Language：English   Publishing type：Research paper (scientific journal)   Publisher：PHYSICAL SOC JAPAN  

We studied the effects of the inhomogeneous density distribution of polar solvent molecules around an ion on the polarization relaxation by using linearized time-dependent density functional theory. This theory, which takes into account the spatial inhomogeneity of the number density of solvent molecules, enabled us to calculate the spatial distribution of the relaxation time under certain initial conditions. The results of our calculations show that the spatial distribution of the relaxation time correlates with that of the number density. The negative correlation becomes positive as the translational diffusion coefficient increases. This dependence on the translational diffusion coefficient is not affected by the initial condition.

DOI： 10.7566/JPSJ.90.073801

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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. In one-component solvent systems, the diffusion coefficient depends on the first-minimum value of the radial distribution function. The results of the MHNC closure are in good agreement with those of calculation using the radial distribution functions of Monte Carlo simulations since the MHNC closure very closely reproduces the radial distribution function of Monte Carlo simulations. In binary-solvent mixtures, the diffusion coefficient is affected by the larger solvent density distribution in the short-range part, particularly the height and sharpness of the first peak and the depth of the first minimum. Since the HNC closure gives the first peak that is higher and sharper than that of the MHNC closure, the calculated diffusion coefficient is smaller than the MHNC closure result. In contrast, the results of the PY closure are qualitatively and quantitatively different from those of the MHNC and HNC closures.

DOI： 10.1063/5.0038894

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IOP Publishing  

DOI： 10.1209/0295-5075/129/66001

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Other Link： https://iopscience.iop.org/article/10.1209/0295-5075/129/66001

Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER INST PHYSICS  

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. The profiles between the solute and solvent particles were compared with those calculated by Monte Carlo simulations. The profiles given by the integral equations with the bridge functions were much more accurate than those calculated by conventional integral equation theories, such as the Ornstein-Zernike (OZ) equation with the PY closure. The accuracy of the MHNC-OZ theory was maintained even when the particle size ratio of solute to solvent was 50. For example, the contact values were 5.7 (Monte Carlo), 5.6 (MHNC), 7.8 (HNC), and 4.5 (PY), and the first minimum values were 0.48 (Monte Carlo), 0.46 (MHNC), 0.54 (HNC), and 0.40 (PY) when the packing fraction of the hard-sphere solvent was 0.38 and the size ratio was 50. The asymptotic decay and the oscillation period for MHNC-OZ were also very accurate, although those given by the HNC-OZ theory were somewhat faster than those obtained by Monte Carlo simulations.

DOI： 10.1063/1.5100040

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We study universal relationships in linear responses to instances when mechanical and thermal perturbations are applied to a nonequilibrium steady state. For perturbations in nonequilibrium Langevin systems, we consider a time-dependent external force exerted on a particle along with a time-dependent temperature for the heat bath. In this system, by calculating heat currents and particle velocity, we obtain the kinetic coefficients (Onsager's coefficients) and the time correlation functions using the Fokker-Planck equations. With these quantities, we derive the reciprocal relation associated with the violation of the fluctuation response relation. We obtain the relation by integrating the extent of the violation with respect to the frequency. We also find the reciprocity in the first moment of the frequency integration. These frequency sum rules hold for both overdamped and underdamped regimes for any type of potential and any strength of the external force.

DOI： 10.1103/PhysRevE.98.042120

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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. When the size ratio is 1: 2, the boundary condition lies close to the slip boundary condition. By contrast, when the size ratio becomes large, the boundary condition approaches the stick boundary condition with the addition of larger solvent spheres. We find that the transition to the stick boundary condition is caused by the increase in the solvent density around the solute due to an entropic effect. Published by AIP Publishing.

DOI： 10.1063/1.5025202

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(Received June 26, 2016; revised December 26, 2016; accepted May 12, 2017; published online June 22, 2017) On the basis of time-dependent density functional theory (TDDFT), we develop a method for calculating the spatial distribution of interacting particles in a nonequilibrium state. The particles flow around spatially fixed matter. Using this method, we clarify the many-particle effects due to particle interactions on the distribution of flowing hard spheres around a spatially fixed hard sphere (probe particle). We numerically calculate the TDDFT equations assuming axial symmetry, using the discrete Hankel transform. From this numerical calculation, we obtain the forces exerted on the probe particle by the flowing hard spheres. The calculated forces are compared with those due to noninteracting flowing particles at various particle flow velocities and volume fractions. This comparison shows that the force in the interactingparticle case is reduced by the hard-sphere interaction at low velocities and small volume fractions. In contrast, at high velocities and large volume fractions, the force in the hard-sphere system is stronger than that in the noninteracting particle system.

DOI： 10.7566/JPSJ.86.074604

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：EPL ASSOCIATION, EUROPEAN PHYSICAL SOCIETY  

We derive the reciprocal relation between the linear mechanical and thermal response functions in a driven diffusive model. In this model, we consider the violation of the fluctuation-response relation (FRR) of the velocity of a particle to the thermal perturbation. In addition, we also consider the FRR violation of the heat current of the system to a mechanical perturbation. We show the equality for the extent of these FRR violations using the Fokker-Planck equation. Copyright (C) EPLA, 2017

DOI： 10.1209/0295-5075/117/20005

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：EPL ASSOCIATION, EUROPEAN PHYSICAL SOCIETY  

Fluid-solid phase diagrams for binary hard-sphere systems were calculated to study the effects of interactions between depletants. Two effective potentials between large hard spheres were examined. One was the Asakura-Oosawa (AO) potential, and the other was an effective potential obtained by using an integral equation theory (IE potential). The IE potential has oscillations caused by the interactions between depletants, whereas in the AO potential, the inter-depletant correlation is ignored. The phase diagrams were obtained by using the thermodynamic perturbation theory with the density functional theory. The phase diagrams for the IE potential systems differed from those for the AO potential systems because of the inter-depletant correlation. The differences in the present calculation were caused by the first minimum of the effective potential. Copyright (C) EPLA, 2016

DOI： 10.1209/0295-5075/116/38004

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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. The solute and the vessel are immersed in small spheres forming the solvent. We develop a theoretical method formulated using the Fokker-Planck equation. The spatial distribution of solute-vessel entropic potential, which is calculated by the three-dimensional integral equation theory combined with rigid-body models, serves as input data. The key quantity analyzed is the density of the probability of finding the solute at any position at any time. It is found that the solute is inserted along the central axis of the vessel cavity and trapped at a position where the entropic potential takes a local minimum value. The solute keeps being trapped without touching the vessel inner surface. In a significantly long time tau, the solute transfers to the position in contact with the vessel bottom possessing the global potential minimum along the central axis. As the solute size increases, tau becomes remarkably longer. We also discuss the relevance of our result to the functional expression of a chaperonin/cochaperonin in the assistance of protein folding. (C) 2016 AIP Publishing LLC.

DOI： 10.1063/1.4943394

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Language：Japanese   Publisher：The Physical Society of Japan  

DOI： 10.11316/jpsgaiyo.71.2.0_3112

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DOI： 10.11316/jpsgaiyo.71.1.0_3281

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DOI： 10.11316/jpsgaiyo.71.1.0_3289

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We formulate a theoretical method for studying the solvent particle dynamics around a moving solute, using time-dependent density functional theory. The theoretical method is applied to the insertion process of a large sphere into a cylindrical vessel immersed in solvent particles. For various velocities of the large sphere, we calculate the nonequilibrium spatial distribution of number density of solvent particles. We find a nonequilibrium effect on the distribution, which is characterized by the total number of solvent particles inside of the vessel. The number is 32.5% larger for a velocity of D-S/2d(S) than for the equilibrium state, where, d(S) and D-S are the diameter and diffusion coefficient of a solvent particle, respectively.

DOI： 10.7566/JPSJ.84.123601

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We formulate a theory for calculating the viscosity of a dilute solution, considering the solute-solvent interaction. We consider an inhomogeneous density distribution of solvent particles caused by the interaction, using the equilibrium solute-solvent radial distribution function. The theory is a microscopic extension of Einstein's viscosity formula. We formulate the theory by a perturbation expansion, assuming that a solvent particle is much smaller than a solute particle. From the perturbation theory, we obtain hydrodynamic equations with new boundary conditions on the surface of the solute. The theory is applied to a system with a simple radial distribution function.

DOI： 10.7566/JPSJ.84.043602

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We extend the relationship between the fluctuation-response relation (FRR) violation and the stationary energy dissipation rate to the Langevin system expressed by field variable. We propose two methods for extending: the operator method and the multiple-scale analysis. By these methods, we expand the FRR violation for the underdamped field system in power series of epsilon = m/gamma to establish the relationship between underdamped and overdamped systems. Here, gamma and m are the friction coefficient and mass of a Brownian particle, respectively. By the expansion, we obtain a unified expression including the relations in the underdamped and overdamped field systems as special cases. The expression shows that the relations have the same form in the underdamped and overdamped field systems. In addition, we show that the relation also holds in the time region difference from that in the underdamped or overdamped system.

DOI： 10.7566/JPSJ.84.044008

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Language：Japanese   Publisher：The Physical Society of Japan (JPS)  

DOI： 10.11316/jpsgaiyo.70.1.0_3441

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DOI： 10.11316/jpsgaiyo.70.1.0_3326

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DOI： 10.11316/jpsgaiyo.70.1.0_3327

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DOI： 10.11316/jpsgaiyo.70.1.0_3004

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DOI： 10.11316/jpsgaiyo.70.1.0_3336

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DOI： 10.11316/jpsgaiyo.70.2.0_2887

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DOI： 10.11316/jpsgaiyo.70.2.0_2542

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

We have studied the effects of interactions between particles on the dynamics in a colloidal dispersion system using the time-dependent density functional theory. We consider a hard-sphere probe particle fixed at the origin and hard-sphere colloidal particles suspended in a solvent that flows at a constant velocity against the probe particle. We calculated the density fields of colloidal particles, forces acting on the probe particle, and friction coefficients for small volume fractions of colloidal particles. The results show that hard-sphere interactions between colloidal particles decrease the forces and friction coefficients. The effect of the interactions is more significant for small colloidal particles than for large particles. The effect also becomes weak with increasing velocity of the solvent. (C) 2014 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.molliq.2014.05.029

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We study the effects of the solvation structure on the diffusion of a large particle in a binary mixture. Using our recently developed perturbation theory, we calculate the diffusion coefficient of a large hard-sphere solute particle immersed in a binary solvent mixture of hard spheres with two different sizes. The calculation results show that the Stokes-Einstein (SE) relation breaks down in the hard-sphere system. When the size ratio of binary solvent spheres is three or more, the deviation from the SE relation increases with the packing fraction of larger solvent spheres. In contrast, at the size ratio of two, the diffusion coefficient approaches the value predicted by the SE relation as larger solvent spheres are added. We show that the large deviation from the SE relation is caused by the high density of larger solvent spheres around the solute sphere. (C) 2014 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.molliq.2014.06.021

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We study the diffusion of a large spherical particle immersed in a binary compressive liquid mixture using a perturbation theory. We focus on the breakdown of the Stokes-Einstein (SE) relation caused by the microscopic solvation structure of binary solvent particles around a solute particle. In order to consider the solvation structure, we solve multicomponent generalized Langevin equations by singular perturbation expansion. Then, we assume that solvent particles are much smaller than the solute particle. Solving the equations, we express the diffusion coefficient analytically using the radial distribution functions of a binary mixture. The expression shows the breakdown of the SE relation if the density distribution of a binary solvent is inhomogeneous around a solute particle. Actually, we show that the SE relation breaks down when a large hard sphere diffuses in a binary hard-sphere mixture. We observe the large deviation from the SE relation, which is a result specific to the binary solvent.

DOI： 10.7566/JPSJ.83.064601

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER INST PHYSICS  

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). We show that the fcc crystallizes even at zero pressure when the position of the Gaussian pocket is coincident with the first or third nearest neighbor site of the fcc crystal. The bcc crystal is more stable than the fcc crystal when the position of the Gaussian pocket is coincident with the second nearest neighbor sites of the bcc crystal. The stable crystal structure is determined by the position of the Gaussian pocket. These results show that we can control the stability of the solid phase by tuning the potential function. (C) 2014 AIP Publishing LLC.

DOI： 10.1063/1.4884021

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A new expression of the Harada-Sasa equality is derived by multiple-scale analysis. The new expression unifies the equality for the underdamped and overdamped Langevin models in special cases. In addition, the expression shows that the equality is available in a new time region, which differs from that in the underdamped or overdamped model. The expression is obtained by the expansion of the fluctuation response relation (FRR) violation in the underdamped model in powers of epsilon=m/gamma, where gamma is the friction coefficient and m is the mass of a Brownian particle. The violation of the FRR is in agreement with the energy dissipation rate up to the second order of epsilon.

DOI： 10.7566/JPSJ.83.053001

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DOI： 10.1016/j.molliq.2014.03.015

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Exact equations of motion for the microscopically defined collective density (rho) over cap (x, t) and the momentum density (g) over cap (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. Our analysis demonstrates that on thermal averaging the dependence of the exact equations on the bare interaction potential is converted to dependence on the corresponding thermodynamic direct correlation functions in the coarse-grained equations.

DOI： 10.1103/PhysRevE.88.043008

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On the basis of the free energy landscape theory, we develop a framework to calculate the structural relaxation time in supercooled liquids and glasses. By the framework, the relaxation time is obtained by an escaping time from a basin in a given free energy surface. In order to demonstrate its usefulness, we apply the framework to monodisperse hard-sphere glass systems. Then we show that the relaxation time increases drastically with the density. Additionally, we discuss an explicit picture of the cooperatively rearranging region by analyzing the spatial distribution of an activation free energy of one particle. (C) 2013 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.cplett.2013.05.051

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A new inhomogeneous time-dependent density functional theory is proposed to study an effect of external field on the polarization relaxation of molecular liquids. The effect of external field is considered by the number density of solvent molecules, and the homogeneous approximation introduced by many previous studies is not employed. To demonstrate the validity of the theory, the spatial distribution of the relaxation time is calculated in a polar solvent system with an ion. The calculated results show a notable effect of translational diffusion on the spatial distribution of the polarization relaxation time.

DOI： 10.7566/JPSJ.82.013001

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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. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4769972]

DOI： 10.1063/1.4769972

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A new theory is developed to study the effects of the granularity of a liquid on the diffusion of a large particle in the liquid. Inhomogeneous Langevin equations are expanded in powers of the size ratio between the solvent and large particles. From the expansion, we obtain hydrodynamic equations with new boundary conditions on the surface of the large particle in the first order. The new boundary conditions can be obtained from the radial distribution function between diffusing and solvent particles. The present theory is formulated by perturbation expansion and can thus deal with a large particle. In addition, using analytical solutions of hydrodynamic equations, we consider the effects of solvent particles at an infinite distance in contrast to the case for other methods. The theory is applied to a model radial distribution function, a hard-sphere system, and a Kihara potential system.

DOI： 10.1143/JPSJ.81.114603

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We present a new method of deriving the relation between the dissipation of energy and the violation of the fluctuation response relation in nonequilibrium states. The method is obtained using the Fokker-Planck equation in underdamped cases. Using the method, we show that the relation obtained by Harada and Sasa can be derived from an energy balance in nonequilibrium steady states. In addition, applying the method to colloidal many-particle systems, we derive a new expression for the relation using the current and density fields. The new expression has a simple form with a linear response coefficient for a nonconservative external force, in contrast to that in a previous study.

DOI： 10.1143/JPSJ.81.094002

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We have investigated the crystallization of a monatomic simple liquid in equilibrium, where the constituents interact through the Lennard-Jones-Gauss (LJG) potential. By incorporating a perturbation expansion into a density functional approach, we obtain a phase diagram covering a wide range of the parameter space. The phase diagram agrees qualitatively with that obtained by molecular dynamics (MD) simulations. The MD simulations show that the system cannot be crystallized, even if the temperature is sufficiently low, in a certain region of the parameter space. In this parameter region, we find that the coexisting density of the fcc crystal is unexpectedly high owing to a decrease in the free energy and show that the third-nearest-neighbor site of the fcc crystal coincides with the second minimum in the LJG potential.

DOI： 10.1143/JPSJS.81SA.SA020

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A new theory of a binary solvent is developed to study the effects of the density of solvent particles around a large solute particle on friction. To develop the theory, the solvent particles are assumed to be much smaller than the solute particle, and then a perturbation expansion is employed. The expansion allows one to derive hydrodynamic equations with boundary conditions on the surface of a solute. The boundary conditions are calculated from the radial distribution functions of a binary solvent. The hydrodynamic equations with the boundary conditions provide an analytical expression for the friction. The developed theory is applied to a binary hard-sphere system. The present theory shows that the friction in the system has larger values than those predicted by the Stokes law.

DOI： 10.1143/JPSJS.81SA.SA026

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A theory, which was previously applied to electron transfer in DNA, is applied to hole transfer between a dye molecule and an electrode coupled through a DNA bridge, because the applicability to such hole transfer has not yet been studied. The results calculated using the theory are compared with the experimental results for the same system. The theory reproduces the dependence of the current between the dye molecule and the electrode on the length of DNA. However, the agreement with experimental results requires that the reorganization energy in the ground state of a dye molecule be larger than that employed in previous studies of electron transfer.

DOI： 10.1143/JPSJ.81.093801

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：Institute of Physics Publishing  

Freezing of various classical liquids is successfully described by density functional theory (DFT). On the other hand, so far no report has been published that DFT describes the freezing of superfuid 4He correctly. In fact, DFT gives too stable solid phase and the superfuid phase does not exist at finite positive pressures within a second order perturbation. In this paper we try a non-perturbative version of DFT, that is modified weighted density approximation (MWDA) to go beyond second order perturbation for the freezing of superfuid 4He. Via an exact zero temperature quantum Monte-Carlo (QMC) method we have computed the equation of state and the compressibility of superfuid 4He. By utilizing a recently introduced analytic continuation method (the GIFT method), we have obtained also density response functions at different densities from QMC imaginary time correlation functions. Contrary to second order perturbation, by employing these QMC data as DFT input we find a too stable superfuid phase, preventing freezing around the experimentally observed freezing pressure. We find the same pathological behavior by using another model energy functional of superfuid 4He (Orsay-Trento model). We conclude that the straightforward MWDA calculation gives such a poor result when liquid-gas transition is present. © Published under licence by IOP Publishing Ltd.

DOI： 10.1088/1742-6596/400/1/012050

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We establish the general relationship between the configurational entropy and heat capacity in a supercooled liquid within the framework of equilibrium statistical mechanics. The relationship shows that the configurational entropy is different from the entropy obtained by the integration of the glass heat capacity. In addition, the difference shows the correlation between the energy and entropy in liquid structures. Applying the general results to a simple model, we demonstrate that the difference can be too large to neglect. We also discuss new experiments using the present results.

DOI： 10.1143/JPSJ.80.064601

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A theory for studying nonlinear dynamics of molecular liquids is developed. The theory is based on the extension of the time-dependent density functional theory to a rigid interaction-site model. From the theory, one can calculate time changes in interaction-site densities using molecular parameters such as the inertial moment of a molecule. The theory has a differential and integral basic equation with a kernel function, which is not included in the time-dependent density functional theory of simple liquids. The application of the theory to diatomic and three-site molecules allows one to obtain explicit expressions of kernel functions.

DOI： 10.1143/JPSJ.80.034801

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DOI： 10.1143/JPSJ.80.025001

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We derive the fluctuating hydrodynamic equation for the number and momentum densities exactly from the underdamped Langevin equation. This derivation is an extension of the Kawasaki-Dean formula in the underdamped case. The steady-state probability distribution of the number and momentum densities field can be expressed by the kinetic and potential energies. In the massless limit, the obtained fluctuating hydrodynamic equation reduces to the Kawasaki-Dean equation. Moreover, the derived equation corresponds to the field equation derived from the canonical equation when the friction coefficient is zero.

DOI： 10.1088/1751-8113/42/6/065001

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DOI： 10.1016/j.jnoncrysol.2008.10.018

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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. Since the size of the cooperatively rearranging region (CRR) is also increased as the density is raised [Yoshidome , Phys. Rev. E 76, 021506 (2007)], the present result is consistent with the Adam-Gibbs theory in which the increase of the activation energy is due to the increase of the size of the CRR.

DOI： 10.1103/PhysRevE.77.061503

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DOI： 10.1063/1.2897786

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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. Analyzing the relaxation process in the CRR, we also find that the string motion is the elementary process for the structural relaxation, which leads to the natural definition of the simultaneously rearranging region as the particles displaced in the string motion.

DOI： 10.1103/PhysRevE.76.021506

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：National Academy of Sciences of Ukraine  

The limit of a large solute in the molecular theory of diffusion developed by Yamaguchi et al. [Yamaguchi T. et al., J. Chem. Phys., 2005, 123, 034504] is studied. By the limit, the Stokes approximation to the hydrodynamic equations is derived in the outside region of a diffusing solute. The limit of a large solute also leads to equations in the inside region of the solute. The analytical solution of the inside equation allows one to derive the boundary condition, which is needed on the surface of the solute when the hydrodynamic equations are calculated. The boundary condition includes stick and slip boundary conditions employed by the Stokes law, in the special case. Besides stick and slip conditions, other conditions can be expressed. The boundary condition depends on properties of a solvent. © A.Yoshimori.

DOI： 10.5488/CMP.10.4.563

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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. In this case, the TDDFM showed that the solvation time decreased monotonically with a mole fraction of the solvent strongly interacting with the solute. The monotonical decreases agreed with experimental results, while the linear model did not reproduce these results. The authors also calculated the solvation time by changing the interaction of both components. The calculation showed that the mole fraction dependence had the peak. The TDDFM presented a much higher peak than the linear model. The difference between the TDDFM and the linear model was caused by a nonlinear effect on an exchange process of solvent particles. (c) 2006 American Institute of Physics.

DOI： 10.1063/1.2409713

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DOI： 10.1016/j.jnoncrysol.2006.02.146

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We propose a new method to construct the free energy landscape in the configurational space, where the density functional approach to the thermodynamic function is exploited. In order to demonstrate the validity of the method, we construct the free energy landscape for rearrangement of atoms in an FCC crystal of hard spheres. Analyzing the relaxation process, we deduce two concepts of rearranging region, one is the simultaneously rearranging region (SRR) which is defined by the difference between two adjacent regions. The other is the cooperatively rearranging region (CRR) which is the spheres involved in the saddle configuration between two adjacent regions. The latter region corresponds to the region introduced by Adam and Gibbs. We show that the SRR and the CRR can be determined explicitly from the free energy landscape.

DOI： 10.1143/JPSJ.75.054005

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We propose a method to calculate the size of the cooperatively rearranging region (CRR), N-CRR, from the free energy landscape. In the free energy landscape picture, the particles in the CRR correspond to those involved in determinig the saddle point between two adjacent basins. By using this method, we estimate N-CRR of the 3-D random configuration of hard spheres. We also find that the system can transit to the adjacent basin via the lower height of the saddle point by the string motion.

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The time-dependent energy distribution of solvation dynamics is studied by molecular dynamics simulations of a Lennard-Jones mixture. We calculate the response functions of the average and the variance which correspond to the spectral peak shift and bandwidth. Our calculation shows that the variance relaxation is slower than that of the average. The result agrees qualitatively with the experimental results. Dividing the obtained response functions into subcomponents caused by each solvent, we find that the relaxation is dominated by that solvent which strongly interacts with the solute. Extracting the redistribution component from the response functions, we find that it causes the slower relaxation of the response function. Thus, we conclude that the difference of the slower relaxations between the average and variance is caused by the redistribution process. © 2005 American Institute of Physics.

DOI： 10.1063/1.1857480

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：3 Pt 1  

Time-dependent density functional methods (TDDFM) are studied from the microscopic viewpoint using projection operator methods in classical liquids. A density field is denned 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. The projection operator method provides the exact expression of the free energy functional. Another definition of the density field by an average leads to the equation of the TDDFM. In addition, an equation describing fluctuations is also derived. (c)2005 The American Physical Society.

DOI： 10.1103/PhysRevE.71.031203

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

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. The projection operator method provides the exact expression of the free energy functional. Another definition of the density field by an average leads to the equation of the TDDFM. In addition, an equation describing fluctuations is also derived.

DOI： 10.1103/PhysRevE.71.031203

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：The Physical Society of Japan (JPS)  

We study distribution of jump rates in supercooled liquids and glass by activation theories developed in studies of chemical reactions. Defining jump conditions, we explain the physical origin giving rise to the jump rate distribution. Jump rates distribute if some kinds of relaxation have different time scales. In addition, we express the distribution by the microscopic parameters of liquids using appropriate approximations. The obtained expression is the power law distribution in the limit of small jump rates. We relate the exponents of the power law with the time scale in the mode coupling theory.

DOI： 10.1143/JPSJ.74.1206

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DOI： 10.1063/1.1840488

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A simple binary-solvent model is theoretically employed to study the size-effect on selective solvation. We consider multi-component hard-sphere molecules with solute-solvent attraction. We employ the PY approximation to calculate coordination numbers. The calculated coordination number shows that the solute attracts more large solvent molecules than small solvent molecules at a weak attraction. The solute, however, attracts small solvent molecules at strong attraction. To study the selectivity, we divide the size-effect into the exclude effect and the steric hindrance. Attractive strength increases the steric hindrance of large solvent molecules more than that of the small solvent molecules. © 2003 Elsevier Science B.V. All rights reserved.

DOI： 10.1016/S0009-2614(03)00182-9

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DOI： 10.1063/1.1519237

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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. For a given observation time, a transition from annealed to quenched system occurs at the temperature when the time scale of jumps exceeds the observation time. The transition occurs at lower temperature and becomes sharper for longer observation time. © 2002 The American Physical Society.

DOI： 10.1103/PhysRevE.66.041103

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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. For a given observation time, a transition from annealed to quenched system occurs at the temperature when the time scale of jumps exceeds the observation time. The transition occurs at lower temperature and becomes sharper for longer observation time. © 2002 The American Physical Society.

DOI： 10.1103/PhysRevE.66.041103

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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. For a given observation time, a transition from annealed to quenched system occurs at the temperature when the time scale of jumps exceeds the observation time. The transition occurs at lower temperature and becomes sharper for longer observation time.

DOI： 10.1103/PhysRevE.66.041103

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Uncovering why spatial mosaics of mimetic morphs are maintained in a Mullerian mimicry system has been a challenging issue in evolutionary biology. In this article, we analyze the reaction diffusion system that describes two-species Mullerian 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. We then analyze the interfacial dynamics of the boundaries to find whether a stable cline is maintained and to obtain the wave speed if the cline is unstable. The results are: (1) In a spatially uniform habitat the morph with greater base fitness spreads both in one and two species system. (2) The strength of cross-species interaction determines whether the mimetic morph clines of model and mimic species coalesce into the same geographical region or pass through each other. The joint wave speed of clines decreases by increasing the number of comimicking species in the mimicry ring. (3) In spatial heterogeneous habitats, stable clines can be maintained due to the balance between the base fitness gradient and the biased gene flow by negative curvature of boundary. This allows the persistence of a spatial mosaic even if one of the morphs is in every place advantageous over the other. A balanced cline is also maintained if there is a gradient in the population density. (4) A new advantageous morph occurring at a local region is doomed to go to extinction in a finite time if the "radius" of initial distribution is below a threshold. Possible applications to the heliconiine butterfly mimicry ring, heterozygous disadvantage systems of chromosomal rearrangement and hybrid zone, the third phase of Wright's Shifting Balance theory, and cytoplasmic incompatibility are discussed. (C) 2002 Elsevier Science (USA).

DOI： 10.1006/tpbi.2001.1552

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DOI： 10.1016/S0022-3093(02)01501-6

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We propose a general framework of calculating the specific heat of the system in nonequilibrium, where the dynamics of the representative point can be separated into fast motion in a basin of energy landscape and the slow stochastic jump motion among basins. We apply this framework to gaseous hydrogen and obtain the observation time (t(obs)) dependence of the specific heat. We find that the specific heat gives the quenched and the annealed one in the limit of t(obs)-->0 and t(obs)--> infinity, respectively. We also investigate the waiting time and the observation time dependence of the specific heat and show that, for shorter waiting time, the observation time must be Ion-er to obtain the same degree of annealing. This tendency is consistent with the observation that the glass transition temperature is higher for faster quenching.

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DOI： 10.1016/S0921-4526(00)00796-1

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DOI： 10.1088/0953-8984/12/29/322

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Monte Carlo simulation calculations were made for investigating the structure and the mechanism of the electron transfer reactions at the metal-electrolyte interface. All the particles are assumed to be spherical with the same radii and the metal was treated as a source of the mirror image force. We obtained a result that many electrolyte ions are directly adsorbed to the metal surface in the presence and absence of the external field, indicating that the structure of the interface is non-uniform and a strong alternating local field is produced. Free energy surfaces for the electron transfer reaction are calculated using the simulation data. We found that the distance fluctuation of a reactant from the metal surface makes significant contribution to the free energy surfaces as well as the orientational and positional fluctuations of solvent and electrolyte ions do, and that the distribution of these fluctuations deviate greatly from the Gaussian, bringing about large nonlinear response effects in the relation between the activation free energy and energy gap of the reaction.

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Optical absorption spectra of 13-trans-locked-bacteriorhodopsin, which contains a chemically modified retinal chromophore inhibiting photoisomerization, were obtained at five temperatures. Analysis of the excited-state dynamics of the time-correlation function (tcf) of the modified wavepacket was made by the Fourier transform of the optical absorption spectra. Even though the photoisomerization of the chromophore was inhibited, the normalized tcf decayed rapidly until the level of about 10(-6) at 200 fs almost independently of the temperature. The ratio of the tcf between 13-trans-locked-bacteriorhodopsin and native bacteriorhodopsin displayed some oscillations. Its mean value was close to 1 until about 100 fs, and it increased, gradually up to the level of 10(0.5)-10(1) at about 200 fs. Namely, the excited-state dynamics of 13-trans-locked-bacteriorhodopsin appears globally quite similar to that of native bacteriorhodopsin up to about 100 fs, and the difference of them becomes slightly evident after 100 fs up to about 200 fs. Those data suggest that the excited-state dynamics of bacteriorhodopsin is not solely determined by the conformation change of the chromophore but also by another factor such as the movement of the microenvironment of the protein.

DOI： 10.1021/jp961580i

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The spring bloom of phytoplankton is a well-established, regular, seasonal event in the western subarctic Pacific and is considered one of the most important conditions of massive production of pelagic fishes. A series of 12 cruises was conducted from 1990 to 1992 to examine the timing and magnitude of the spring phytoplankton bloom in the Oyashio region, the western subarctic Pacific off Hokkaido, Japan. An interannual variability in the bloom events was also analysed. On the basis of hydrographical characteristics, the study area was divided into three water masses: the Oyashio Water Mass, the Mixed Water Mass, and the Coastal Water Mass. Spring blooms were observed first in April in the Oyashio and the Coastal Water Masses, and continued to May in 1991 and 1992. However, no bloom was recorded in the Mixed Water Mass. High nutrient supply into the surface mixed layer during winter is likely to be one of the factors supporting an intense spring bloom in the Oyashio Water Mass. A significant positive relationship between log-transformed surface chlorophyll a concentration and maximum density gradient (MDG) within the euphotic layer was obtained in April, indicating the importance of vertical stability of the water column in the initiation of spring blooms in the Oyashio and the Coastal Water Masses. The spring blooms in 1991 were much more extensive and lasted longer than in 1990. It is suggested that meteorological conditions and abundance of grazers were responsible for this interannual difference.

DOI： 10.1046/j.1365-2419.1997.00034.x

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The spin-boson model was applied to analyze the temperature dependence of excited state dynamics for the cis-trans photoisomerization of the chromophore in bacteriorhodopsin which was obtained by the Fourier transform of the optical absorption spectrum. The results indicate that the model is valid in the short time region less than about 30 fs and that the excited state dynamics in the time region larger than 30 fs is dominated by the non-harmonic slow vibrational motion, which is temperature independent. It is suggested that this specific vibrational motions might reflect the ultrafast cis-trans isomerization of the chromophore as well as conformation change of the protein environment.

DOI： 10.1016/0009-2614(96)00434-4

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier  

The refraction of active waves is analyzed for a stable-metastable reaction-diffusion system consisting of two regions with different diffusion coefficients. The equations governing the evolution of wavefronts are derived by means of an asymptotic perturbation method for boundary layers. These equations describe non-stationary refraction near the steady state regime. It is shown that the dynamics of wavefronts separates into that in the region near the boundary and that far from the boundary.

DOI： 10.1016/S0375-9601(96)80008-9

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The nonlinear Smoluchowski-Vlasov equation is calculated to investigate nonlinear effects on solvation dynamics. While a linear response has been assumed for free energy in equilibrium solvent, the equation includes dynamical nonlinear terms. The solvent density function is expanded in terms of spherical harmonics for orientation of solvent molecules, and then only terms for ℓ=0 and 1, and m=0 are taken. The calculated results agree qualitatively with that obtained by many molecular dynamics simulations. In the long-term region, solvent relaxation for a change from a neutral solute to a charged one is slower than that obtained by the linearized equation. Further, in the model, the nonlinear terms lessen effects of acceleration by the translationai diffusion on solvent relaxation. © 1995, Elsevier Ltd. All rights reserved.

DOI： 10.1016/S0167-6881(06)80794-9

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The nonlinear Smoluchowski-Vlasov equation is calculated to investigate nonlinear effects on solvation dynamics. While a linear response has been assumed for free energy in equilibrium solvent, the equation includes dynamical nonlinear terms. The solvent density function is expanded in terms of spherical harmonics for orientation of solvent molecules, and then only terms for ℓ=0 and 1, and m=0 are taken. The calculated results agree qualitatively with that obtained by many molecular dynamics simulations. In the long-term region, solvent relaxation for a change from a neutral solute to a charged one is slower than that obtained by the linearized equation. Further, in the model, the nonlinear terms lessen effects of aceleration by the translational diffusion on solvent relaxation. © 1995.

DOI： 10.1016/0167-7322(95)00881-6

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER CHEMICAL SOC  

We have investigated energy pp laws of the intermolecular charge separation (CS) and charge recombination (CR) reactions by considering the distance distribution between donor and acceptor molecules. The experimentally obtained energy gap dependence of the CS reaction rate constant, which shows a large width and flat shape, has been theoretically explained as follows. The sharp increase in the normal region is due to the donor-acceptor molecules in close contact which give the energy pp laws with small widths and are located at small energy gaps. The flat shapes of the top region and the inverted region arc due to the donor-acceptor molecules at large mutual distances which give the energy gap laws with large widths and are located at large energy gaps. The experimentally obtained energy gap law of the CR reaction, which is nearly bell-shaped and located at thc rather large energy gap, cannot be explained by assuming thc same distance distribution as in the CS reaction. A narrow distance distribution of the geminate radical ion pair was necessary for the satisfactory interpretation of the energy gap law of thc CR reaction. It was also shown that the energy gap law of the CR reaction can be reproduced rather well by considering a dynamical process of relaxation of the initial distance distribution of the geminate radical ion pair which is produced by the photoinduced CS reaction.

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

We conducted Monte Carlo simulations of polar solutions by explicitly treating the effect of electronic polarizability of solvent molecules. Based on these data, we calculated the energy-gap dependence of electron-transfer rates. It was found that a considerable asymmetry of the energy-gap dependence of the charge-separation rate is brought about by the electronic polarizability. It was also found that the inverted region of the charge-recombination reaction shifts considerably to the smaller energy gap from that of the charge-separation reaction, due to the non-linearity of solvent polarization.

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We have conducted Monte Carlo simulations of polar solutions with a spherical hard core model by properly taking into account the electronic polarizability of solvent molecules. We have calculated the free energy curve as a function of the reaction coordinate of electron transfer reactions in cases where the reactant is neutral and charged. From the analysis of the free energy curvature ratio between the two cases, we have found that the electronic polarizability contributes to enhance the nonlinear response of solvent polarizations and that this enhancement is greatly strengthened if the translational motion of solvent molecules is frozen. © 1991, Taylor &amp
Francis Group, LLC. All rights reserved.

DOI： 10.1080/08927029108022428

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The reorganization energy of electron-transfer reactions as a function of the distance between donor and acceptor molecules is calculated by Monte Carlo simulation. It is found that the reorganization energy of charge-separation reactions is appreciably different from that of charge-recombination reactions. The average of these values agrees very well with the value obtained by a mean-spherical-approximation theory.

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The electron-transfer rate as a function of the free energy gap (energy-gap law) was formulated by including the solvent nonlinear response effect and averaging over the distribution of donor-acceptor distances. Using the same parameter values, we fit the theoretical energy-gap laws to three independent experimental measurements: the photoinduced charge-separation (CS) rate as measured from fluorescence quenching in the stationary state, the actual photoinduced charge-separation rate as obtained from analysis of the transient effect in the fluorescence decay curve, and the charge-recombination (CR) rate of the geminate radical-ion pair. The different energy-gap laws among those reactions can be reproduced reasonably well by adopting different distributions of the donor-acceptor distance: that of the CS reaction covering those over various distances and more specified ones corresponding to the contact ion-pair (CIP) and solvent-separated ion-pair (SSIP) models for the CR reaction. The nonlinear effect in those homogeneous reactions is small when the CIP model applies and appreciable when the SSIP model applies.

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Other Link： http://dl.ndl.go.jp/info:ndljp/pid/10942537

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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. The comparison of these equations leads to conditions under which the RPMD and CMD correlation functions agree approximately with the full-quantum canonical correlation function. The condition for the RPMD is that the memory effects of the full-quantum and RPMD equations vanish quickly with the same time constants. The CMD correlation function requires additional conditions concerning static correlation. (C) 2008 American Institute of Physics.

DOI： 10.1063/1.2939480

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Language：English   Publishing type：Book review, literature introduction, etc.  

This article reviews microscopic development of time dependent functional method and its application to chemical physics. It begins with the formulation of density functional theory. The time dependent extension is discussed after the equilibrium formulation. Its application is explained by solvation dynamics. In addition, it reviews studies of nonlinear effects on polar liquids and simple mixtures.

DOI： 10.1142/S0219633604000878

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Dynamics of distributions in a solvation process is studied using the Smoluchowski equation. Time evolution of distributions is calculated on a two-dimensional nonlinear free energy surface. The number density of solvent molecules is considered as well as the polarization density. The calculations show that widths of the distribution relax more slowly than peak shifts for slow relaxation of the number density. The result agrees qualitatively with that obtained by time-resolved fluorescence spectroscopy.

DOI： 10.1143/JPSJ.70.1833

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A new method is developed to study nonlinear dynamics of molecular liquids. It is a time dependent density functional method for the interaction site model. The nonlinear Langevin theory provides the formulation of the method. An approximation is introduced to calculate the reversible term. (C) 2001 Elsevier Science B.V. All rights reserved.

DOI： 10.1016/S0167-7322(00)00177-X

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Language：English   Publisher：AMERICAN PHYSICAL SOC  

To study the time dependent density functional method (TDDFM), two streaming velocity (reversible) terms are reformulated in the nonlinear Langevin equation. Mori's [Prog. Theor. Phys. 33, 423 (1965)] projection operator method shows a variety of nonlinear Langevin equations. This is because the equations depend on the choice of phase space functions employed in the projection. If phase space functions include particular functions, however, the streaming velocity term has an invariable form. The form is independent of the choice of other phase space functions. Since the invariable streaming velocity term does not introduce the TDDFM, the second viewpoint is presented. In this, the linearization of the streaming velocity term agrees with the frequency term in the linear Langevin equation. Since only the second streaming velocity term introduces the TDDFM, one needs to be cautious in the derivation of the TDDFM. [S1063-651X(99)10506-3].

DOI： 10.1103/PhysRevE.59.6535

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Fermi's golden rule is expanded in Planck's constant to study quantum effects of nuclear baths on transitions between electronic states. For six approximations, the second-order expansion of the transition rates is compared with the exact expansion. The comparison provides the conditions for agreement between the exact and approximate rate constants in the second order. Two of the conditions show that the change in electronic states of the solute does not affect solvent structure much. The other concerns linearity of the reaction coordinate. Besides the comparison of analytical expressions, the expansion of approximations is numerically compared, using a simple model. Most approximations show similar values for a parameter set. The values approximate the value obtained by quantum molecular simulations. (C) 1998 American Institute of Physics. [S0021-9606(98)00844-7].

DOI： 10.1063/1.477549

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Time dependent density functional theory in its "extended linear" or "surrogate" form is used to investigate the dynamics of selective ion solvation in binary dipolar solvents. It is shown that simple analytical approximations that trap the basic physics of the solvation process can be obtained. In particular, it is found that the relaxation of:the solvent number densities about a charged solute is governed by two distinct modes clearly associated with electrostriction and redistribution processes. This is consistent with the physical picture suggested by molecular dynamics (MD) simulations. The solvent polarization relaxation is also dominated by two modes associated with the-two rotational diffusion constants of the binary solvent. In addition to the analytical approximations, full numerical solutions of the extended linear theory are obtained and the dependence of the relaxation on solvent density and solute charge is discussed. Detailed comparisons of the theory with MD simulations for a closely related model indicate that the theory is qualitatively correct, but quantitatively poor generally predicting relaxation rates which are too fast. This is due mainly to the neglect of inertial or non-Markovian effects in the theoretical approach. (C) 1998 American Institute of Physics. [S0021-9606(98)50132-8]

DOI： 10.1063/1.476912

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Language：English   Publisher：BLACKWELL SCIENCE LTD  

Theoretical and numerical models were developed to investigate the effects of water temperature on the population dynamics of the kelp, Laminaria religiosa. The models describe seasonal changes in the biomass of kelp by calculation of growth and grazing rates of sea urchins, Strongylocentrotus nudus. Using the theoretical model, conditions were obtained to satisfy the statistical analysis of a relationship between water temperature and kelp harvests from a fishery census. The conditions require the negative second derivative Of the growth rate with respect to temperatures, or the positive second derivative of the grazing rate. By using the numerical model, harvests of kelp were calculated for a change in water temperature over a given period. The period of a temperature change giving the maximum effects an the harvest was determined primarily by temperature dependence on the growth rate. Grazing by sea urchins had large effects on the harvest of kelp. A value of 10(4) was obtained for a ratio between harvests at the higher and the lower temperatures differing by +/- 1 degrees C.

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Linear and nonlinear versions of time dependent density functional theory are solved for a single solute particle in a simple binary solvent. All particles interact with Lennard-Jones potentials. The theoretical results are compared with molecular dynamics calculations. It is shown that the nonlinear theory is necessary in order to obtain a good quantitative description of selective solvation dynamics. The linear theory is only of qualitative value. Also, attention is drawn to a previously little appreciated problem which arises when one attempts to compare time dependent density functional theory with computer simulation or experimental results. The difficulty involves matching the theoretical and absolute time scales and is discussed in detail in this paper. (C) 1998 American Institute of Physics. [S0021-9606(98)50615-0].

DOI： 10.1063/1.476044

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Language：English   Publisher：Elsevier  

To study nuclear quantum effects on electron transfer reactions, the non-adiabatic rate constant is expanded in terms of Planck's constant. The expansion to the second order reproduces well the quantum correction in the activation free energy for a quantum Monte Carlo simulation of water. In addition, the spin-boson model is discussed using the expansion. The validity of the rate constant given by the spin-boson model is investigated in non-linear systems. Conditions for obtaining exact values of the rate constant are established in the second order of Planck's constant. In liquids, the conditions are satisfied if the one-body distribution function does not change during the electron transfer reaction. © 1997 Elsevier Science S.A.

DOI： 10.1016/S0022-0728(96)04997-2

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For the number density of solvent molecules, nonlinear effects on solvation dynamics are studied using the dynamical density functional method. The present method includes nonlinear coupling between the number density and a polarization field only in the free energy functional. By means of the nonlinear free energy functional, nonlinear differential-integral equations are developed for the polarization field and number density. Numerical calculations show that solvent molecules relax more slowly around an ion than around a neutral solute. This result agrees qualitatively with nonlinear effects observed in many molecular dynamics simulations. In addition, the nonlinear dynamics of hydrogen bonds can be understood, by considering the slow relaxation of the number density of solvent molecules. (C) 1996 American Institute of Physics.

DOI： 10.1063/1.472454

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A method of calculating nonlinear terms in free energy is studied for the density functional theory of a molecular system with orientational freedoms. In the method, a free energy functional is expanded into Taylor series of density fields, and then the coefficients are calculated from the cumulant expansion. Using the method, expansion coefficients of third and forth orders are explicitly derived by the three-point and four-point coefficients of the cumulant expansion. For the third-order coefficient, two approximations are compared by calculations of the triplet direct correlation function. The approximation obtained by expansion in terms of pair correlation functions gives abrupt changes in the triplet direct correlation function. The simplified Kirkwood superposition approximation gives slow changes in the function, though its value should be scaled down by a small parameter. (C) 1996 American Institute of Physics.

DOI： 10.1063/1.471700

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Language：English   Publisher：ELSEVIER SCIENCE BV  

Diffusion effects on geminate charge recombination are investigated for intermolecular electron transfer system. Analytical and numerical calculations are presented for reaction-diffusion equations. In some limiting cases of the equations, a condition is established where the population of geminate ion pairs decreases exponentially by charge recombination. This condition is that the ion pairs are produced inside the zone of recombination and charge recombination takes place before ion pairs diffuse into separated ions. Numerical calculations are made in realistic cases where reorganization energy in the expression of the rate constant depends on the reactant distance. As a result, we found that the population of ion pairs has both components of exponential decrease and a root inverse tail (t(-1/2)). The component of exponential decrease is large when the recombination rate is fast.

DOI： 10.1016/0301-0104(95)00305-3

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Language：English   Publisher：Kluwer Academic Publishers  

Effects of vertical stability on spring blooms of phytoplankton were investigated for the western subarctic Pacific ocean using a one-dimensional (depth) ecosystem model. In the model, vertical stability was expressed by diffusion constants calculated from observed density distribution. Dynamics of phytoplankton in blooms was calculated by the model using the vertical diffusion. Then, the calculated results were compared with the Coastal Zone Color Scanner (CZCS) data. The comparison shows that the shallow surface mixed layer causes early start days of spring blooms at inshore (northern) stations. In addition, spring blooms continue long at inshore (northern) stations since a water column has weak stability. This is because weak stability of a water column causes large nutrient supply from a deep layer and large diffusive transport of phytoplankton biomass from the subsurface maximum. © 1995 Journal of the Oceanographic Society of Japan.

DOI： 10.1007/BF02286393

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An approximate expression is developed for a nonadiabatic electron transfer rate to estimate quantum effects of nuclear rearrangements. The time-dependent formula for Fermi's golden rule is expanded by Plank's constant to the second order, using the Wigner transformation. The method of ($) over bar h-expansion is applicable to systems with nonlinear potentials or many degrees of freedom. Using a continuum approximation, from the expansion, a rate expression is obtained, including sizes of reactants and a distance between reactants explicitly. The ratio of the obtained rate to the classical rate agrees well with a ratio by a quantum Monte Carlo simulation.

DOI： 10.1016/0009-2614(95)00109-H

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Two kinds of symmetry causing a symmetric shape of the free energy curve are presented in a Hamiltonian of a neutral reactant state for Polar solution. They are the symmetry for inversion of solvent molecules and a reactant molecule. In addition, the deviation from the symmetry is formulated using a perturbation method. The antisymmetric part of the free energy curve is expressed by the symmetric part using a thermal average of the deviation in the Hamiltonian and the reaction coordinate.

DOI： 10.1016/0009-2614(94)87117-5

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Language：English   Publisher：PERGAMON-ELSEVIER SCIENCE LTD  

A modeling study was conducted to investigate the effects of interaction between two warm-core rings on the phytoplankton distribution. Using a quasi-geostrophic reduced-gravity model, the interaction between two vortices was calculated to reproduce the partial vortex merger between two warm-core rings, 86B and OR. On the calculated flow field, the three-dimensional model of plankton dynamics generated high phytoplankton biomass at the edge of the merged vortex. In the model, phytoplankton grew due to nutrient transport into the euphotic zone by upward motion of water caused by meanders of the current followed by the partial vortex merger. Further, the model reproduced the horizontal distribution of phytoplankton observed in 86B.

DOI： 10.1016/0967-0637(94)90017-5

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Language：English   Publisher：AMER METEOROLOGICAL SOC  

To study horizontal divergence, the thin jet model is applied to meanders of a continuous potential vorticity front in a 1 1/2-layer (divergent barotropic) model. The distributions of the depth of the layer and the velocity component normal to the front are calculated on a coordinate system along the front. The distributions of the horizontal divergence are also investigated for some values of the Rossby number. In the model, divergence appears on the front from the cyclonic curve to the anticyclonic curve, and convergence appears on the front from the anticyclonic curve to the cyclonic curve. Further, a large Rossby number is found to cause an asymmetrical distribution of the horizontal divergence. The calculated values of the divergence are compared with the observational data.

DOI： 10.1175/1520-0485(1994)024<0345:HDCBMO>2.0.CO;2

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Language：English   Publisher：Kluwer Academic Publishers  

Semi-geostrophic dynamics of jets are studied using a potential vorticity front in an equivalent barotropic model. Meandering processes of the front are examined in the thin-jet limit on a β-plane by a curvilinear coordinate system. For calculated along-front velocity fields, asymmetrical profiles are caused by meandering. This asymmetry of the velocity profile is enhanced as the Rossby number becomes large. Using the along-front velocity fields, the normal velocity of front is expressed so that the Rossby number is explicitly included. This expression can be rewritten in the form of the mKdV equation. © 1993 Journal of the Oceanographic Society of Japan.

DOI： 10.1007/BF02237459

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Language：English   Publisher：PHYSICAL SOCIETY JAPAN  

Energy gap dependences of solvent dynamics effects on the electron transfer rate in polar solutions are investigated by solving the diffusion-reaction equation. New points in this study are that (1) we treat non-linear response systems where the translational motion couples non-linearly with the rotational motion and (2) we investigate systematically the energy gap dependence of the solvent dynamics effect for the charge separation (CS) and charge recombination (CR) reactions. The non-linear free energy functions are characterized, based on the Monte Carlo simulation data for model systems where solvent translational positions are either allowed to move or fixed. The calculated results are that so far as the non-linear coupling is substantial, the energy gap law of the CS reaction is little affected by the solvent dynamics, while that of the CR reaction is greatly modified.

DOI： 10.1143/JPSJ.61.2577

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We study the non-linear effects on the dynamical process of the solvation in a polar solvent. On the basis of the non-linear generalized Smoluchowski equation with the linear-response free energy, we calculate the time dependence of the solvent-solute interaction. It is shown that the solvation process becomes slow in the long-time region where the non-linear coupling between the dynamics of the solvent number density and the orientational relaxation is significant.

DOI： 10.1016/0009-2614(91)87166-9

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DOI： 10.1063/1.458651

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Language：English   Publisher：AMER CHEMICAL SOC  

DOI： 10.1021/j100363a009

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Language：English   Publisher：AMER CHEMICAL SOC  

DOI： 10.1021/j100346a064

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