Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session G62: Computational Methods for Statistical Mechanics: Advances and Applications IFocus
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Sponsoring Units: DCOMP Chair: Markus Eisenbach, Oak Ridge National Laboratory Room: Room 417 |
Tuesday, March 7, 2023 11:30AM - 12:06PM |
G62.00001: Generating constrained stochastic processes Invited Speaker: Gregory Schehr I will review recent progress on generating constrained stochastic processes. Starting from constrained Brownian trajectories, I will highlight the notion of an effective Langevin equation and generalise it to the case of discrete-time processes, including the case of Lévy flights. I will then extend these results to the case of non-Markovian processes, including the run-and-tumble particles which are commonly used as a toy model of active matter. Finally, I will show how this method not only allows to generate efficiently constrained multi-particles dynamics, such as nonintersecting Brownian bridges, but also provides a useful framework to obtain exact analytical results for such interacting particles systems. |
Tuesday, March 7, 2023 12:06PM - 12:18PM |
G62.00002: Robust computational algorithm for temperature-dependant phonon frequencies and lifetimes calculation beyond the perturbation approximation Jalaan Avritte, David E Crawford, Jianjun Dong Recent advancements of machine-learning interatomic potentials provide new opportunities to accurately simulate lattice vibrations of complex materials using a computer cluster of moderate size. We have implemented a robust algorithm to compute temperature-dependent phonon frequencies and lifetimes of crystals based on the molecular dynamics (MD) simulations of atomic velocity-velocity correlation functions. This method calculates effects of all orders of lattice anharmonicity beyond the perturbation approximation. A robust reciprocal q-space symmetrization algorithm significantly reduces numerical fluctuations found in the MD simulations with thousand-atom material systems over hundreds of picoseconds. We have adopted this algorithm to predict phonon frequencies and lifetimes of crystalline silicon from 300K to 1500K. Our MD simulation results are compared to results from perturbation calculations based on the bare-phonon spectra and third order lattice anharmonicity, as well as the latest neutron-scattering data. This comparison shows that the onset of the break-down of single relaxation time approximation starts around 600K in many optical phonon modes. Current developments are in the works to accurately predict the lattice thermal conductivity from these temperature-dependent phonon properties. This approach can be readily extended to structurally more complex materials, such as nano-materials or materials interfaces. |
Tuesday, March 7, 2023 12:18PM - 12:30PM |
G62.00003: Adaptive power method for estimating large deviations of Markov chains Francesco Coghi, Hugo Touchette I will discuss a stochastic algorithm based on a power method that adaptively learns the large deviation functions characterising the fluctuations of additive functionals of Markov processes. I will show a convergence study of the algorithm close to dynamical phase transitions, exploring the speed of convergence as a function of the learning rate and the effect of including transfer learning in parameter space. As a test example for the optimal perfomance of the algorithm, I will discuss the mean degree of a uniform random walk on Erd¨os–R´enyi random graphs, which appears to show a delocalisation-localisation transition in the infinite size limit. |
Tuesday, March 7, 2023 12:30PM - 12:42PM |
G62.00004: Brownian Bridge Approximations for Barrier-Crossing Problems George Curtis The simulation of rare events is an important problem in chemical physics with numerous challenges and applications. To investigate such phenomena, we study a process known as a generalized Brownian bridge – i.e., a continuous random walk conditioned to lie in a specified region of phase space and/or end in a given region. This random process has broad applicability when one wants to control the endpoint of stochastic systems, which is often the case in fields like polymer physics and reaction systems. However, construction of a bridge requires solving a Backwards Fokker-Planck (BFP) equation which suffers from the “Curse of Dimensionality” and thus is impractical to compute on complex and high dimensional potential energy surfaces. Therefore, we propose leveraging approximate solutions in conjunction with an importance sampling scheme to correct (re-weight) any errors which occur. Specifically, we exploit asymptotic properties of the BFP to generate simple approximate bridges that reach one region before another, and efficiently generate barrier-crossing trajectories in systems with either large potential energy barriers or in a low temperature (low noise) regime. We see that this drastically simplifies the bridge construction while maintaining statistical accuracy. |
Tuesday, March 7, 2023 12:42PM - 12:54PM |
G62.00005: Accelerating Multicanonical Monte Carlo Simulations with Irreversibility Ying-Wai Li, Thomas Vogel Monte Carlo simulations are robust methods to study statistical physics. However, the unpredictable convergence time and the ease of being trapped in local minima have plagued the efficiency of both traditional and modern Monte Carlo algorithms. We review and design new strategies of introducing irreversibility to suppress the random walk behavior in Monte Carlo simulations. These strategies violate detailed balance condition, yet they satisfy the global balance condition that ensures correct statistics. When applied to multicanonical sampling, our new strategies showed significant speedup compared to the original algorithm. We will demonstrate the advantage of our new algorithms with Monte Carlo simulations on spin systems and alloys. |
Tuesday, March 7, 2023 12:54PM - 1:06PM |
G62.00006: Scaling dimensions from linearized tensor renormalization group transformations Xinliang Lyu, Naoki Kawashima, RuQing G Xu Tensor network renormalization group (TNRG) is a novel numerical technique for 2D and 3D classical statistical models. The approximation accuracy is controlled by an integer called bond dimension χ, roughly corresponding to the number of coupling kept in a conventional RG scheme. The estimation of the free energy of 2D Ising model converges to the exact value when χ increases; TNRG also provides a highly-accurate estimation of the critical temperature of 3D Ising model. However, it is the universal properties, like scaling dimensions of a critical model, that are more interesting and important. In 2D, methods based on conformal field theory (CFT) arguments exist, but are not applicable in 3D. |
Tuesday, March 7, 2023 1:06PM - 1:18PM |
G62.00007: Leveraging Enhanced, Recursively Stratified Sampled Monte Carlo Integration for Accurate Molecular Partition Functions Gabriel Rath, Kai Leonhard, Mohammed Azzaoui, Wassja A Kopp Accurate molecular thermodynamics predictions are important for the modeling of atmospheric, industrial, and combustion processes. Most state-of-the-art methods handle thermodynamic contributions from the motions of nuclei using approximate partition functions calculated from high-quality electronic models. Configuration Integral Monte Carlo Integration (CIMCI) [1] instead calculates full partition functions via numerical integrations over all phase space, usually of a coarser electronic model. However, state-of-the-art Monte Carlo (MC) integration techniques like MISER [2] and VEGAS [3] proved to be insufficient for CIMCI, so new enhancements were developed. These include support for multiple parallel integrations over the same phase space, a pair of improved variants of MISER (PMISER and RMISER) that allow pre-sampling results to be included in final results, and a more mathematically rigorous way to predict sub-region variances when performing stratified sampling recursively the way MISER does. Preliminary benchmarking shows efficiency gains equivalent to what one would get from a ca. 9x to 100x increase in sampling budget. While these were mainly created for CIMCI, MC integration's widespread use means many more applications can also benefit. |
Tuesday, March 7, 2023 1:18PM - 1:30PM |
G62.00008: Rényi entanglement entropy in complex quantum systems Miha Srdinsek Despite being a well-established operational approach to quantify entanglement, R'enyi entropy calculations have been plagued by their computational complexity [1-3]. We introduce a theoretical framework based on an optimal thermodynamic integration scheme, where the R'enyi entropy can be efficiently evaluated using regularizing paths [4]. This approach avoids slowly convergent fluctuating contributions and leads to low-variance estimates. In this way, large system sizes and high levels of entanglement in model or first-principles Hamiltonians are within our reach. We demonstrate it in the one-dimensional quantum Ising model and perform the first evaluation of entanglement entropy in the formic acid dimer, by discovering that its two shared protons are entangled even above room temperature. |
Tuesday, March 7, 2023 1:30PM - 1:42PM |
G62.00009: Markov State Model Optimization of Self-Assembly Protocols for Finite Subunit Pool Systems Anthony S Trubiano, Michael F Hagan A large body of recent theoretical and experimental work in self-assembly has shown that designing time-dependent protocols for system parameters can greatly boost assembly yields and target state selectivity, as well as structure reconfigurability. We recently developed a gradient-based optimization algorithm that combines Markov state model (MSM) analysis with optimal control theory to efficiently compute time-dependent protocols that maximize the finite time assembly yield of a target structure. Although the method performed well on diverse self-assembly systems, it was limited to systems with approximately constant (or negligible) chemical potential. Here, we describe extending the method to systems where subunit depletion is non-negligible, by constructing MSMs as a function of the free monomer concentration. We test the extended method on a system of triangular subunits designed to assemble into icosahedral capsids. |
Tuesday, March 7, 2023 1:42PM - 1:54PM Author not Attending |
G62.00010: Thermodynamic Limit in Computer Simulations via Finite-Size Integral Equations Jose M Sevilla Moreno, Robinson Cortes Huerto, Kurt Kremer Integral equations (IE) connect the local structure of a liquid with equilibrium thermodynamic quantities such as isothermal compressibility, activity coefficients and excess entropy. IE are usually defined in the grand canonical ensemble and calculated in the thermodynamic limit (TL). By contrast, computer simulations typically consider finite-size systems and mimic the TL using periodic boundary conditions (PBC). This practice introduces various finite-size effects whose effects must be identified and corrected to approximate the simulation results in the TL. |
Tuesday, March 7, 2023 1:54PM - 2:06PM |
G62.00011: From Molecular Dynamics to lattice Boltzmann Alexander Wagner Lattice Boltzmann methods have been hugely successful for the simulation of fluid systems at the Navier-Stokes level, but for phenomena bejond Navier-Stokes (like fluctuating systems) it is often unclear how to correctly incorporate those effects. We will show that is is possible to directly derive lattice gas and lattice Boltzmann from Molecular Dynamics throught a coarse-graining procedur [1]. Doing so leads to the definition of novel integer lattice gases [2,3,4] and shows that standard assumptions regarding fluctuations are often incorrect [5]. It can also establish a physical justification for the so called "over-relaxation" process [7], which in turn justifies the definition of integer lattice gas methods with such a collision operator [4]. |
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