Wen-Jong Ma

A molecular dynamics study of freezing in a confined geometry

The dynamics of freezing of a Lennard‐Jones liquid in narrow channels bounded by molecular walls is studied by computer simulation. We quantify the time development of ordering and observe a novel freezing mechanism. The liquid forms layers and subsequent in‐plane ordering within a layer is accompanied by a sharpening of the layer in the transverse direction. The effects of channel size, the methods of quench, the liquid–wall interaction and the roughness of walls on the freezing mechanism are elucidated. Comparison with recent experiments on freezing in confined geometries is presented.

Crossover behavior of stock returns and mean square displacements of particles governed by the Langevin equation

It is found that the mean square log-returns calculated from the high-frequency one-day moving average of US and Taiwan stocks with the time internal τ show ballistic behavior with the exponent for small τ and show diffusion-like behavior with the exponent for large τ. Such a crossover behavior can be well described by the mean square displacements of particles governed by the Langevin equation of motion. Thus, θ and D can be considered, respectively, as the temperature-like and diffusivity-like kinetic parameters of the market, and they can be used to characterize the behavior of the market.

Universal geometrical factor of protein conformations as a consequence of energy minimization

The biological activity and functional specificity of proteins depend on their native three-dimensional structures determined by inter- and intra-molecular interactions. In this paper, we investigate the geometrical factor of protein conformation as a consequence of energy minimization in protein folding. Folding simulations of 10 polypeptides with chain length ranging from 183 to 548 residues manifest that the dimensionless ratio (V/Ar) of the van der Waals volume V to the surface area A and average atomic radius r of the folded structures, calculated with atomic radii setting used in SMMP (Eisenmenger F. et al., Comput. Phys. Commun., 138 (2001) 192), approach 0.49 quickly during the course of energy minimization. A large scale analysis of protein structures shows that the ratio for real and well-designed proteins is universal and equal to 0.491±0.005. The fractional composition of hydrophobic and hydrophilic residues does not affect the ratio substantially. The ratio also holds for intrinsically disordered proteins, while it ceases to be universal for polypeptides with bad folding properties.

Polydispersity Effect and Universality of Finite-Size Scaling Function

We derive an equation for the existence probability Ep for general percolation problem using an analytical argument based on exponential-decay behaviour of spatial correlation function. It is shown that the finite-size scaling function is well approximated by the error function. The present argument explain why it is universal. We use Monte Carlo simulation to calculate Ep for polydisperse continuum percolation and find that mono- and polydisperse system have the same finite-size scaling function.

Characteristics of instantaneous resonant modes in simple dense fluids with short- ranged repulsive interactions

We manifest the characteristics of the low-frequency, quasilocalized instantaneous normal modes, named as the instantaneous resonant modes (IRMs), in simple dense fluids with short-ranged repulsive interactions. The analyses include the potential energy profiles of the IRMs, and the local geometric structures and the number of the interacting neighbors of the particles at which the centers of the quasilocalization are located. We conclude that an IRM is created due to fluctuations in the local density, and has a barely-isolated center, which slightly interacts with one or two nearest neighbors, and the potential energy profile of an IRM is basically single-well with strong anharmonicity. The differences in character between the IRMs and the high-frequency localized instantaneous normal modes are also examined. Based on the barely isolated center picture, a necessary criterion for the occurrence of the IRMs is proposed. While only the imaginary-frequency IRMs are found in dense fluids with purely repulsive interactions satisfying the criterion, a tiny attractive well in the pair potential allows the occurrence of the real-frequency IRMs. The physical systems to detect the presence of the IRMs are discussed.

Dynamics of supercooled Lennard-Jones system

Abstract The /β-relaxation dynamics in a simple monatomic Lennard-Jones system is re-visited for both quenching and crushing by the molecular dynamics technique. We obtain for each process the pairwise liquid structures and use them as input data to numerically solve for the dynamical transition point within the idealized version of the mode-coupling theory. It is found that near the dynamical transition point the dynamical behavior of the Lennard-Jones liquid such as the master function, the tagged-particle distribution function, etc. deviates more from a purely repulsive hard-sphere system but is closer to that of a liquid metal. This indicates, from the details of inter-particle interactions that, the attractive tail of the pair potential does play a non-negligible role in the feedback effects addressed in the mode-coupling theory. To quantify our studies, we have performed simulation also for the self-part intermediate scattering function for a temperature range that spans over the dynamical transition point. Compared with the prediction of mode-coupling theory, the simulated tagged particle self-part density-density correlation function displays a sluggish and stretched relaxation, although its retarded signature is observed to be extremely weak. This implies that a simple monatomic liquid because of this basic nature of interparticle interactions is structurally much more difficult to exemplify the β-relaxation process.

Molecular dynamics of viscous flows

Molecular dynamics techniques are used to study the microscopic aspects of several slow viscous flows past a solid wall, where both fluid and wall have a molecular structure. Systems of several thousand molecules are found to exhibit reasonable continuum behavior, albeit with significant thermal fluctuations. In Couette and Poiseuille flow of liquids it is found that the no‐slip boundary condition arises naturally as a consequence of molecular roughness, and that the velocity and stress fields agree with the solutions of the Stokes equations. At lower densities slip appears, which can be incorporated into a flow‐independent slip‐length boundary condition. An immiscible two‐fluid system is stimulated by a species‐dependent intermolecular interaction. The local velocity field near a moving contact line shows a breakdown of the no‐slip condition and, up to substantial statistical fluctuations, is consistent with earlier predictions of Dussan. [Work supported by NSF.]