Bulletin of the American Physical Society
APS March Meeting 2021
Volume 66, Number 1
Monday–Friday, March 15–19, 2021; Virtual; Time Zone: Central Daylight Time, USA
Session S22: Computational Methods for Statistical Mechanics: Advances and Applications  IFocus Live

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Sponsoring Units: DCOMP GSNP Chair: Ying Wai Li, Los Alamos National Laboratory 
Thursday, March 18, 2021 11:30AM  12:06PM Live 
S22.00001: Doing “Statistical Mechanics” with Big Data: Understanding Protein Allostery Invited Speaker: Andrea Liu Statistical mechanics has been the workhorse that condensed matter physicists have used to make the connection between microscopic properties and macroscopic, collective phenomena. Establishing this connection requires reducing masses of microscopic information (dimensional reduction) to a few relevant microscopic variables and their distributions. Data science methods are designed for dimensional reduction, so they are a natural tool to turn to when statistical mechanics fails. But it requires physics to identify the relevant microscopic quantities as well as the most appropriate data science methods to use to access them. I will discuss our application of persistent homology to develop microscopic understanding of the phenomenon of allostery in proteins. 
Thursday, March 18, 2021 12:06PM  12:18PM Live 
S22.00002: Simulated annealing with adaptive cooling rates Mariia Karabin, Steven Stuart Simulated annealing is known to be among the most robust optimization methods and many variations of it have attempted to improve the original algorithm. Here we present the molecular dynamicsbased adaptivecooling simulated annealing (ACSA) method, where the cooling rates are adaptively adjusted during the optimization based on the instantaneous values of the heat capacity. At the temperatures where more states are thermally accessible and the heat capacity is above a certain threshold, the algorithm chooses a slow cooling rate to ensure that the system is well optimized and doesn’t get trapped in one of the undesirable minima, and a faster cooling rate is chosen at all other times to decrease the optimization time. The efficiency of the ACSA algorithm is calculated with respect to the original simulated annealing algorithm, when applied to the LennardJones cluster optimization. The ACSA is about twice as efficient as the original algorithm for the LennardJones clusters with 2540 atoms and its performance improves for lager clusters. 
Thursday, March 18, 2021 12:18PM  12:30PM Live 
S22.00003: Machine Learning Regression of Quantum ManyBody Operator Dynamics Justin Reyes, Sayandip Dhara, Eduardo R Mucciolo The accurate determination of the longtime dynamics of operator expectation values for quantum many body systems is a computationally demanding problem, with traditional methods scaling exponentially with the system size. We develop a machine learning method which determines the long time dynamics by performing a regression over expectation values calculated exactly over short time intervals. WIth this approach, the longtime dynamics can be determined independent of system size. We demonstrate this computational advantage for both the Ising model in transverse field and the XXZ model. 
Thursday, March 18, 2021 12:30PM  12:42PM Live 
S22.00004: Why is uncertainty quantification of sloppy models challenging? Yonatan Kurniawan, Mark K Transtrum, Cody Petrie, Kinamo Jahali Williams Mathematical models are widely used in science. They summarize what we know about a physical system and probe domains that are experimentally challenging or impossible. Uncertainty quantification helps us determine how much we can trust the predictions a model makes. Multiparameter models are often sloppy, i.e., they have cost surfaces with long, narrow canyons and broad, flat plateaus. Typically, contours on these surfaces do not close; they extend to the limit of physically allowed parameter values such as zero or infinity. These features on the likelihood surface make uncertainty quantification of sloppy models challenging. To show this, I use both Bayesian (Markov Chain Monte Carlo) and Frequentist (profile likelihood) methods to quantify parametric uncertainty of two interatomic potentials, LennardJones and StillingerWeber. I calibrate these models on energy and force data for several atomic configurations from the OpenKIM database. I demonstrate that these models have infinite uncertainty in some of their parameters and discuss challenges this poses for uncertainty quantification in sloppy models. 
Thursday, March 18, 2021 12:42PM  12:54PM Live 
S22.00005: Confinement Potential Inside Rare Gas Plated MCM41 Nanopores Nathan Nichols, Timothy R Prisk, Garfield T Warren, Paul E Sokol, Juan M Vanegas, Adrian G Del Maestro Motivated by recent experimental and simulation results reporting on the use of rare gas preplated nanoporous materials to explore one dimensional superfluidity, we describe an approach towards constructing a microscopically accurate description of the confinement potential in these systems. By combining grand canonical Monte Carlo adsorption isotherms with molecular dynamics simulations and experimental results, we can resolve atomicscale detail of the energetic environment inside MCM41 crystals. The results support a previous conjecture that the adsorption of a rare gas monolayer can screen imperfections and roughness near the pore walls and yield a smooth confinement potential that can be incorporated into more costly quantum simulations of lowdimensional superfluids. 
Thursday, March 18, 2021 12:54PM  1:06PM Live 
S22.00006: Method of the matrix permanent in the theory of critical phenomena: Asymptotics for the largesize powerlaw circulant matrices William Shannon, Vladimir Kocharovsky, Sergey Tarasov, Vitaly Kocharovsky A microscopic theory of phase transitions in a critical region suggested recently in [V.V. Kocharovsky et al., Physica Scripta 90, 108002 (2015); Entropy 22, 322 (2020)] reduces calculation of an order parameter and various correlation functions to computing the permanents of certain matrices given by the wellknown meanfield equations. It is known that an exact computation of a permanent is a #Pproblem that can’t be solved by a classical computer in a polynomial time. Hence, finding adequate approximations and asymptotics of the permanent is of great importance. In this talk, we present our recent results in this direction for the case of powerlaw circulant matrices, including comparison with the known results on a randomphase approximation, exponentiallaw circulant matrices, and McCullagh asymptotics for doublystochastic matrices with a moderate variation of entries. 
Thursday, March 18, 2021 1:06PM  1:18PM Live 
S22.00007: Realspace renormalization group transformation from CNN and maximum likelihood estimation Chak Ming Chan, WANG DING, Liang Tian, LeiHan Tang We report a novel scheme to perform realspace renormalization group (RG) transformation based on supervised machine learning. The 2D Potts model on a square lattice is used as an example. System configurations generated by Monte Carlo simulations at selected temperatures below and above the transition temperature are fed into a convolutional neural network with the network weights optimized to produce the best match under a classifier. Effective model parameters that characterize the distribution of transformed configurations in one step are then extracted using maximum likelihood estimation. This allows us to construct the RG flow in the Hamiltonian space and obtain critical exponents for the transition. Results are presented for different q values. 
Thursday, March 18, 2021 1:18PM  1:30PM Live 
S22.00008: 2D vortex fluctuations above the critical KosterlitzThouless transition temperature Mingyu Fan, Karla Galdamez, Charlie McDowell, Gary Williams Vortex fluctuations above the critical KosterlitzThouless (KT) transition temperature are characterized using simulations of the 2D XY model. The asymptotic vortexvortex correlation function is found to be a power law in the vortex separation at all temperatures. The correlation of plusminus vortex pairs has the expected exponent of 4 at T_{KT}, but then rises to a sharp peak of nearly 3 at T = 1.1 T_{KT}, close to the specific heat peak at 1.15 T_{KT}. It then decreases back to the value of 4 at infinite temperature. The plusplus and minusminus correlations have an exponent of 4 at all temperatures. Also studied is the net winding number of vortices fluctuated in a circle of radius R. The averaged net winding number squared is found to vary linearly with the circle perimeter at all temperatures above and below T_{KT}, contrary to several speculations in the literature. The slope of the variation with R is found to sharply peak at a temperature close to the correlation function and specific heat peaks, and then decreases to a value at infinite temperature that is in complete agreement with an early theory by D. Dhar. These results show that significant correlations between the vortices persist even to infinite temperature. 
Thursday, March 18, 2021 1:30PM  1:42PM Live 
S22.00009: New Developments of Variationally Enhanced Sampling Omar Valsson Variationally enhanced sampling (VES) is a collective variable based enhanced sampling method where we construct the external bias potential via a variational principle by minimizing a convex functional [1,2]. We can employ VES to obtain both free energy landscapes and kinetics of rare events. The method is available in the VES code [3], an opensource library for the PLUMED 2 plugin [4], allowing usage of the technique in a wide range of molecular dynamics codes. 
Thursday, March 18, 2021 1:42PM  1:54PM Live 
S22.00010: Coarsegraining of polyisoprene melts using inverse Monte Carlo and local density potentials Nobahar Shahidi, Antonis Chazirakis, Vagelis Harmandaris, Manolis Doxastakis Bottomup coarsegraining of polymers is commonly performed by matching structural order parameters such as pair distribution functions and distribution of bond lengths, bending angles and dihedrals. We introduce the distribution of nearestneighbors as an additional multibody order parameter to improve the representability of the coarsegrain model. We develop the forcefield using the inverseMonte Carlo method to overcome the challenges associated with crosscorrelation of interaction terms in polymer systems. 
Thursday, March 18, 2021 1:54PM  2:06PM Live 
S22.00011: Effects of Lattice Constraints in CoarseGrained Protein Models: A WangLandau Study Alfred Farris, Daniel Seaton, David P Landau Using WangLandau sampling [1], we compare and contrast folding behavior in coarsegrained models for Crambin  a 46 amino acid protein. We investigate Crambin in the context of the hydrophobic polar (HP) lattice model [2] and the semiflexible H0P lattice model [3]  an extension to the HP model in which an additional monomer type and an interaction accounting for chainstiffness are included. We also examine folding behavior in the analogous continuum models, with potentials designed specifically to mimic the lattice models. Through analysis of thermodynamic and structural behavior, we paint a clear picture of the folding process in all cases, and gain an understanding of the effects of certain interactions on the folding process, as well as how lattice constraints impact the folding process. As the complexity of the model interactions increases, the two major transitions observed in nature  the coilglobule collapse and the folding transition, split into multistep pro 
Thursday, March 18, 2021 2:06PM  2:18PM Live 
S22.00012: Spin dynamics simulations on the Surface of a nanoscale Heisenberg antiferromagnet Zhuofei Hou, David P Landau Monte Carlo and spin dynamics techniques with fourthorder SuzukiTrotter decompositions of the exponential operator have been used to perform largescale simulations of the dynamic behavior of a nanoscale, classical, Heisenberg antiferromagnet on a simple cubic lattice at a temperature below the Nèel temperature 1 . A classical isotropic Heisenberg model with an antiferromagnetic nearestneighbor exchange interaction was studied. A simple cubic lattice with free boundary conditions was used. The assumption of qspace spinwave reflections with broken momentum conservation due to freesurface confinements was developed and used to explain multiple excitation peaks for wave vectors within the first Brillouin zone that appear in the spinwave spectra of the transverse component of dynamic structure factor S^{T}(q, ω) in the nanoscale classical Heisenberg antiferromagnet. In this study, we applied the same simulation techniques to the nanoscale classical Heisenberg antiferromagnet we studied before for studying spin dynamic behavior on the surfaces of a nanoscale antiferromagnet. 
Thursday, March 18, 2021 2:18PM  2:30PM Live 
S22.00013: Finding free energy barriers for complex mesophases Ankita Mukhtyar, Fernando A Escobedo Block copolymers are known to selfassemble into a multitude of phases with vastly different geometries. Amongst these, the double gyroid holds a special place due to its highly symmetric, complex and ordered network that imparts it with many useful properties. In order to tap into the unique properties of the double gyroid phase, we need to be able to design and control its formation. This requires a deeper understanding of the nucleation and growth mechanisms through which it selfassembles. In this paper we attempt to evaluate the nucleation pathway for the disorder to gyroid phase transition, simulated using molecular / dissipative particle dynamics, that to the best of our knowledge still remains largely unknown. We make use of a local order parameter framework developed in an earlier study and put forth multiple approaches to evaluate the free energy barriers for the transition, such as the mean first passage time, hybrid monte carlo, and other novel variants of the umbrella sampling technique. 
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