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Register a new userNon-uniqueness of local stress of three-body potentials in molecular simulations
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Microscopic stress fields are widely used in molecular simulations to understand mechanical behavior. Recently, decomposition methods of multibody forces to central force pairs between the interacting particles have been proposed. Here, we introduce a force center of a three-body potential and propose different force decompositions that also satisfy the conservation of translational and angular momentum. We compare the force decompositions by stress-distribution magnitude and discuss their difference in the stress profile of a bilayer membrane using coarse-grained and atomistic molecular dynamics simulations.
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The complex scaling method, which consists in continuing spatial coordinates into the complex plane, is a well-established method that allows to compute resonant eigenfunctions of the time-independent Schroedinger operator. Whenever it is desirable to apply the complex scaling to investigate resonances in physical systems defined on numerical discrete grids, the most direct approach relies on the application of a similarity transformation to the original, unscaled Hamiltonian. We show that such an approach can be conveniently implemented in the Daubechies wavelet basis set, featuring a very promising level of generality, high accuracy, and no need for artificial convergence parameters. Complex scaling of three dimensional numerical potentials can be efficiently and accurately performed. By carrying out an illustrative resonant state computation in the case of a one-dimensional model potential, we then show that our wavelet-based approach may disclose new exciting opportunities in the field of computational non-Hermitian quantum mechanics.
Large-scale clustering of highly biased tracers of large-scale structure has emerged as one of the best observational probes of primordial non-Gaussianity of the local type (i.e. f_{NL}^{local}). This type of non-Gaussianity can be generated in multifield models of inflation such as the curvaton model. Recently, Tseliakhovich, Hirata, and Slosar showed that the clustering statistics depend qualitatively on the ratio of inflaton to curvaton power xi after reheating, a free parameter of the model. If xi is significantly different from zero, so that the inflaton makes a non-negligible contribution to the primordial adiabatic curvature, then the peak-background split ansatz predicts that the halo bias will be stochastic on large scales. In this paper, we test this prediction in N-body simulations. We find that large-scale stochasticity is generated, in qualitative agreement with the prediction, but that the level of stochasticity is overpredicted by ~30%. Other predictions, such as xi independence of the halo bias, are confirmed by the simulations. Surprisingly, even in the Gaussian case we do not find that halo model predictions for stochasticity agree consistently with simulations, suggesting that semi-analytic modeling of stochasticity is generally more difficult than modeling halo bias.
We present a new method for sampling stochastic displacements in Brownian Dynamics (BD) simulations of colloidal scale particles. The method relies on a new formulation for Ewald summation of the Rotne-Prager-Yamakawa (RPY) tensor, which guarantees that the real-space and wave-space contributions to the tensor are independently symmetric and positive-definite for all possible particle configurations. Brownian displacements are drawn from a superposition of two independent samples: a wave-space (far-field or long-ranged) contribution, computed using techniques from fluctuating hydrodynamics and non-uniform Fast Fourier Transforms; and a real-space (near-field or short-ranged) correction, computed using a Krylov subspace method. The combined computational complexity of drawing these two independent samples scales linearly with the number of particles. The proposed method circumvents the super-linear scaling exhibited by all known iterative sampling methods applied directly to the RPY tensor that results from the power law growth of the condition number of tensor with the number of particles. Calculations for hard sphere dispersions and colloidal gels are illustrated and used to explore the role of microstructure on performance of the algorithm. In practice, the logarithmic part of the predicted scaling is not observed and the algorithm scales linearly for up to 4 million particles, obtaining speed ups of over an order of magnitude over existing iterative methods, and making the cost of computing Brownian displacements comparable the cost of computing deterministic displacements in BD simulations. A high-performance implementation employing non-uniform fast Fourier transforms implemented on graphics processing units and integrated with the software package HOOMD-blue is used for benchmarking.
The fluid flow through porous media is described by Darcys law, while the fluid/wall interactions can be neglected. In nanopores, where adsorption dominates, Darcys extension has been made, but approaches able to describe flows in mesopores are still lacking. We show here that molecular flows through nano-constrictions is well described by Berverloos law, predicting the mass flow rate of granular material through macro-apertures. This molecular and granular analogy, allows to derive a relationship providing a theoretical framework for the molecular flow in disordered mesoporous systems.
In this letter we show that the late-time scaling state in spinodal decomposition is not unique. We performed lattice Boltzmann simulations of the phase-ordering of a 50%-50% binary mixture using as initial conditions for the phase-ordering both a symmetric morphology that was created by symmetric spinodal decomposition and a morphology of one phase dispersed in the other, created by viscoelastic spinodal decomposition. We found two different growth laws at late times, although both simulations differ only in the early time dynamics. The new scaling state consists of dispersed droplets. The growth law associated with this scaling state is consistent with a $Lsim t^{1/2}$ scaling law.
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