We study the orientational ordering on the surface of a sphere using Monte Carlo and Brownian dynamics simulations of rods interacting with an anisotropic potential. We restrict the orientations to the local tangent plane of the spherical surface and fix the position of each rod to be at a discrete point on the spherical surface. On the surface of a sphere, orientational ordering cannot be perfectly nematic due to the inevitable presence of defects. We find that the ground state of four +1/2 point defects is stable across a broad range of temperatures. We investigate the transition from disordered to ordered phase by decreasing the temperature and find a very smooth transition. We use fluctuations of the local directors to estimate the Frank elastic constant on the surface of a sphere and compare it to the planar case. We observe subdiffusive behavior in the mean square displacement of the defect cores and estimate their diffusion constants.

Swimming velocity and rate of dissipation of a sphere with surface distortions are discussed on the basis of the Stokes equations of low-Reynolds-number hydrodynamics. At first the surface distortions are assumed to cause an irrotational axisymmetric flow pattern. The efficiency of swimming is optimized within this class of flows. Subsequently, more general axisymmetric polar flows with vorticity are considered. This leads to a considerably higher maximum efficiency. An additional measure of swimming performance is proposed based on the energy consumption for given amplitude of stroke.

We study the degeneracy of the ground-state energy $E$ of the two-component Bose-Hubbard model and of the perturbative correction $E_1$. We show that the degeneracy properties of $E$ and $E_1$ are closely related to the connectivity properties of the lattice. We determine general conditions under which $E$ is nondegenerate. This analysis is then extended to investigate the degeneracy of $E_1$. In this case, in addition to the lattice structure, the degeneracy also depends on the number of particles present in the system. After identifying the cases in which $E_1$ is degenerate and observing that the standard (degenerate) perturbation theory is not applicable, we develop a method to determine the zeroth-order correction to the ground state by exploiting the symmetry properties of the lattice. This method is used to implement the perturbative approach to the two-component Bose-Hubbard model in the case of degenerate $E_1$ and is expected to be a valid tool to perturbatively study the asymmetric character of the Mott insulator to superfluid transition between the particle and hole side.

We show numerically that introducing the next-nearest-neighbor interactions (of appropriate strength) into the one-dimensional (1D) Fermi-Pasta-Ulam-$\beta$ (FPU-$\beta$) lattice can result in an unusual, nonmonotonic temperature dependent divergence behavior in a wide temperature range, which is in clear contrast to the universal divergence manner independent of temperature as suggested previously in the conventional 1D FPU-$\beta$ models with nearest-neighbor (NN) coupling only. We also discuss the underlying mechanism of this finding by analyzing the temperature variations of the properties of discrete breathers, especially that with frequencies having the intraband components. The results may provide useful information for establishing the connection between the macroscopic heat transport properties and the underlying dynamics in general 1D systems with interactions beyond NN couplings.

The adsorption isotherm for the recently proposed parallel Kawasaki (PK) lattice-gas model [Phys. Rev. E 88, 062144 (2013)] is calculated exactly in one dimension. To do so, a third-order difference equation for the grand-canonical partition function is derived and solved analytically. In the present version of the PK model, the attraction and repulsion effects between two neighboring particles and between a particle and a neighboring empty site are ruled, respectively, by the dimensionless parameters $\varphi$ and $\theta$. We discuss the inflections induced in the isotherms by situations of high repulsion, the role played by finite lattice sizes in the emergence of substeps, and the adequacy of the two most widely used mean-field approximations in lattice gases, namely, the Bragg-Williams and the Bethe-Peierls approximations.

The failure dynamics in $\mathrm{Si}{\mathrm{O}}_2$-based porous materials under compression, namely the synthetic glass Gelsil and three natural sandstones, has been studied for slowly increasing compressive uniaxial stress with rates between 0.2 and 2.8 kPa/s. The measured collapsed dynamics is similar to Vycor, which is another synthetic porous $\mathrm{Si}{\mathrm{O}}_2$ glass similar to Gelsil but with a different porous mesostructure. Compression occurs by jerks of strain release and a major collapse at the failure point. The acoustic emission and shrinking of the samples during jerks are measured and analyzed. The energy of acoustic emission events, its duration, and waiting times between events show that the failure process follows avalanche criticality with power law statistics over ca. 4 decades with a power law exponent $\varepsilon \simeq$ 1.4 for the energy distribution. This exponent is consistent with the mean-field value for the collapse of granular media. Besides the absence of length, energy, and time scales, we demonstrate the existence of aftershock correlations during the failure process.

We consider the dynamics in infinite population evolution models with a general symmetric fitness landscape. We find shock waves, i.e., discontinuous transitions in the mean fitness, in evolution dynamics even with smooth fitness landscapes, which means that the search for the optimal evolution trajectory is more complicated. These shock waves appear in the case of positive epistasis and can be used to represent punctuated equilibria in biological evolution during long geological time scales. We find exact analytical solutions for discontinuous dynamics at the large-genome-length limit and derive optimal mutation rates for a fixed fitness landscape to send the population from the initial configuration to some final configuration in the fastest way.

In this paper, we propose a nonlinear transport model for an aviation network. The takeoff rate from an airport is characterized by the degree of ground congestion. Due to the effect of surface congestion, the performance of an airport deteriorates because of inefficient configurations of waiting aircraft on the ground. Using a simple transport model, we performed simulations on a United States airport network and found a global jamming transition induced by local surface congestion. From a physical perspective, the mechanism of the transition is studied analytically and the resulting aircraft distribution is discussed considering system dynamics. This study shows that the knowledge of the relationship between a takeoff rate and a congestion level on the ground is vital for efficient air traffic operations.

We present analytical results for the first-passage statistics of Brownian particles near a comblike absorbing boundary. Our approach is based on the method of boundary homogenization (or boundary smoothing) when an equivalent flat boundary is introduced to maintain the same diffusion flux as the original rough boundary. By using the conformal invariance of the Laplace equation we derive an analytic expression for the position of an equivalent boundary in terms of its spatial period and amplitude. The main analytical results being initially obtained for the steady state system provide important insights into the statistical characteristics of diffusive transport near rough boundaries (high order moments of the trapping time statistics).

We present a thermodynamic theory for a generic population of $M$ individuals distributed into $N$ groups (clusters). We construct the ensemble of all distributions with fixed $M$ and $N$, introduce a selection functional that embodies the physics that governs the population, and obtain the distribution that emerges in the scaling limit as the most probable among all distributions consistent with the given physics. We develop the thermodynamics of the ensemble and establish a rigorous mapping to regular thermodynamics. We treat the emergence of a so-called giant component as a formal phase transition and show that the criteria for its emergence are entirely analogous to the equilibrium conditions in molecular systems. We demonstrate the theory by an analytic model and confirm the predictions by Monte Carlo simulation.

Maximally random jammed (MRJ) sphere packing is a prototypical example of a system naturally poised at the margin between underconstraint and overconstraint. This marginal stability has traditionally been understood in terms of isostaticity, the equality of the number of mechanical contacts and the number of degrees of freedom. Quasicontacts, pairs of spheres on the verge of coming in contact, are irrelevant for static stability, but they come into play when considering dynamic stability, as does the distribution of contact forces. We show that the effects of marginal dynamic stability, as manifested in the distributions of quasicontacts and weak contacts, are consequential and nontrivial. We study these ideas first in the context of MRJ packing of $d$-dimensional spheres, where we show that the abundance of quasicontacts grows at a faster rate than that of contacts. We reexamine a calculation of Jin et al. [Phys. Rev. E 82, 051126 (2010)], where quasicontacts were originally neglected, and we explore the effect of their inclusion in the calculation. This analysis yields an estimate of the asymptotic behavior of the packing density in high dimensions. We argue that this estimate should be reinterpreted as a lower bound. The latter part of the paper is devoted to Bravais lattice packings that possess the minimum number of contacts to maintain mechanical stability. We show that quasicontacts play an even more important role in these packings. We also show that jammed lattices are a useful setting for studying the Edwards ensemble, which weights each mechanically stable configuration equally and does not account for dynamics. This ansatz fails to predict the power-law distribution of near-zero contact forces, $P\left(f\right)\sim f^{\theta }$.

A simple and computationally inexpensive core-softened model, originally proposed by Franzese [G. Franzese, J. Mol. Liq. 136, 267 (2007)], was adopted to show that it exhibits properties of waterlike fluid and hydrophobic effect. The potential used between particles is spherically symmetric with two characteristic lengths. Thermodynamics of nonpolar solvation were modeled as an insertion of a modified Lennard-Jones particle. It was investigated how the anomalous predictions of the model as well as the nonpolar solvation compare with the experimental data for water anomalies and the temperature dependence of noble gases hydration. It was shown that the model qualitatively follows the same trends as water. The model is able to reproduce waterlike anomalous properties (density maximum, heat capacity minimum, isothermal compressibility, etc.) and hydrophobic effect (minimum solubility for nonpolar solutes near ambient conditions, increased solubility of larger noble gases, etc.). It is argued that the model yields similar results as more complex and computationally expensive models.

We formulate and implement a generalized island-dynamics model of epitaxial growth based on the level-set technique to include the effect of an additional energy barrier for the attachment and detachment of atoms at step edges. For this purpose, we invoke a mixed, Robin-type, boundary condition for the flux of adsorbed atoms (adatoms) at each step edge. In addition, we provide an analytic expression for the requisite equilibrium adatom concentration at the island boundary. The only inputs are atomistic kinetic rates. We present a numerical scheme for solving the adatom diffusion equation with such a mixed boundary condition. Our simulation results demonstrate that mounds form when the step-edge barrier is included, and that these mounds steepen as the step-edge barrier increases.

We investigate the quantum transport dynamics governed by the nonlinear Schrödinger equation with a periodically-$\delta$-kicking potential and discover the emergence of a directed current in momentum space. With the increase of nonlinearity, we find strikingly that the momentum current decreases, reverses, and finally vanishes, indicating that the quantum transport can be effectively manipulated through adjusting the nonlinearity. The underlying dynamic mechanism is uncovered and some important implications are addressed.

Scalar dispersion has complex interactions between advection and diffusion that depend on the values of the scalar diffusivity and of the (possibly large) set of parameters controlling the flow. Using a spectral method which is three to four orders of magnitude faster than traditional methods, we calculate the fine-scale structure of the global solution space of the advection-diffusion equation for a physically realizable chaotic flow. The solution space is rich: spatial pattern locking, an order-disorder transition, and optima in dispersion rates that move discontinuously with Peclét number and boundary condition type are some of the discoveries. We uncover the mechanisms which control pattern locking and govern the global structure of dispersion across the parameter space and Peclét number spectrum.

In this paper, we develop an approach to achieve either frequency or amplitude modulation of an oscillator merely through feedback control. We present and implement a unified theory of our approach for any finite-dimensional continuous dynamical system that exhibits oscillatory behavior. The approach is illustrated not only for the normal forms of dynamical systems but also for representative biological models, such as the isolated and coupled FitzHugh-Nagumo model. We demonstrate the potential usefulness of our approach to uncover the mechanisms of frequency and amplitude modulations experimentally observed in a wide range of real systems.

A Langevin process describing diffusion in a periodic potential landscape has a time-dependent diffusion constant, which means that its average mean-squared displacement (MSD) only becomes linear at late times. The long-time, or effective diffusion, constant can be estimated from the slope of a linear fit of the MSD at late times. Due to the crossover between a short time microscopic diffusion constant, which is independent of the potential, to the effective late-time diffusion constant, a linear fit of the MSD will not in general pass through the origin and will have a nonzero constant term. Here we address how to compute the constant term and provide explicit results for Brownian particles in one dimension in periodic potentials. We show that the constant is always positive and that at low temperatures it depends on the curvature of the minimum of the potential. For comparison we also consider the same question for the simpler problem of a symmetric continuous time random walk in discrete space. Here the constant can be positive or negative and can be used to determine the variance of the hopping time distribution.