The Experts below are selected from a list of 279 Experts worldwide ranked by ideXlab platform
Michele Colturato - One of the best experts on this subject based on the ideXlab platform.
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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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Well-posedness and longtime behavior for a singular phase field system with perturbed phase dynamics
Evolution Equations & Control Theory, 2018Co-Authors: Michele ColturatoAbstract:We consider a singular phase field system located in a smooth bounded domain. In the Entropy Balance Equation appears a logarithmic nonlinearity. The second Equation of the system, deduced from a Balance law for the microscopic forces that are responsible for the phase transition process, is perturbed by an additional term involving a possibly nonlocal maximal monotone operator and arising from a class of sliding mode control problems. We prove existence and uniqueness of the solution for this resulting highly nonlinear system. Moreover, under further assumptions, the longtime behavior of the solution is investigated.
Heng Liang - One of the best experts on this subject based on the ideXlab platform.
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Integral optimizing functional of separation efficiency
Journal of Chromatography A, 1999Co-Authors: Heng LiangAbstract:Abstract According to thermodynamics, the integral optimizing functional of separation efficiency (ΔSS), which is the mixed Entropy change between initial and final states directly associated with separation efficiency, was presented to indicate integral separation efficiency for any zone separation method by further considering the Entropy change from the uniform to the arbitrary distribution of solute zones. Physically, as a system property, ΔSS is equal to the amount of information that the solute system obtains from its separation surrounding, or separation system. It can be quantitatively related to the irreversibility of separation processes in the Entropy Balance Equation, and corresponds to the extent of Boltzmann order. In separation science, ΔSS corresponds to the quantity of separated solutes. For any arbitrary distribution of solute zones, ΔSS can be calculated directly from the distributions and relative positions of solute zones and the number of moles of solutes. Thus ΔSS can be calculated directly from the separation results of chromatography and electrophoresis to indicate separation efficiency integrally and quantitatively. For example, for Gaussian distributions of zones, ΔSS can be calculated directly from the standard deviations of the peaks (σ), the distance between the centers of gravity of adjoining zones (Δx) and the number of moles of the solutes (n) or the peak height (h). A quasi-inverse relation between ΔSS and separation pureness of solutes (ϕ) was found numerically. In any effective separation process, ΔSS is always a negative value, and the more negative ΔSS is, the better the separation efficiency is. The computer simulation supported the above characters of ΔSS. The discovery of ΔSS is a part of the nonequilibrium thermodynamic separation theory, which can be used to integrally optimize and time-varying control the complete separation systems – the aggregates of solute systems and separation systems.
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Frameworks of separation theories from two separate worlds : dynamics and thermodynamics
Journal of Chromatography A, 1998Co-Authors: Heng Liang, Bingcheng LinAbstract:Abstract Contemporary separation theories are based on the mass conservation Equation with the methods of dynamics, lose the Entropy Balance Equation as a restriction condition, and draw very little from non-equilibrium thermodynamics, cybernetics, information theory and systematology. Thus, they cannot account for the irreversibility of separation processes. In natural sciences, the Entropy Balance Equation is an exclusive way to reveal the evolution that separation systems undergo in order to make solute systems evolve from Boltzmann's disorder to order. The irreversibility of separation processes, which is caused by thermodynamic forces, and described by the Entropy Balance Equation only, is the source of both the separation and mixing of solute systems. Therefore, Clausius' heat death (band spreading of one component) and Darwin's evolutionism (separation among different components) simultaneously coexist in separation processes. The framework of non-equilibrium thermodynamic separation theory is made up of three parts. First, the integral optimization function is found on the part of the mixed Entropy change of the solute system between the final state and the initial one relating directly to the net separation. It corresponds to the information quantity that solute systems gain from separation systems. The more negative the integral optimization function is, the more information solute systems gain and the better the integral separation efficiency of big separation systems is. Second, according to the Entropy Balance Equation and the conditions of practical separation processes, a separation state function can be discovered to show how separation systems described by macroscopic physicochemical parameters affect the integral optimization function. Lastly, with the methods of modern cybernetics, we will be able to optimize and time-varyingly control separation processes through controlling the operation parameters in separation processes with the separation state function. The non-equilibrium thermodynamic separation theory will keep separation theories up to date with modern physics and intersecting sciences.
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Frameworks of separation theories from two separate worlds: dynamics and thermodynamics
Journal of Chromatography A, 1998Co-Authors: Heng Liang, Bingcheng LinAbstract:Contemporary separation theories are based on the mass conservation Equation with the methods of dynamics, lose the Entropy Balance Equation as a restriction condition, and draw very little from non-equilibrium thermodynamics, cybernetics, information theory and systematology. Thus, they cannot account for the irreversibility of separation processes. In natural sciences, the Entropy Balance Equation is an exclusive way to reveal the evolution that separation systems undergo in order to make solute systems evolve from Boltzmann's disorder to order. The irreversibility of separation processes, which is caused by thermodynamic forces, and described by the Entropy Balance Equation only, is the sourer of both the separation and mixing of solute systems. Therefore, Clausius' heat death (band spreading of one component) and Darwin's evolutionism (separation among different components) simultaneously coexist in separation processes. The framework of non-equilibrium thermodynamic separation theory is made up of three parts. First, the integral optimization function is found on the part of the mixed Entropy change of the solute system between the final state and the initial one relating directly to the net separation. It corresponds to the information quantity that solute systems gain from separation systems. The more negative the integral optimization function is, the more information solute systems gain and the better the integral separation efficiency of big separation systems is. Second, according to the Entropy Balance Equation and the conditions of practical separation processes, a separation state function can be discovered to show how separation systems described by macroscopic physicochemical parameters affect the integral optimization function. Lastly, with the methods of modern cybernetics, we will be able to optimize and time-varyingly control separation processes through controlling the operation parameters in separation processes with the separation state function. The non-equilibrium thermodynamic separation theory will keep separation theories up to date with modern physics and intersecting sciences. (C) 1998 Elsevier Science B.V. All rights reserved
Bingcheng Lin - One of the best experts on this subject based on the ideXlab platform.
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Frameworks of separation theories from two separate worlds : dynamics and thermodynamics
Journal of Chromatography A, 1998Co-Authors: Heng Liang, Bingcheng LinAbstract:Abstract Contemporary separation theories are based on the mass conservation Equation with the methods of dynamics, lose the Entropy Balance Equation as a restriction condition, and draw very little from non-equilibrium thermodynamics, cybernetics, information theory and systematology. Thus, they cannot account for the irreversibility of separation processes. In natural sciences, the Entropy Balance Equation is an exclusive way to reveal the evolution that separation systems undergo in order to make solute systems evolve from Boltzmann's disorder to order. The irreversibility of separation processes, which is caused by thermodynamic forces, and described by the Entropy Balance Equation only, is the source of both the separation and mixing of solute systems. Therefore, Clausius' heat death (band spreading of one component) and Darwin's evolutionism (separation among different components) simultaneously coexist in separation processes. The framework of non-equilibrium thermodynamic separation theory is made up of three parts. First, the integral optimization function is found on the part of the mixed Entropy change of the solute system between the final state and the initial one relating directly to the net separation. It corresponds to the information quantity that solute systems gain from separation systems. The more negative the integral optimization function is, the more information solute systems gain and the better the integral separation efficiency of big separation systems is. Second, according to the Entropy Balance Equation and the conditions of practical separation processes, a separation state function can be discovered to show how separation systems described by macroscopic physicochemical parameters affect the integral optimization function. Lastly, with the methods of modern cybernetics, we will be able to optimize and time-varyingly control separation processes through controlling the operation parameters in separation processes with the separation state function. The non-equilibrium thermodynamic separation theory will keep separation theories up to date with modern physics and intersecting sciences.
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Frameworks of separation theories from two separate worlds: dynamics and thermodynamics
Journal of Chromatography A, 1998Co-Authors: Heng Liang, Bingcheng LinAbstract:Contemporary separation theories are based on the mass conservation Equation with the methods of dynamics, lose the Entropy Balance Equation as a restriction condition, and draw very little from non-equilibrium thermodynamics, cybernetics, information theory and systematology. Thus, they cannot account for the irreversibility of separation processes. In natural sciences, the Entropy Balance Equation is an exclusive way to reveal the evolution that separation systems undergo in order to make solute systems evolve from Boltzmann's disorder to order. The irreversibility of separation processes, which is caused by thermodynamic forces, and described by the Entropy Balance Equation only, is the sourer of both the separation and mixing of solute systems. Therefore, Clausius' heat death (band spreading of one component) and Darwin's evolutionism (separation among different components) simultaneously coexist in separation processes. The framework of non-equilibrium thermodynamic separation theory is made up of three parts. First, the integral optimization function is found on the part of the mixed Entropy change of the solute system between the final state and the initial one relating directly to the net separation. It corresponds to the information quantity that solute systems gain from separation systems. The more negative the integral optimization function is, the more information solute systems gain and the better the integral separation efficiency of big separation systems is. Second, according to the Entropy Balance Equation and the conditions of practical separation processes, a separation state function can be discovered to show how separation systems described by macroscopic physicochemical parameters affect the integral optimization function. Lastly, with the methods of modern cybernetics, we will be able to optimize and time-varyingly control separation processes through controlling the operation parameters in separation processes with the separation state function. The non-equilibrium thermodynamic separation theory will keep separation theories up to date with modern physics and intersecting sciences. (C) 1998 Elsevier Science B.V. All rights reserved
Hong Qian - One of the best experts on this subject based on the ideXlab platform.
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Stochastic Limit-Cycle Oscillations of a Nonlinear System Under Random Perturbations
Journal of Statistical Physics, 2021Co-Authors: Yu-chen Cheng, Hong QianAbstract:Dynamical systems with $$\varepsilon $$ ε small random perturbations appear in both continuous mechanical motions and discrete stochastic chemical kinetics. The present work provides a detailed analysis of the central limit theorem (CLT), with a time-inhomogeneous Gaussian process, near a deterministic limit cycle in $$\mathbb {R}^n$$ R n . Based on respectively the theory of random perturbations of dynamical systems and the WKB approximation that codes the large deviations principle (LDP), results are developed in parallel from both standpoints of stochastic trajectories and transition probability density and their relations are elucidated. We show rigorously the correspondence between the local Gaussian fluctuations and the curvature of the large deviation rate function near its infimum, connecting the CLT and the LDP of diffusion processes. We study uniform asymptotic behavior of stochastic limit cycles through the interchange of limits of time $$t\rightarrow \infty $$ t → ∞ and $$\varepsilon \rightarrow 0$$ ε → 0 . Three further characterizations of stochastic limit cycle oscillators are obtained: (i) An approximation of the probability flux near the cycle; (ii) Two special features of the vector field for the cyclic motion; (iii) A local Entropy Balance Equation along the cycle with clear physical meanings. Lastly and different from the standard treatment, the origin of the $$\varepsilon $$ ε in the theory is justified by a novel scaling hypothesis via constructing a sequence of stochastic differential Equations.
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Representations and divergences in the space of probability measures and stochastic thermodynamics
Journal of Computational and Applied Mathematics, 2020Co-Authors: Liu Hong, Hong Qian, Lowell F. ThompsonAbstract:Abstract Radon–Nikodym (RN) derivative between two measures arises naturally in the affine structure of the space of probability measures with densities. Entropy, free energy, relative Entropy, and Entropy production as mathematical concepts associated with RN derivatives are introduced. We identify a simple Equation that connects two measures with densities as a possible mathematical basis of the Entropy Balance Equation that is central in nonequilibrium thermodynamics. Application of this formalism to Gibbsian canonical distribution yields many results in classical thermomechanics. An affine structure based on the canonical representation and two divergences are introduced in the space of probability measures. It is shown that thermodynamic work, as a conditional expectation, is indicative of the RN derivative between two energy representations being singular. The Entropy divergence and the heat divergence yield respectively a Massieu–Planck potential based and a generalized Carnot inequalities.
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nonequilibrium thermodynamic formalism of nonlinear chemical reaction systems with waage guldberg s law of mass action
Chemical Physics, 2016Co-Authors: Hong QianAbstract:Macroscopic Entropy production rate σ(tot) in the general nonlinear isothermal chemical reaction system with mass action kinetics is decomposed into a free energy dissipation rate and a house-keeping heat dissipation rate: σ(tot)=σ(fd)+σ(hk); σ(fd)=-dA/dt, where A is a generalized free energy function. This yields a novel nonequilibrium free energy Balance Equation dA/dt=-σ(tot)+σ(hk), which is on a par with celebrated Entropy Balance Equation dS/dt=σ(tot)+η(ex) where η(ex) is the rate of Entropy exchange with the environment. For kinetic systems with complex Balance, σ(fd) and σ(hk) are the macroscopic limits of stochastic free energy dissipation rate and house-keeping heat dissipation rate, which are both nonnegative, in the Delbruck–Gillespie description of the stochastic chemical kinetics. A full kinetic and thermodynamic theory of chemical reaction systems that transcends mesoscopic and macroscopic levels emerges.
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physical origins of Entropy production free energy dissipation and their mathematical representations
Physical Review E, 2010Co-Authors: Hao Ge, Hong QianAbstract:A unifying mathematical theory of nonequilibrium thermodynamics of stochastic systems in terms of master Equations is presented. As generalizations of isothermal Entropy and free energy, two functions of state play central roles: the Gibbs Entropy $S$ and the relative Entropy $F$, which are related via the stationary distribution of the stochastic dynamics. $S$ satisfies the fundamental Entropy Balance Equation $dS/dt={e}_{p}\ensuremath{-}{h}_{d}/T$ with Entropy production rate ${e}_{p}\ensuremath{\ge}0$ and heat dissipation rate ${h}_{d}$, while $dF/dt=\ensuremath{-}{f}_{d}\ensuremath{\le}0$. For closed systems that satisfy detailed Balance: $T{e}_{p}(t)={f}_{d}(t)$. For open systems, one has $T{e}_{p}(t)={f}_{d}(t)+{Q}_{hk}(t)$, where the housekeeping heat, ${Q}_{hk}\ensuremath{\ge}0$, was first introduced in the phenomenological nonequilibrium steady-state thermodynamics put forward by Oono and Paniconi. ${Q}_{hk}$ represents the irreversible work done by the surrounding to the system that is kept away from reaching equilibrium. Hence, Entropy production ${e}_{p}$ consists of free energy dissipation associated with spontaneous relaxation (i.e., self-organization), ${f}_{d}$, and active energy pumping that sustains the open system ${Q}_{hk}$. The amount of excess heat involved in the relaxation ${Q}_{ex}={h}_{d}\ensuremath{-}{Q}_{hk}={f}_{d}\ensuremath{-}T(dS/dt)$. Two kinds of irreversibility, and the meaning of the arrow of time, emerge. Quasistationary processes, adiabaticity, and maximum principle for Entropy are also generalized to nonequilibrium settings.
Alexander Zlotnik - One of the best experts on this subject based on the ideXlab platform.
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On aggregated regularized Equations for homogeneous binary gas mixture flows with viscous compressible components
INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2019, 2020Co-Authors: Tatiana G. Elizarova, Alexander ZlotnikAbstract:We consider binary gas mixture flows with viscous compressible components in the absence of chemical reactions. We aggregate the previously derived regularized Equations for inhomogeneous mixtures and thus derive new simpler regularized Equations for homogeneous ones (i.e., with the common velocity and temperature). The Entropy Balance Equation with the non-negative Entropy production is stated for the new Equations. They are constructed for numerical simulations of flows.
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On some properties of multidimensional hyperbolic quasi-gasdynamic systems of Equations
Russian Journal of Mathematical Physics, 2017Co-Authors: B. N. Chetverushkin, Alexander ZlotnikAbstract:We study a multidimensional hyperbolic quasi-gasdynamic (HQGD) system of Equations containing terms with a regularizing parameter τ > 0 and 2nd order space and time derivatives; the body force is taken into account. We transform it to a form close to the compressible Navier–Stokes system of Equations. Then we derive the Entropy Balance Equation and show that the Entropy production is similar to the latter system plus a term of the order of O (τ^2). We analyze an Equation for the total Entropy as well. We also show that the corresponding residuals in the HQGD Equations with respect to the compressible Navier–Stokes ones are of the order of O (τ^2) too. Finally we treat the simplified barotropic HQGD system of Equations with the general state Equation and the stationary potential body force and obtain the corresponding results for it.
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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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on quasi gasdynamic and quasi hydrodynamic Equations for binary gas mixtures
Doklady Mathematics, 2014Co-Authors: T G Elizarova, Alexander Zlotnik, B. N. ChetverushkinAbstract:The quasigasdynamic (QGD) approach makes it possible to construct convenient and reliable differ� ence schemes for the numerical solution of various gasdynamic problems. Its description can be found in (1-3). More specifically, in (2, Chapter 9) (see also (4)), the Boltzmann kinetic Equation for a mixture of monatomic gases (5) is used to derive and test QGD Equations for binary mixtures of nonreactive ideal polytropic gases. In this paper, we analyze and expand the capabili� ties of the QGD approach in this area. The original Equations from (2) are rewritten as conservation laws, which are more conventional in viscous gas dynamics and convenient for discretization. Additionally, an external force and a heat source are taken into account. We briefly discuss the parabolicity of the sys� tem in the sense of Petrovskii, which ensures that the system is well defined. An Entropy Balance Equation is derived, and the Entropy production for a gas mixture is shown to be nonnegative, which ensures that the sys� tem is physically consistent (but does not hold in all available descriptions of gas mixtures). Importantly, to achieve the latter property, the expressions for the exchange terms in the total energy Balance Equation (initially derived only for monatomic gas mixtures) are properly generalized. Additionally, we introduce a simplification of the QGD system for binary mixtures, which is referred to as a quasihydrodynamic system and is used for the numerical simulation of weakly compressible suband transonic flows. At the end of this paper, we present simplified barotropic versions of both systems and derive a corresponding energy bal� ance Equation with nonpositive energy production. The QGD system for binary gas mixtures a and b (see (2)) consists of the following mass Balance, momentum, and total energy Equations for the gas α: