Session W48: Computational Methods for Statistical Mechanics: Advances and Applications III

Accelerated Monte Carlo sampling through non-reversibility and factorisation

In the context of the high-dimensionality and multimodality of the potentials encountered in chemical physics, massive efforts have been devoted into the development of efficient simulation methodologies. Since the first works of Molecular dynamics (MD) and Markov-chain Monte Carlo (MCMC) methods, bidimensional particle systems, in particular with hard-core interactions, have played the role of a challenging but inspiring test bed. In spite of their apparent simplicity, they exhibit a rich behavior where topological defects bind or unbind themselves in pair, ruling by doing so the transition phases. Standard detailed-balance (or reversible) Markov chains then often fail at exploring efficiently the related configuration space. I will first present the MCMC simulation strategies known as Event-Chain Monte Carlo and based on rejection-free and non-reversible processes, which were first developed to address this challenge. These methods are based on the breaking of detailed balance in the underlying stochastic sampling processes, upgrading them from discrete Markov chains to piecewise deterministic Markov processes (PDMP). PDMP sampling has now shown performances competing with its MD counterparts in chemical physics and, beyond, with state-of-the-art sampling schemes, e.g. Hamiltonian Monte Carlo, in statistical inference. I will discuss how the generalisation of these methods to most systems was made possible by consistently replacing the time-reversibility symmetry of detailed balance by potential or global symmetries. I will finally address the question of practical implementation, in particular regarding computational complexity and how the factorisation, first used to design the first PDMP for sphere systems, can be used even in standard MCMC schemes to reduce the computational complexity cost, as e.g. in long-range systems.   

Distribution of conductance in disordered mesoscopic systems

We present numerical studies of the conductance distribution of disordered mesoscopic conductors based on random matrix theories. These studies explore the dependence of the conductance distribution on different parameters, dimensionality of the system, and disorder.   

Choosing the right event (in non-reversible event-chain Monte Carlo)

The general framework of event-chain Monte Carlo (ECMC) constructs non-reversible Markov chains for continuous statistical-physics models ranging from hard-disk systems to long-range interacting molecular systems. Over recent years, several algorithms from the family of ECMC have been proposed, which, in the event-driven formulation of ECMC, only differ in their treatment of events (that is, e.g., of disk collisions in a hard-disk system). Still, we show that different variants can have widely different performances. As a first example, we consider locally stable sparse hard-disk packings [1]. Using a scaling theory confirmed by simulation results, we obtain two classes for the escape from slightly relaxed hard-disk packings parameterized by a relaxation parameter. In one class, the escape time varies algebraically with the relaxation parameter. In the other class, the escape time only scales as the logarithm of the relaxation parameter. As a second example, we consider integrated autocorrelation times in dense systems of flexible extended hard-disk dipoles [2]. Here, the ECMC variants show order-of-magnitude spreads. We expect the performance differences to carry over to long-range interacting molecular systems, where the choice of the optimal ECMC variant is thus highly important.   

Axial Nucleus Density for DFT, Symmetry Axis Rotating Toward Electron Clusters with ½, Zeta Related to Two Locked-at-180o Dirac Monopoles, Inter-dimensional Hemispherical (r#,θ#,φ#,z) Relativity Stress

I provide a DFT axial nucleus density to apply that is not in current set.

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We present improved estimators that can be used along with Quantum Typicality (QT) to reduce statistical noise in thermal expectation values at low temperatures with minimal extra overhead. The estimators use Randomized Low-rank approximations to capture the low-energy states of the thermal density matrix, $e^{-\beta H}$. We demonstrate the efficacy of the improved estimators by looking at the statistical fluctuations in finite-temperature expectation values of a frustrated quantum antiferromagnet.    

Rejection-Free Population Annealing and Frustrated Ising Models

Population annealing (PA) is a sequential Monte Carlo technique suited for massively parallel simulations of systems with sampling diffiulties. While simulating a population of system copies, population control allows the algorithm to amplify well equilibrated copies while getting rid of lesss well adapted ones and hence speed up the overall relaxation process. While this works well for systems with many competing states, it does nothing to speed up sampling in cases where the embedded conventional Markov chain Monte Carlo dynamics is slow due to small acceptance rates, such as for simulations at low temperatures. We show here that a combination of rejection-free or event-driven simulation algorithms such as the n-fold way with the meta-heuristic provided by population annealing allows to successfully tackle problems where low acceptance rates would otherwise make a standard PA simulation inefficient. The method is used to study the behavior of a frustrated Ising model on the honeycomb lattice with ferromagnetic nearest-neighbor interactions of strength $J_1$ and antiferromagnetic next-nearest-neighbor interactions of strength $J_2$ close to the special point $J_2 = -J_1/4$. While conventional methods seemed to indicate slowing-down effects reminiscent of a first-order phase transition, these are found to be artifacts of the transition temperature approaching zero and the accompanying Metropolis acceptance rates disappearing. In contrast, rejection-free PA allows to study this problem in detail and map out the phase diagram.   

Construction of CRSS model for sapphire with rate theory and molecular dynamic simulations

Compression test is a popular experiment to study the mechanical behavior of materials during uniaxial loading. In such tests, the critical resolved shear stress (CRSS) is often determined as the characteristic property of material strength. The current work studies CRSS of sapphire under uniaxial compressive stress using molecular dynamic simulations. During each test, a cubic model is subjected to a constant strain rate until plastic deformation is observed, and the CRSS is calculated for each case by applying the Schmid's law. The test is run under various model sizes, strain rates, temperatures, as well as orientations; the CRSS dependencies of these variables are investigated. Furthermore, with the application of rate theory, a mathematical model of CRSS is developed to interpret the variable dependencies. Such a model is fitted to the simulation results to obtain a statistical model. It is found that CRSS of sapphire has a positive relation with strain rate, and negative relations with model size and temperature. For future work, the resulting model can be compared to experimental data, where its effectiveness can be investigated.   

Computational studies of the glass-forming ability of binary alloys

Some alloys easily form glasses, while others do not. The critical cooling rates of good versus poor glass-formers can differ by more than 14 orders of magnitude. An important, open problem is to identify the elemental features that give rise to this wide variation in the glass-forming ability of alloys. In recent studies, we have performed large-scale molecular dynamics simulations of Lennard-Jones and patchy-particle models of alloys to determine how several elemental features, such as the cohesive energy, atomic size ratio, and symmetry of the atomic bonds, affect glass formation in binary alloys. We find that combinations of features that give rise to local icosahedral order possess good glass-forming ability. In addition, chemical frustration, characterized by the degree to which the local concentration of different atomic species deviates from that in the liquid state, strongly enhances the glass-forming ability. We also identify a new mechanism of “bond shortening” for improving the glass-forming ability, where atomic species with weaker repulsive interactions are closer to each other than the other atom types are to each other. These findings for binary alloys can also be used to guide glass design in ternary and multicomponent alloys.   

Reversible and irreversible plastic events in a sheared amorphous solid - a mesoscopic approach

It was recently shown that the dynamics of a sheared amorphous solid under athermal and quasistatic shear (AQS) can be rigorously mapped into a state transition graph, where the vertices correspond to ensembles of microscopic particle configuration that remain mechanically stable over a range of strains [1,2]. We have called these ensembles mesostates, and the transitions between them constitute purely plastic events. This approach permits tracing out on a transition graph the AQS response under arbitrary shear protocols. The topology of the transition graph thus encodes the possible dynamics. Moreover, such transition graphs can be extracted from standard atomistic simulations of amorphous solids. At the same time, the transition graph topology provides a way of comparing the dynamics of different driven disordered systems. Here we show that graphs obtained from a mesoscopic model of a sheared amorphous solid faithfully reproduce key topological features of those extracted from atomistic simulations, providing a validation of our mesoscopic model [3,4]. We use the mesoscopic model to compare the topologies of transition graphs extracted from well- and poorly annealed amorphous solids.   

Pico-Scale Ideas for People-Scale Problems: Leveraging Molecular Simulation Tools for the Modeling of Urban Systems

Techniques from computational science, especially particle-based methods for molecular simulation, have played an enormous role in understanding the physics of amorphous matter. In such simulations, the particles that are amorphously arranged may represent atoms or (in appropriately coarse-grained simulations) molecular/macromolecular-scale entities. In this talk, we discuss the power of adapting molecular simulation tools to model amorphous "materials" at the scale of urban phenomena, namely, at the scale of crowds (with particles representing pedestrians) or even at the scale of cities (with particles representing buildings). We argue that the fields of pedestrian dynamics and urban-systems modeling could benefit to a significant extent from this interdisciplinary approach, by leveraging, e.g., the computationally efficient solvers and the descriptors for spatiotemporal correlation popularized by the molecular-simulation community. We provide several representative examples in support of this premise, and close by highlighting future opportunities for synergistic growth between these two communities.   

Stereo-chemistry controlled mechanical properties of cross-linked Poly (N-isopropyl acrylamide) in aqueous medium using molecular simulations

Poly (N-isopropyl acrylamide) or PNIPAM is one of the most promising hydrogels with diverse applications in tissue engineering and drug delivery due to biocompatibility and tunability of temperature response close to human body. Density of crosslinker primarily limits water absorption of hydrogels below LCST (swollen state). In this work, we use all-atom molecular dynamics to simulate the dynamic bond formation between PNIPAM and its cross-linker to study the influence of stereochemistry and degree of cross-linking (DOC) in aqueous medium in swollen and collapsed states of cross-linked PNIPAM to engineer mechanical properties. Specifically, we obtain radius of gyration (Rg), stress-strain curve, shear modulus (G) and Young's modulus (E) in compression and tension. This study provides a better understanding of customized hydrogel behavior and fine-tuning of its mechanical properties for different applications.   

Not Saved by the Bell: Non-Gaussianity and Fluid Transport Measurements in Molecular-Dynamics Simulations

 In interpreting molecular-dynamics (MD) simulations, it is frequently taken for granted that measurements meet (seemingly vanilla) standards of statistical regularity, enabling the use of commonplace statistical procedures for model fitting and uncertainty quantification. In this talk, we explore several systems in which such assumptions break down in subtle and surprising ways, with a specific focus on fluid diffusion under spatial confinement. In a wide-ranging array of MD simulations reflecting systems of engineering interest, we demonstrate that distributions of mean-squared displacement exhibit significant non-Gaussianity at fixed times as well as significant heteroscedasticity over time. If unaccounted for, these statistical qualities tend to lead to underestimates of the simulation time required to characterize fluid transport and, ultimately, overconfident estimates of transport quantities. Drawing on modern tools for regression analysis of time series, we discuss strategies for ameliorating these issues. Our work highlights the unusual statistical challenges posed by (and numerous opportunities to improve the interpretation of) MD simulations of fluids, especially in confined and heterogeneous environments.