We study boundary lubrication characteristics of a liquid crystal (LC) monolayer sheared between two crystalline surfaces by nonequilibrium molecular dynamics simulations, using a simplified rigid bead-necklace model of the LC molecules. We consider LC monolayers confined by surfaces with three different atomic structures, subject to different shearing velocities, thus approximating a wide variety of materials and driving conditions. The time dependence of the friction force is studied and correlated with that of the orientational order exhibited by the LC molecules, arising from the competition between the effect of the structure of the confining surfaces and that of the imposed sliding direction. We show that the observed stick-slip events for low shear rates involve order-disorder transitions, and that the LC monolayer no longer has enough time to reorder at high shear rates, resulting in a smooth sliding regime. An irregular stick-slip phase between the regular stick-slip and smooth sliding is observed for intermediate shear rates regardless of the surface structure.

Recent years have witnessed the development of a large body of algorithms for community detection in complex networks. Most of them are based upon the optimization of objective functions, among which modularity is the most common, though a number of alternatives have been suggested in the scientific literature. We present here an effective general search strategy for the optimization of various objective functions for community detection purposes. When applied to modularity, on both real-world and synthetic networks, our search strategy substantially outperforms the best existing algorithms in terms of final scores of the objective function. In terms of execution time for modularity optimization this approach also outperforms most of the alternatives present in literature with the exception of fastest but usually less efficient greedy algorithms. The networks of up to $30000$ nodes can be analyzed in time spans ranging from minutes to a few hours on average workstations, making our approach readily applicable to tasks not limited by strict time constraints but requiring the quality of partitioning to be as high as possible. Some examples are presented in order to demonstrate how this quality could be affected by even relatively small changes in the modularity score stressing the importance of optimization accuracy.

The effect of various velocity boundary condition is studied in two-dimensional Rayleigh-Bénard convection. Combinations of no-slip, stress-free, and periodic boundary conditions are used on both the sidewalls and the horizontal plates. For the studied Rayleigh numbers $\text{Ra}$ between ${10}^8$ and ${10}^{11}$ the heat transport is lower for $\Gamma =0.33$ than for $\Gamma =1$ in case of no-slip sidewalls. This is, surprisingly, the opposite for stress-free sidewalls, where the heat transport increases for a lower aspect ratio. In wider cells the aspect-ratio dependence is observed to disappear for $\text{Ra}\ge {10}^{10}$. Two distinct flow types with very different dynamics can be seen, mostly dependent on the plate velocity boundary condition, namely roll-like flow and zonal flow, which have a substantial effect on the dynamics and heat transport in the system. The predominantly horizontal zonal flow suppresses heat flux and is observed for stress-free and asymmetric plates. Low aspect-ratio periodic sidewall simulations with a no-slip boundary condition on the plates also exhibit zonal flow. In all the other cases, the flow is roll like. In two-dimensional Rayleigh-Bénard convection, the velocity boundary conditions thus have large implications on both roll-like and zonal flow that have to be taken into consideration before the boundary conditions are imposed.

We present a detailed direct numerical simulation of statistically steady, homogeneous, isotropic, two-dimensional magnetohydrodynamic turbulence. Our study concentrates on the inverse cascade of the magnetic vector potential. We examine the dependence of the statistical properties of such turbulence on dissipation and friction coefficients. We extend earlier work significantly by calculating fluid and magnetic spectra, probability distribution functions (PDFs) of the velocity, magnetic, vorticity, current, stream-function, and magnetic-vector-potential fields, and their increments. We quantify the deviations of these PDFs from Gaussian ones by computing their flatnesses and hyperflatnesses. We also present PDFs of the Okubo-Weiss parameter, which distinguishes between vortical and extensional flow regions, and its magnetic analog. We show that the hyperflatnesses of PDFs of the increments of the stream function and the magnetic vector potential exhibit significant scale dependence and we examine the implication of this for the multiscaling of structure functions. We compare our results with those of earlier studies.

We numerically examine run-and-tumble active matter particles in Casimir geometries composed of two finite parallel walls. We find that there is an attractive force between the two walls of a magnitude that increases with increasing run length. The attraction exhibits an unusual exponential dependence on the wall separation, and it arises due to a depletion of swimmers in the region between the walls by a combination of the motion of the particles along the walls and a geometric shadowing effect. This attraction is robust as long as the wall length is comparable to or smaller than the swimmer run length, and is only slightly reduced by the inclusion of steric interactions between swimmers. We also examine other geometries and find regimes in which there is a crossover from attraction to repulsion between the walls as a function of wall separation and wall length.

We study the $k$-NN hard-core lattice gas model in which the first $k$ next-nearest-neighbor sites of a particle are excluded from occupation by other particles on a two-dimensional square lattice. This model is the lattice version of the hard-disk system with increasing $k$ corresponding to decreasing lattice spacing. While the hard-disk system is known to undergo a two-step freezing process with increasing density, the lattice model has been known to show only one transition. Here, based on Monte Carlo simulations and high-density expansions of the free energy and density, we argue that for $k=4,10,11,14,\cdots$, the lattice model undergoes multiple transitions with increasing density. Using Monte Carlo simulations, we confirm the same for $k=4,...,11$. This, in turn, resolves an existing puzzle as to why the 4-NN model has a continuous transition against the expectation of a first-order transition.

Considering any Hamiltonian, any initial state, and measurements with a small number of possible outcomes compared to the dimension, we show that most measurements are already equilibrated. To investigate nontrivial equilibration, we therefore consider a restricted set of measurements. When the initial state is spread over many energy levels, and we consider the set of observables for which this state is an eigenstate, most observables are initially out of equilibrium yet equilibrate rapidly. Moreover, all two-outcome measurements, where one of the projectors is of low rank, equilibrate rapidly.

Order-disorder phase transition of the ferromagnetic Ising model is investigated on a series of two-dimensional lattices that have negative Gaussian curvatures. Exceptional lattice sites of coordination number seven are distributed on the triangular lattice, where the typical distance between the nearest exceptional sites is proportional to an integer parameter $n$. Thus, the corresponding curvature is asymptotically proportional to $-n_{}^{-2}$. Spontaneous magnetization and specific heat are calculated by means of the corner transfer matrix renormalization group method. For all the finite $n$ cases, we observe the mean-field-like phase transition. It is confirmed that the entanglement entropy at the transition temperature is linear in $(c/6)lnn$, where $c=1/2$ is the central charge of the Ising model. The fact agrees with the presence of the typical length scale $n$ being proportional to the curvature radius.

The temporal evolution of equilibrium fluctuations for surface steps of monatomic height is analyzed studying one-dimensional solid-on-solid models. Using Monte Carlo simulations, fluctuations due to periphery diffusion (PD) as well as due to evaporation and condensation are considered, both for isolated steps and for steps confined by the presence of straight steps. For isolated steps, the dependence of the characteristic power laws, their exponents, and prefactors on temperature, slope, and curvature is elucidated, with the main emphasis on PD, taking into account finite-size effects. The entropic repulsion due to a second straight step may lead, among other things, to an interesting transient power-law-like growth of the fluctuations, for PD. Findings are compared to results of previous Monte Carlo simulations and predictions based, mostly, on scaling arguments and Langevin theory.

We study the dynamics of inertial particles in three-dimensional incompressible maps, as representations of volume-preserving flows. The impurity dynamics has been modeled, in the Lagrangian framework, by a six-dimensional dissipative bailout embedding map. The fluid-parcel dynamics of the base map is embedded in the particle dynamics governed by the map. The base map considered for the present study is the Arnold-Beltrami-Childress (ABC) map. We consider the behavior of the system both in the aerosol regime, where the density of the particle is larger than that of the base flow, as well as the bubble regime, where the particle density is less than that of the base flow. The phase spaces in both the regimes show rich and complex dynamics with three types of dynamical behaviors—chaotic structures, regular orbits, and hyperchaotic regions. In the one-action case, the aerosol regime is found to have periodic attractors for certain values of the dissipation and inertia parameters. For the aerosol regime of the two-action ABC map, an attractor merging and widening crisis is identified using the bifurcation diagram and the spectrum of Lyapunov exponents. After the crisis an attractor with two parts is seen, and trajectories hop between these parts with period 2. The bubble regime of the embedded map shows strong hyperchaotic regions as well as crisis induced intermittency with characteristic times between bursts that scale as a power law behavior as a function of the dissipation parameter. Furthermore, we observe a riddled basin of attraction and unstable dimension variability in the phase space in the bubble regime. The bubble regime in the one-action case shows similar behavior. This study of a simple model of impurity dynamics may shed light upon the transport properties of passive scalars in three-dimensional flows. We also compare our results with those seen earlier in two-dimensional flows.

An alternative way for the derivation of the new Korteweg–de Vries (KdV)-type equation is presented. The equation contains terms depending on the bottom topography (there are six new terms in all, three of which are caused by the unevenness of the bottom). It is obtained in the second-order perturbative approach in the weakly nonlinear, dispersive, and long wavelength limit. Only treating all these terms in the second-order perturbation theory made the derivation of this KdV-type equation possible. The motion of a wave, which starts as a KdV soliton, is studied according to the new equation in several cases by numerical simulations. The quantitative changes of a soliton's velocity and amplitude appear to be directly related to bottom variations. Changes of the soliton's velocity appear to be almost linearly anticorrelated with changes of water depth, whereas correlation of variation of soliton's amplitude with changes of water depth looks less linear. When the bottom is flat, the new terms narrow down the family of exact solutions, but at least one single soliton survives. This is also checked by numerics.

Recently, anomalous scaling properties of front broadening during spontaneous imbibition of water in Vycor glass, a nanoporous medium, were reported: the mean height and the width of the propagating front increase with time $t$ both proportional to $t^{1/2}$. Here, we propose a simple lattice imbibition model and elucidate quantitatively how the correlation range of the hydrostatic pressure and the disorder strength of the pore radii affect the scaling properties of the imbibition front. We introduce an effective tension of liquid across neighboring pores, which depends on the aspect ratio of each pore, and show that it leads to a dynamical crossover: both the mean height and the roughness grow faster in the presence of tension in the intermediate-time regime but eventually saturate in the long-time regime. The universality class of the long-time behavior is discussed by examining the associated scaling exponents and their relation to directed percolation.

The mechanical response of a circularly driven disk in a dissipative medium is considered. We focus on the role played by viscous friction in the spinning motion of the disk, especially on the effect called reverse rotation, where the intrinsic and orbital rotations are antiparallel. Contrary to what happens in the frictionless case, where steady reverse rotations are possible, we find that this dynamical behavior may exist only as a transient when dissipation is considered. Whether or not reverse rotations in fact occur depends on the initial conditions and on two parameters, one related to dragging, inertia, and driving, the other associated with the geometric configuration of the system. The critical value of this geometric parameter (separating the regions where reverse rotation is possible from those where it is forbidden) as a function of viscosity is well adjusted by a $q$-exponential function.

Kinetic and fluid equations are derived for the dynamics of classical inhomogeneous trapped plasmas in the strong coupling regime. The starting point is an extended Singwi-Tosi-Land-Sjölander (STLS) ansatz for the dynamic correlation function, which is allowed to depend on time and both particle coordinates separately. The time evolution of the correlation function is determined from the second equation of the Bogolyubov-Born-Green-Kirkwood-Yvon hierarchy. We study the equations in the linear limit and derive a nonlocal equation for the fluid displacement field. Comparisons to first-principles molecular dynamics simulations reveal an excellent quality of our approach thereby overcoming the limitations of the broadly used STLS scheme.

In this article we use optimal control to maximize the efficiency of a quantum heat engine executing the Otto cycle in the presence of external noise. We optimize the engine performance for both amplitude and phase noise. In the case of phase damping we additionally show that the ideal performance of a noiseless engine can be retrieved in the adiabatic (long time) limit. The results obtained here are useful in the quest for absolute zero, the design of quantum refrigerators that can cool a physical system to the lowest possible temperature. They can also be applied to the optimal control of a collection of classical harmonic oscillators sharing the same time-dependent frequency and subjected to similar noise mechanisms. Finally, our methodology can be used for the optimization of other interesting thermodynamic processes.

We present a detailed analysis of the morphology of granular systems composed of frictionless pentagonal particles by varying systematically both the size span and particle shape irregularity, which represent two polydispersity parameters of the system. The microstructure is characterized in terms of various statistical descriptors such as global and local packing fractions, radial distribution functions, coordination number, and fraction of floating particles. We find that the packing fraction increases with the two parameters of polydispersity, but the effect of shape polydispersity for all the investigated structural properties is significant only at low size polydispersity where the positional and/or orientational ordering of the particles prevail. We focus in more detail on the class of side/side contacts, which is the interesting feature of our system as compared to a packing of disks. We show that the proportion of such contacts has weak dependence on the polydispersity parameters. The side- side contacts do not percolate but they define clusters of increasing size as a function of size polydispersity and decreasing size as a function of shape polydispersity. The clusters have anisotropic shapes but with a decreasing aspect ratio as polydispersity increases. This feature is argued to be a consequence of strong force chains (forces above the mean), which are mainly captured by side-side contacts. Finally, the force transmission is intrinsically multiscale, with a mean force increasing linearly with particle size.

Leukocytes and other circulating cells deform and move relatively to the channel flow in the lateral and translational directions. Their migratory property is important in immune response, hemostasis, cancer progression, delivery of nutrients, and microfluidic technologies such as cell separation and enrichment, and flow cytometry. Using our three-dimensional computational algorithm for multiphase viscoelastic flow, we have investigated the effect of pairwise interaction on the lateral and translational migration of circulating cells in a microchannel. The numerical simulation data show that when two cells with the same size and small separation distance interact, repulsive interaction take place until they reach the same lateral equilibrium position. During this process, they undergo swapping or passing, depending on the initial separation distance between each other. The threshold value of this distance increases with cell deformation, indicating that the cells experiencing larger deformation are more likely to swap. When a series of closely spaced cells with the same size are considered, they generally undergo damped oscillation in both lateral and translational directions until they reach equilibrium positions where they become evenly distributed in the flow direction (self-assembly phenomenon). A series of cells with a large lateral separation distance could collide repeatedly with each other, eventually crossing the centerline and entering the other side of the channel. For a series of cells with different deformability, more deformable cells, upon impact with less deformable cells, move to an equilibrium position closer to the centerline. The results of our study show that the bulk deformation of circulating cells plays a key role in their migration in a microchannel.

We consider a model for the diffusion of epidemics in a population that is partitioned into local communities. In particular, assuming a mean-field approximation, we analyze a continuous-time susceptible-infected-susceptible (SIS) model that has appeared recently in the literature. The probability by which an individual infects individuals in its own community is different from the probability of infecting individuals in other communities. The aim of the model, compared to the standard, nonclustered one, is to provide a compact description for the presence of communities of local infection where the epidemic process is faster compared to the rate at which it spreads across communities. Ultimately, it provides a tool to express the probability of epidemic outbreaks in the form of a metastable infection probability. In the proposed model, the spatial structure of the network is encoded by the adjacency matrix of clusters, i.e., the connections between local communities, and by the vector of the sizes of local communities. Thus, the existence of a nontrivial metastable occupancy probability is determined by an epidemic threshold which depends on the clusters' size and on the intercommunity network structure.

We investigate numerically the dynamics of a propagating front in the presence of a spatiotemporally chaotic flow field. The flow field is the three-dimensional time-dependent state of spiral defect chaos generated by Rayleigh-Bénard convection in a spatially extended domain. Using large-scale parallel numerical simulations, we simultaneously solve the Boussinesq equations and a reaction-advection-diffusion equation with a Fischer-Kolmogorov-Petrovskii-Piskunov reaction for the transport of the scalar species in a large-aspect-ratio cylindrical domain for experimentally accessible conditions. We explore the front dynamics and geometry in the low-Damköhler-number regime, where the effect of the flow field is significant. Our results show that the chaotic flow field enhances the front propagation when compared with a purely cellular flow field. We quantify this enhancement by computing the spreading rate of the reaction products for a range of parameters. We use our results to quantify the complexity of the three-dimensional front geometry for a range of chaotic flow conditions.