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  • Papers

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  • Recent Results
  • Test of MCT
The numerical solutions of the mode-coupling theory for the Lennard-Jones binary colloids are tested by performing extensive Brownian-dynamics simulations from a unified point of view based on the mean-field theory proposed recently [1]. As a liquid is cooled, a discrepancy between the simulation results and the MCT solutions for the mean-square displacements starts to appear around the so-called β stage. This becomes more obvious at lower temperatures. We note that this is just due to the basic formulation (Mori formalism) employed by MCT but not due to the approximations made by it [2].

[1] M. Tokuyama and Y. Kimura, Physica A 387, 4749 (2008).
[2] M. Tokuyama, Physica A 387, 1926 (2008).






  • Master Curve
    The mean-square displacements in any different systems are collapsed on a master curve given by the mean-field theory if the values of their long-time self-diffusion coefficients (universal parameter) are the same.

     

    • Mean-Free Path
    The mean-free paths in any different systems are the same if the values of their long-time self-diffusion coefficients (universal parameter u) are the same.     

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    • Books
    • M. Tokuyama, I. Oppenheim, and H. Nishiyama, eds.
    Complex Systems
    American Institute of Physics Conference Proceedings No. 982 (2008).
    • M. Tokuyama and S. Maruyama, eds.
    Flow Dynamics
    American Institute of Physics Conference Proceedings No. 832 (2006).
    • M. Tokuyama and I. Oppenheim, eds.
    Slow Dynamics in Complex Systems
    American Institute of Physics Conference Proceedings No. 708 (2004).
    • M. Tokuyama and H. Eugene Stanley, eds.
    Statistical Physics
    American Institute of Physics Conference Proceedings No. 519 (2000).
    • M. Tokuyama and I. Oppenheim, eds.
    Slow Dynamics in Complex Systems
    American Institute of Physics Conference Proceedings No. 469 (1999).
    • M. Tokuyama and I. Oppenheim, eds.
    Statistical Physics
    World Scientific (Singapore, 1998).
    • M. Tokuyama, ed.
    Statistical Physics
    Bussei Kenkyu (Kyoto) 66 (1996).
    • K. Kawasaki, M. Tokuyama, and T. Kawakatsu, eds.
    Slow Dynamics in Condensed Matters
    American Institute of Physics Conference Proceedings No. 256 (1992).

     

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    • Papers

    [1] Mean-Field Theory of Glass Transitions

    [2] Time-Convolutionless Projection Operator Method

    [3] Hard-Sphere Systems

    [4] Dynamics of Spatial Heterogeneities

    [5] Brownian Motion

    [6] Charged Colloidal Suspensions

    [7] Fractal

    [8] Phase Separations

    [9] Chemical Reactions

    [10] Gas Kinetics

    [11] Long-Time Tail

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    • Mean-Field Theory of Glass Transition
    • M. Tokuyama
    Test of the mode-coupling theory near the colloidal glass transition by extensive Brownian-dynamics simulations
    Physica A 387, 4749-4754 (2008).
    • M. Tokuyama, T. Narumi, and E. Kohira
    Mapping from a Fragile Glass-Forming System to a Simpler One near their Glass Transitions
    Physica A 385, 439-455 (2007).
    • M. Tokuyama
    Similarities in Diversely Different Glass-Forming Systems
    Physica A 378, 157-166 (2007)
    • M. Tokuyama
    Mean-Field Theory of Glass Transitions
    Physica A 364, 23-62 (2006).
    • M. Tokuyama, H. Yamazaki, and Y. Terada
    Universal Effects of Collective Interactions on Long-Time Self-Diffusion Coefficients in Hard-Sphere Systems
    Physica A 328, 367-379 (2003).
    • M. Tokuyama, H. Yamazaki, and Y. Terada
    Test of Mean-Field Equations for Two Types of Hard-Sphere Systems by Brownian-Dynamics Simulation and a Molecular-Dynamics Simulation
    Phys. Rev. E 67, 062403 (2003).
    • M. Tokuyama
    Slow Dynamics ofEquilibrium Density Fluctuations in Suspensions of Colloidal Hard Shperes near the Glass Transition
    Phys. Rev. E 62, R5915-R5918 (2000). 

     

    • Time-Convolutionless Projection Operator Method
    • M. Tokuyama
    A statistical-mechanical theory of self-diffusion in colloidal suspensions -- application to colloidal glass transitions
    Physica A 387, 4015-4032 (2008).
    • M. Tokuyama
    Erratum to "A statistical mechanical theory of self-diffusion in colloidal suspensions -- Application to colloidal glass transitions"
    Physica A 387, 5675-5677 (2008)
    • M. Tokuyama
    A statistical-mechanical theory of self-diffusion in glass-forming liquids
    Physica A 387, 5003-5011 (2008).
    • M. Tokuyama
    Comparison of the Tokuyama-Mori type projection-operator method to that of Mori type near the glass transition
    Physica A 387, 1926-1936 (2008).
    • M. Tokuyama
    Statistical-Dynamical Theory of Nonlinear Stochastic Processes
    Physica A 109, 128-160 (1981).
    • M. Tokuyama
    On the Theory of Fluctuations around Non-equilibrium Staedy States
    Physica A 102, 399-430 (1980).
    • M. Tokuyama and H. Mori
    Statistical-Mechanical Theory of Random Frequency Modulation and Generalized Brownian Motions
    Prog. Theor. Phys. 55, 411-429 (1976).
    • M. Tokuyama and H. Mori
    Statistical-Mechanical Approach to Random Frequency Modulation and the Gaussian memory Function
    Prog. Theor. Phys. 55, 411-429 (1976).

     

     

    • Hard-Sphere Systems
    • M. Tokuyama and Y. Terada
    How Different is a Hard-Sphere Fluid from a Suspension of Hard-Sphere Colloids near the Glas Transitions
    Physica A 375, 18-36 (2007).
    • M. Tokuyama and Y. Terada
    Slow Dynamics and Re-entrant Melting in a Polydisperse Hard-Sphere Fluid
    J. Phys. Chem. B 109, 21357-21363 (2005).
    • M. Tokuyama, Y. Terada, and I. Oppenheim
    On the Slow Dynamics of Density Fluctuations near the Colloidal Glass Transition
    EPJ E 9,271-275 (2002).
    • M. Tokuyama
    Slow Dynamics of Equilibrium Density Fluctuations in Suspensions of Hard Spheres near the Glass Transition
    J. Korean Physical Society 38, 512-515 (2001).
    • M. Tokuyama
    On the Derivation of a Nonlinear Stochastic Diffusion Equation for Supercooled Colloidal Liquids and Glasses
    Physica A 294, 23-43 (2001).
    • M. Tokuyama
    Slow Dynamics of Equilibrium Density Fluctuations in a Supercooled Colloidal Liquid
    Physica A 289, 57-85 (2001).
    • M. Tokuyama, Y. Enomoto, and I. Oppenheim
    Slow Dynamics of Supercooled Colloidal Fluids
    Physica A 270, 380-402 (1999).
    • M. Tokuyama
    Effective Diffusion Model on Brownian Dynamics of Hard-Sphere Colloidal Suspensions
    Physica A 265, 333-340 (1999).
    • M. Tokuyama, Y. Enomoto, and I. Oppenheim
    Slow Dynamics of Nonequilibrium Density Fluctuations in Concentrated Hard-Sphere Suspensions
    International Journal of Thermophysics 19, 877-885 (1998).
    • M. Tokuyama, Y. Enomoto, and I. Oppenheim
    Slow Dynamics of Structure and Fluctuations in Supercooled Colloidal Fluids
    Phy. Rev. E 56, 2302-2305 (1997).
    • M. Tokuyama, Y. Enomoto, and I. Oppenheim
    Slow Dynamics of Nonequilibrium Density Fluctuations in Hard-Sphere Suspensions
    Phy. Rev. E 55, R29-R32 (1997).
    • M. Tokuyama
    Nonequilibrium Effects on Slow Dynamics in Concentrated Colloidal Suspensions
    Phys. Rev. E 54, R1062-R1065 (1996).
    • M. Tokuyama
    Slow Dynamics of Self-Diffusion in Metastable Colloidal Fluids
    Physica A 229, 36-46 (1996).
    • M. Tokuyama and I. Oppenheim
    On the Theory of Concentrated Hard-Sphere Suspensions
    Physica A 216, 85-119 (1995).
    • M. Tokuyama and I. Oppenheim
    Dynamics of Hard-Sphere Suspensions
    Phys. Rev. E 50, R16-R19 (1994).

     

     

    • Dynamics of Spatial heterogeneities
    • M. Tokuyama, Y. Terada, and I. Oppenheim
    Nonlinear Equilibrium Density Fluctuations and Spatial Heterogeneities near the Colloidal Glass Transition
    Physica A 321, 193-206 (2003).
    • M. Tokuyama, Y. Terada, and I. Oppenheim
    Effect of Spatial Heterogeneities on the Slow Dynamics of Density Fluctuations near the Colloidal Glass Transition
    Physica A 307, 27-40 (2002).
    • M. Tokuyama, Y. Enomoto and I. Oppenheim
    Slow Dynamics of Supercooled Colloidal Fluids: Spatial Heterogeneities and Nonequilibrium Density Fluctuations"
    Physica A 270, 380-402 (1999).

     

     

    • Brownian Motion and Long-Time Tails
    • M. Tokuyama
    On the Theory of Nonlinear Shear Viscosity and Long-Time Tails
    Physics Letters A 102, 21-24 (1984).
    • M. Tokuyama and I. Oppenheim
    Statistical-Mechanical Theory of Brownian Motion
    Physica A 94, 501-520 (1978). 

     

    • Charged Colloidal Suspensions
    • M. Tokuyama
    Statistical-mechanical Theory of Short-Time Self-Diffusion in Dilute Suspensions of Highly Charged Colloids
    Physica A 352, 252-264 (2005).
    • M. Tokuyama
    Effective Forces between Macroions in Highly Charged Colloidal Suspensions
    Phys. Rev. E 59, R2550-R2553 (1999).
    • M. Tokuyama
    Theory of Slow Dynamics in Highly Charged Colloidal Suspensions
    Phys. Rev. E 58, R2729-2732 (1998). 

     

    • Fractal
    • M. Tokuyama and K. Kawasaki
    Fractal Dimensions for Diffusion-Limited Aggregation
    Phys. Letts. A 100, 337-340 (1984). 

     

    • Phase Separations
    • Y. and M. Tokuyama
    Encounter Effects on the Dynamics of Fluctuations in Phase Separations of Off-Critically Quenched Binary Systems
    Physica A 232, 304-314 (1996).
    • M. Tokuyama and Y. Enomoto
    Effects of Encounters on Phase-Separating Dynamics from Diffusion-Controlled Growth to Coarsening
    Physica A 220, 261-276 (1995).
    • M. Tokuyama and Y. Enomoto
    Dynamics of Crossover from Diffusion Growth to Coarsening in Quenched Binary Mixtures
    International Journal of Thermophysics 15, 1145-1155 (1994).
    • M. Tokuyama and Y. Enomoto
    On the Theory of Late-Stage Phase Separation in Off-Critically Quenched Binary Systems
    Physica A 204, 673-692 (1994).
    • M. Tokuyama and Y. Enomoto
    Theory of Phase-Separation Dynamics in Quenched Binary Mixtures
    Physical Review E 47, 1156-1179 (1993).
    • M. Tokuyama and Y. Enomoto
    Dynamics of Crossover Phenomenon in Phase-Separating Systems
    Physical Review Letters 69, 312-315 (1992).
    • M. Tokuyama and Y. Enomoto
    Kinetic equations and Fluctuations in Electrochemical Nucleation: Studies of Many-Body Effects on Diffusion-Controlled Particle Growth on a Substrate
    Journal of Chemical Physics 94, 8234-8243 (1991).
    • M. Tokuyama
    Statistical-Mechanical Theory of Diffusion-Controlled Particle Growth on a Surface: Kinetics of Diffusion-Limited Currents
    Physica A 169, 147-190 (1990).
    • M. Tokuyama, Y. Enomoto, and K. Kawasaki
    Dynamics of Fluctuations in Ostwald Ripening - A New Equation of Motion for the Structure Function
    Physica A 143, 183-209 (1987).
    • Y. Enomoto, K. Kawasaki, and M. Tokuyama
    The Time Dependent Behavior of the Ostwald Ripening
    Acta. Metall. 35, 915-922 (1987).
    • Y. Enomoto, K. Kawasaki, and M. Tokuyama
    Computer Modeling of Ostwald Ripening
    Acta. Metall. 35, 907-913 (1987).
    • K. Kawasaki, Y. Enomoto, and M. Tokuyama
    Elementary derivation of Kinetic Equations for Ostwald Ripening
    Physica A 135, 426-445 (1986).
    • Y. Enomoto, M. Tokuyama, and K. Kawasaki
    Finite Volume Fraction Effects on Ostwald Ripening
    Acta. Metall. 34, 2119-2128 (1986).
    • M. Tokuyama, K. Kawasaki, and Y. Enomoto
    Kinetic Equations for Ostwald Ripening
    Physica A 134, 323-338 (1986).
    • M. Tokuyama and K. Kawasaki
    Statistical-Mechanical Theory of Coarsening of Spherical Droplets
    Physica A 123, 386-411 (1984).

     

    • Chemical Reactions
    • M. Tokuyama and J. Ross
    Statistical-Mechanical Theory of Many-Body effects in Reaction Rates
    J. Chem. Phys. 91, 4043-4060 (1989).
    • M. Tokuyama and R. I. Cukier
    Dynamics of Diffusion-Controlled Reactions Among Stationary Sinks- Scaling Expansion Approach
    J. Chem. Phys. 76, 6202-6214 (1982).
    • M. Tokuyama and R. I. Cukier
    Hydrodynamics of a Suspension of Non-Dilute Stationary Spheres
    Physical Review Letters 48, 1604-1607 (1982).

     

    • Gas Kinetics
    • M. Tokuyama and H. Mori
    Kinetic Equations and Fluctuations in µ Space of One-Component Dilute Plasmas
    Prog. of Theor. Phys. 58, 92-112 (1977). 
    • M. Tokuyama and H. Mori
    Statistical-Mechanical Theory of the Boltzmann Equation and Fluctuations in µ Space
    Prog. of Theor. Phys. 56, 1073-1092 (1976). 
    • M. Tokuyama and H. Mori
    Derivation of the Boltzmann Equation by the Scaling Method for Reduction of Processes
    Prog. of Theor. Phys. 55, 1322-1323 (1976).