Based on a general model of Brownian motors, the Onsager coefficients and generalized efficiency of a thermal Brownian motor are calculated analytically. It is found that the Onsager reciprocity relation holds and the...Based on a general model of Brownian motors, the Onsager coefficients and generalized efficiency of a thermal Brownian motor are calculated analytically. It is found that the Onsager reciprocity relation holds and the Onsager coefficients are not affected by the kinetic energy change due to the particle＇s motion. Only when the heat leak in the system is negligible can the determinant of the Onsager matrix vanish. Moreover, the influence of the main parameters characterizing the model on the generalized efficiency of the Brownian motor is discussed in detail. The characteristic curves of the generalized efficiency varying with these parameters are presented, and the maximum generalized efficiency and the corresponding optimum parameters are determined. The results obtained here are of general significance. They are used to analyze the performance characteristics of the Brownian motors operating in the three interesting cases with zero heat leak, zero average drift velocity or a linear response relation, so that some important conclusions in current references are directly included in some limit cases of the present paper.展开更多
The viscous dissipation limit of weak solutions is considered for the Navier-Stokes equations of compressible isentropic flows confined in a bounded domain.We establish a Kato-type criterion for the validity of the in...The viscous dissipation limit of weak solutions is considered for the Navier-Stokes equations of compressible isentropic flows confined in a bounded domain.We establish a Kato-type criterion for the validity of the inviscid limit for the weak solutions of the Navier-Stokes equations in a function space with the regularity index close to Onsager’s critical threshold.In particular,we prove that under such a regularity assumption,if the viscous energy dissipation rate vanishes in a boundary layer of thickness in the order of the viscosity,then the weak solutions of the Navier-Stokes equations converge to a weak admissible solution of the Euler equations.Our approach is based on the commutator estimates and a subtle foliation technique near the boundary of the domain.展开更多
By using the Onsager principle as an approximation tool,we give a novel derivation for the moving finite element method for gradient flow equations.We show that the discretized problem has the same energy dissipation ...By using the Onsager principle as an approximation tool,we give a novel derivation for the moving finite element method for gradient flow equations.We show that the discretized problem has the same energy dissipation structure as the continuous one.This enables us to do numerical analysis for the stationary solution of a nonlinear reaction diffusion equation using the approximation theory of free-knot piecewise polynomials.We show that under certain conditions the solution obtained by the moving finite element method converges to a local minimizer of the total energy when time goes to infinity.The global minimizer,once it is detected by the discrete scheme,approximates the continuous stationary solution in optimal order.Numerical examples for a linear diffusion equation and a nonlinear Allen-Cahn equation are given to verify the analytical results.展开更多
According to the general principle of non-equilibrium thermodynamics, we propose a set of macroscopic transport equations for the spin transport and the charge transport, In particular, the spin torque is introduced a...According to the general principle of non-equilibrium thermodynamics, we propose a set of macroscopic transport equations for the spin transport and the charge transport, In particular, the spin torque is introduced as a generalized ＇current density＇ to describe the phenomena associated with the spin non-conservation in a unified framework. The Einstein relations and the Onsager relations between different transport phenomena are established. Specifically, the spin transport properties of the isotropic non-magnetic and the isotropic magnetic two-dimensional electron gases are fully described by using this theory, in which only the macroscopic-spin-related transport phenomena allowed by the symmetry of the system are taken into account.展开更多
The purpose of this paper is to introduce to you, the Western people, nowadays a “widely unknown” Japanese thermodynamicist by the name of Motoyosi Sugita and his study on the thermodynamics of transient phenomena a...The purpose of this paper is to introduce to you, the Western people, nowadays a “widely unknown” Japanese thermodynamicist by the name of Motoyosi Sugita and his study on the thermodynamics of transient phenomena and his theory of life. This is because although he was one of the top theoretical physicists in Japan before, during and after WWII and after WWII he promoted the establishment of the biophysical society of Japan as one of the founding members, he himself and his studies themselves have seemed to be totally forgotten nowadays in spite that his study was absolutely important for the study of life. Therefore, in this paper I would like to present what kind of person he was and what he studied in physics as a review on the physics work of Motoyosi Sugita for the first time. I will follow his past studies to introduce his ideas in theoretical physics as well as in biophysics as follows: He proposed the bright ideas such as the quasi-static change in the broad sense, the virtual heat, and the field of chemical potential etc. in order to establish his own theory of thermodynamics of transient phenomena, as the generalization of the Onsager-Prigogine’s theory of the irreversible processes. By the concept of the field of chemical potential that acquired the nonlinear transport, he was seemingly successful to exceed and go beyond the scope of Onsager and Prigogine. Once he established his thermodynamics, he explored the existence of the 4th law of thermodynamics for the foundation of theory of life. He applied it to broad categories of transient phenomena including life and life being such as the theory of metabolism. He regarded the 4th law of thermodynamics as the maximum principle in transient phenomena. He tried to prove it all life long. Since I have recently found that his maximum principle can be included in more general maximum principle, which was known as the Pontryagin’s maximum principle in the theory of optimal control, I would like to explain such theories produced by Motoyosi Sugita as de展开更多
When a film of soft matter solutions is being dried, a skin layer often forms at its surface, which is a gel-like elastic phase made of concentrated soft matter solutions. We study the dynamics of this process by usin...When a film of soft matter solutions is being dried, a skin layer often forms at its surface, which is a gel-like elastic phase made of concentrated soft matter solutions. We study the dynamics of this process by using the solute based Lagrangian scheme which was proposed by us recently. In this scheme, the process of the gelation（i.e., the change from sol to gel） can be naturally incorporated in the diffusion equation. Effects of the elasticity of the skin phase, the evaporation rate of the solvents, and the initial concentration of the solutions are discussed. Moreover, the condition for the skin formation is provided.展开更多
A new variational method is proposed to investigate the dynamics of the thin film in a coating flow where a liquid is delivered through a fixed slot gap onto a moving substrate. A simplified ODE system has also been d...A new variational method is proposed to investigate the dynamics of the thin film in a coating flow where a liquid is delivered through a fixed slot gap onto a moving substrate. A simplified ODE system has also been derived for the evolution of the thin film whose thickness hf is asymptotically constant behind the coating front. We calculate the phase diagram as well as the film profiles and approximate the film thickness theoretically, and agreement with the well-known scaling law as Ca2/3 is found.展开更多
Loschmidt’s paradox is extended by replacing its assumption of time reversibility with full CPT symmetry. Mobility is identified as a means for expressing collisions or dissipation, and the cross product of its gradi...Loschmidt’s paradox is extended by replacing its assumption of time reversibility with full CPT symmetry. Mobility is identified as a means for expressing collisions or dissipation, and the cross product of its gradient with the magnetic field, for expressing parity. Three phenomena incorporating such cross products are identified. The first is the cross product of the mobility gradient with the magnetic field. The second combines this cross product with the E cross B drift. The third is the reciprocal of the Nernst effect expressed as a cross product of the temperature gradient and the magnetic field. Simulations are conducted for testing Loschmidt’s extended paradox. Onsager’s exclusion of magnetic fields and rotation from reciprocals violates CPT symmetry and is unjustified. All three cross-product phenomena skew statistics in a fashion unanticipated by Boltzmann’s assumptions in his H-Theorem. CPT symmetric systems fall outside the assumptions of the theorem which is not rendered invalid but simply limited to its domain of applicability. Therefore, these systems do not violate the second law as Boltzmann defines it. They bypass it.展开更多
In this paper, we introduce the progress of the Euler equation and Onsager conjecture. We also introduce the Euler＇s life, the researches about the incompressible Euler equation, and the Onsager conjecture.
The drying of liquid droplets is a common daily life phenomenon that has long held a special interest in scientific research.When the droplet includes nonvolatile solutes,the evaporation of the solvent induces rich de...The drying of liquid droplets is a common daily life phenomenon that has long held a special interest in scientific research.When the droplet includes nonvolatile solutes,the evaporation of the solvent induces rich deposition patterns of solutes on the substrate.Understanding the formation mechanism of these patterns has important ramifications for technical applications,ranging from coating to inkjet printing to disease detection.This topical review addresses the development of physical understanding of tailoring the specific ring-like deposition patterns of drying droplets.We start with a brief introduction of the experimental techniques that are developed to control these patterns of sessile droplets.We then summarize the development of the corresponding theory.Particular attention herein is focused on advances and issues related to applying the Onsager variational principle(OVP)theory to the study of the deposition patterns of drying droplets.The main obstacle to conventional theory is the requirement of complex numerical solutions,but fortunately there has been recent groundbreaking progress due to the OVP theory.The advantage of the OVP theory is that it can be used as an approximation tool to reduce the high-order conventional hydrodynamic equations to first-order evolution equations,facilitating the analysis of soft matter dynamic problems.As such,OVP theory is now well poised to become a theory of choice for predicting deposition patterns of drying droplets.展开更多
Let D be an integer at least 3 and let H(D, 2) denote the hypercube. It is known that H(D, 2) is a Q-polynomial distance-regular graph with diameter D, and its eigenvalue sequence and its dual eigenvalue sequence are ...Let D be an integer at least 3 and let H(D, 2) denote the hypercube. It is known that H(D, 2) is a Q-polynomial distance-regular graph with diameter D, and its eigenvalue sequence and its dual eigenvalue sequence are all {D-2i}D i=0. Suppose that denotes the tetrahedron algebra. In this paper, the authors display an action of ■ on the standard module V of H(D, 2). To describe this action, the authors define six matrices in Mat X(C), called A, A*, B, B*, K, K*.Moreover, for each matrix above, the authors compute the transpose and then compute the transpose of each generator of ■ on V.展开更多
We analytically and numerically compute the Onsager dissociation rate(exciton dissociation)on an interface induced by a piezoelectric potential in an inorganicorganic hybrid p-n junction system(ZnO+(poly(p-phenylene v...We analytically and numerically compute the Onsager dissociation rate(exciton dissociation)on an interface induced by a piezoelectric potential in an inorganicorganic hybrid p-n junction system(ZnO+(poly(p-phenylene vinylene));PPV).When a positive piezoelectric potential is created at the interface region owing to the deformation of the system,free electrons accumulate at the interface.Hence,screening effects are observed.It is assumed that the electron layer formed at the interface then attracts free holes from the p-type PPV region,which leads to exciton formation,possibly via the Langevin recombination process.The increased exciton density can then contribute to the Onsager dissociation rate,which is maximum around the interface.This paper focuses on the role of piezoelectric effects in promoting exciton formation at the interface and its relation with the exciton dissociation rate.展开更多
The drying of liquid droplets is a common phenomenon in daily life,and has long attracted special interest in scientific research.We propose a simple model to quantify the shape evolution of drying droplets.The model ...The drying of liquid droplets is a common phenomenon in daily life,and has long attracted special interest in scientific research.We propose a simple model to quantify the shape evolution of drying droplets.The model takes into account the friction constant between the contact line(CL)and the substrate,the capillary forces,and the evaporation rate.Two typical evaporation processes observed in experiments,i.e.,the constant contact radius(CCR)and the constant contact angle(CCA),are demonstrated by the model.Moreover,the simple model shows complicated evaporation dynamics,for example,the CL first spreads and then recedes during evaporation.Analytical models of no evaporation,CCR,and CCA cases are given,respectively.The scaling law of the CL or the contact angle as a function of time obtained by analytical model is consistent with the full numerical model,and they are all subjected to experimental tests.The general model facilitates a quantitative understanding of the physical mechanism underlying the drying of liquid droplets.展开更多
基金supported by the National Natural Science Foundation of China (Grant No 10575084)
文摘Based on a general model of Brownian motors, the Onsager coefficients and generalized efficiency of a thermal Brownian motor are calculated analytically. It is found that the Onsager reciprocity relation holds and the Onsager coefficients are not affected by the kinetic energy change due to the particle＇s motion. Only when the heat leak in the system is negligible can the determinant of the Onsager matrix vanish. Moreover, the influence of the main parameters characterizing the model on the generalized efficiency of the Brownian motor is discussed in detail. The characteristic curves of the generalized efficiency varying with these parameters are presented, and the maximum generalized efficiency and the corresponding optimum parameters are determined. The results obtained here are of general significance. They are used to analyze the performance characteristics of the Brownian motors operating in the three interesting cases with zero heat leak, zero average drift velocity or a linear response relation, so that some important conclusions in current references are directly included in some limit cases of the present paper.
基金supported by National Science Foundation of USA(Grant No.DMS-1907584)supported by the Fundamental Research Funds for the Central Universities(Grant No.JBK 2202045)+1 种基金supported by National Science Foundation of USA(Grant Nos.DMS-1907519 and DMS-2219384)supported by National Natural Science Foundation of China(Grant No.12271122)。
文摘The viscous dissipation limit of weak solutions is considered for the Navier-Stokes equations of compressible isentropic flows confined in a bounded domain.We establish a Kato-type criterion for the validity of the inviscid limit for the weak solutions of the Navier-Stokes equations in a function space with the regularity index close to Onsager’s critical threshold.In particular,we prove that under such a regularity assumption,if the viscous energy dissipation rate vanishes in a boundary layer of thickness in the order of the viscosity,then the weak solutions of the Navier-Stokes equations converge to a weak admissible solution of the Euler equations.Our approach is based on the commutator estimates and a subtle foliation technique near the boundary of the domain.
基金supported in part by NSFC grants DMS-11971469the National Key R&D Program of China under Grant 2018YFB0704304 and Grant 2018YFB0704300.
文摘By using the Onsager principle as an approximation tool,we give a novel derivation for the moving finite element method for gradient flow equations.We show that the discretized problem has the same energy dissipation structure as the continuous one.This enables us to do numerical analysis for the stationary solution of a nonlinear reaction diffusion equation using the approximation theory of free-knot piecewise polynomials.We show that under certain conditions the solution obtained by the moving finite element method converges to a local minimizer of the total energy when time goes to infinity.The global minimizer,once it is detected by the discrete scheme,approximates the continuous stationary solution in optimal order.Numerical examples for a linear diffusion equation and a nonlinear Allen-Cahn equation are given to verify the analytical results.
基金Project supported by the National Key Basic Research Special Foundation of China (Grant No 2006CB921300)the National Natural Science Foundation of China (Grant No 10604063)
文摘According to the general principle of non-equilibrium thermodynamics, we propose a set of macroscopic transport equations for the spin transport and the charge transport, In particular, the spin torque is introduced as a generalized ＇current density＇ to describe the phenomena associated with the spin non-conservation in a unified framework. The Einstein relations and the Onsager relations between different transport phenomena are established. Specifically, the spin transport properties of the isotropic non-magnetic and the isotropic magnetic two-dimensional electron gases are fully described by using this theory, in which only the macroscopic-spin-related transport phenomena allowed by the symmetry of the system are taken into account.
文摘The purpose of this paper is to introduce to you, the Western people, nowadays a “widely unknown” Japanese thermodynamicist by the name of Motoyosi Sugita and his study on the thermodynamics of transient phenomena and his theory of life. This is because although he was one of the top theoretical physicists in Japan before, during and after WWII and after WWII he promoted the establishment of the biophysical society of Japan as one of the founding members, he himself and his studies themselves have seemed to be totally forgotten nowadays in spite that his study was absolutely important for the study of life. Therefore, in this paper I would like to present what kind of person he was and what he studied in physics as a review on the physics work of Motoyosi Sugita for the first time. I will follow his past studies to introduce his ideas in theoretical physics as well as in biophysics as follows: He proposed the bright ideas such as the quasi-static change in the broad sense, the virtual heat, and the field of chemical potential etc. in order to establish his own theory of thermodynamics of transient phenomena, as the generalization of the Onsager-Prigogine’s theory of the irreversible processes. By the concept of the field of chemical potential that acquired the nonlinear transport, he was seemingly successful to exceed and go beyond the scope of Onsager and Prigogine. Once he established his thermodynamics, he explored the existence of the 4th law of thermodynamics for the foundation of theory of life. He applied it to broad categories of transient phenomena including life and life being such as the theory of metabolism. He regarded the 4th law of thermodynamics as the maximum principle in transient phenomena. He tried to prove it all life long. Since I have recently found that his maximum principle can be included in more general maximum principle, which was known as the Pontryagin’s maximum principle in the theory of optimal control, I would like to explain such theories produced by Motoyosi Sugita as de
基金Project supported by the National Natural Science of China(Grant Nos.21434001,51561145002,and 11421110001)
文摘When a film of soft matter solutions is being dried, a skin layer often forms at its surface, which is a gel-like elastic phase made of concentrated soft matter solutions. We study the dynamics of this process by using the solute based Lagrangian scheme which was proposed by us recently. In this scheme, the process of the gelation（i.e., the change from sol to gel） can be naturally incorporated in the diffusion equation. Effects of the elasticity of the skin phase, the evaporation rate of the solvents, and the initial concentration of the solutions are discussed. Moreover, the condition for the skin formation is provided.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.91630208,91641107,and 11771437)
文摘A new variational method is proposed to investigate the dynamics of the thin film in a coating flow where a liquid is delivered through a fixed slot gap onto a moving substrate. A simplified ODE system has also been derived for the evolution of the thin film whose thickness hf is asymptotically constant behind the coating front. We calculate the phase diagram as well as the film profiles and approximate the film thickness theoretically, and agreement with the well-known scaling law as Ca2/3 is found.
文摘Loschmidt’s paradox is extended by replacing its assumption of time reversibility with full CPT symmetry. Mobility is identified as a means for expressing collisions or dissipation, and the cross product of its gradient with the magnetic field, for expressing parity. Three phenomena incorporating such cross products are identified. The first is the cross product of the mobility gradient with the magnetic field. The second combines this cross product with the E cross B drift. The third is the reciprocal of the Nernst effect expressed as a cross product of the temperature gradient and the magnetic field. Simulations are conducted for testing Loschmidt’s extended paradox. Onsager’s exclusion of magnetic fields and rotation from reciprocals violates CPT symmetry and is unjustified. All three cross-product phenomena skew statistics in a fashion unanticipated by Boltzmann’s assumptions in his H-Theorem. CPT symmetric systems fall outside the assumptions of the theorem which is not rendered invalid but simply limited to its domain of applicability. Therefore, these systems do not violate the second law as Boltzmann defines it. They bypass it.
基金supported by the National Natural Science Foundation of China No.11731014supported by the Foundation of Guangzhou University:2700050357
文摘In this paper, we introduce the progress of the Euler equation and Onsager conjecture. We also introduce the Euler＇s life, the researches about the incompressible Euler equation, and the Onsager conjecture.
基金supported by the National Natural Science Foundation of China(Grant No.21822302)the joint NSFCISF Research Program,China(Grant No.21961142020)the Fundamental Research Funds for the Central Universities,China。
文摘The drying of liquid droplets is a common daily life phenomenon that has long held a special interest in scientific research.When the droplet includes nonvolatile solutes,the evaporation of the solvent induces rich deposition patterns of solutes on the substrate.Understanding the formation mechanism of these patterns has important ramifications for technical applications,ranging from coating to inkjet printing to disease detection.This topical review addresses the development of physical understanding of tailoring the specific ring-like deposition patterns of drying droplets.We start with a brief introduction of the experimental techniques that are developed to control these patterns of sessile droplets.We then summarize the development of the corresponding theory.Particular attention herein is focused on advances and issues related to applying the Onsager variational principle(OVP)theory to the study of the deposition patterns of drying droplets.The main obstacle to conventional theory is the requirement of complex numerical solutions,but fortunately there has been recent groundbreaking progress due to the OVP theory.The advantage of the OVP theory is that it can be used as an approximation tool to reduce the high-order conventional hydrodynamic equations to first-order evolution equations,facilitating the analysis of soft matter dynamic problems.As such,OVP theory is now well poised to become a theory of choice for predicting deposition patterns of drying droplets.
基金supported by the National Natural Science Foundation of China(Nos.11471097,11271257)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20121303110005)+1 种基金the Natural Science Foundation of Hebei Province(No.A2013205021)the Key Fund Project of Hebei Normal University(No.L2012Z01)
文摘Let D be an integer at least 3 and let H(D, 2) denote the hypercube. It is known that H(D, 2) is a Q-polynomial distance-regular graph with diameter D, and its eigenvalue sequence and its dual eigenvalue sequence are all {D-2i}D i=0. Suppose that denotes the tetrahedron algebra. In this paper, the authors display an action of ■ on the standard module V of H(D, 2). To describe this action, the authors define six matrices in Mat X(C), called A, A*, B, B*, K, K*.Moreover, for each matrix above, the authors compute the transpose and then compute the transpose of each generator of ■ on V.
基金This research was supported by the Office of the Theory&Modeling Based Design of Energy Harvesting,Korea.
文摘We analytically and numerically compute the Onsager dissociation rate(exciton dissociation)on an interface induced by a piezoelectric potential in an inorganicorganic hybrid p-n junction system(ZnO+(poly(p-phenylene vinylene));PPV).When a positive piezoelectric potential is created at the interface region owing to the deformation of the system,free electrons accumulate at the interface.Hence,screening effects are observed.It is assumed that the electron layer formed at the interface then attracts free holes from the p-type PPV region,which leads to exciton formation,possibly via the Langevin recombination process.The increased exciton density can then contribute to the Onsager dissociation rate,which is maximum around the interface.This paper focuses on the role of piezoelectric effects in promoting exciton formation at the interface and its relation with the exciton dissociation rate.
基金Project supported by the National Natural Science Foundation of China(Grant No.21822302)the joint NSFC-ISF Research Program,China(Grant No.21961142020)+1 种基金the Fundamental Research Funds for the Central Universities,Chinathe National College Students'Innovative and Entrepreneurial Training Plan Program,China(Grant No.201910006142).
文摘The drying of liquid droplets is a common phenomenon in daily life,and has long attracted special interest in scientific research.We propose a simple model to quantify the shape evolution of drying droplets.The model takes into account the friction constant between the contact line(CL)and the substrate,the capillary forces,and the evaporation rate.Two typical evaporation processes observed in experiments,i.e.,the constant contact radius(CCR)and the constant contact angle(CCA),are demonstrated by the model.Moreover,the simple model shows complicated evaporation dynamics,for example,the CL first spreads and then recedes during evaporation.Analytical models of no evaporation,CCR,and CCA cases are given,respectively.The scaling law of the CL or the contact angle as a function of time obtained by analytical model is consistent with the full numerical model,and they are all subjected to experimental tests.The general model facilitates a quantitative understanding of the physical mechanism underlying the drying of liquid droplets.
