Acknowledging the significance of awareness diffusion and behavioral response in contagion outbreaks has been regarded as an indispensable prerequisite for a complete understanding of epidemic spreading. Recent studies from the research community have accumulated overwhelming evidence for the incessantly evolving structure of the underlying networks. Thus there is an impelling need to capture the interplay between the epidemic spreading and awareness diffusion on time-varying networks. In this paper, we consider a behavioral model in which susceptible individuals become alert and adopt a preventive behavior under the local risk perception characterized by a decision-making threshold. The impact of awareness diffusion on the epidemic threshold is investigated under the framework of activity-driven network. Results show that the local epidemic situation in risk perception and the duration of preventive effect are crucial for raising the epidemic threshold. The analytical results are corroborated by Monte Carlo simulations.

Scaling in complex supply networks is a population-level optimization phenomenon thought to arise from the evolutions of the underlying individual networks, but the evolution-scaling connection has not been empirically demonstrated. Here, using individually resolved, temporally serial, and population-scope datasets from public water supply networks, we empirically demonstrate this connection. On the log-log plot, structural properties of individual supply networks trace out evolutionary paths describable as linear projectiles, each characterized by a slope reflecting optimized physical economies of scale and an intercept reflecting morphological adaptation to settlement contexts. The universality in scaling slope coexists with the variability in scaling intercept, so that networks of diverse morphologies advance in time along a “common evolutionary track.” This cross-level observation establishes that individual-level dynamic evolutions cumulatively manifest population-level optimal scaling in complex water supply networks.

We show that collective chaotic behavior emerging from the Boltzmann picture of gases provides an alternate conceptual framework to analyze and create apparent randomness on computers. For instance, at equilibrium the distribution of various physical quantities such as position or velocities or two-dimensional projection of kinetic energy can be used to generate uniform, Gaussian, and exponential distributions. Finally, based on these ideas we present a simplified but highly efficient mesoscopic Boltzmann-type algorithm to generate random distributions at a computational efficiency which is orders of magnitude higher than contemporary algorithms. We illustrate the effectiveness by considering two representative examples: spinodal decomposition of a binary alloy and rare event sampling in biological systems.

Deformable elastic bodies in viscous and viscoelastic media constitute a large portion of synthetic and biological complex fluids. We present a parallelized three-dimensional simulation methodology which fully resolves the momentum balance in the solid and fluid domains. An immersed boundary algorithm is exploited known as the immersed-finite-element method (IFEM) which accurately determines the internal forces in the solid domain. The scheme utilized has the advantages of requiring no costly remeshing, handling finite Reynolds number, as well as incorporating nonlinear viscoelasticity in the fluid domain. Our algorithm is designed for computationally efficient simulation of multiparticle suspensions with mixed structure types. The internal force calculation in the solid domain in the IFEM is coupled with a finite volume based incompressible fluid solver, both of which are massively parallelized for distributed memory architectures. We performed extensive case studies to ensure the fidelity of our algorithm. Namely, a series of single particle simulations for capsules, red blood cells, and elastic solid deformable particles were conducted in viscous and viscoelastic media. All of our results are in excellent quantitative agreement with the corresponding reported data in the literature which are based on different simulation platforms. Furthermore, we assess the accuracy of multiparticle simulation of blood suspensions (red blood cells in plasma) with and without platelets. Finally, we present the results of a simulation of multiple solid deformable objects in a viscoelastic medium.

Macroscopic properties of heterogeneous materials, including thermal and electrical conductivity, elastic moduli, and fluid permeability, depend crucially on their microstructure. Optimal design of such materials with desired properties, as well as characterization of their microstructure, are fundamental problems that have been studied for a long time. Accurate characterization of the microstructure is possible if several $n$-point correlation functions that describe their statistical properties can be computed. While the limits $n=1$, corresponding to phase fractions, and $n=2$, that represents such two-point correlation functions as the radial distribution function, have yielded useful information and insights and have been utilized for reconstruction of models of heterogeneous materials, in many cases higher-order correlation functions are required in order to develop deeper understanding of materials' properties, as well as obtaining accurate estimates for them. We describe an algorithm for computing third-order correlation functions. We test the accuracy of the algorithm for a model of fully penetrable disks, i.e., the so-called cherry-pit model in the limit of the penetrability parameter $\lambda =0$, for which an exact expression for the three-point probability function $S_3({\mathbf{x}}_1,{\mathbf{x}}_2,{\mathbf{x}}_3)$ is known. Excellent agreement between the computed results and the theoretical predictions is demonstrated. We then report on the results of extensive computations for several types of heterogeneous materials and the analysis of their three-point correlation functions. They include the probability and cluster functions $S_3$ and $C_3$, as well as the three-point surface and surface-surface-void correlation functions $F_{sss}$ and $F_{ssv}$, for a variety of two- and three-dimensional disordered materials and media.

We investigate neighbor-avoiding walks on the simple cubic lattice in the presence of an adsorbing surface. This class of lattice paths has been less studied using Monte Carlo simulations. Our investigation follows on from our previous results using self-avoiding walks and self-avoiding trails. The connection is that neighbor-avoiding walks are equivalent to the infinitely repulsive limit of self-avoiding walks with monomer-monomer interactions. Such repulsive interactions can be seen to enhance the excluded volume effect. We calculate the critical behavior of the adsorption transition for neighbor-avoiding walks, finding a critical temperature of $T_{\mathrm{a}}=3.274\left(9\right)$ and a crossover exponent of $\varphi =0.482\left(13\right)$, which is consistent with the exponent for self-avoiding walks and trails, leading to an overall combined estimate for three dimensions of ${\varphi }_{\text{3D}}=0.484\left(7\right)$. While questions of universality have previously been raised regarding the value of adsorption exponents in three dimensions, our results indicate that the value of $\varphi$ in the strongly repulsive regime does not differ from its noninteracting value. However, it is clearly different from the mean-field value of $1/2$ and therefore not superuniversal.

Using Monte Carlo simulation, we study the percolation of sticks, i.e., zero-width rods, on a plane, paying special attention to the effects of stick alignment and their length dispersity. The stick lengths are distributed in accordance with log-normal distributions, providing a constant mean length with different widths of distribution. Scaling analysis is performed to obtain the percolation thresholds in the thermodynamic limits for all values of the parameters. Greater alignment of the sticks leads to increases in the percolation threshold, while an increase in length dispersity decreases the percolation threshold. A fitting formula is proposed for the dependence of the percolation threshold both on stick alignment and on length dispersity.

We revisit the scaling properties of the energy spectra in fully developed incompressible homogeneous turbulence in forced magnetofluids (MHD) in three dimensions (3D), which are believed to be characterized by universal scaling exponents in the inertial range. Enumerating these universal scaling exponents that characterize the energy spectra remains a theoretical challenge. To study this, we set up a scaling analysis of the 3D MHD equations, driven by large-scale external forces and with or without a mean magnetic field. We use scaling arguments to bring out various scaling regimes for the energy spectra. We obtain a variety of scaling in the inertial range, ranging from the well-known Kolmogorov spectra in the isotropic 3D ordinary MHD to more complex scaling in the anisotropic cases that depend on the magnitude of the mean magnetic field. We further dwell on the possibility that the energy spectra scales as $k^{-2}$ in the inertial range, where $k$ is a wave vector belonging to the inertial range, and also speculate on unequal scaling of the kinetic and magnetic energy spectra in the inertial range of isotropic 3D ordinary MHD. We predict the possibilities of scale-dependent anisotropy and intriguing weak dynamic scaling in the Hall MHD and electron MHD regimes of anisotropic MHD turbulence. Our results can be tested in large-scale simulations and relevant laboratory-based and solar wind experiments.

Twisted states with nonzero winding numbers composed of sinusoidally coupled identical oscillators have been observed in a ring. The phase of each oscillator in these states constantly shifts, following its preceding neighbor in a clockwise direction, and the summation of such phase shifts around the ring over $2\pi$ characterizes the winding number of each state. In this work, we consider finite-sized $d$-dimensional hypercubic lattices, namely, square ($d=2$) and cubic ($d=3$) lattices with periodic boundary conditions. For identical oscillators, we observe new states in which the oscillators belonging to each line (plane) for $d=2$ ($d=3$) are phase synchronized with nonzero winding numbers along the perpendicular direction. These states can be reduced into twisted states in a ring with the same winding number if we regard each subset of phase-synchronized oscillators as one single oscillator. For nonidentical oscillators with heterogeneous natural frequencies, we observe similar patterns with slightly heterogeneous phases in each line $(d=2)$ and plane $(d=3)$. We show that these states generally appear for random configurations when the global coupling strength is larger than the critical values for the states.

We demonstrate the existence of solitary waves of synchrony in one-dimensional arrays of oscillator populations with Laplacian coupling. Characterizing each community with its complex order parameter, we obtain lattice equations similar to those of the discrete nonlinear Schrödinger system. Close to full synchrony, we find solitary waves for the order parameter perturbatively, starting from the known phase compactons and kovatons; these solutions are extended numerically to the full domain of possible synchrony levels. For nonidentical oscillators, the existence of dissipative solitons is shown.

We study finite-size fluctuations in a network of spiking deterministic neurons coupled with nonuniform synaptic coupling. We generalize a previously developed theory of finite-size effects for globally coupled neurons with a uniform coupling function. In the uniform coupling case, mean-field theory is well defined by averaging over the network as the number of neurons in the network goes to infinity. However, for nonuniform coupling it is no longer possible to average over the entire network if we are interested in fluctuations at a particular location within the network. We show that if the coupling function approaches a continuous function in the infinite system size limit, then an average over a local neighborhood can be defined such that mean-field theory is well defined for a spatially dependent field. We then use a path-integral formalism to derive a perturbation expansion in the inverse system size around the mean-field limit for the covariance of the input to a neuron (synaptic drive) and firing rate fluctuations due to dynamical deterministic finite-size effects.

We investigate the linearized hydrodynamic equations of interacting self-propelled particles in two-dimensional space. It is found that the small perturbations of density and polarization fields satisfy the hyperbolic partial differential equations—that admit analytical propagating wave solutions. These solutions uncover the questionable traveling band formation in the flocking state of self-propelled particles. Below the critical noise strength, an unstable disordered state (random motion) undergoes a transient vortex and evolves to an ordered state (flocking motion) as unidirectional traveling waves. There appear two possible longitudinal wave patterns depending on the noise strength, including a single band in the stable state and multiplebands in the unstable state. A comparison of theoretical and experimental studies is presented.

Based on Brownian dynamics simulations, we investigate the thermodynamic signatures of nonequilibrium steady states in a confined colloidal suspension under shear flow. Specifically, we consider a thin film consisting of charged particles in narrow slit-pore confinement, forming two layers with quadratic in-plane structure in equilibrium. This many-body system displays three distinct steady states, characterized by unique dynamical and rheological response to the applied shear flow. Calculating the work and heat, we find that both quantities indicate the different states by their mean and by their distributions. A particularly interesting situation occurs at large shear rates, where the particles perform a collective zigzag motion. Here, we find a bistability regarding the degree of phase synchronization of the particle motion. It turns out that this bistability is key to understanding the resulting ensemble-averaged work distributions. For all states, we compare the work and heat distributions to those of effective single-particle systems. By this, we aim at identifying the many-body character of the stochastic thermodynamic quantities.

A simple extension of the thermodynamic dislocation theory is proposed for an analysis of bars subjected to torsion. Employing a small set of physics-based parameters, which we expect to be approximately independent of strain rate and temperature, we are able to simulate the torque-twist curves for bars made of single crystal copper that agree with the experimental ones.

One of the most intriguing features of Earth's axial magnetic dipole field, well known from the geological record, is its occasional and unpredictable reversal of polarity. Understanding the phenomenon is rendered very difficult by the highly nonlinear nature of the underlying magnetohydrodynamic problem. Numerical simulations of the liquid outer core, where regeneration occurs, are only able to model conditions that are far from Earth-like. On the analytical front, the situation is not much better; basic calculations, such as relating the average rate of reversals to various core parameters, have apparently been intractable. Here, we present a framework for solving such problems. Starting with the magnetic induction equation, we show that by considering its sources to be stochastic processes with fairly general properties, we can derive a differential equation for the joint probability distribution of the dominant toroidal and poloidal modes. This can be simplified to a Fokker-Planck equation and, with the help of an adiabatic approximation, reduced even further to an equation for the dipole amplitude alone. From these equations various quantities related to the magnetic field, including the average reversal rate, field strength, and time to complete a reversal, can be computed as functions of a small number of numerical parameters. These parameters in turn can be computed from physical considerations or constrained by paleomagnetic, numerical, and experimental data.

We develop a hybrid method to extract the frequency-dependent dielectric susceptibility $\mathbf{\chi }\left(\omega \right)$ from a $5\text{−}\mu \text{s}$ molecular dynamics trajectory of the Drew-Dickerson DNA dodecamer. Using nonparametric regression, polarization fluctuations are broken into slow and fast parts, each part treated by a different method optimal for its behavior. Our calculation reproduces the peak near ${10}^8\mathrm{Hz}$ in $\text{Im}\left[\mathbf{\chi }\right(\omega \left)\right]$ observed in recent experiments. This feature arises from the motion of the negatively charged DNA backbone and tightly bound counterions. Toward the low-frequency side of the peak, the DNA and counterions tend to move together and hence their contributions to the dielectric susceptibility cancel. At higher frequency the counterions disengage from the backbone and they each respond constructively to the time-varying electric field.

We consider the one-magnon subspace of a quantum Heisenberg Hamiltonian with ferromagnetic ground state. In this model, the spins belong to a chain which contains a cubic interaction between the nearest neighbors atoms. The quantum Heisenberg spin-spin coupling is a function of the distance between them. By providing a numerical solution of the Heisenberg nonlinear lattice model, we found that magnon-lattice coupling affects the magnon dynamics in distinct ways: for a specific range of magnon-lattice interaction values, a magnon-soliton pair is observed. Moreover, an effective repulsion between the magnon's excitation and the lattice deformation is noticed for other cases.

We analyze the scaling behavior of the fidelity, and the corresponding susceptibility, emerging in finite-size many-body systems whenever a given control parameter $\lambda$ is varied across a quantum phase transition. For this purpose we consider a finite-size scaling (FSS) framework. Our working hypothesis is based on a scaling assumption of the fidelity in terms of the FSS variables associated with $\lambda$ and its variation $\delta \lambda$. This framework entails the FSS predictions for continuous transitions and enables one to extend them to first-order transitions, where the FSS becomes qualitatively different. The latter is supported by analytical and numerical analyses of the quantum Ising chain along its first-order quantum transition line, driven by an external longitudinal field.

Casimir forces in a critical medium are produced by the spatial suppression of order parameter fluctuations. In this paper we address the question of how fluctuations of a critical medium are related to the magnitude of critical Casimir interactions. Namely, for the Ising model we express the potential of critical Casimir interactions in terms of Fortuin-Kasteleyn site-bond correlated percolation clusters. These clusters are a quantitative representation of fluctuations in a medium. We propose a Monte Carlo method for the computation of the Casimir force potential which is based on this relation. We verify this method by computation of Casimir interactions between two disks for the two-dimensional Ising model. The method is also applied to the investigation of a nonadditivity of the critical Casimir potential. The nonadditive contribution to three-particle interaction is computed as a function of the temperature and the separation between disks. The benefit of the proposed method is that it lets us compute the multiparticle interaction explicitly.

The most common way of estimating the anomalous-diffusion exponent from single-particle trajectories consists in a linear fitting of the dependence of the time averaged mean square displacement on the lag time at the log-log scale. However, various measurement noises that are unavoidably present in experimental data can strongly deteriorate the quality of this estimation procedure and bias the estimated exponent. To investigate the impact of noises and to improve the estimation quality, we compare three approaches for estimating the anomalous-diffusion exponent and check their efficiency on fractional Brownian motion corrupted by Gaussian noise. We discuss how the parameters of both the anomalous-diffusion model and the estimation techniques influence the estimated exponent. We show that the conventional linear fitting is the least optimal method for the analysis of noisy data.