Ken Sekimoto

Kinetic Characterization of Heat Bath and the Energetics of Thermal Ratchet Models

Langevin equations have been employed to describe thermally fluctuating systems, such as thermal ratchet models . Their role of the heat bath in these contexts has not been clearly understood. We introduce an approach to this issue and, by using it, propose a method to study the energetics of those models. As a example, we calculate the efficiency of energy conversion of “Feynmans ratchet”.

Protein friction exerted by motor enzymes through a weak-binding interaction

Recently Vale et al. (1989, Cell 59, 915-925.) reported an observation of the one-dimensional Brownian movement of microtubules bound to flagellar dynein through a weak-binding interaction. In this study, we propose a theoretical model of this phenomenon. Our model consists of a rigid microtubule associated with a number of elastic dynein heads through a weak-binding interaction at equilibrium. The model implies that (1) the Brownian motion of the microtubule is not directly driven by the atomic collision of the solvent particles, but is driven by the thermally-generated structural fluctuations of the dynein heads which interact with the microtubule; (2) dynein heads through a weak-binding interaction exert a frictional drag force on the sliding motion of the microtubule and the drag force is proportional to the sliding velocity the same as in hydrodynamic viscous friction. This protein friction, with such viscous-like characteristics, may well play a role as a velocity-limiting factor in the normal ATP-induced sliding movement of motile proteins.

Complementarity Relation for Irreversible Process Derived from Stochastic Energetics

When the process of a system in contact with a heat bath is described by the classical Langevin equation, use of the method of stochastic energetics [K. Sekimoto: J. Phys. Soc. Jpn. 66 (1997) 1234] enables us to derive the form of Helmholtz free energy and the dissipation function of the system. We are able to prove that the irreversible heat Q irr and the time lapse Δ t of an isothermal process obey the complementarity relation, Q irr Δ t ≥ k B T S min , where S min depends on the initial and the final values of the control parameters, but does not depend on the pathway between these values.

Evolution of the domain structure during the nucleation-and-growth process with non-conserved order parameter

We generalize the model of the nucleation-and-growth process studied by Kolmogorov, Johnson, Mehl and Avrami. We then derive the exact space-time correlation functions of the two-phase structure which consist of metastable phase and stable phase. The result includes the case in which the nucleation rate and/or the growth velocity is a function of space and time.

Unattainability of carnot efficiency in the brownian heat engine

We discuss the reversibility of the Brownian heat engine. We perform an asymptotic analysis of the Kramers equation on a Buttiker-Landauer system and show quantitatively that Carnot efficiency is unattainable even in the fully overdamped limit. The unattainability is attributed to inevitable irreversible heat flow over the temperature boundary.

Elastic instabilities and phase coexistence of gels

We develop a macroscopic static theory of gels upon swelling or volume phase transition. After deriving the linear elasticity theory of strained systems from the general nonlinear formalism of deformation, we show that the surface modulational instability of a gel plate occurs as the result of softening of (generalized) Rayleigh surface waves. We also derive the stability criteria for uniaxially strained bulk gels. In addition to these linear analyses we developed, for the first time to our knowledge, a theory of three-dimensional phase coexistence of gels exhibiting a volume phase transition. Our study is limited mostly to the case of spherically symmetric geometry with the outer boundary of the gel having a finite radius. Various features of the two phase coexistence are found, some of which have no counterparts in the usual phase separation in binary fluids or gas-liquid systems.

Elastic Instability of Gels upon Swelling

We consider theoretically the equilibrium pattern formation of the get stab which is observed upon the volume-phase transition if one of the two surfaces of the slab is mechanically fixed prior to the transition. We show that the elastic theory for that geometry can predict the linear instability of some spatially periodic modes of deformation.

Dynamical theory of polymer melt morphology

A general kinetic equation of the monomer density variables for polymer blends and block copolymer melts is obtained which describes slow morphology variations. The general theory is applied to a polymer blend adopting the biased reptation model of a polymer chain under mean field. We obtain an equation of motion of interfaces in a phase-separated polymer blend, which contains an interface reaction term for length scales shorter than lc ≡ R2G/ξ, where RG is the gyration radius of a polymer chain and ξ the interfacial width. We also discuss some problems associated with the incompressibility requirement for phase separation kinetics of binary systems not limited to polymers. For length scales greater than lc the interface dynamics involves diffusion in bulk pure phases even in the strong segregation limit in a way different from that for the usual time-dependent Ginzburg-Landau equation for the conserved order parameter. Implications of the existence of the new term on the late stage phase separation kinetics of polymer blend are discussed.

Polarity Sorting in a Bundle of Actin Filaments by Two-Headed Myosins

A theoretical model is presented for sorting of the polarity of actin filaments in the presence of actin-activated ATP-hydrolysis of two-headed myosin (heavy meromyosin, HMM). In methyl-cellulose aqueous solution, actin filaments form a nonpolar bundlelike aggregate. Upon addition of HMM and ATP to this, the HMM-driven mutual sliding of the actin filaments is known to lead to gradual segregation of the filaments according to their polarity directions, as well as to contraction of the length of the bundle. We found crucial role of frictional drag between the actin filaments, which is not mediated by active sliding force of the two-headed myosins. We show why regions of actins with sorted polarity emerge and how they undergo coarsening in the presence of frictional drag between filaments.

A Mechanism for Shear Thickening of Polymer-Bearing Surfaces: Elasto-Hydrodynamic Coupling

We propose a mechanism for non-contact repulsive interaction between elastic bodies moving past each other in a fluid. A lateral flow along the curved surface and the resulting deformation lead to dissipative lubrication forces that act normal to the surfaces. Forces between polymer-bearing surfaces undergoing shear are calculated and seem to be important for the interpretation of surface force apparatus measurements such as those by Klein et al.