Mcmahonbates6679

Surface roughening is found only at stresses and shear rates in and above the shear thickening range. These observed relations between surface roughening and stresses confirm that dilation and stresses are coupled in the high-stress state of DST.We present a framework exploiting the cascade of phase transitions occurring during a simulated annealing of the expectation-maximization algorithm to cluster datasets with multiscale structures. Using the weighted local covariance, we can extract, a posteriori and without any prior knowledge, information on the number of clusters at different scales together with their size. We also study the linear stability of the iterative scheme to derive the threshold at which the first transition occurs and show how to approximate the next ones. Finally, we combine simulated annealing together with recent developments of regularized Gaussian mixture models to learn a principal graph from spatially structured datasets that can also exhibit many scales.Rigidity percolation (RP) is the emergence of mechanical stability in networks. Motivated by the experimentally observed fractal nature of materials like colloidal gels and disordered fiber networks, we study RP in a fractal network where intrinsic correlations in particle positions is controlled by the fractal iteration. Specifically, we calculate the critical packing fractions of site-diluted lattices of Sierpiński gaskets (SG's) with varying degrees of fractal iteration. Our results suggest that although the correlation length exponent and fractal dimension of the RP of these lattices are identical to that of the regular triangular lattice, the critical volume fraction is dramatically lower due to the fractal nature of the network. Furthermore, we develop a simplified model for an SG lattice based on the fragility analysis of a single SG. This simplified model provides an upper bound for the critical packing fractions of the full fractal lattice, and this upper bound is strictly obeyed by the disorder averaged RP threshold of the fractal lattices. Our results characterize rigidity in ultralow-density fractal networks.Multiple scattering of light by resonant vapor is characterized by Lévy-type superdiffusion with a single-step size distribution p(x)∝1/x^1+α. We investigate Lévy flight of light in a hot rubidium vapor collisional-broadened by 50 torr of He gas. The frequent collisions produce Lorentzian absorptive and emissive profiles with α less then 1 and a corresponding divergent mean step size. We extract the Lévy parameter α≈0.5 in a multiple-scattering regime from radial profile of the transmission and from violation of the Ohm's law. The measured radial transmission profile and the total diffusive transmission curves are well reproduced by numerical simulations for Lorentzian line shapes.The Fortuin-Kasteleyn (FK) random-cluster model, which can be exactly mapped from the q-state Potts spin model, is a correlated bond percolation model. By extensive Monte Carlo simulations, we study the FK bond representation of the critical Ising model (q=2) on a finite complete graph, i.e., the mean-field Ising model. We provide strong numerical evidence that the configuration space for q=2 contains an asymptotically vanishing sector in which quantities exhibit the same finite-size scaling as in the critical uncorrelated bond percolation (q=1) on the complete graph. Moreover, we observe that, in the full configuration space, the power-law behavior of the cluster-size distribution for the FK Ising clusters except the largest one is governed by a Fisher exponent taking the value for q=1 instead of q=2. This demonstrates the percolation effects in the FK Ising model on the complete graph.When the interactions of agents on a network are assumed to follow the Deffuant opinion dynamics model, the outcomes are known to depend on the structure of the underlying network. This behavior cannot be captured by existing mean-field approximations for the Deffuant model. In this paper, a generalized mean-field approximation is derived that accounts for the effects of network topology on Deffuant dynamics through the degree distribution or community structure of the network. The accuracy of the approximation is examined by comparison with large-scale Monte Carlo simulations on both synthetic and real-world networks.The time evolution of an occupation number is studied for a fermionic or bosonic oscillator linearly fully coupled to several fermionic and bosonic heat baths. The influence of the characteristics of thermal reservoirs of different statistics on the nonstationary population probability is analyzed at large times. Applications of the absence of equilibrium in such systems for creating a dynamic (nonstationary) memory storage are discussed.The noisy voter model is a stylized representation of opinion dynamics. Individuals copy opinions from other individuals, and are subject to spontaneous state changes. In the case of two opinion states this model is known to have a noise-driven transition between a unimodal phase, in which both opinions are present, and a bimodal phase, in which one of the opinions dominates. Gefitinib mw The presence of zealots can remove the unimodal and bimodal phases in the model with two opinion states. Here we study the effects of zealots in noisy voter models with M>2 opinion states on complete interaction graphs. We find that the phase behavior diversifies, with up to six possible qualitatively different types of stationary states. The presence of zealots removes some of these phases, but not all. We analyze situations in which zealots affect the entire population, or only a fraction of agents, and show that this situation corresponds to a single-community model with a fractional number of zealots, further enriching the phase diagram. Our study is conducted analytically based on effective birth-death dynamics for the number of individuals holding a given opinion. Results are confirmed in numerical simulations.The azobenzene-containing crosslinked liquid crystalline polymer is a potential candidate for a stimuli-responsive soft robot, as it provides contactless actuation without the implementation of any separate component. For facilitating practical applications of this novel material, complicated and predefined motions have been realized by tailoring the chemical structure of the polymer network. However, conventional multiscale mechanical analysis, which utilizes the all-atom molecular dynamics to represent a microscopic model, is unsuitable for handling diverse material design parameters due to excessive computational costs. Hence, a multiscale optomechanical simulation framework, which combines the coarse-grained molecular dynamics (CG MD) and the finite-element (FE) method, is developed in this study. The CG MD simulation satisfactorily reproduces the light-induced phase transition and photosoftening effect on the mechanical properties. In particular, using the mesoscale analysis, the presented methodology can treat diverse morphology parameters (liquid crystal phase, spacer length, and crosslinking density) to observe the associated photodeformations.