Nonintegral form of the reciprocal relation associated with violation of the fluctuation response relation.

We extend Onsager's reciprocal relation to systems in a nonequilibrium steady state. While Onsager's reciprocal relation concerns the kinetic (Onsager) coefficient, the extended reciprocal relation concerns violation of the fluctuation response relation (FRR) for mechanical and thermal perturbations. This extended relation holds at each frequency when the extent of the FRR violation is expressed in a frequency domain.

Dynamic Monte Carlo calculation generating particle trajectories that satisfy the diffusion equation for heterogeneous systems with a position-dependent diffusion coefficient and free energy.

A series of new Monte Carlo (MC) transition probabilities was investigated that could produce molecular trajectories statistically satisfying the diffusion equation with a position-dependent diffusion coefficient and potential energy. The MC trajectories were compared with the numerical solution of the diffusion equation by calculating the time evolution of the probability distribution and the mean first passage time, which exhibited excellent agreement. The method is powerful when investigating, for example, the long-distance and long-time global transportation of a molecule in heterogeneous systems by coarse-graining them into one-particle diffusive molecular motion with a position-dependent diffusion coefficient and free energy.

Solvation effects on diffusion processes of a macromolecule: Accuracy required for radial distribution function to calculate diffusion coefficient.

We investigate the dependence of the diffusion coefficient of a large solute particle on the solvation structure around a solute. The diffusion coefficient of a hard-sphere system is calculated by using a perturbation theory of large-particle diffusion with radial distribution functions around the solute. To obtain the radial distribution function, some integral equation theories are examined, such as the Percus-Yevick (PY), hypernetted-chain (HNC), and modified HNC theories using a bridge function proposed by Kinoshita (MHNC) closures.

Reduced density profile of small particles near a large particle: Results of an integral equation theory with an accurate bridge function and a Monte Carlo simulation.

Solute-solvent reduced density profiles of hard-sphere fluids were calculated by using several integral equation theories for liquids. The traditional closures, Percus-Yevick (PY) and the hypernetted-chain (HNC) closures, as well as the theories with bridge functions, Verlet, Duh-Henderson, and Kinoshita (named MHNC), were used for the calculation. In this paper, a one-solute hard-sphere was immersed in a one-component hard-sphere solvent and various size ratios were examined.

Stick boundary condition at large hard sphere arising from effective attraction in binary hard-sphere mixtures.

We have studied the diffusion of a large hard-sphere solute immersed in binary hard-sphere mixtures. We reveal how the boundary condition at the solute surface is affected by the solvent density around the solute. Solving equations for a binary compressible mixture by perturbation expansions, we obtain the boundary condition depending on the size ratio of binary solvent spheres.

Dynamics of the entropic insertion of a large sphere into a cylindrical vessel.

Insertion of a solute into a vessel comprising biopolymers is a fundamental function in a biological system. The entropy originating from the translational displacement of solvent particles plays an essential role in the insertion. Here we study the dynamics of entropic insertion of a large spherical solute into a cylindrical vessel.

Solid phase stability of a double-minimum interaction potential system.

We study phase stability of a system with double-minimum interaction potential in a wide range of parameters by a thermodynamic perturbation theory. The present double-minimum potential is the Lennard-Jones-Gauss potential, which has a Gaussian pocket as well as a standard Lennard-Jones minimum. As a function of the depth and position of the Gaussian pocket in the potential, we determine the coexistence pressure of crystals (fcc and bcc).

Coarse-grained forms for equations describing the microscopic motion of particles in a fluid.

Exact equations of motion for the microscopically defined collective density ρ(x,t) and the momentum density ĝ(x,t) of a fluid have been obtained in the past starting from the corresponding Langevin equations representing the dynamics of the fluid particles. In the present work we average these exact equations of microscopic dynamics over the local equilibrium distribution to obtain stochastic partial differential equations for the coarse-grained densities with smooth spatial and temporal dependence. In particular, we consider Dean's exact balance equation for the microscopic density of a system of interacting Brownian particles to obtain the basic equation of the dynamic density functional theory with noise.

Molecular dynamics study of fast dielectric relaxation of water around a molecular-sized ion.

We have calculated the dielectric relaxation of water around an ion using molecular dynamics simulations. The collective motion of water near the ion showed fast relaxation, whereas the reorientational motion of individual water molecules does not have the fast component. The ratio of the relaxation time for the fast component and the bulk water was consistent with the experimental results, known as hyper-mobile water, for alkali halide aqueous solution.

Free-energy landscape for a tagged particle in a dense hard-sphere fluid.

Exploiting the thermodynamic potential functional provided by density functional theory, we determine analytically the free-energy landscape (FEL) in a hard-sphere fluid. The FEL is represented in the three-dimensional coordinate space of the tagged particle. We also analyze the distribution of the free-energy barrier between adjacent basins and show that the most provable value and the average of the free-energy barrier are increasing functions of the density.

New conditions for validity of the centroid molecular dynamics and ring polymer molecular dynamics.

Validity of the centroid molecular dynamics (CMD) and ring polymer molecular dynamics (RPMD) in quantum liquids is studied on an assumption that momenta of liquid particles relax fast. The projection operator method allows one to derive the generalized Langevin equation including a memory effect for the full-quantum canonical (Kubo-transformed) correlation function. Similar equations for the CMD and RPMD correlation functions can be derived too.

Free energy landscape and cooperatively rearranging region in a hard sphere glass.

Exploiting the density functional theory, we calculate the free energy landscape (FEL) of the hard sphere glass in three dimensions. From the FEL, we estimate the number of the particles in the cooperatively rearranging region (CRR). We find that the density dependence of the number of the particles in the CRR is expressed as a power law function of the density.

Nonlinear effects on solvation dynamics in simple mixtures.

The authors applied the time dependent density functional method (TDDFM) and a linear model to solvation dynamics in simple binary solvents. Changing the solute-solvent interactions at t=0, the authors calculated the time evolution of density fields for solvent particles after the change (t>0) by the TDDFM and linear model. First, the authors changed the interaction of only one component of solvents.

Microscopic derivation of time-dependent density functional methods.

Time-dependent density functional methods (TDDFM) are studied from the microscopic viewpoint using projection operator methods in classical liquids. A density field is defined without averaging, so that a time evolution equation of the density field is derived with a random force. The derived equation includes a free energy functional, which is different from that defined in the TDDFM.

Specific heat in a nonequilibrium system composed of Einstein oscillators.

In order to understand the behavior of thermodynamic quantities near the glass transition temperature, we put the energy landscape picture and the particle's jump motion together and calculate the specific heat of a nonequilibrium system. Taking the finite observation time into account, we study the observation time dependence of the specific heat. We assume the Einstein oscillators for the dynamics of each basin in the landscape structure of phase space and calculate the specific heat of a system with 20 basins.

Spatial mosaic and interfacial dynamics in a Müllerian mimicry system.

Uncovering why spatial mosaics of mimetic morphs are maintained in a Müllerian mimicry system has been a challenging issue in evolutionary biology. In this article, we analyze the reaction diffusion system that describes two-species Müllerian mimicry in one- and two-dimensional habitats. Due to positive frequency-dependent selection, a local population first approaches the state where one of the comimicking patterns predominates, which is followed by slow movement of boundaries where different patterns meet.