heat and particle transport, including cross effects, and the associated Entropy Balance is given in the framework of a deterministic dynamical system. This is achieved by a multibaker map where, in addition to the phase-space density of the multibaker, a second field with appropriate source terms is included in order to mimic a spatial temperature distribution and its time evolution. Conditions are given to ensure consistency in an appropriately defined continuum limit with the thermodynamic Entropy Balance. They leave as the only free parameter of the model the Entropy flux let directly into the surroundings. If it vanishes in the bulk, the transport properties of the model are described by the thermodynamic transport equations. Another choice leads to a uniform temperature distribution. It represents transport problems treated by means of a thermostating algorithm, similar to the one considered in nonequilibrium molecular dynamics. Irreversibility in transport models based on dynamical systems with only a few degrees of freedomhas become the subject of intensive recent studies @1‐11#. They illustrate how macroscopic transport coefficients are related to the properties of the microscopic dynamics. It is a remarkable discovery that in chaotic dynamical systems a rate of irreversible Entropy production can be defined @4,6,7,9,12‐20#. This development opens the possibility of requiring for a consistent dynamical-system modeling of an irreversible process the derivation of both the transport equations and the Entropy Balance. In our approach we shall observe this constraint.
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Entropy Balance, Multibaker Maps, and the Dynamics of the Lorentz Gas
Hard Ball Systems and the Lorentz Gas, 2000Co-Authors: Tamás Tél, Jürgen VollmerAbstract:We extend and review recent results on nonequilibrium transport processes described by multibaker maps. The relation of these maps to the dynamics of the Lorentz gas is discussed. Special emphasis is put on the concept of coarse graining and its use in defining the analog of thermodynamic Entropy and in deriving an Entropy Balance. A full analogy with Irreversible Thermodynamics can only be obtained if at certain points we deviate from traditional dynamical system theory, and allow for open boundary conditions which make the system to converge to a ‘forced’ stationary measure. This measure differs from the natural SRB measure which can be realized with periodic boundary conditions only.
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Entropy Balance in the presence of drift and diffusion currents: An elementary chaotic map approach
Physical Review E, 1998Co-Authors: Jürgen Vollmer, Tamás Tél, Wolfgang BreymannAbstract:We study the rate of irreversible Entropy production and the Entropy flux generated by low-dimensional dynamical systems modeling transport processes induced by the simultaneous presence of an external field and a density gradient. The key ingredient for understanding Entropy Balance is the coarse graining of the phasespace density. This mimics the fact that ever refining phase-space structures caused by chaotic dynamics can only be detected by finite resolution. Calculations are carried out for a generalized multibaker map. For the time-reversible dissipative ~thermostated! version of the model, results of nonequilibrium thermodynamics are recovered in the large system limit. Independent of the choice of boundary conditions, we obtain the rate of irreversible Entropy production per particle as u 2 /D, where u is the streaming velocity ~current per density! and
L Matya - One of the best experts on this subject based on the ideXlab platform.
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shear flow viscous heating and Entropy Balance from dynamical systems
EPL, 2001Co-Authors: Jürgen Vollmer, L MatyaAbstract:A consistent description of a shear flow, the accompanied viscous heating, and the associated Entropy Balance is given in the framework of a deterministic dynamical system, where a multibaker dynamics drives two fields: the velocity and the temperature distributions. In an appropriate macroscopic limit their transport equations go over into the Navier-Stokes and the heat conduction equation of viscous flows. The inclusion of an artificial heat sink can stabilize steady states with constant temperatures. It mimics a thermostating algorithm used in non-equilibrium molecular-dynamics simulations.
Laszlo Matyas - One of the best experts on this subject based on the ideXlab platform.
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multibaker map for shear flow and viscous heating
Physical Review E, 2001Co-Authors: Laszlo Matyas, Jürgen VollmerAbstract:A consistent description of shear flow and the accompanying viscous heating as well as the associated Entropy Balance is given in the framework of a deterministic dynamical system. The laminar shear flow is modeled by a Hamiltonian multibaker map which drives velocity and temperature fields. In the appropriate macroscopic limit one recovers the Navier-Stokes and heat conduction equations along with the associated Entropy Balance. This indicates that results of nonequilibrium thermodynamics can be described by means of an abstract, sufficiently chaotic, and mixing dynamics. A thermostating algorithm can also be incorporated into this framework.
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Multibaker map for thermodynamic cross effects in dynamical systems
Physical Review E, 2000Co-Authors: Laszlo Matyas, Tamás Tél, Jürgen VollmerAbstract:A consistent description of simultaneous heat and particle transport, including cross effects, and the associated Entropy Balance is given in the framework of a deterministic dynamical system. This is achieved by a multibaker map where, in addition to the phase-space density of the multibaker, a second field with appropriate source terms is included in order to mimic a spatial temperature distribution and its time evolution. Conditions are given to ensure consistency in an appropriately defined continuum limit with the thermodynamic Entropy Balance. They leave as the only free parameter of the model the Entropy flux let directly into the surroundings. If it vanishes in the bulk, the transport properties of the model are described by the thermodynamic transport equations. Another choice leads to a uniform temperature distribution. It represents transport problems treated by means of a thermostating algorithm, similar to the one considered in nonequilibrium molecular dynamics. Irreversibility in transport models based on dynamical systems with only a few degrees of freedomhas become the subject of intensive recent studies @1‐11#. They illustrate how macroscopic transport coefficients are related to the properties of the microscopic dynamics. It is a remarkable discovery that in chaotic dynamical systems a rate of irreversible Entropy production can be defined @4,6,7,9,12‐20#. This development opens the possibility of requiring for a consistent dynamical-system modeling of an irreversible process the derivation of both the transport equations and the Entropy Balance. In our approach we shall observe this constraint.
Alexander Zlotnik - One of the best experts on this subject based on the ideXlab platform.
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Entropy Balance for the one-dimensional hyperbolic quasi-gasdynamic system of equations
Doklady Mathematics, 2017Co-Authors: Alexander Zlotnik, Boris N. ChetverushkinAbstract:Entropy Balance in the one-dimensional hyperbolic quasi-gasdynamic (HQGD) system of equations is analyzed. In particular, in regular flow regimes, it is shown that the behavior of Entropy in the HQGD system is mainly determined by terms involving the natural viscosity and thermal conductivity coefficients. The total Entropy production differs from the Navier–Stokes equations for viscous compressible heat-conducting gases by O(τ2) terms, where τ is a relaxation parameter. Additionally, a similar analysis of energy Balance is performed for the simpler case of the barotropic HQGD system, which is of interest for some applications.
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on spatial discretization of the one dimensional quasi gasdynamic system of equations with general equations of state and Entropy Balance
Computational Mathematics and Mathematical Physics, 2015Co-Authors: Vladimir Gavrilin, Alexander ZlotnikAbstract:The one-dimensional quasi-gasdynamic system of equations in the form of mass, momentum, and total energy conservation laws with general gas equations of state is considered. A family of three-point symmetric spatial discretizations of this system is studied for which the internal energy equation has a suitable form (without imBalance terms). An Entropy Balance equation is derived, and the influence exerted by the choice of discretizations of various terms on the form of difference imBalance terms in this equation is determined. Special discretizations are presented for which the corresponding nondivergence imBalance terms are zero. The Euler system of equations is solved numerically in the cases of a perfect polytropic gas, stiffened gas, and the van der Waals equations of state.
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On spatial discretization of the one-dimensional quasi-gasdynamic system of equations with general equations of state and Entropy Balance
Computational Mathematics and Mathematical Physics, 2015Co-Authors: Vladimir Gavrilin, Alexander ZlotnikAbstract:The one-dimensional quasi-gasdynamic system of equations in the form of mass, momentum, and total energy conservation laws with general gas equations of state is considered. A family of three-point symmetric spatial discretizations of this system is studied for which the internal energy equation has a suitable form (without imBalance terms). An Entropy Balance equation is derived, and the influence exerted by the choice of discretizations of various terms on the form of difference imBalance terms in this equation is determined. Special discretizations are presented for which the corresponding nondivergence imBalance terms are zero. The Euler system of equations is solved numerically in the cases of a perfect polytropic gas, stiffened gas, and the van der Waals equations of state.
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spatial discretization of the one dimensional quasi gasdynamic system of equations and the Entropy Balance equation
Computational Mathematics and Mathematical Physics, 2012Co-Authors: Alexander ZlotnikAbstract:For the quasi-gasdynamic system of equations, there holds the law of nondecreasing Entropy. Difference methods based on this system have been successfully used in numerous applications and test gasdynamic computations. In theoretical terms, however, for standard spatial discretizations of this system, the nondecreasing Entropy law does not hold exactly even in the one-dimensional case because of the mesh imBalance terms. For the quasi-gasdynamic equations, a new conservative spatial discretization is proposed for which the Entropy Balance equation has an appropriate form and the Entropy production is guaranteed to be nonnegative (which also holds in the presence of body forces and heat sources). An important element of this discretization is that it makes use of nonstandard space-averaging techniques, including a nonlinear “logarithmic” averaging of the density and internal energy. The results hold on arbitrary nonuniform meshes.
Pierluigi Colli - One of the best experts on this subject based on the ideXlab platform.
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Global existence for a phase separation system deduced from the Entropy Balance.
arXiv: Analysis of PDEs, 2019Co-Authors: Pierluigi Colli, Shunsuke KurimaAbstract:This paper is concerned with a thermomechanical model describing phase separation phenomena in terms of the Entropy Balance and equilibrium equations for the microforces. The related system is highly nonlinear and admits singular potentials in the phase equation. Both the viscous and the non-viscous cases are considered in the Cahn--Hilliard relations characterizing the phase dynamics. The Entropy Balance is written in terms of the absolute temperature and of its logarithm, appearing under time derivative. The initial and boundary value problem is considered for the system of partial differential equations. The existence of a global solution is proved via some approximations involving Yosida regularizations and a suitable time discretization.
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Global existence for a singular phase field system related to a sliding mode control problem
Nonlinear Analysis: Real World Applications, 2018Co-Authors: Pierluigi Colli, Michele ColturatoAbstract:Abstract In the present contribution we consider a singular phase field system located in a smooth and bounded three-dimensional domain. The Entropy Balance equation is perturbed by a logarithmic nonlinearity and by the presence of an additional term involving a possibly nonlocal maximal monotone operator and arising from a class of sliding mode control problems. The second equation of the system accounts for the phase dynamics, and it is deduced from a Balance law for the microscopic forces that are responsible for the phase transition process. The resulting system is highly nonlinear; the main difficulties lie in the contemporary presence of two nonlinearities, one of which under time derivative, in the Entropy Balance equation. Consequently, we are able to prove only the existence of solutions. To this aim, we will introduce a backward finite differences scheme and argue on this by proving uniform estimates and passing to the limit on the time step.
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Singular limit of an integrodifferential systemrelated to the Entropy Balance
Discrete & Continuous Dynamical Systems - B, 2014Co-Authors: Elena Bonetti, Pierluigi Colli, Gianni GilardiAbstract:A thermodynamic model describing phase transitions with thermal memory, in terms of an Entropy equation and a momentum Balance for the microforces, is adressed. Convergence results and error estimates are proved for the related integrodifferential system of PDE as the sequence of memory kernels converges to a multiple of a Dirac delta, in a suitable sense.
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Singular limit of an integrodifferential system related to the Entropy Balance
arXiv: Analysis of PDEs, 2013Co-Authors: Elena Bonetti, Pierluigi Colli, Gianni GilardiAbstract:A thermodynamic model describing phase transitions with thermal memory, in terms of an Entropy equation and a momentum Balance for the microforces, is adressed. Convergence results and error estimates are proved for the related integrodifferential system of PDE as the sequence of memory kernels converges to a multiple of a Dirac delta, in a suitable sense.
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global solution to a singular integro differential system related to the Entropy Balance
Nonlinear Analysis-theory Methods & Applications, 2007Co-Authors: Elena Bonetti, Pierluigi Colli, Mauro Fabrizio, Gianni GilardiAbstract:This paper is devoted to the mathematical analysis of a thermodynamic model describing phase transitions with thermal memory in terms of an Entropy equation and a momentum Balance for the microforces. The initial and boundary value problem is addressed for the related integro-differential system of partial differential equations (PDEs). Existence and uniqueness, continuous dependence on the data, and regularity results are proved for the global solution, in a finite time interval.