Understanding mixing processes that occur in the human vitreous chamber is of fundamental importance due to the relevant clinical implications in drug delivery treatments of several eye conditions. In this article we rely on experimental observations (which demonstrated that dispersion coefficients largely dominate diffusive coefficients) on a physical model of the human eye to perform an analysis based on Lagrangian trajectories. In particular, we study barriers to transport in a particularly significant two-dimensional section of the eye model by using nonlinear dynamical systems theoretical and numerical tools. Bifurcations in the system dynamics are investigated by varying the main physical parameters of the problem.

We model structural transitions of small-size Wigner crystals in laterally compressed two-dimensional traps. Ground and metastable configurations are calculated and their transformations are linked to conspicuous changes in the heat capacity of the system. We show that various types of structural transitions are reflected by characteristic features in the behavior of the heat capacity. For deeper understanding, results produced by the Monte Carlo numerical calculations are compared to predictions of simple one-dimensional models.

An analytical solution of the radiative transfer equation for the radiance caused by an isotropic source which is located in an infinitely extended medium was derived using the $P_N$ method. The results were compared with Monte Carlo simulations and excellent agreement was found. In addition, the radiance of the ${\mathit{SP}}_N$ approximation for the same geometry was derived. Comparison with Monte Carlo simulations showed that the ${\mathit{SP}}_N$ radiance, although being more exact than the radiance derived from diffusion theory, has relatively large errors in many relevant cases.

An epidemiological model for dengue propagation using cellular automata is constructed. Dependence on temperature and rainfall index are taken into account. Numerical results fit pretty well with the registered cases of dengue for the city of Rio de Janeiro for the period from 2006 to 2008. In particular, our approach explains very well an abnormally high number of cases registered in 2008. A phase transition from endemic to epidemic regimes is discussed.

The nonlinear dynamics of coupled electrostatic upper-hybrid (UH) and Alfvén waves (AWs) is revisited in a magnetized electron-ion plasma with charged dust impurities. A pair of nonlinear equations that describe the interaction of UH wave envelopes (including the relativistic electron mass increase) and the density as well as the compressional magnetic field perturbations associated with the AWs are solved numerically to show that many coherent solitary patterns can be excited and saturated due to modulational instability of unstable UH waves. The evolution of these solitary patterns is also shown to appear in the states of spatiotemporal coherence, temporal as well as spatiotemporal chaos, due to collision and fusion among the patterns in stochastic motion. Furthermore, these spatiotemporal features are demonstrated by the analysis of wavelet power spectra. It is found that a redistribution of wave energy takes place to higher harmonic modes with small wavelengths, which, in turn, results in the onset of Alfvénic turbulence in dusty magnetoplasmas. Such a scenario can occur in the vicinity of Saturn’s magnetosphere as many electrostatic solitary structures have been observed there by the Cassini spacecraft.

We report measurements of electrical conductivity of eight metals in the plasma state at densities ranging from 0.002 to 0.5 times solid density, and with internal energy from 2 to 30 kJ/gm. Data are presented as functions of internal energy and specific volume. Conductivity is observed to fall as the plasma expands for fixed internal energy, and for all but tantalum and titanium shows a minimum at approximately 0.01 times solid density, followed by an increase as the density decreases further.

We perform numerical simulations to determine the shear stress and pressure of steady-state shear flow in a soft-disk model in two dimensions at zero temperature in the vicinity of the jamming transition ${\varphi }_J$. We use critical point scaling analyses to determine the critical behavior at jamming, and we find that it is crucial to include corrections to scaling for a reliable analysis. We find that the relative size of these corrections are much smaller for pressure than for shear stress. We furthermore find a superlinear behavior for pressure and shear stress above ${\varphi }_J$, both from the scaling analysis and from a direct analysis of pressure data extrapolated to the limit of vanishing shear rate.

We have developed an alternate description of dynamics of nucleation in terms of an extended set of order parameters. The order parameters consist of an ordered set of $k$th largest clusters, ordered such that $k=$ 1 is the largest cluster in the system, $k=$ 2 is the second largest cluster, and so on. We have derived an analytic expression for the free energy for the $k$th largest cluster, which is in excellent agreement with the simulated results. At large supersaturation, the free energy barrier for the growth of the $k$th largest cluster disappears and the nucleation becomes barrierless. The major success of this extended theoretical formalism is that it can clearly explain the observed change in mechanism at large metastability [P. Bhimalapuram et al., Phys. Rev. Lett. 98, 206104 (2007)] and the associated dynamical crossover. The classical nucleation theory cannot explain this crossover. The crossover from activated to barrierless nucleation is found to occur at a supersaturation where multiple clusters cross the critical size. We attribute the crossover as the onset of the kinetic spinodal. We have derived an expression for the rate of nucleation in the barrierless regime by modeling growth as diffusion on the free energy surface of the largest cluster. The model reproduces the slower increase in the rate of growth as a function of supersaturation, as observed in experiments.

Filled and cross-linked elastomeric rubbers are versatile network materials with a multitude of applications ranging from artificial organs and biomedical devices to cushions, coatings, adhesives, interconnects, and seismic-isolation, thermal, and electrical barriers. External factors such as mechanical stress, temperature fluctuations, or radiation are known to create chemical changes in such materials that can directly affect the molecular weight distribution (MWD) of the polymer between cross-links and alter the structural and mechanical properties. From a materials science point of view it is highly desirable to understand, affect, and manipulate such property changes in a controlled manner. Unfortunately, that has not yet been possible due to the lack of experimental characterization of such networks under controlled environments. In this work we expose a known rubber material to controlled dosages of γ radiation and utilize a newly developed multiquantum nuclear-magnetic-resonance technique to characterize the MWD as a function of radiation. We show that such data along with mechanical stress-strain measurements are amenable to accurate analysis by simple network models and yield important insights into radiation-induced molecular-level processes.

In light of the issue of oscillation propagation in neural networks, various topologies of FitzHugh-Nagumo neuron populations are investigated. External Gaussian white noise is injected into the first neuron only. Before the oscillation spreads to the other neurons in the network, some of the inherent stochasticity within the noise-induced oscillation of the first neuron is filtered out due to the neuron's nonlinear dynamics. Both the temporal and the spatial coherence of the evoked activity's propagation are analyzed in conjunction with the network topology randomness $p$, the coupling strength between neurons $g$, and the noise amplitude $D$. The temporal periodicity of the global neural network presents a typical coherence biresonance (CBR) characteristic with regard to the noise intensity. The network topology randomness exerts different influences on the resonance effects for different coupling strength regimes. At an intermediate coupling strength, the random shortcuts reinforce the interactions between the neurons, and then more stochasticity in the firings of the first neuron spreads within the network. Consequently, CBR is decreased with the increase of the network topology randomness. At a large coupling strength, the random shortcuts assist the nonlinearity in impairing the stochastic components, and consequently help to enhance the resonance effects, which differed significantly from previous related work. However, the degree of the spatial synchronization of the systems increases monotonically as the network topology randomness increases at any coupling strength.

The assembly properties of F-actin filaments in the presence of different biological cross-linker concentrations and types have been investigated using a combined approach of fluorescence confocal microscopy and coarse-grained molecular dynamics simulation. In particular for highly cross-linked regimes, new network morphologies are observed. Complex network formation and the details of the resulting structure are strongly dependent on the ratio of cross-linkers to actin monomers and cross-linker shape but only weakly dependent on overall actin concentration and filament length. The work presented here may help to provide some fundamental understanding of how excessive cross-linkers interact with the actin filament solution, creating different structures in the cell under high cross-linker concentrations. F-actin is not only of biological importance but also, as an example of a semiflexible polymer, has attracted significant interest in its physical behavior. In combination with different cross-linkers semiflexible filaments may provide new routes to bio-materials development and act as the inspiration for new hierarchical network-based materials.

Time-delayed feedback is a practical method for controlling various nonlinear dynamical systems. We consider its influence on the dynamics of a multicycle van der Pol oscillator that is birhythmic in nature. It has been shown that depending on the strength of delay the bifurcation space can be divided into two subspaces for which the dynamical response of the system is generically distinct. We observe an interesting collapse and revival of birhythmicity with the variation of the delay time. Depending on the parameter space the system also exhibits a transition between birhythmicity and monorhythmic behavior. Our analysis of amplitude equation corroborates with the results obtained by numerical simulation of the dynamics.

We study the kinetics of water escape from balls folded from square aluminum foils of different thickness and edge size. We found that the water discharge rate obeys the scaling relation $Q\propto V_P(M-M_r){}^{\alpha }$ with the universal scaling exponents $\alpha =3\pm 0.1$, where $V_P$ is the volume of pore space, $M(t)$ is the actual mass of water in the ball, and $M_r$ is the mass of residual water. The last is found to be a power-law function of $V_P$. The relation of these findings to the fractal geometry of randomly folded matter is discussed.

An analytical fluid model is proposed for artificially collimating fast electron beams produced in the interaction of ultraintense laser pulses with specially engineered low-density-core–high-density-cladding structure targets. Since this theory clearly predicts the characteristics of the spontaneously generated magnetic field and its dependence on the plasma parameters of the targets transporting fast electrons, it is of substantial relevance to the target design for fast ignition. The theory also reveals that the rapid changing of the flow velocity of the background electrons in a transverse direction (perpendicular to the flow velocity) caused by the density jump dominates the generation of a spontaneous interface magnetic field for these kinds of targets. It is found that the spontaneously generated magnetic field reaches as high as $100$ MG, which is large enough to collimate fast electron transport in overdense plasmas. This theory is also supported by numerical simulations performed using a two-dimensional particle-in-cell code. It is found that the simulation results agree well with the theoretical analysis.

We deal with the three-dimensional Gross-Pitaevskii equation which is used to describe a cloud of dilute bosonic atoms that interact under competing two- and three-body scattering potentials. We study the case where the cloud of atoms is strongly confined in two spatial dimensions, allowing us to build an unidimensional nonlinear equation,controlled by the nonlinearities and the confining potentials that trap the system along the longitudinal coordinate. We focus attention on specific limits dictated by the cubic and quintic coefficients, and we implement numerical simulations to help us to quantify the validity of the procedure.

Diffusion processes are relevant for a variety of phenomena in the natural sciences, including diffusion of cells or biomolecules within cells, diffusion of molecules on a membrane or surface, and diffusion of a molecular conformation within a complex energy landscape. Many experimental tools exist now to track such diffusive motions in single cells or molecules, including high-resolution light microscopy, optical tweezers, fluorescence quenching, and Förster resonance energy transfer (FRET). Experimental observations are most often indirect and incomplete: (1) They do not directly reveal the potential or diffusion constants that govern the diffusion process, (2) they have limited time and space resolution, and (3) the highest-resolution experiments do not track the motion directly but rather probe it stochastically by recording single events, such as photons, whose properties depend on the state of the system under investigation. Here, we propose a general Bayesian framework to model diffusion processes with nonlinear drift based on incomplete observations as generated by various types of experiments. A maximum penalized likelihood estimator is given as well as a Gibbs sampling method that allows to estimate the trajectories that have caused the measurement, the nonlinear drift or potential function and the noise or diffusion matrices, as well as uncertainty estimates of these properties. The approach is illustrated on numerical simulations of FRET experiments where it is shown that trajectories, potentials, and diffusion constants can be efficiently and reliably estimated even in cases with little statistics or nonequilibrium measurement conditions.

It is shown how to explicitly coarse-grain the microscopic dynamics of the rule-based Vicsek model for self-propelled agents. The hydrodynamic equations are derived by means of an Enskog-type kinetic theory. Expressions for all transport coefficients are given. The transition from a disordered to a flocking state, which at large particle speeds appears to be a fluctuation-induced first-order phase transition, is studied numerically and analytically.

We study the response of one-dimensional diffusive systems, consisting of particles interacting via symmetric or asymmetric exclusion, to time-periodic driving from two reservoirs coupled to the ends. The dynamical response of the system can be characterized in terms of the structure factor. We find an interesting frequency-dependent response; the current-carrying majority excitons cyclically crosses over from a short wavelength mode to a long wavelength mode with an intermediate regime of coexistence. This effect being boundary driven decays inversely with system size. Analytic calculations show that this behavior is common to diffusive systems, both in the absence and presence of correlations.

We investigate the dynamics of the majority-rule opinion formation model when voters experience differential latencies. With this extension, voters that just adopted an opinion go into a latent state during which they are excluded from the opinion formation process. The duration of the latent state depends on the opinion adopted by the voter. This leads to a bias toward consensus on the opinion that is associated with the shorter latency. We determine the exit probability and time to consensus for systems of $N$ voters. Additionally, we derive an asymptotic characterization of the time to consensus by means of a continuum model.

We consider open quantum systems with dynamics described by master equations that have perturbative expansions in the system-environment interaction. We show that, contrary to intuition, full-time solutions of order-$2n$ accuracy require an order-$(2n+2)$ master equation. We give two examples of such inaccuracies in the solutions to an order-$2n$ master equation: order-$2n$ inaccuracies in the steady state of the system and order-$2n$ positivity violations. We show how these arise in a specific example for which exact solutions are available. This result has a wide-ranging impact on the validity of coupling (or friction) sensitive results derived from second-order convolutionless, Nakajima-Zwanzig, Redfield, and Born-Markov master equations.