We study the vertical Brownian motion of a gold particle levitated by a repulsive Casimir force to a silica plate immersed in bromobenzene. The time evolution of the particle distribution starting from an equilibrium position, where the Casimir force and gravitational force are balanced, is considered by solving the Langevin equation using the Monte Carlo method. When the gold particle is very close to the silica plate, the Casimir force changes from repulsive to attractive, and the particle eventually sticks to the surface. The escape rate from a metastable position is calculated by solving the Fokker-Plank equation; it agrees with the value obtained by Kramers’ escape theory. The duration of levitation increases as the particle radius increases up to around 2.3 $\mu$m. As an example, we show that a 1-$\mu$m-diameter gold particle can be levitated for a significantly long time by the repulsive Casimir force at room temperature.

Information exchange dynamics of the two-dimensional $XY$ model is studied by means of the entropic sampling algorithm. Combining the analytic and numerical results, we obtain the entropy in the whole range of the energy at various system sizes. The time evolution of the order parameter and of the number of vortices is explored, and the corresponding relaxation times are found to grow algebraically with the system size. Such absence of characteristic time scales in the thermodynamic limit manifests the emergent criticality of the exchanging process of information with the environment. The mechanism of information exchange in the $XY$ model is discussed in terms of the dynamic exponents, in comparison with the Ising model.

We study the thermal phase transitions in a classical (hard-core) lattice gas model with nearest-neighbor three-body interactions on the honeycomb lattice, based on parallel tempering Monte Carlo simulations. This system realizes incompressible low-temperature phases at fractional fillings of $9/16$, $5/8,$ and $3/4$ that were identified in a previous study of a related quantum model. In particular, both the $9/16$ and the $5/8$ phase exhibit an extensive ground-state degeneracy reflecting the frustrated nature of the three-body interactions on the honeycomb lattice. The thermal melting of the $9/16$ phase is found to be a first-order, discontinuous phase transition. On the other hand, from the thermodynamic behavior we obtain indications for a four-states Potts-model thermal transition out of the $5/8$ phase. We find that this thermal Potts-model transition relates to the selection of one out of four extensive sectors within the low-energy manifold of the $5/8$ phase, which we obtain via an exact mapping of the ground-state manifold to a hard-core dimer model on an embedded honeycomb superlattice.

We perform numerical simulations of repulsive, frictionless athermal disks in two and three spatial dimensions undergoing cyclic quasistatic simple shear to investigate particle-scale reversible motion. We identify three classes of steady-state dynamics as a function of packing fraction $\varphi$ and maximum strain amplitude per cycle ${\gamma }_{\max }$. Point-reversible states, where particles do not collide and exactly retrace their intracycle trajectories, occur at low $\varphi$ and ${\gamma }_{\max }$. Particles in loop-reversible states undergo numerous collisions and execute complex trajectories but return to their initial positions at the end of each cycle. For sufficiently large $\varphi$ and ${\gamma }_{\max }$, systems display irreversible dynamics with nonzero self-diffusion. Loop-reversible dynamics enables the reliable preparation of configurations with specified structural and mechanical properties over a broad range of $\varphi$.

We revisit the mean-field limiting law screening excess sum rule that holds for rodlike polyelectrolytes. We present an efficient derivation of this law that clarifies its region of applicability: The law holds in the limit of small polymer radius, measured relative to the Debye screening length. From the limiting law, we determine the individual ion excess values for single-salt electrolytes. We also consider the mean-field excess sum away from the limiting region, and we relate this quantity to the osmotic pressure of a dilute polyelectrolyte solution. Finally, we consider numerical simulations of many-body polymer-electrolyte solutions. We conclude that the limiting law often accurately describes the screening of physical charged polymers of interest, such as extended DNA.

We investigate evolution models with recombination and neutrality. We consider the Crow-Kimura (parallel) mutation-selection model with the neutral fitness landscape, in which there is a central peak with high fitness $A$, and some of 1-point mutants have the same high fitness $A$, while the fitness of other sequences is 0. We find that the effect of recombination and neutrality depends on the concrete version of both neutrality and recombination. We consider three versions of neutrality: (a) all the nearest neighbor sequences of the peak sequence have the same high fitness $A$; (b) all the $l$-point mutations in a piece of genome of length $l\ge 1$ are neutral; (c) the neutral sequences are randomly distributed among the nearest neighbors of the peak sequences. We also consider three versions of recombination: (I) the simple horizontal gene transfer (HGT) of one nucleotide; (II) the exchange of a piece of genome of length $l$, HGT-$l$; (III) two-point crossover recombination (2CR). For the case of (a), the 2CR gives a rather strong contribution to the mean fitness, much stronger than that of HGT for a large genome length $L$. For the random distribution of neutral sequences there is a critical degree of neutrality ${\nu }_c$, and for $\mu <{\mu }_c$ and (${\mu }_c-\mu$) is not large, the 2CR suppresses the mean fitness while HGT increases it; for $\nu$ much larger than ${\nu }_c$, the 2CR and HGT-$l$ increase the mean fitness larger than that of the HGT. We also consider the recombination in the case of smooth fitness landscapes. The recombination gives some advantage in the evolutionary dynamics, where recombination distinguishes clearly the mean-field-like evolutionary factors from the fluctuation-like ones. By contrast, mutations affect the mean-field-like and fluctuation-like factors similarly. Consequently, recombination can accelerate the non-mean-field (fluctuation) type dynamics without considerably affecting the mean-field-like factors.

In this work, we develop a theoretical model to explain the equilibrium spheroidal deformation of a giant unilamellar vesicle (GUV) under an alternating (ac) electric field. Suspended in a leaky dielectric fluid, the vesicle membrane is modeled as a thin capacitive spheroidal shell. The equilibrium vesicle shape results from the balance between mechanical forces from the viscous fluid, the restoring elastic membrane forces, and the externally imposed electric forces. Our spheroidal model predicts a deformation-dependent transmembrane potential, and is able to capture large deformation of a vesicle under an electric field. A detailed comparison against both experiments and small-deformation (quasispherical) theory showed that the spheroidal model gives better agreement with experiments in terms of the dependence on fluid conductivity ratio, permittivity ratio, vesicle size, electric field strength, and frequency. The spheroidal model also allows for an asymptotic analysis on the crossover frequency where the equilibrium vesicle shape crosses over between prolate and oblate shapes. Comparisons show that the spheroidal model gives better agreement with experimental observations.

A one-dimensional hyperbolic reaction-diffusion model of epidemics is developed to describe the dynamics of diseases spread occurring in an environment where three kinds of individuals mutually interact: the susceptibles, the infectives, and the removed. It is assumed that the disease is transmitted from the infected population to the susceptible one according to a nonlinear convex incidence rate. The model, based upon the framework of extended thermodynamics, removes the unphysical feature of instantaneous diffusive effects, which is typical of parabolic models. Linear stability analyses are performed to study the nature of the equilibrium states against uniform and nonuniform perturbations. Emphasis is given to the occurrence of Hopf and Turing bifurcations, which break the temporal and the spatial symmetry of the system, respectively. The existence of traveling wave solutions connecting two steady states is also discussed. The governing equations are also integrated numerically to validate the analytical results and to characterize the spatiotemporal evolution of diseases.

Adapting grid density to flow behavior provides the advantage of increasing solution accuracy while decreasing the number of grid elements in the simulation domain, therefore reducing the computational time. One method for grid adaptation requires successive refinement of grid density based on observed solution behavior until the numerical errors between successive grids are negligible. However, such an approach is time consuming and it is often neglected by the researchers. We present a technique to calculate the grid size distribution of an adaptive grid for computational fluid dynamics (CFD) simulations in a complex cerebral aneurysm geometry based on the kinematic curvature and torsion calculated from the velocity field. The relationship between the kinematic characteristics of the flow and the element size of the adaptive grid leads to a mathematical equation to calculate the grid size in different regions of the flow. The adaptive grid density is obtained such that it captures the more complex details of the flow with locally smaller grid size, while less complex flow characteristics are calculated on locally larger grid size. The current study shows that kinematic curvature and torsion calculated from the velocity field in a cerebral aneurysm can be used to find the locations of complex flow where the computational grid needs to be refined in order to obtain an accurate solution. We found that the complexity of the flow can be adequately described by velocity and vorticity and the angle between the two vectors. For example, inside the aneurysm bleb, at the bifurcation, and at the major arterial turns the element size in the lumen needs to be less than $10\%$ of the artery radius, while at the boundary layer, the element size should be smaller than $1\%$ of the artery radius, for accurate results within a $0.5\%$ relative approximation error. This technique of quantifying flow complexity and adaptive remeshing has the potential to improve results accuracy and reduce computational time for patient-specific hemodynamics simulations, which are used to help assess the likelihood of aneurysm rupture using CFD calculated flow patterns.

From transportation networks to complex infrastructures, and to social and communication networks, a large variety of systems can be described in terms of multiplexes formed by a set of nodes interacting through different networks (layers). Multiplexes may display an increased fragility with respect to the single layers that constitute them. However, so far the overlap of the links in different layers has been mostly neglected, despite the fact that it is an ubiquitous phenomenon in most multiplexes. Here, we show that the overlap among layers can improve the robustness of interdependent multiplex systems and change the critical behavior of the percolation phase transition in a complex way.

The increasing availability of time- and space-resolved data describing human activities and interactions gives insights into both static and dynamic properties of human behavior. In practice, nevertheless, real-world data sets can often be considered as only one realization of a particular event. This highlights a key issue in social network analysis: the statistical significance of estimated properties. In this context, we focus here on the assessment of quantitative features of specific subset of nodes in empirical networks. We present a method of statistical resampling based on bootstrapping groups of nodes under constraints within the empirical network. The method enables us to define acceptance intervals for various null hypotheses concerning relevant properties of the subset of nodes under consideration in order to characterize by a statistical test its behavior as “normal” or not. We apply this method to a high-resolution data set describing the face-to-face proximity of individuals during two colocated scientific conferences. As a case study, we show how to probe whether colocating the two conferences succeeded in bringing together the two corresponding groups of scientists.

A time series analysis method for predicting the probability density of a dynamical system is proposed. A nonstationary parametric model of the probability density is estimated from data within a maximum likelihood framework and then extrapolated to forecast the future probability density and explore the system for critical transitions or tipping points. A full systematic account of parameter uncertainty is taken. The technique is generic, independent of the underlying dynamics of the system. The method is verified on simulated data and then applied to prediction of Arctic sea-ice extent.

The onset of transient Soret-driven convection is investigated experimentally in a colloidal suspension of thermosensitive nanoparticles by the shadowgraph technique and by particle tracking observations. From the shadowgraph images, the concentration profile is reconstructed, giving evidence of a convective motion inside the transient boundary layer. Furthermore, the latency times for the convection onset are extracted from the measurements. The results point out that particle tracking is superior to the shadowgraph method for detecting the onset of convection. The onset latency times obtained from these experiments obey scaling laws which are in accordance with the predictions from theoretical treatments.

The lattice Boltzmann method has been shown to be successful for microscale gas flows, and it has attracted significant research interest. In this paper, the recently proposed filter-matrix lattice Boltzmann (FMLB) model is first applied to study the microchannel gas flows, in which a Bosanquet-type effective viscosity is used to capture the flow behaviors in the transition regime. A kinetic boundary condition, the combined bounce-back and specular-reflection scheme with the second-order slip scheme, is also designed for the FMLB model. By analyzing a unidirectional flow, the slip velocity and the discrete effects related to the boundary condition are derived within the FMLB model, and a revised scheme is presented to overcome such effects, which have also been validated through numerical simulations. To gain an accurate simulation in a wide range of Knudsen numbers, covering the slip and the entire transition flow regimes, a set of slip coefficients with an introduced fitting function is adopted in the revised second-order slip boundary condition. The periodic and pressure-driven microchannel flows have been investigated by the present model in this study. The numerical results, including the velocity profile and the mass flow rate, as well as the nonlinear pressure distribution along the channel, agree fairly well with the solutions of the linearized Boltzmann equation, the direct simulation Monte Carlo results, the experimental data, and the previous results of the multiple effective relaxation lattice Boltzmann model. Also, the present results of the velocity profile and the mass flow rate show that the present model with the fitting function can yield improved predictions for the microchannel gas flow with higher Knudsen numbers in the transition flow regime.

The study of the packing of hard hyperspheres in $d$-dimensional Euclidean space ${\mathbb{R}}^d$ has been a topic of great interest in statistical mechanics and condensed matter theory. While the densest known packings are ordered in sufficiently low dimensions, it has been suggested that in sufficiently large dimensions, the densest packings might be disordered. The random sequential addition (RSA) time-dependent packing process, in which congruent hard hyperspheres are randomly and sequentially placed into a system without interparticle overlap, is a useful packing model to study disorder in high dimensions. Of particular interest is the infinite-time saturation limit in which the available space for another sphere tends to zero. However, the associated saturation density has been determined in all previous investigations by extrapolating the density results for nearly saturated configurations to the saturation limit, which necessarily introduces numerical uncertainties. We have refined an algorithm devised by us [S. Torquato, O. U. Uche, and F. H. Stillinger, Phys. Rev. E 74, 061308 (2006)] to generate RSA packings of identical hyperspheres. The improved algorithm produce such packings that are guaranteed to contain no available space in a large simulation box using finite computational time with heretofore unattained precision and across the widest range of dimensions ($2\le d\le 8$). We have also calculated the packing and covering densities, pair correlation function $g_2\left(r\right)$, and structure factor $S\left(k\right)$ of the saturated RSA configurations. As the space dimension increases, we find that pair correlations markedly diminish, consistent with a recently proposed “decorrelation” principle, and the degree of “hyperuniformity” (suppression of infinite-wavelength density fluctuations) increases. We have also calculated the void exclusion probability in order to compute the so-called quantizer error of the RSA packings, which is related to the second moment of inertia of the average Voronoi cell. Our algorithm is easily generalizable to generate saturated RSA packings of nonspherical particles.

We synthesize colloidal particles with various anisotropic shapes and track their orientationally resolved Brownian trajectories using confocal microscopy. An analysis of appropriate short-time correlation functions provides direct access to the hydrodynamic friction tensor of the particles revealing nontrivial couplings between the translational and rotational degrees of freedom. The results are consistent with calculations of the hydrodynamic friction tensor in the low-Reynolds-number regime for the experimentally determined particle shapes.

Kinetics of the deposition process of dimers in the presence of desorption is studied by Monte Carlo method on a one-dimensional lattice. The aim of this work is to investigate how do various temporal dependencies of the desorption rate hasten or slow down the deposition process. The growth of the coverage $\theta \left(t\right)$ above the jamming limit to its steady-state value ${\theta }_{\infty }$ is analyzed when the desorption probability $P_{\mathrm{des}}$ decreases both stepwise and linearly (continuously) over a certain time domain. We report a numerical evidence that the time needed for a system to reach the given coverage $\theta$ can be significantly reduced if $P_{\mathrm{des}}$ decreases in time. Finally, a self-consistent optimization procedure, when the probability $P_{\mathrm{des}}$ depends on the current coverage density $\theta \left(t\right)$, is formulated and tested. The present model reproduces qualitatively the densification kinetics and the memory effects of vibrated granular materials. Our results suggest that the process of vibratory compaction of granular materials can be optimized by using a time dependent intensity of external excitations.

Understanding the mechanisms of how colloidal solution properties and drying processes result in dry colloidal structures is essential for industrial applications such as paint, ceramics, and electrodes. In this study, we develop a computational method to simulate the drying process of colloidal suspensions containing solid particles and polymers. The method consists of a solvent evaporation model, a fluid particle dynamics method, and a two-phase lattice Boltzmann method. We determine that a high-viscosity solvent, small surface tension, and a high evaporation rate of the solvent lead to a structure with dispersed particles and interconnected pores. When these conditions are not present, the particles agglomerate and the pores are disconnected.

We investigate the peculiarity of the interaction between particles immersed into a smectic liquid crystal with a layered structure. Such a structure of a liquid crystal imposes restrictions on possible deformations of the layer displacement field. Previous studies neglect this fact and give improper results for the interaction potential within one molecular layer. The present paper shows that such restrictions yield an interaction potential substantially different from those of previous studies. Oscillatory behavior, which was not present in the potentials of previous studies, might give rise to superstructures of immersed particles with finite interparticle distance.

In the framework of the modified model [S. V. Burylov and A. N. Zakhlevnykh, Phys. Rev. E 88, 012511 (2013)] of soft ferronematic liquid crystals, i.e., suspensions of needlelike ferroparticles in nematic solvents, we consider the ferronematic states with different mutual orientations of the director and magnetization. We study the transitions between states in an external magnetic field and show that these transitions are characterized by either continuous or discontinuous changes in the order parameter; i.e., they can be both the second-order and the first-order, respectively. In the latter case the magnetic field induced orientational hysteresis arises, which can be observed in experiments on the birefringence of ferronematic liquid crystals.