arXiv subjects

Shin-ichi Sasa

Publications and source records attributed to Shin-ichi Sasa.

139 records · Page 8Linked to original sources

arXiv1999

Thermodynamic Irreversibility from high-dimensional Hamiltonian Chaos

This paper discusses the thermodynamic irreversibility realized in high-dimensional Hamiltonian systems with a time-dependent parameter. A new quantity, the irreversible information loss, is defined from the Lyapunov analysis so as to characterize the thermodynamic irreversibility. It is proved that this new quantity satisfies an inequality associated with the second law of thermodynamics. Based on the assumption that these systems possess the mixing property and certain large deviation properties in the thermodynamic limit, it is argued reasonably that the most probable value of the irreversible information loss is equal to the change of the Boltzmann entropy in statistical mechanics, and that it is always a non-negative value. The consistency of our argument is confirmed by numerical experiments with the aid of the definition of a quantity we refer to as the excess information loss.

cond-mat.stat-mech↗

arXiv1998

Stochastic Energetics of Non-uniform Temperature Systems

We propose an energetic interpretation ofstochastic processes described by Langevin equations with non-uniform temperature. In order to avoid Itô-Stratonovich dilemma, we start with a Kramers equation, and derive a Fokker-Plank equation by the renormalization group method. We give a proper definition of heat for the system. Based on our formulations,we analyze two examples, the Thomson effect and a Brownian motor which realizes the Carnot efficiency.

cond-mat.stat-mech↗

arXiv1998

Dynamical Scaling Behavior of the Swift-Hohenberg Equation Following a Quench to the Modulated State

We study the kinetics of phase transitions in a Rayleigh-Benard system after onset of convection using 2D Swift-Hohenberg equation. An initially uniform state evolves to one whose ground state is spatially periodic. We confirmed previous results which showed that dynamical scaling occurs at medium quench ($ε= 0.25$) with scaling exponents 1/5 and 1/4 under zero noise and finite noise respectively. We find logarithmic scaling behavior for a deep quench ($ε= 0.75$) at zero noise. A simple method is devised to measure the proxy of domain wall length. We find that the energy and domain wall length exhibit scaling behavior with the same exponent. For $ε= 0.25$, the scaling exponents are 1/4 and 0.3 at zero and finite noise respectively.

patt-sol↗

arXiv1998

Numerical simulations on Szilard's engine and information erasure

We present a computational model for Szilard's engine and the information discarding process. Taking advantage of a fact that the one is essentially the reversed cycle of the other, we can discuss the both by employing the same model. Through numerical simulations we calculate the work extracted by the engine and the heat generation in the information discarding process. It is found that these quantities depend on some realistic ingredients, which means that the work done by the engine is no longer canceled by the heat generation in the information erasure.

physics.class-ph↗

arXiv1997

Brownian Motors driven by Particle Exchange

We extend the Langevin dynamics so that particles can be exchanged with a particle reservoir. We show that grand canonical ensembles are realized at equilibrium and derive the relations of thermodynamics for processes between equilibrium states. As an application of the proposed evolution rule, we devise a simple model of Brownian motors driven by particle exchange. KEYWORDS: Langevin Dynamics, Thermodynamics, Open Systems

cond-mat.stat-mech↗

arXiv1997

Equilibrium Chemical Engines

An equilibrium reversible cycle with a certain engine to transduce the energy of any chemical reaction into mechanical energy is proposed. The efficiency for chemical energy transduction is also defined so as to be compared with Carnot efficiency. Relevance to the study of protein motors is discussed. KEYWORDS: Chemical thermodynamics, Engine, Efficiency, Molecular machine.

cond-mat.soft↗

arXiv1997

Complementarity relation for irreversible process derived from stochastic energetics

When the process of a system in contact with a heat bath is described by classical Langevin equation, the method of stochastic energetics [K. Sekimoto, J. Phys. Soc. Jpn. vol. 66 (1997) p.1234] enables to derive the form of Helmholtz free energy and the dissipation function of the system. We prove that the irreversible heat Q_irr and the time lapse $Delta t} of an isothermal process obey the complementarity relation, Q_irr {Delta t} >= k_B T S_min, where S_min depends on the initial and the final values of the control parameters, but it does not depend on the pathway between these values.

cond-mat.stat-mech↗

arXiv1996

Renormalization Group Derivation of Phase Equations

Phase equations describing the evolution of large scale modulation of spatially periodic patterns in two dimensional systems are derived by employing the renormalization group method. A general formula for phase diffusion coefficients is given under certain conditions.

patt-sol↗

arXiv1995

Pattern selection of cracks in directionally drying fracture

We study pattern selection of cracks in directionally drying fractures by analyzing the experimental systems recently devised by C. Allain and L. Limat. [Phys. Rev. Lett. {\bf 74}, 2981 (1995).] Proposing a simple picture of crack formation, we clarify the mechanism of how cracks array regularly and find that the interval between neighboring cracks is proportional to the $2/3$ power of the cell thickness. This result explains well the experimental data of Allain and Limat.

patt-sol↗

arXiv1995

A Kink Soliton Characterizing Traffic Congestion

We study traffic congestion by analyzing a one dimensional traffic flow model. Developing an asymptotic method to investigate the long time behavior near a critical point, we derive the modified Korteweg-de Vries (mKdV) equation as the lowest order model. There are an infinite number of kink solitons to the mKdV equation, while it has been found by numerical simulations that the kink pattern arising in traffic congestion is uniquely determined irrespective of initial conditions. In order to resolve this selection problem, we consider higher order corrections to the mKdV equation and find that there is a kink soliton which can deform continuously with the perturbation represented by the addition of these corrections. With numerical confirmation, we show that this continuously deformable kink soliton characterizes traffic congestion. We also discuss the relationship between traffic congestion and slugging phenomenon in granular flow.

patt-sol↗

arXiv1995

Collective patterns arising out of spatio-temporal chaos

We present a simple mathematical model in which a time averaged pattern emerges out of spatio-temporal chaos as a result of the collective action of chaotic fluctuations. Our evolution equation possesses spatial translational symmetry under a periodic boundary condition. Thus the spatial inhomogeneity of the statistical state arises through a spontaneous symmetry breaking. The transition from a state of homogeneous spatio-temporal chaos to one exhibiting spatial order is explained by introducing a collective viscosity which relates the averaged pattern with a correlation of the fluctuations.

chao-dyn↗

arXiv1994

Weakly Chaotic Population Dynamics in Random Ecological Networks

Population dynamics in random ecological networks are investigated by analyzing a simple deterministic equation. It is found that a sequence of abrupt changes of populations punctuating quiescent states characterize the long time behavior. An asymptotic analysis is developed by introducing a log-scaled time, and it is shown that such a dynamical process behaves as non-steady weak chaos in which population disturbances grow algebraically in time. Also, some relevance of our study to taxonomic data of biological extinction is mentioned.

chao-dyn↗

arXiv1993

Oscillatory instability of crack propagations in quasi-static fracture

Crack propagations in quasi-static fracture are studied theoretically. The Griffith theory is applied to discuss a crack extension condition and motion of crack tips in straight propagations. Stability of the straight propagations is investigated based on the simple assumption that a curvature near the crack tip is determined by a singular shear stress. It is shown that straight propagations become unstable under ceatain conditions. Combined with boundary effects, this instability leads to an oscillatory propagation of cracks. The critical conditions are calculated quantitatively.

patt-sol↗