We discuss a way to exploit conformal mapping to study the response of a finite metallic film of arbitrary shape to an external electromagnetic field at finite frequencies. This provides a simple way to understand different physics issues and provides insights that include the issue of vorticity and eddy current and the nature of the divergent electric field at the boundaries and at corners. We study an example of an equilateral triangular plate and find good agreement with results obtained with traditional numerical techniques.

We study a two-dimensional binary mixture of patchy colloids in sedimentation-diffusion equilibrium using Monte Carlo simulation and Wertheim's theory. By tuning the buoyant masses of the colloids we can control the gravity-induced sequence of fluid stacks of differing density and percolation properties. We find complex stacking sequences with up to four layers and reentrant network formation, consistently in simulations and theoretically using only the bulk phase diagram as input. Our theory applies to general patchy colloidal mixtures and is relevant to understanding experiments under gravity.

Disks moving in a narrow channel have many features in common with the glassy behavior of hard spheres in three dimensions. In this paper we study the caging behavior of the disks that sets in at characteristic packing fraction ${\varphi }_d$. Four-point overlap functions similar to those studied when investigating dynamical heterogeneities have been determined from event-driven molecular dynamics simulations and the time-dependent dynamical length scale has been extracted from them. The dynamical length scale increases with time and, on the equilibration time scale, it is proportional to the static length scale associated with the zigzag ordering in the system, which grows rapidly above ${\varphi }_d$. The structural features responsible for the onset of caging and the glassy behavior are easy to identify as they show up in the structure factor, which we have determined exactly from the transfer-matrix approach.

In this paper we study the properties of the chaotic wave fields generated in the frame of the Kundu-Eckhaus equation (KEE). Modulation instability results in a chaotic wave field which exhibits small-scale filaments with a free propagation constant, $k$. The average velocity of the filaments is approximately given by the average group velocity calculated from the dispersion relation for the plane-wave solution; however, direction of propagation is controlled by the $\beta$ parameter, the constant in front of the Raman-effect term. We have also calculated the probabilities of the rogue wave occurrence for various values of propagation constant $k$ and showed that the probability of rogue wave occurrence depends on $k$. Additionally, we have showed that the probability of rogue wave occurrence significantly depends on the quintic and the Raman-effect nonlinear terms of the KEE. Statistical comparisons between the KEE and the cubic nonlinear Schrödinger equation have also been presented.

Nanocomposites consist of nanofillers and matrices, thus allowing one to design novel materials with desirable properties of both nanofillers and matrices. The percolating network formation of nanofillers in matrices is critical to such desired properties. Some nanofillers such as carbon nanotubes and graphene nanosheets are so flexible that they become either wavy or crumpled. Such a variability in the nanofiller conformation may affect the percolating network formation but has been often (but not always) ignored in the theoretical and computational investigation. In this work, we investigate how the flexibility of different kinds of nanofillers influences the formation of the percolating network by performing extensive Langevin dynamics simulations. We consider three kinds of nanofillers of different shape: nanospheres, nanorods, and nanoplates. When the sizes of nanofillers (or the radius of gyration, $R_g$) are comparable, nanorods form a percolating network at a lower volume fraction than nanoplates while nanofillers require the highest volume fraction to form the percolating network, which is consistent with previous experiments. The percolation threshold concentration $\left({\varphi }_c\right)$ of nanospheres increases with an increase in their $R_g$, while ${\varphi }_c$ of nanorods and nanoplates decrease with $R_g$. However, the effect of flexibility on the percolation threshold volume fraction is much more significant for nanoplates than nanorods. We also estimate the electric conductivity and find that the electric conductivity follows a scaling relation faithfully but with different critical exponents depending on the shape and flexibility.

The coefficient of restitution may be determined from the sound signal emitted by a sphere bouncing repeatedly off the ground. Although there is a large number of publications exploiting this method, so far, there is no quantitative discussion of the error related to this type of measurement. Analyzing the main error sources, we find that even tiny deviations of the shape from the perfect sphere may lead to substantial errors that dominate the overall error of the measurement. Therefore, we come to the conclusion that the well-established method to measure the coefficient of restitution through the emitted sound is applicable only for the case of nearly perfect spheres. For larger falling height, air drag may lead to considerable error, too.

We formulate a damped oscillating particle method to solve the stationary nonlinear Schrödinger equation (NLSE). The ground-state solutions are found by a converging damped oscillating evolution equation that can be discretized with symplectic numerical techniques. The method is demonstrated for three different cases: for the single-component NLSE with an attractive self-interaction, for the single-component NLSE with a repulsive self-interaction and a constraint on the angular momentum, and for the two-component NLSE with a constraint on the total angular momentum. We reproduce the so-called yrast curve for the single-component case, described in [A. D. Jackson et al., Europhys. Lett. 95, 30002 (2011)], and produce for the first time an analogous curve for the two-component NLSE. The numerical results are compared with analytic solutions and competing numerical methods. Our method is well suited to handle a large class of equations and can easily be adapted to further constraints and components.

Anomalously slow relaxation of clusters of a liquid confined in a disordered system of pores has been studied for the (water-L23 nanoporous medium) system. The evolution of the system of confined liquid clusters consists of a fast formation stage followed by slow relaxation of the system and its decay. The characteristic time for the formation of the initial state is ${\tau }_p\sim 10$ s after the reduction of excess pressure after complete filling. Anomalously slow relaxation has been observed for times of ${10}^1–{10}^5$ s, and decay has been observed at times of $>{10}^5$ s. The time dependence of the volume fraction $\theta$ of pores filled with the confined liquid is described by a power law $\theta \sim t^{-\alpha }$ with the exponent $\alpha <0.15$. The exponent $\alpha$ and temperature dependence $\alpha \left(T\right)$ are qualitatively described theoretically for the case of a slightly polydisperse medium in a mean-field approximation with the inclusion of the interaction of liquid clusters and averaging over various degenerate local configurations of clusters. In this approximation, slow relaxation is represented as a continuous transition through a sequence of metastable states of the system of clusters with a decreasing barrier.

Modeling a temporal process as if it is Markovian assumes that the present encodes all of a process's history. When this occurs, the present captures all of the dependency between past and future. We recently showed that if one randomly samples in the space of structured processes, this is almost never the case. So, how does the Markov failure come about? That is, how do individual measurements fail to encode the past? and How many are needed to capture dependencies between the past and future? Here, we investigate how much information can be shared between the past and the future but not reflected in the present. We quantify this elusive information, give explicit calculational methods, and outline the consequences, the most important of which is that when the present hides past-future correlation or dependency we must move beyond sequence-based statistics and build state-based models.

This paper investigates dynamics of a management system for controlling a pair of energy storages. The system involves the following two characteristics: each storage behaves in a manner that reduces the number of charge noncharge cycles and begins to be charged when the price of power is lower than a particular price threshold. The price is proportional to the past total power flow from a power grid to all storages. A peak of the total power flow occurs when these storages are charged simultaneously. From the viewpoint of nonlinear dynamics, the energy storages can be considered as relaxation oscillators coupled by a delay connection. Our analytical results suggest that the peak can be reduced by inducing an antiphase synchronization in coupled oscillators. We confirm these analytical results through numerical simulations. In addition, we numerically investigate the dynamical behavior in 10 storages and find that time delay in the connection is important in reducing the peak.

Delay-coordinate reconstruction is a proven modeling strategy for building effective forecasts of nonlinear time series. The first step in this process is the estimation of good values for two parameters, the time delay and the embedding dimension. Many heuristics and strategies have been proposed in the literature for estimating these values. Few, if any, of these methods were developed with forecasting in mind, however, and their results are not optimal for that purpose. Even so, these heuristics—intended for other applications—are routinely used when building delay coordinate reconstruction-based forecast models. In this paper, we propose an alternate strategy for choosing optimal parameter values for forecast methods that are based on delay-coordinate reconstructions. The basic calculation involves maximizing the shared information between each delay vector and the future state of the system. We illustrate the effectiveness of this method on several synthetic and experimental systems, showing that this metric can be calculated quickly and reliably from a relatively short time series, and that it provides a direct indication of how well a near-neighbor based forecasting method will work on a given delay reconstruction of that time series. This allows a practitioner to choose reconstruction parameters that avoid any pathologies, regardless of the underlying mechanism, and maximize the predictive information contained in the reconstruction.

How long people live depends on their health, and how it changes with age. Individual health can be tracked by the accumulation of age-related health deficits. The fraction of age-related deficits is a simple quantitative measure of human aging. This quantitative frailty index ($F$) is as good as chronological age in predicting mortality. In this paper, we use a dynamical network model of deficits to explore the effects of interactions between deficits, deficit damage and repair processes, and the connection between the $F$ and mortality. With our model, we qualitatively reproduce Gompertz's law of increasing human mortality with age, the broadening of the $F$ distribution with age, the characteristic nonlinear increase of the $F$ with age, and the increased mortality of high-frailty individuals. No explicit time-dependence in damage or repair rates is needed in our model. Instead, implicit time-dependence arises through deficit interactions—so that the average deficit damage rates increase, and deficit repair rates decrease, with age. We use a simple mortality criterion, where mortality occurs when the most connected node is damaged.

We consider the constrained Schelling model of social segregation in which the utility factor of agents strictly increases and nonlocal jumps of the agents are allowed. In the present study, the utility factor $u$ is defined in a way such that it can take continuous values and depends on the tolerance threshold as well as the fraction of unlike neighbors. Two models are proposed: in model A the jump probability is determined by the sign of $u$ only, which makes it equivalent to the discrete model. In model B the actual values of $u$ are considered. Model A and model B are shown to differ drastically as far as segregation behavior and phase transitions are concerned. In model A, although segregation can be achieved, the cluster sizes are rather small. Also, a frozen state is obtained in which steady states comprise many unsatisfied agents. In model B, segregated states with much larger cluster sizes are obtained. The correlation function is calculated to show quantitatively that larger clusters occur in model B. Moreover for model B, no frozen states exist even for very low dilution and small tolerance parameter. This is in contrast to the unconstrained discrete model considered earlier where agents can move even when utility remains the same. In addition, we also consider a few other dynamical aspects which have not been studied in segregation models earlier.

In this work we have developed and implement a new approach for the study of magnetoliposomes using Monte Carlo simulations. Our model is based on interaction among nanoparticles considering magnetic dipolar, van der Waals, ionic-steric, and Zeeman interaction potentials. The ionic interaction between nanoparticles and the lipid bilayer is represented by an ionic repulsion electrical surface potential that depends on the nanoparticle-lipid bilayer distance and the concentration of ions in the solution. A direct comparison among transmission electron microscopy, vibrating sample magnetometer, dynamic light scattering, nanoparticle tracking analysis, and experimentally derived static magnetic birefringence and simulation data allow us to validate our implementation. Our simulations suggest that confinement plays an important role in aggregate formation.

Deformability is a central feature of many types of microswimmers, e.g., for artificially generated self-propelled droplets. Here, we analyze deformable bead-spring microswimmers in an externally imposed solvent flow field as simple theoretical model systems. We focus on their behavior in a circular swirl flow in two spatial dimensions. Linear (straight) two-bead swimmers are found to circle around the swirl with a slight drift to the outside with increasing activity. In contrast to that, we observe for triangular three-bead or squarelike four-bead swimmers a tendency of being drawn into the swirl and finally getting drowned, although a radial inward component is absent in the flow field. During one cycle around the swirl, the self-propulsion direction of an active triangular or squarelike swimmer remains almost constant, while their orbits become deformed exhibiting an “egglike” shape. Over time, the swirl flow induces slight net rotations of these swimmer types, which leads to net rotations of the egg-shaped orbits. Interestingly, in certain cases, the orbital rotation changes sense when the swimmer approaches the flow singularity. Our predictions can be verified in real-space experiments on artificial microswimmers.

We perform numerical simulations of non-Brownian suspensions in the laminar flow regime to study the scaling behavior of particle clusters and collisions under shear. As the particle fraction approaches the maximum packing fraction, large transient clusters appear in the system. We use methods from percolation theory to discuss the cluster size distribution. We also give a scaling relation for the percolation threshold as well as system size effects through time-dependent fluctuations of this threshold and relate them to system size. System size effects are important close to the maximum packing fraction due to the divergence of the cluster length scale. We then investigate the transient nature of the clusters through characterization of particle collisions and show that collision times exhibit scale-invariant properties. Finally, we show that particle collision times can be modeled as first-passage processes.

This article describes how an embedded bubble changes the surface wave of a suspended liquid drop, and how such modifications, if recorded experimentally, can be used to detect voids in typically opaque interior of the fluid. The analysis uses a matrix formalism to predict the frequencies for natural oscillation and the deformation for acoustically induced forced vibration. The theory shows that the embedded cavity causes major shifts in the frequency and amplitude values as well as twofold increase in number of natural modes, indicating multifacetted utility of the results in process diagnostics, material characterizations, and combustion technology.

Based on the Darcy-Brinkman-Forchheimer equation, a finite-volume computational model with lattice Boltzmann flux scheme is proposed for incompressible porous media flow in this paper. The fluxes across the cell interface are calculated by reconstructing the local solution of the generalized lattice Boltzmann equation for porous media flow. The time-scaled midpoint integration rule is adopted to discretize the governing equation, which makes the time step become limited by the Courant-Friedricks-Lewy condition. The force term which evaluates the effect of the porous medium is added to the discretized governing equation directly. The numerical simulations of the steady Poiseuille flow, the unsteady Womersley flow, the circular Couette flow, and the lid-driven flow are carried out to verify the present computational model. The obtained results show good agreement with the analytical, finite-difference, and/or previously published solutions.

In this paper, we developed a unified lattice Boltzmann model (LBM) to simulate electroconvection in a dielectric liquid induced by unipolar charge injection. Instead of solving the complex set of coupled Navier-Stokes equations, the charge conservation equation, and the Poisson equation of electric potential, three consistent lattice Boltzmann equations are formulated. Numerical results are presented for both strong and weak injection regimes, and different scenarios for the onset and evolution of instability, bifurcation, and chaos are tracked. All LBM results are found to be highly consistent with the analytical solutions and other numerical work.