Session V22: Classical Monte Carlo and Molecular Dynamics

Monte Carlo Simulation of a Novel Classical Spin Model with a Tricritical Point

Recent experimental findings along with motivation from the well known Blume-Capel model has led to the development of a novel two-dimensional classical spin model defined on a square lattice. This model consists of two Ising spin species per site with each species interacting with its own kind as perpendicular one dimensional Ising chains along with complex and frustrating interactions between species. Probing this model with Mean Field Theory, Metropolis Monte Carlo, and Wang Landau sampling has revealed a rich phase diagram which includes a tricritical point separating a first order magnetic phase transition from a continuous one, along with three ordered phases. Away from the tricritical point, the expected 2D Ising critical exponents have been recovered. Ongoing work focuses on finding the tricritical exponents and their connection to a supersymmetric critical point.   

Molecular dynamics simulations of Leidenfrost droplets on a vibrating nano ratchet

Asymmetrically nanostructured surfaces can function as Brownian ratchets, that is, create a bias in mass or energy flows in response to thermal noise or in a more general case, isotropic excitations. Recently, experimental studies have shown that it is possible to induce directional movement of water droplets deposited on a vertically vibrating hydrophobic substrate made of inclined nanopillars. To investigate this issue, we have performed large-scale molecular dynamics (MD) simulations of a water droplet on a pillared graphitic substrate. We have found that our results not only reproduce the experimental behavior but also reveal new phenomena. In particular, it was found that at certain critical amplitude and frequency, the motion of the droplet transits from circular to linear-oscillatory along the substrate. The transition ultimately depends on the relative size of droplet and pillars, suggesting new ways of controlling the movement of water droplets on superhydrophobic substrates.   

Observation of 2D Ising criticality of liquid-gas transition by the flowgram method

We study the critical properties of the transition in 2D liquid-gas system with the square-well potential interaction by Monte Carlo simulations in the grand canonical ensemble. Due to lack of the underlying Ising symmetry, the analysis cannot be done reliably by the standard methods applicable to lattice systems. In contrast, the analysis based on the flowgram method \footnote{ A. B. Kuklov, N.V. Prokof'ev, B.V. Svistunov, and M. Troyer, Ann. of Phys., {\bf 321}, 1602 (2006).} allowed us to find the critical point to significantly higher (and controllable) accuracy than in previous studies by other authors. Simulations were performed in a progression of sizes $L$ up to size $L = 84$, with the particle numbers varying over 3 orders of magnitude and the subcritical behavior not extending beyond $L=10-15$. The finite size scaling analysis of the critical exponents and their ratio, $\mu$ and $\gamma/\nu$, gives values consistent with the 2D Ising universality class within 1-2\% of errors. Our result essentially closes proposals that the nature of the liquid-gas transition might be different from the Ising model in systems with short-range interactions.   

Heat Transfer in Porous Crystals Containing Adsorbed Gases

Using molecular modeling, we investigated heat transfer phenomena in a porous crystal containing gases. This study was motivated by the challenge of quickly dissipating heat generated in metal-organic frameworks (MOFs) during gas adsorption. Our study reveals that thermal conductance is dominated by lattice thermal conductivity in the crystal, and that conductance decreases as the density of gas in the pores increases. We show that the observed decreased conductivity is due to phonon scattering in the crystal due to interactions with gas molecules. We have also investigated the effect of pore size and shape on thermal transport in these structures. We show that thermal conductivity of pure nanoporous crystals decreases with pore size. For nanoporous crystals with small pores, gas adsorption reduces thermal conductivity due to more phonon scatterings, whereas for larger pores, the increase in gas loading does not affect lattice thermal conductivity. We show that the probability of gas-crystal collisions is smaller for larger pores, which explains why loaded gases do not significantly affect thermal conductivity of large pore structures.   

Renormalized Multicanonical Sampling in Two-Dimensional Systems

This presentation considers the relative speed and accuracy of the recently introduced renormalized multicanonical sampling method [D. Yevick, Int. J. Mod. Phys. C, 1650033] in the context of the 2 dimensional Ising model. In particular, the technique is compared to a method in which the transition matrix is constructed during a multicanonical determination of the density of states. In the comparison, the simulation speed is significantly increased by the renormalized sampling and the calculations with the transition matrices obtained from the multicanonical refinement steps of the renormalized algorithm improves the simulation speed and accuracy further.   

Dynamic Algorithms for Transition Matrix Generation

The methods of [D. Yevick, Int. J. Mod. Phys. C, 1650041] for constructing transition matrices are applied to the two dimensional Ising model. Decreasing the system temperature during the acquisition of the matrix elements yields a reasonably precise specific heat curve for a 32x32 spin system for a limited number (50-100M) of realizations. If the system is instead evolved to first higher and then lower energies within a restricted interval that is steadily displaced in energy as the computation proceeds, a modification which permits backward displacements up to a certain lower bound for each forward step ensures acceptable accuracy. Additional constraints on the transition rule are also investigated.   

``Binless Wang-Landau sampling'' - a multicanonical Monte Carlo algorithm without histograms

Inspired by the very successful Wang-Landau (WL) sampling \footnote{F. Wang and D. P. Landau, Phys. Rev. Lett. \textbf{86}, 2050 (2001).}, we innovated a multicanonical Monte Carlo algorithm to obtain the density of states (DOS) for physical systems with continuous state variables. Unlike the original WL scheme where the DOS is obtained as a numerical array of finite resolution, our algorithm assumes an analytical form for the DOS using a well chosen basis set, with coefficients determined iteratively similar to the WL approach. To avoid undesirable artificial errors caused by the discretization of state variables, we get rid of the use of a histogram for keeping track of the number of visits to energy levels, but store the visited states directly for the fitting of coefficients. This new algorithm has the advantage of producing an analytical expression for the DOS, while the original WL sampling can be readily recovered.   

Critical nonequilibrium relaxation in cluster algorithms in the BKT and weak first-order phase transitions

Recently we showed that the critical nonequilibrium relaxation in cluster algorithms is widely described by the stretched-exponential decay of physical quantities in the Ising [1] or Heisenberg [2] models. Here we make a similar analysis in the Berezinsky-Kosterlitz-Thouless (BKT) phase transition in the 2D XY model (simple exponential decay) and in the weak first-order phase transition in the 2D $q=5$ Potts model (power-law decay) [3], which means that these phase transitions can clearly be characterized by the present analysis. These relaxation behaviors are compared with those in the 3D and 4D XY models (second-order phase transition) and in the 2D $q$-state Potts models ($2 \le q \le 4$ for second-order and $q \ge 6 $ for strong first-order phase transitions. \smallskip \par \noindent [1] Y.~Nonomura, J.\ Phys.\ Soc.\ Jpn.\ {\bf 83}, 113001 (2014); [2] Y.~Nonomura and Y.~Tomita, arXiv:1508.05218; [3] Y.~Nonomura and Y.~Tomita, arXiv:1509.08352.   

Real Space Alternatives to the Ewald: Shifted Electrostatics for Multipoles

We have developed three real-space methods for computing electrostatic interactions in Molecular Dynamics (MD): Gradient Shifted Force (GSF), Shifted Potential (SP), and Taylor Shifted Force (TSF) [1]. Electrostatic interaction energies, forces, and torques of the molecules obtained from these methods were tested against an analytical as well as a reference method in a variety of condensed phase environments. Tests show that electrostatic energies, forces, and torques evaluated from our real-space methods show excellent agreement with the computationally expensive Ewald method. Total energy is conserved in molecular systems interacting using GSF and TSF methods. Different structural and dynamical properties of the multipolar fluids have been investigated. Recently, we have developed methods for evaluating dielectric properties for dipolar and quadrupolar fluids. Results for the dielectric constant of dipolar and quadrupolar fluids evaluated using the fluctuation and perturbation method will also be discussed. [1] M. Lamichhane \textit{et al.,} J. Chem. Phys \textbf{141}, 134109 (2014); \textbf{141}, 134110 (2014).   

A robust high-order ideal magnetohydrodynamic solver

In this work we present a robust high-order numerical method for the ideal magnetohydrodynamics (MHD) equations. Our method is single-stage and single-step, and hence amenable to adaptive mesh refinement (AMR) technology. The numerical robustness of the scheme is realized by accomplishing a total of two unrelated tasks: we retain positivity of the density and pressure by limiting fluxes similar to what happens in a flux corrected transport method, and we obtain divergence free magnetic fields by implementing an unstaggered transport method for the evolution of the magnetic potential. We present numerical results in two and three dimensions that indicate the utility of the scheme. These results include several classical test problems such as Orzag-Tang, cloud shock interactions and blast wave problems.