Robert H. Swendsen

MULTIDIMENSIONAL FREE-ENERGY CALCULATIONS USING THE WEIGHTED HISTOGRAM ANALYSIS METHOD

The recently formulated weighted histogram analysis method (WHAM)1 is an extension of Ferrenberg and Swendsens multiple histogram technique for free‐energy and potential of mean force calculations. As an illustration of the method, we have calculated the two‐dimensional potential of mean force surface of the dihedrals gamma and chi in deoxyadenosine with Monte Carlo simulations using the all‐atom and united‐atom representation of the AMBER force fields. This also demonstrates one of the major advantages of WHAM over umbrella sampling techniques. The method also provides an analysis of the statistical accuracy of the potential of mean force as well as a guide to the most efficient use of additional simulations to minimize errors.

Cluster Monte Carlo algorithms

Abstract The Swendsen-Wang and Wolff Monte Carlo algorithms are described in some detail, using the Potts model as an example. Various generalizations are then reviewed and some applications are discussed. Two complete Fortran programs for the algorithms are provided.

Feeling textures through a probe: Effects of probe and surface geometry and exploratory factors

Vibratory roughness perception occurs when people feel a surface with a rigid probe. Accordingly, perceived roughness should reflect probe and surface geometry, exploratory speed, and force. Experiments 1 and 2 compared magnitude estimation of roughness with the bare finger and two types of probes, one designed to eliminate force moments, under the subject’s active control. Experiments 3 and 4 varied speed under passive control. Log magnitude was consistently a quadratic function of log spacing between elements in the surface. The location of the function’s peak was related to the drop point—that is, the spacing at which the probe can just drop between elements—which is affected by probe tip diameter, element height, and speed. Other parameters of the quadratic were affected by probe type and speed.

Monte Carlo simulation of particulate matter segregation

Abstract Size segregation occurs when particulate matter is subjected to some form of shaking or vibration. This segregation has been the subject of much interest to industries dealing with granular materials. We present the results of new Monte Carlo simulations, which provide insight into the essentially geometric origin of the segregation effect. Results show excellent agreement with segregation observed in experimental systems by other researchers.

TRANSITION MATRIX MONTE CARLO REWEIGHTING AND DYNAMICS

Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213(10 September 1998)We study an induced dynamics in the space of energy ofsingle-spin-flip Monte Carlo algorithm. The method gives anefficient reweighting technique. This dynamics is shown tohave relaxation times proportional to the specific heat. Thus,it is plausible for a logarithmic factor in the correlation timeof the standard 2D Ising local dynamics.05.50.+q, 02.70Lq, 64.60.Ht.

Magnetic ground state of semiconducting transition-metal trichalcogenide monolayers

Layered transition-metal trichalcogenides with the chemical formula ABX3 have attracted recent interest as potential candidates for two-dimensional magnets. Using first-principles calculations within density functional theory, we investigate the magnetic ground states of monolayers of Mn- and Cr-based semiconducting trichalcogenides.We show that the second and third nearest-neighbor exchange interactions (J2 and J3) between magnetic ions, which have been largely overlooked in previous theoretical studies, are crucial in determining the magnetic ground state. Specifically, we find that monolayer CrSiTe3 is an antiferromagnet with a zigzag spin texture due to significant contribution from J3, whereas CrGeTe3 is a ferromagnet with a Curie temperature of 106 K. Monolayers of Mn compounds (MnPS3 and MnPSe3) always show antiferromagnetic N eel order. We identify the physical origin of various exchange interactions, and demonstrate that strain can be an effective knob for tuning the magnetic properties. Possible magnetic ordering in the bulk is also discussed. In conclusion, our study suggests that ABX3 can be a promising platform to explore two-dimensional magnetic phenomena.

Modern methods of analyzing Monte Carlo computer simulations

In the past few years, new approaches to Monte Carlo simulations have produced substantial improvements in the efficiency of both simulation techniques and data analysis. This paper will focus on the recent renewal of interest in histogram methods and the new developments in this field. This approach to data analysis has proven very effective in improving the efficiency and ultimate accuracy of Monte Carlo calculations. The methods will be described along with several new applications.

Spiral growth of crystals: Simulations on a stochastic model

Abstract We present the results of computer simulations of spiral growth on relatively large crystal surfaces (up to 600 x 600 lattice constants). This provides a microscopic test for phenomenological thermodynamic theories. In particular we have found that deviations from the linear theory only occur for cases, in which the radius of the critical nucleus is of the order of one lattice constant.

Statistical mechanics of colloids and Boltzmann's definition of the entropy

The Boltzmann entropy as traditionally presented in statistical mechanics textbooks is only a special case and not Boltzmanns fundamental definition. The difference becomes important when the traditional expression for the entropy is applied to colloids, for which it makes incorrect predictions. Boltzmanns original definition of the entropy in terms of the probabilities of states of composite systems leads to consistent and correct statistical mechanics and thermodynamics.

Statistical mechanics and disordered systems

Since computers are able to simulate the equilibrium properties of model systems, they may also prove useful for solving the hard optimization problems that arise in the engineering of complex systems.