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Register a new userInference of hidden structures in complex physical systems by multi-scale clustering
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We survey the application of a relatively new branch of statistical physics--community detection-- to data mining. In particular, we focus on the diagnosis of materials and automated image segmentation. Community detection describes the quest of partitioning a complex system involving many elements into optimally decoupled subsets or communities of such elements. We review a multiresolution variant which is used to ascertain structures at different spatial and temporal scales. Significant patterns are obtained by examining the correlations between different independent solvers. Similar to other combinatorial optimization problems in the NP complexity class, community detection exhibits several phases. Typically, illuminating orders are revealed by choosing parameters that lead to extremal information theory correlations.
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Algorithms for simulating complex physical systems or solving difficult optimization problems often resort to an annealing process. Rather than simulating the system at the temperature of interest, an annealing algorithm starts at a temperature that is high enough to ensure ergodicity and gradually decreases it until the destination temperature is reached. This idea is used in popular algorithms such as parallel tempering and simulated annealing. A general problem with annealing methods is that they require a temperature schedule. Choosing well-balanced temperature schedules can be tedious and time-consuming. Imbalanced schedules can have a negative impact on the convergence, runtime and success of annealing algorithms. This article outlines a unifying framework, ensemble annealing, that combines ideas from simulated annealing, histogram reweighting and nested sampling with concepts in thermodynamic control. Ensemble annealing simultaneously simulates a physical system and estimates its density of states. The temperatures are lowered not according to a prefixed schedule but adaptively so as to maintain a constant relative entropy between successive ensembles. After each step on the temperature ladder an estimate of the density of states is updated and a new temperature is chosen. Ensemble annealing is highly practical and broadly applicable. This is illustrated for various systems including Ising, Potts, and protein models.
Recent DFT (density functional theory) simulations showed that metals have a hitherto overlooked symmetry termed hidden scale invariance [Hummel {em et al.}, Phys. Rev. B {bf{92}}, 174116 (2015)]. According to isomorph theory, this scaling property implies the existence of lines in the thermodynamic phase diagram, so-called isomorphs, along which structure and dynamics are invariant to a good approximation when given in properly reduced units. This means that the phase diagram becomes effectively one-dimensional with regard to several physical properties. This paper investigates consequences and implications of the isomorph theory in six metallic crystals; Au, Ni, Cu, Pd, Ag and Pt. The data are obtained from molecular dynamics simulations employing many body effective medium theory (EMT) to model the atomic interactions realistically. We test the predictions from isomorph theory for structure and dynamics by means of the radial distribution and the velocity autocorrelation functions, as well as the rather dramatic prediction of instantaneous equilibration after a jump between two isomorphic points. Many properties of crystals tend to be dominated by defects and many of the properties associated with these defects are expected to be isomorph invariant as well. This is investigated in this paper for the case of vacancy diffusion. We find the predicted invariance of structure and also of dynamics, though less rigorous. We show results on the variation of the density scaling exponent $gamma$, which can be related to the Gruneisen-parameter, for all six metals. We consider large density changes up to a factor of two, corresponding to very high pressures. Unlike systems modelled using the Lennard-Jones potential where the density scaling-exponent $gamma$ is almost constant, it varies substantially when using the EMT potential and is also strongly material dependent.
In recent years lines along which structure and dynamics are invariant to a good approximation, so-called isomorphs, have been identified in the thermodynamic phase diagrams of several model liquids and solids. This paper reports computer simulations of the transverse and longitudinal collective dynamics at different length scales along an isomorph of the Lennard-Jones system. Our findings are compared to corresponding results along an isotherm and an isochore. Confirming the theoretical prediction, the reduced-unit dynamics of the transverse momentum density is invariant to a good approximation along the isomorph at all time and length scales. Likewise, the wave-vector dependent shear-stress autocorrelation function is found to be isomorph invariant. A similar invariance is not seen along the isotherm or the isochore. Using a spatially non-local hydrodynamic model for the transverse momentum-density time-autocorrelation function, the macroscopic shear viscosity and its wave dependence are determined, demonstrating that the shear viscosity is isomorph invariant on all length scales studied. This analysis implies the existence of a novel length scale which characterizes each isomorph. The transverse sound-wave velocity, the Maxwell relaxation time, and the rigidity shear modulus are also isomorph invariant. In contrast, the reduced-unit dynamics of the mass density is not invariant at length scales longer than the inter-particle distance. By fitting to a generalized hydrodynamic model, we extract values for the wave-vector-dependent thermal diffusion coefficient, sound attenuation coefficient, and adiabatic sound velocity. The isomorph variation of these quantities in reduced units at long length scales can be eliminated by scaling with $gamma$, a fundamental quantity in the isomorph theory framework, an empirical observation that remains to be explained theoretically.
Two dimensionless fundamental physical constants, the fine structure constant $alpha$ and the proton-to-electron mass ratio $frac{m_p}{m_e}$ are attributed a particular importance from the point of view of nuclear synthesis, formation of heavy elements, planets, and life-supporting structures. Here, we show that a combination of these two constants results in a new dimensionless constant which provides the upper bound for the speed of sound in condensed phases, $v_u$. We find that $frac{v_u}{c}=alphaleft(frac{m_e}{2m_p}right)^{frac{1}{2}}$, where $c$ is the speed of light in vacuum. We support this result by a large set of experimental data and first principles computations for atomic hydrogen. Our result expands current understanding of how fundamental constants can impose new bounds on important physical properties.
Recently, monolayer SnS, a two-dimensional group IV monochalcogenide, was grown on a mica substrate at the micrometer-size scale by the simple physical vapor deposition (PVD), resulting in the successful demonstration of its in-plane room temperature ferroelectricity. However, the reason behind the monolayer growth remains unclear because it had been considered that the SnS growth inevitably results in a multilayer thickness due to the strong interlayer interaction arising from lone pair electrons. Here, we investigate the PVD growth of monolayer SnS from two different feed powders, highly purified SnS and commercial phase-impure SnS. Contrary to expectations, it is suggested that the mica substrate surface is modified by sulfur evaporated from the Sn2S3 contaminant in the as-purchased powder and the lateral growth of monolayer SnS is facilitated due to the enhanced surface diffusion of SnS precursor molecules, unlike the growth from the highly purified powder. This insight provides a guide to identify further controllable growth conditions.
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