As an indicator of cooperative motion in a system of Brownian particles that models two-dimensional colloidal liquids, a displacement correlation tensor is calculated analytically and compared with numerical results. The key idea for the analytical calculation is to relate the displacement correlation tensor, which is a kind of four-point space-time correlation, to the Lagrangian two-time correlation of the deformation gradient tensor. Tensorial treatment of the statistical quantities, including the displacement correlation itself, allows capturing the vortical structure of the cooperative motion. The calculated displacement correlation also implies a negative long-time tail in the velocity autocorrelation, which is a manifestation of the cage effect. Both the longitudinal and transverse components of the displacement correlation are found to be expressible in terms of a similarity variable, suggesting that the cages are nested to form a self-similar structure in the space-time.

Uncertain recognition success, unfavorable scaling of connection complexity, or dependence on complex external input impair the usefulness of current oscillatory neural networks for pattern recognition or restrict technical realizations to small networks. We propose a network architecture of coupled oscillators for pattern recognition which shows none of the mentioned flaws. Furthermore we illustrate the recognition process with simulation results and analyze the dynamics analytically: Possible output patterns are isolated attractors of the system. Additionally, simple criteria for recognition success are derived from a lower bound on the basins of attraction.

We consider a class of adaptive network models where links can only be created or deleted between nodes in different states. These models provide an approximate description of a set of systems where nodes represent agents moving in physical or abstract space, the state of each node represents the agent's heading direction, and links indicate mutual awareness. We show analytically that the adaptive network description captures a phase transition to collective motion in some swarming systems, such as the Vicsek model, and that the properties of this transition are determined by the number of states (discrete heading directions) that can be accessed by each agent.

A complete lattice Boltzmann model (LBM) is proposed for the steady radiative transfer equation (RTE). The RTE can be regarded as a pure convection equation with a source term. To derive the expressions for the equilibrium distribution function and the relaxation time, an artificial isotropic diffusion term is introduced to form a convection-diffusion equation. When the dimensionless relaxation time has a value of 0.5, the lattice Boltzmann equation (LBE) is exactly applicable to the original steady RTE. We also perform a multiscale analysis based on the Chapman-Enskog expansion to recover the macroscopic RTE from the mesoscopic LBE. The D2Q9 model is used to solve the LBE, and the numerical results obtained by the LBM are comparable to the results obtained by other methods or analytical solutions, which demonstrates that the proposed model is highly accurate and stable in simulating multidimensional radiative transfer. In addition, we find that the convergence rate of the LBM depends on the transport properties of RTE: for diffusion-dominated RTE with a large optical thickness, the LBM shows a second-order convergence rate in space, while for convection-dominated RTE with a small optical thickness, a lower convergence rate is observed.

We consider continuous-time quantum walks (CTQWs) on multilayer dendrimer networks (MDs) and their application to quantum transport. A detailed study of properties of CTQWs is presented and transport efficiency is determined in terms of the exact and average return probabilities. The latter depends only on the eigenvalues of the connectivity matrix, which even for very large structures allows a complete analytical solution for this particular choice of network. In the case of MDs we observe an interplay between strong localization effects, due to the dendrimer topology, and good efficiency from the linear segments. We show that quantum transport is enhanced by interconnecting more layers of dendrimers.

We present an exact analysis of the physical properties of bimodal networks specified by the two peak degree distribution fully incorporating the degree-degree correlation between node connections. The structure of the correlated bimodal network is uniquely determined by the Pearson coefficient of the degree correlation, keeping its degree distribution fixed. The percolation threshold and the giant component fraction of the correlated bimodal network are analytically calculated in the whole range of the Pearson coefficient from $-1$ to 1 against two major types of node removal, which are the random failure and the degree-based targeted attack. The Pearson coefficient for next-nearest-neighbor pairs is also calculated, which always takes a positive value even when the correlation between nearest-neighbor pairs is negative. From the results, it is confirmed that the percolation threshold is a monotonically decreasing function of the Pearson coefficient for the degrees of nearest-neighbor pairs increasing from $-1$ and 1 regardless of the types of node removal. In contrast, the node fraction of the giant component for bimodal networks with positive degree correlation rapidly decreases in the early stage of random failure, while that for bimodal networks with negative degree correlation remains relatively large until the removed node fraction reaches the threshold. In this sense, bimodal networks with negative degree correlation are more robust against random failure than those with positive degree correlation.

Microswimmers such as bacteria perform random walks known as run-and-tumbles to move up chemoattractant gradients and as a result aggregate with others. It is also known that such micro-swimmers can self-organize into macroscopic patterns due to interactions with neighboring cells through the fluidic environment they live in. While the pattern formation resulting from chemotactic and hydrodynamic interactions separately and together have been previously investigated, the effect of the anisotropy in the tumbles of microswimmers has been unexplored. Here we show through linear analysis and full nonlinear simulations that the slight anisotropy in the individual swimmer tumbles can alter the collective pattern formation in nontrivial ways. We show that tumbling anisotropy diminishes the magnitude of the chemotactic aggregates but may result in more such aggregation peaks.

We present a data-driven framework to study the relationship between fluid flow at the macroscale and the internal pore structure, across the micro- and mesoscales, in porous, granular media. Sphere packings with varying particle size distribution and confining pressure are generated using the discrete element method. For each sample, a finite element analysis of the fluid flow is performed to compute the permeability. We construct a pore network and a particle contact network to quantify the connectivity of the pores and particles across the mesoscopic spatial scales. Machine learning techniques for feature selection are employed to identify sets of microstructural properties and multiscale complex network features that optimally characterize permeability. We find a linear correlation (in log-log scale) between permeability and the average closeness centrality of the weighted pore network. With the pore network links weighted by the local conductance, the average closeness centrality represents a multiscale measure of efficiency of flow through the pore network in terms of the mean geodesic distance (or shortest path) between all pore bodies in the pore network. Specifically, this study objectively quantifies a hypothesized link between high permeability and efficient shortest paths that thread through relatively large pore bodies connected to each other by high conductance pore throats, embodying connectivity and pore structure.

Velocity distributions in normal shock waves obtained in dilute granular flows are studied. These distributions cannot be described by a simple functional shape and are believed to be bimodal. Our results show that these distributions are not strictly bimodal but a trimodal distribution is shown to be sufficient. The usual Mott-Smith bimodal description of these distributions, developed for molecular gases, and based on the coexistence of two subpopulations (a supersonic and a subsonic population) in the shock front, can be modified by adding a third subpopulation. Our experiments show that this additional population results from collisions between the supersonic and subsonic subpopulations. We propose a simple approach incorporating the role of this third intermediate population to model the measured probability distributions and apply it to granular shocks as well as shocks in molecular gases.

The primary and key task of binary fluid flow modeling is to track the interface with good accuracy, which is usually challenging due to the sharp-interface limit and numerical dispersion. This article concentrates on further development of the conservative Allen-Cahn equation (ACE) [Geier et al., Phys. Rev. E 91, 063309 (2015)] under the framework of the lattice Boltzmann method (LBM), with incorporation of the incompressible hydrodynamic equations [Liang et al., Phys. Rev. E 89, 053320 (2014)]. Utilizing a modified equilibrium distribution function and an additional source term, this model is capable of correctly recovering the conservative ACE through the Chapman-Enskog analysis. We also simulate four phase-tracking benchmark cases, including one three-dimensional case; all show good accuracy as well as low numerical dispersion. By coupling the incompressible hydrodynamic equations, we also simulate layered Poiseuille flow and the Rayleigh-Taylor instability, illustrating satisfying performance in dealing with complex flow problems, e.g., high viscosity ratio, high density ratio, and high Reynolds number situations. The present work provides a reliable and efficient solution for binary flow modeling.

When a droplet of water impacts a heated surface, the drop may be observed to bounce. Recently is has been found that small quantities ($\sim 100$ ppm) of polymer additives such as polyethylene oxide can significantly increase the maximum bouncing height of drops. This effect has been explained in terms of the reduction of energy dissipation caused by polymer additives during the drop retraction and rebound, resulting in higher mechanical energy available for bouncing. Here we demonstrate, by comparing three types of fluids (Newtonian, shear-thinning, and viscoelastic), that the total kinetic energy carried by low-viscosity Newtonian drops during retraction is partly transformed into rotational kinetic energy rather than dissipated when compared with high-viscosity or non-Newtonian drops. We also show that non-Newtonian effects play little role in the energy distribution during drop impact, while the main effect is due to the symmetry break observed during the retraction of low-viscosity drops.

We outline a basic strategy of how self-propulsion can be used to improve the yield of a typical colloidal self-assembly process. The success of this approach is predicated on the thoughtful design of the colloidal building block as well as how self-propulsion is endowed to the particle. As long as a set of criteria are satisfied, it is possible to significantly increase the rate of self-assembly, and greatly expand the window in parameter space where self-assembly can occur. In addition, we show that by tuning the relative on-off time of the self-propelling force it is possible to modulate the effective speed of the colloids allowing for further optimization of the self-assembly process.

The shock dissemination of granular rings or shells is characterized by the formation of coherent particle jets that have different dimensions from those associated with the constituent grains. In order to identify the mechanisms governing the formation of particle jets, we carry out the simulations of the shock dispersal of quasi-two-dimensional particle rings based on the discrete-element method. The evolution of the particle velocities and contact forces on the time scales ranging from microseconds to milliseconds reveals a two-stage development of particle jets before they are expelled from the outer surface. Much effort is made to understand the particle agglomeration around the inner surface that initiates the jet formation. The shock interaction with the innermost particle layers generates a heterogeneous network of force chains with clusters of strong contacts regularly spaced around the inner surface. Momentum alongside the stresses is primarily transmitted along the strong force chains. Therefore, the clustering of strong force chains renders the agglomeration of fast-moving particles connected by strong force chains. The fast-moving particle clusters subsequently evolve into the incipient particle jets. The following competition among the incipient jets that undergo unbalanced growth leads to substantial elimination of the minor jets and the significant multiplication of the major jets, the number of jets thus varying with time. Moreover, the number of jets is found to increase with the strength of the shock loading due to an increased number of jets surviving the retarding effect of major jets.

We extend the (1+1)-dimensional fluid solid-on-solid (SOS) model to include a confining flat surface opposite to the SOS surface subject to a constant load. This load is balanced by a repulsive surface-surface interaction given by an ansatz which agrees with known analytical solutions in the limit of two separated flat surfaces. Mechanical equilibrium is imposed at all times by repositioning the confining surface. By the use of kinetic Monte Carlo (KMC) we calculate how the equilibrium concentration (deposition rate) depends on the applied load, and find it to reproduce analytical thermodynamics independent of the parameters of the interaction ansatz. We also study the dependency between the surface roughness and the saturation level as we vary the surface tension, and expand on previous analyses of the asymmetry between growth and dissolution by parametrizing the linear growth rate constant for growth and dissolution separately. We find the presence of a confining surface to affect the speed of growth and dissolution equally.

An accurate understanding of burn dynamics in implosions of cryogenically layered deuterium (D) and tritium (T) filled capsules, obtained partly through precision diagnosis of these experiments, is essential for assessing the impediments to achieving ignition at the National Ignition Facility. We present measurements of neutrons from such implosions. The apparent ion temperatures $T_{\mathrm{ion}}$ are inferred from the variance of the primary neutron spectrum. Consistently higher DT than DD $T_{\mathrm{ion}}$ are observed and the difference is seen to increase with increasing apparent DT $T_{\mathrm{ion}}$. The line-of-sight rms variations of both DD and DT $T_{\mathrm{ion}}$ are small, $\sim 150\mathrm{eV}$, indicating an isotropic source. The DD neutron yields are consistently high relative to the DT neutron yields given the observed $T_{\mathrm{ion}}$. Spatial and temporal variations of the DT temperature and density, DD-DT differential attenuation in the surrounding DT fuel, and fluid motion variations contribute to a DT $T_{\mathrm{ion}}$ greater than the DD $T_{\mathrm{ion}}$, but are in a one-dimensional model insufficient to explain the data. We hypothesize that in a three-dimensional interpretation, these effects combined could explain the results.

Particle simulations confined by sharp walls usually develop an oscillatory density profile. For some applications, most notably soft matter liquids, this behavior is often unrealistic and one expects a monotonic density climb instead. To reconcile simulations with experiments, we propose mirror-and-shift boundary conditions where each interface is mapped to a distant part of itself. The main result is that the particle density increases almost monotonically from zero to bulk, over a short distance of about one particle diameter. The method is applied to simulate a polymer brush in explicit solvent, grafted on a flat silicon substrate. The simulated density profile agrees favorably with neutron reflectometry measurements and self-consistent field theory results.

A recent proposal of an effective temperature $\theta$, conjugated to a generalized entropy $s_q$, typical of nonextensive statistical mechanics, has led to a consistent thermodynamic framework in the case $q=2$. The proposal was explored for repulsively interacting vortices, currently used for modeling type-II superconductors. In these systems, the variable $\theta$ presents values much higher than those of typical room temperatures $T$, so that the thermal noise can be neglected ($T/\theta \simeq 0$). The whole procedure was developed for an equilibrium state obtained after a sufficiently long-time evolution, associated with a nonlinear Fokker-Planck equation and approached due to a confining external harmonic potential, $\varphi \left(x\right)=\alpha x^2/2$ ($\alpha >0$). Herein, the thermodynamic framework is extended to a quite general confining potential, namely $\varphi \left(x\right)={\alpha \left|x\right|}^z/z$ ($z>1$). It is shown that the main results of the previous analyses hold for any $z>1$: (i) The definition of the effective temperature $\theta$ conjugated to the entropy $s_2$. (ii) The construction of a Carnot cycle, whose efficiency is shown to be $\eta =1-({\theta }_2/{\theta }_1)$, where ${\theta }_1$ and ${\theta }_2$ are the effective temperatures associated with two isothermal transformations, with ${\theta }_1>{\theta }_2$. The special character of the Carnot cycle is indicated by analyzing another cycle that presents an efficiency depending on $z$. (iii) Applying Legendre transformations for a distinct pair of variables, different thermodynamic potentials are obtained, and furthermore, Maxwell relations and response functions are derived. The present approach shows a consistent thermodynamic framework, suggesting that these results should hold for a general confining potential $\varphi \left(x\right)$, increasing the possibility of experimental verifications.

The purpose of this paper is to provide a formula for the effective diffusion operator obtained by projecting the three-dimensional diffusion equation onto a two-dimensional plane, assuming reflective boundary conditions at two surfaces in three-dimensional space and a finite transversal stabilization rate.

Disordered many-particle hyperuniform systems are exotic amorphous states of matter that lie between crystal and liquid: They are like perfect crystals in the way they suppress large-scale density fluctuations and yet are like liquids or glasses in that they are statistically isotropic with no Bragg peaks. These exotic states of matter play a vital role in a number of problems across the physical, mathematical as well as biological sciences and, because they are endowed with novel physical properties, have technological importance. Given the fundamental as well as practical importance of disordered hyperuniform systems elucidated thus far, it is natural to explore the generalizations of the hyperuniformity notion and its consequences. In this paper, we substantially broaden the hyperuniformity concept along four different directions. This includes generalizations to treat fluctuations in the interfacial area (one of the Minkowski functionals) in heterogeneous media and surface-area driven evolving microstructures, random scalar fields, divergence-free random vector fields, and statistically anisotropic many-particle systems and two-phase media. In all cases, the relevant mathematical underpinnings are formulated and illustrative calculations are provided. Interfacial-area fluctuations play a major role in characterizing the microstructure of two-phase systems (e.g., fluid-saturated porous media), physical properties that intimately depend on the geometry of the interface, and evolving two-phase microstructures that depend on interfacial energies (e.g., spinodal decomposition). In the instances of random vector fields and statistically anisotropic structures, we show that the standard definition of hyperuniformity must be generalized such that it accounts for the dependence of the relevant spectral functions on the direction in which the origin in Fourier space is approached (nonanalyticities at the origin). Using this analysis, we place some well-known energy spectra from the theory of isotropic turbulence in the context of this generalization of hyperuniformity. Among other results, we show that there exist many-particle ground-state configurations in which directional hyperuniformity imparts exotic anisotropic physical properties (e.g., elastic, optical, and acoustic characteristics) to these states of matter. Such tunability could have technological relevance for manipulating light and sound waves in ways heretofore not thought possible. We show that disordered many-particle systems that respond to external fields (e.g., magnetic and electric fields) are a natural class of materials to look for directional hyperuniformity. The generalizations of hyperuniformity introduced here provide theoreticians and experimentalists new avenues to understand a very broad range of phenomena across a variety of fields through the hyperuniformity “lens.”