We present a computer-assisted approach to coarse graining the evolutionary dynamics of a system of nonidentical oscillators coupled through a (fixed) network structure. The existence of a spectral gap for the coupling network graph Laplacian suggests that the graph dynamics may quickly become low dimensional. Our first choice of coarse variables consists of the components of the oscillator states—their (complex) phase angles—along the leading eigenvectors of this Laplacian. We then use the equation-free framework, circumventing the derivation of explicit coarse-grained equations, to perform computational tasks such as coarse projective integration, coarse fixed-point, and coarse limit-cycle computations. In a second step, we explore an approach to incorporating oscillator heterogeneity in the coarse-graining process. The approach is based on the observation of fast-developing correlations between oscillator state and oscillator intrinsic properties and establishes a connection with tools developed in the context of uncertainty quantification.

We study the deterministic spin dynamics of an anisotropic magnetic particle in the presence of a magnetic field with a constant longitudinal and a time-dependent transverse component using the Landau-Lifshitz-Gilbert equation. We characterize the dynamical behavior of the system through calculation of the Lyapunov exponents, Poincaré sections, bifurcation diagrams, and Fourier power spectra. In particular we explore the positivity of the largest Lyapunov exponent as a function of the magnitude and frequency of the applied magnetic field and its direction with respect to the main anisotropy axis of the magnetic particle. We find that the system presents multiple transitions between regular and chaotic behaviors. We show that the dynamical phases display a very complicated structure of intricately intermingled chaotic and regular phases.

We present a model that describes the drying of solutions and colloidal dispersions from droplets confined between two circular plates. This confined geometry, proposed by Clément and Leng [Langmuir 20, 6538 (2004)], casts a perfect control of the evaporation conditions, and thus also of the concentration kinetics of the solutes in the droplet. Our model, based on simple transport equations for binary mixtures, describes the concentration process of the solute inside the droplet. Using dimensionless units, we identify the different numbers that govern the concentration field of the solute, and we detail how to extract kinetic and thermodynamic information on the binary mixture from such drying experiments. We finally discuss, using numerical resolution of the model and analytical arguments, several specific cases: dilute solutions, a colloidal hard sphere dispersion, and a binary molecular mixture.

Single-particle tracking (SPT) microscopy is increasingly used to characterize nanoparticulate systems. We introduce a concept for estimation of particle number concentration in Brownian particle dispersions using SPT based on a model for the trajectory length distribution of particles to estimate the detection region volume. The resulting method is independent of precalibration reference measurements, and robust with respect to image processing settings. Experimentally estimated concentrations of different dilutions of 0.19- and 0.52-$\mu$m polymer nanospheres are in excellent agreement with estimates computed from the concentrations of the stock solutions.

We study a minimal lattice model which describes bidirectional transport of “particles” driven along a one-dimensional track, as is observed in microtubule based, motor protein driven bidirectional transport of cargo vesicles, lipid bodies, and organelles such as mitochondria. This minimal model, a multispecies totally asymmetric exclusion process (TASEP) with directional switching, can provide a framework for understanding the interplay between the switching dynamics of individual particles and the collective movement of particles in one dimension. When switching is much faster than translocation, the steady-state density and current profiles of the particles are homogeneous in the bulk and are well described by mean-field (MF) theory, as determined by comparison to a Monte Carlo simulation. In this limit, we can map this model to the exactly solvable partially asymmetric exclusion-process (PASEP) model. Away from this fast switching regime the MF theory fails, although the average bulk density profile still remains homogeneous. We study the steady-state behavior as a function of the ratio of the translocation and net switching rates $Q$ and find a unique first-order phase transition at a finite $Q$ associated with a discontinuous change of the bulk density. When the switching rate is decreased further (keeping translocation rate fixed), the system approaches a jammed phase with a net current that tends to zero as $J\sim 1/Q$. We numerically construct the phase diagram for finite $Q$.

We study the comparative importance of thermal to nonthermal fluctuations for membrane-based models in the linear regime. Our results, both in $1+1$ and $2+1$ dimensions, suggest that nonthermal fluctuations dominate thermal ones only when the relaxation time $\tau$ is large. For moderate to small values of $\tau$, the dynamics is defined by a competition between these two forces. The results are expected to act as a quantitative benchmark for biological modeling in systems involving cytoskeletal and other nonthermal fluctuations.

Conical points of a leaky dielectric drop surrounded by a dielectric gas in an external ac electric field are investigated. A novel class of steady conical tips depending on the permittivity ratio and applied signal frequency is presented. It is found that conical solutions with very small angles are possible (angles much smaller than the classical Taylor cone angle ${49.3}^{\circ }$ for a conducting drop in a dc field); this result can be relevant to the observations of small cone angles in Chetwani, Maheshwari, and Chang experiments [N. Chetwani, S. Maheshwari, and H.-C. Chang, Phys. Rev. Lett. 101, 204501 (2008)].

The $p$-median problem is a common model for optimal facility location. The task is to place $p$ facilities (e.g., warehouses or schools) in a heterogeneously populated space such that the average distance from a person's home to the nearest facility is minimized. Here we study the special case where the population lives along a line (e.g., a road or a river). If facilities are optimally placed, the length of the line segment served by a facility is inversely proportional to the square root of the population density. This scaling law is derived analytically and confirmed for concrete numerical examples of three US interstate highways and the Mississippi River. If facility locations are permitted to deviate from the optimum, the number of possible solutions increases dramatically. Using Monte Carlo simulations, we compute how scaling is affected by an increase in the average distance to the nearest facility. We find that the scaling exponents change and are most sensitive near the optimum facility distribution.

A population typically consists of agents that continually distribute themselves into different groups at different times. This dynamic grouping has recently been shown to be essential in explaining many features observed in human activities including social, economic, and military activities. We study the effects of dynamic grouping on the level of cooperation in a modified evolutionary $N$-person snowdrift game. Due to the formation of dynamical groups, the competition takes place in groups of different sizes at different times and players of different strategies are mixed by the grouping dynamics. It is found that the level of cooperation is greatly enhanced by the dynamic grouping of agents, when compared with a static population of the same size. As a parameter $\beta$, which characterizes the relative importance of the reward and cost, increases, the fraction of cooperative players $f_C$ increases and it is possible to achieve a fully cooperative state. Analytically, we present a dynamical equation that incorporates the effects of the competing game and group size distribution. The distribution of cooperators in different groups is assumed to be a binomial distribution, which is confirmed by simulations. Results from the analytic equation are in good agreement with numerical results from simulations. We also present detailed simulation results of $f_C$ over the parameter space spanned by the probabilities of group coalescence ${\nu }_m$ and group fragmentation ${\nu }_p$ in the grouping dynamics. A high ${\nu }_m$ and low ${\nu }_p$ promotes cooperation, and a favorable reward characterized by a high $\beta$ would lead to a fully cooperative state.

Changes in the level of synchronization and desynchronization in coupled oscillator systems due to an external stimulus are called event-related synchronization or desynchronization (ERS or ERD). Such changes occur in real-life systems where the collective activity of the entities of a coupled system is affected by some external influence. In order to understand the role played by the external influence in the occurrence of ERD and ERS, we study a system of coupled nonlinear oscillators in the presence of an external stimulus signal. We find that the phenomena of ERS and ERD are generic and occur in all types of coupled oscillator systems. We also find that the same external stimulus signal can cause ERS and ERD depending upon the strength of the signal. We identify the stability of the ERS and ERD states and also find analytical and numerical boundaries between the different synchronization regimes involved in the occurrence of ERD and ERS.

Mixing in viscous fluids is challenging, but chaotic advection in principle allows efficient mixing. In the best possible scenario, the decay rate of the concentration profile of a passive scalar should be exponential in time. In practice, several authors have found that the no-slip boundary condition at the walls of a vessel can slow down mixing considerably, turning an exponential decay into a power law. This slowdown affects the whole mixing region, and not just the vicinity of the wall. The reason is that when the chaotic mixing region extends to the wall, a separatrix connects to it. The approach to the wall along that separatrix is polynomial in time and dominates the long-time decay. However, if the walls are moved or rotated, closed orbits appear, separated from the central mixing region by a hyperbolic fixed point with a homoclinic orbit. The long-time approach to the fixed point is exponential, so an overall exponential decay is recovered, albeit with a thin unmixed region near the wall.

In 2007 an interesting phenomenon was discovered [J. Phys. D 40, 6112 (2007)]: a horizontal thread of water, the so-called water bridge, hangs in a horizontal electrostatic field. A different explanation of the water bridge stability is proposed herein: the force supporting it is the surface tension of water, while the role of the electric field is to not allow the water bridge to reduce its surface energy by breaking into separate drops. It is proven that electrostatic field is not the origin of the tension holding the bridge.

A stochastic treatment yielding to the derivation of a general Fokker-Planck equation is presented to model the slow convergence toward equilibrium of mean-field systems due to finite-$N$ effects. The thermalization process involves notably the disintegration of coherent structures that may sustain out-of-equilibrium quasistationary states. The time evolution of the fraction of particles remaining close to a mean-field potential trough is analytically computed. This indicator enables to estimate the lifetime of coherent structures and thermalization time scale in mean-field systems.

Using the recently introduced simple procedure of dividing Gaussian matrices by a positive random variable, a family of random matrices is generated characterized by a behavior ruled by the generalized hyperbolic distribution. The spectral density evolves from the semicircle law to a Gaussian-like behavior while concomitantly, the local fluctuations show a transition from the Wigner-Dyson to the Poisson statistics. Long range statistics such as number variance exhibit large fluctuations typical of nonergodic ensembles.

Energy transport control in low dimensional nanoscale systems has attracted much attention in recent years. In this paper, we investigate the energy transport properties of the Frenkel-Kontorova lattice subject to a periodic driving force, in particular, the resonance behavior of the energy current by varying the external driving frequency. It is discovered that, in certain parameter ranges, multiple resonance peaks, instead of a single resonance, emerge. By comparing the nonlinear lattice model with a harmonic chain, we unravel the underlying physical mechanism for such a resonance phenomenon. Other parameter dependencies of the resonance behavior are examined as well. Finally, we demonstrate that heat pumping is actually absent in this force-driven model.

Using the phenomenological renormalization group (PRG), we evaluate the low-energy excitation spectrum along the critical line of a quantum spin chain having a local interaction between three Ising spins and longitudinal and transverse magnetic fields, i.e., a Turban model. The low-energy excitation spectrum found with the PRG agrees with the spectrum predicted for the $(D_4,A_4)$ conformal minimal model under a nontrivial correspondence between translations at the critical line and discrete lattice translations. Under this correspondence, the measurements confirm a prediction that the critical line of this quantum spin chain and the critical point of the two-dimensional three-state Potts model are in the same universality class.

A model for the collision between a sand grain and a body of yardang material is established by using the principles of classical mechanics. A new nondimensional parameter, the “abrasion number” $A_n$, is derived from the model. The volume removed per impact for different targets is proportional to $A_n$ approximately. As an indicator of the energy ratio of the impacting material to the target material, $A_n$ not only reflects the previous “abrasion law” but also introduces two dominant mechanical parameters, Young’s modulus and yield stress. We propose $A_n$ to be a similarity criterion for abrasion experiments. The practicability of the model under natural conditions is examined by an example. It is concluded that the abrasion rates of yardangs in the western Qaidam basin, China, are $0.011\text{--}0.398\text{mm/yr}$ in the period of 1986 to 2010 and remarkable abrasion events generally correspond with strong wind conditions. The model will be helpful for reconstructing the history of aeolian activities from the morphologies of yardangs in the arid regions on Mars.

Nonequilibrium structure formation and dynamics in suspensions of superparamagnetic colloids driven by an external rotating magnetic field are studied by particle-based mesoscale hydrodynamics simulations in confined geometry. We address the fundamental question how the rotation of the colloids about their own axes can be converted into a translational motion by breaking the symmetry of the confining geometry. We study a two-dimensional system of colloids with short-range repulsive interactions, which mimics flow in shallow microchannels. In straight channels, we observe a two-way traffic but—for symmetry reasons—no net transport. However, by keeping some colloids fixed near one of the two walls, net transport can be achieved. This approach allows the control and switchability of the flow in complex microchannel networks. A minimal geometry that fulfills the requirement of broken symmetry are ring channels. We determine the translational velocity of the spinning colloids and study its dependence on the channel width for various median radii. We conclude that spinning colloids present a promising alternative for flow generation and control in microfluidic devices.

The influence of an ellipsoid on the angular order of two-dimensional classical clusters is investigated through Brownian dynamics simulations. We found the following: (1) The presence of an ellipsoid does not influence the start of the angular melting, but reduces the rate at which the inner rings can rotate with respect to each other. (2) Even a small eccentricity of the ellipsoid leads to a stabilization of the angular order of the system. (3) Depending on the position of the ellipsoid in the cluster, a reentrant behavior in the angular order is observed before full radial melting of the cluster sets in. (4) The ellipsoid can lead to a two-step angular melting process: First, the rotation of the inner rings with respect to each other is hindered by the ellipsoid, but on further increasing the kinetic energy of the system, the ellipsoid just starts to behave as a spherical particle with different mobility. The effect of an ellipsoid on the molten system does not depend crucially on the interparticle interaction, but a softer parabolic confinement reduces the angular stabilization.

We performed experiments and simulations to investigate the influence of hydrodynamic interaction on the diffusion dynamics of circular and linear λ-DNA confined in nanoslits. Contrary to the common assumption that intrachain hydrodynamic interaction (HI) is completely screened when polymers are confined in channels with height $h$ smaller than the radius of gyration $R_{\mathrm{g}}$, it is found that the HI is partially screened and approaches complete screening only for $R_{\mathrm{g}}\ll h$. For λ-DNA, the HI becomes nearly completely screened only when the channel height is smaller than the Kuhn length. In addition, the dynamics of linear and circular λ-DNA in very strong confinement is shown to be independent of the chain topology.