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We present one effective multicanonical molecular dynamics (MCMD) algorithm accelerating the convergence of rough energy landscapes simulations via an adaptive force-biased iteration scheme. Our method utilizes several short MCMD simulations with dynamically updated weights and combines them to estimate the density of states via multiple histogram technique. The key step of our algorithm is the adaptive refinement for the derivative of multicanonical weight, which allows the system to enlarge the sampling energy range maintaining the statistical accuracy. The performance of our method has been validated for atomic Lennard-Jones clusters.

A generalized version of the simulated tempering operated in the expanded ensembles of non-Boltzmann weights has been proposed to mitigate a quasiergodicity problem occurring in simulations of rough energy landscapes. In contrast to conventional simulated tempering employing the Boltzmann weight, our method utilizes a parametrized, generalized distribution as a workhorse for stochastic exchanges of configurations and subensembles transitions, which allows a considerable enhancement for the rate of convergence of Monte Carlo and molecular dynamics simulations using delocalized weights. A feature of our method is that the exploration of the parameter space encouraging subensembles transitions is greatly accelerated using the dynamic update scheme for the weight via the average guide specific to the energy distribution. The performance and characteristic feature of our method have been validated in the liquid-solid transition of Lennard-Jones clusters and the conformational sampling of alanine dipeptide by taking two types of Tsallis [C. Tsallis, J. Stat. Phys. 52, 479 (1988)] expanded ensembles associated with different parametrization schemes.

The characteristic sampling dynamics of importance samplings driven by the Tsallis weight [C. Tsallis, J. Stat. Phys. 52, 479 (1988)] has been analyzed in terms of recently developed Langevin stochastic model by considering the effects of the density of states and the potential smoothing of the Tsallis transformation. Our study reveals that the fixed points, which are determined by the crossing points of the statistical temperature and the Tsallis effective temperature, play a critical role in overall dynamics of the Tsallis statistics sampling. The dynamical origin of enhanced conformational searches of the Tsallis weight has been investigated by unveiling the intimate relationship between the sampling dynamics and the stability change of corresponding fixed points. Based on this stochastic analysis, we propose one effective method to realize a broad energy distribution in the Tsallis statistics sampling by determining optimal Tsallis parameters systematically based on preliminary canonical samplings. The effectiveness of our method has been validated in the folding simulation of Met-Enkephalin and liquid-solid transition simulation of Lennard-Jones cluster systems., ((c) 2004 American Institute of Physics)

The fundamental relations of the sampling process in the multicanonical ensemble and simulated tempering have been studied in the expanded ensembles formalism. The simulated tempering is identified as the multicanonical sampling with the generalized weight determined by a Laplace transform of the temperature weight. The characteristic dynamics of both sampling methods has been verified in the stochastic formulation of the sampling process. Our study gives a necessary and sufficient condition for the weights to realize a uniform sampling in the energy and temperature spaces. Based on the stochastic model, robust force biased iteration schemes have been proposed to allow automatic determinations of uniform sampling weights.

Two stilbene glycosides, pieceid-2"-O-gallate and pieceid-2"-O-coumarate, were isolated from the MeOH extract of the roots of Pleuropterus ciliinervis Nakai (Polygonaceae), together with two known compounds, resveratrol and pieceid. Their structures were determined spectroscopically, particularly by 2D NMR spectroscopic analysis. The antioxidant activities of stilbenes isolated were determined in vitro against 1,1-diphenyl-2-picrylhydrazyl (DPPH) radicals, superoxide radicals and by determining their lipid peroxidation inhibitory activities. Among the compounds isolated, pieceid-2"-O-gallate had the most potent inhibitory scavenging effect on DPPH, superoxide radicals and upon lipid peroxidation inhibition with IC50 values of 16.5, 23.9 and 5.1 microM, respectively.

The stochastic model describing the sampling process in multicanonical ensemble has been derived by considering the sampling process as an overdamped Brownian motion on the free energy surface. The essential dynamics of the multicanonical sampling has been characterized by a Langevin equation in a piecewise multivalleyed free energy landscape, modulated by a temperature-dependent curvature. Based on the stochastic model we showed that the multicanonical weight can be determined by interpolating maximum probability energy points of the canonical samplings at different temperatures.

The characteristic features of the collapse of the ground state in trapped one-component attractive Bose-Einstein condensates are studied by applying the catastrophe theory. From numerically obtained stable and unstable solutions of the Gross-Pitaevskii equation, we derive the catastrophe function defining the stability of the stationary points on the Gross-Pitaevskii energy functional. The bifurcation diagram and the universal scaling laws stemming from the catastrophe function show quantitative agreement with the numerical results.

We examine the stability properties of the ground state of two-component Bose-Einstein condensates as a function of the interspecies interactions. A stability criterion is identified from the curvature matrix of the Gross-Pitaevskii energy functional subject to the normalization conditions. By analyzing the stability signature, the characteristic features of the spontaneous spatial symmetry breaking are verified in various types of traps. The details of the differences between the continuous symmetry breaking and discrete symmetry breaking are discussed.

A new 27-carboxylic lupane-type triterpene, tiarellic acid (1), was isolated from Tiarella polyphylla together with corosolic acid (2) and tormentic acid (3). Tiarellic acid was characterized as 3,23-dihydroxy-20(29)-lupen-27-oic acid and its NMR data were unambiguously assigned using 2-D NMR techniques.