The role of turbulence in current generation and self-excitation of magnetic fields has been studied in the geometry of a mechanically driven, spherical dynamo experiment, using a three-dimensional numerical computation. A simple impeller model drives a flow that can generate a growing magnetic field, depending on the magnetic Reynolds number $\mathrm{Rm}={\mu }_0\sigma Va$ and the fluid Reynolds number $\mathrm{Re}=Va∕\nu$ of the flow. For $\mathrm{Re}<420$, the flow is laminar and the dynamo transition is governed by a threshold of ${\mathrm{Rm}}_{\mathrm{crit}}=100$, above which a growing magnetic eigenmode is observed that is primarily a dipole field transverse to the axis of symmetry of the flow. In saturation, the Lorentz force slows the flow such that the magnetic eigenmode becomes marginally stable. For $\mathrm{Re}>420$ and $\mathrm{Rm}\sim 100$ the flow becomes turbulent and the dynamo eigenmode is suppressed. The mechanism of suppression is a combination of a time varying large-scale field and the presence of fluctuation driven currents (such as those predicted by the mean-field theory), which effectively enhance the magnetic diffusivity. For higher Rm, a dynamo reappears; however, the structure of the magnetic field is often different from the laminar dynamo. It is dominated by a dipolar magnetic field aligned with the axis of symmetry of the mean-flow, which is apparently generated by fluctuation-driven currents. The magnitude and structure of the fluctuation-driven currents have been studied by applying a weak, axisymmetric seed magnetic field to laminar and turbulent flows. An Ohm’s law analysis of the axisymmetric currents allows the fluctuation-driven currents to be identified. The magnetic fields generated by the fluctuations are significant: a dipole moment aligned with the symmetry axis of the mean-flow is generated similar to those observed in the experiment, and both toroidal and poloidal flux expulsion are observed.

We propose to employ the quasi-isotropic metamaterial (QIMM) slab to construct a polarization insensitive lens, in which both $E$- and $H$-polarized waves exhibit the same refocusing effect. For shallow incident angles, the QIMM slab will provide some degree of refocusing in the same manner as an isotropic negative index material. The refocusing effect allows us to introduce the ideas of paraxial beam focusing and phase compensation by the QIMM slab. On the basis of angular spectrum representation, a formalism describing paraxial beams propagating through a QIMM slab is presented. Because of the negative phase velocity in the QIMM slab, the inverse Gouy phase shift and the negative Rayleigh length of paraxial Gaussian beam are proposed. We find that the phase difference caused by the Gouy phase shift in vacuum can be compensated by that caused by the inverse Gouy phase shift in the QIMM slab. If certain matching conditions are satisfied, the intensity and phase distributions at object plane can be completely reconstructed at image plane. Our simulation results show that the superlensing effect with subwavelength image resolution could be achieved in the form of a QIMM slab.

In this paper, a two-phase lattice Boltzmann (LB) model, developed for simulating fluid flows on a Cartesian grid at high liquid-to-gas density ratios, is adapted to an axisymmetric coordinate system. This is achieved by incorporating additional source terms in the planar evolution equations for the density and pressure distribution functions such that the axisymmetric mass and momentum conservation equations are recovered in the macroscopic limit. Appropriate numerical treatment of the terms is performed to obtain stable computations at high density ratio for this axisymmetric model. The particle collision is modeled by employing multiple relaxation times to attain stability at low viscosity. The model is evaluated by verifying the Laplace-Young relation for a liquid drop, comparing computed frequency of oscillations of an initially ellipsoidal drop with analytical values and comparing the behavior of a spherical drop impinging on a wet wall with prior results. The time evolution of the radial distance of the tip of the corona, formed when the drop impinges, agrees well with prior data.

We probe the nature of the jamming transition of frictional granular media by studying their vibrational properties as a function of the applied pressure $p$ and friction coefficient $\mu$. The density of vibrational states exhibits a crossover from a plateau at frequencies $\omega \gtrsim {\omega }^{*}(p,\mu )$ to a linear growth for $\omega \lesssim {\omega }^{*}(p,\mu )$. We show that ${\omega }^{*}$ is proportional to $\mathrm{\Delta }z$, the excess number of contacts per grain relative to the minimally allowed, isostatic value. For zero and infinitely large friction, typical packings at the jamming threshold have $\mathrm{\Delta }z\to 0$, and then exhibit critical scaling. We study the nature of the soft modes in these two limits, and find that the ratio of elastic moduli is governed by the distance from isostaticity.

Many weighted scale-free networks are known to have a power-law correlation between strength and degree of nodes, which, however, has not been well explained. We investigate the dynamic behavior of resource-traffic flow on scale-free networks. The dynamical system will evolve into a kinetic equilibrium state, where the strength, defined by the amount of resource or traffic load, is correlated with the degree in a power-law form with tunable exponent. The analytical results agree well with simulations.

We study the impact of stochastic payoff variations with different distributions on the evolution of cooperation in the spatial prisoner’s dilemma game. We find that Gaussian-distributed payoff variations are most successful in promoting cooperation irrespective of the temptation to defect. In particular, the facilitative effect of noise on the evolution of cooperation decreases steadily as the frequency of rare events increases. Findings are explained via an analysis of local payoff ranking violations. The relevance of results for economics and sociology is discussed.

Complete chaotic synchronization of end lasers has been observed in a line of mutually coupled, time-delayed system of three lasers, with no direct communication between the end lasers. The present paper uses ideas from generalized synchronization to explain the complete synchronization in the presence of long coupling delays, applied to a model of mutually coupled semiconductor lasers in a line. These ideas significantly simplify the analysis by casting the stability in terms of the local dynamics of each laser. The variational equations near the synchronization manifold are analyzed, and used to derive the synchronization condition that is a function of parameters. The results explain and predict the dependence of synchronization on various parameters, such as time delays, strength of coupling and dissipation. The ideas can be applied to understand complete synchronization in other chaotic systems with coupling delays and no direct communication between synchronized subsystems.

Dynamic phase transition in the Ginzburg-Landau model of the anisotropic $XY$ spin system in a rotating external field is studied. We observe several types of oscillations, limit cycles, quasiperiodic oscillations and chaotic motions. It is found that limit cycle oscillations can have the periodicity of multiple times of the period of the applied field and that the system shows two kinds of scenarios leading to the onset of quasiperiodic oscillations, i.e., the saddle-node and Hopf bifurcations. Furthermore, this paper reports the findings of chaotic behaviors in the context of dynamic phase transition and that there exist two types of chaos with and without a certain kind of symmetry.

A qualitative geometrical analysis of the classical Coulomb three-body problem is developed. Three ions and atom are investigated: namely, ${\mathrm{H}}^{-}$, He, and ${\mathrm{Li}}^{+}$. The dynamics of these atom and ions is treated in the approximation that the nucleus has infinite mass. Geometrical structures of the dynamics starting from the initial conditions with zero velocities are elucidated. In particular, the distribution of the final states in the initial condition space, its fractal structure, and binary collision orbits are specified. As a result, it is found that binary collision orbits form a lobelike structure. It is shown that the lobelike structure is, in fact, fractal. The lobelike structure is continuously connected to the collinear $eZe$ configuration space, in which a well-known binary symbolic dynamics exists. With these observations, it is expected that as well as triple-collision orbits, binary-collision orbits also serve us some clue to find a symbolic dynamics for the full dynamics with zero angular momentum.

We rigorously derive an analytical expression for the energy equilibration rate in nonequilibrium electron-ion systems that is valid for a large class of systems including solid and liquid metals, warm dense matter, and hot, weakly coupled plasmas. To this end we first derive a generalized Langevin equation that describes the motion of the classical ions in the quantum mechanical environment of the electrons. A general expression for the energy relaxation rate is then obtained assuming that each subsystem is in thermal equilibrium with itself. Direct approximations naturally reproduce the popular results of Landau and Spitzer for hot plasmas and the “Fermi golden rule” result for dense matter. We propose a method to evaluate numerically the energy relaxation rate with finite-temperature density functional theory calculations in difficult regimes such as the warm dense matter regime where neither quantum nor strong coupling effects can be ignored.

We experimentally investigated the decay behavior with time $t$ of resonances near and at exceptional points, where two complex eigenvalues and also the associated eigenfunctions coalesce. The measurements were performed with a dissipative microwave billiard, whose shape depends on two parameters. The $t^2$ dependence predicted at the exceptional point on the basis of a two-state matrix model could be verified. Outside the exceptional point the predicted Rabi oscillations, also called quantum echoes in this context, were detected.

The Smoluchowski equation for a system of Brownian particles in a temperature gradient is derived from the Kramers equation by means of a multiple time-scale method. The interparticle interactions are assumed to be represented by a mean-field description. We present numerical results that compare well with the theoretical prediction together with an extensive discussion on the prescription of the Langevin equation in overdamped systems.

Oscillatory Zoning (OZ) is a phenomenon exhibited by many geologically formed crystals. It is characterized by quasiperiodic oscillations in the composition of a solid solution, caused by self-organization. We present a model for OZ. The growth mechanism applied includes species diffusion through the solution bulk, particle adsorption, surface diffusion, and subsequently desorption or incorporation into the crystal. This mechanism, in particular, can provide the synchronization effects necessary to reproduce the layered structure of experimentally obtained crystals, lacking in other models. We conduct a linear stability analysis combined with numerical simulations. Our results reproduce the experimental findings with respect to the patterns formed and a critical supersaturation necessary for OZ to occur.

We present a phenomenological model to interprete the optically induced easy direction in a nematic cell in the slab approximation. One of the surfaces of the sample is supposed to give strong anchoring, whereas the other, covered with photosensible material, very weak anchoring. We assume that a surface nematic molecule is submitted to a potential connected with its interaction with the surface easy direction, with the surface nematic field, and with the optical induced anisotropy. The case in which the coupling with the nematic order in the bulk is important is considered too. A differential equation for the time evolution of the surface director is proposed, in which the viscous torque is balanced by the torque related to the surface fields. We show that our theoretical predictions are in agreement with experimental data on the optical induced surface orientation. The dependence of the anchoring energy strength on the irradiation time for dye-doped liquid crystals is also investigated.

We explore large scale conformations of DNA molecules adsorbed on curved surfaces. For that purpose, we investigate the behavior of DNA adsorbed on periodically shaped cationic lipid membranes. These unique membrane morphologies are supported on grooved, one-dimensionally periodic microstructured surfaces. Strikingly, we find that these periodically structured membranes are capable to stretch DNA coils. We elucidate this phenomenon in terms of surface curvature dependent potential energy attained by the adsorbed DNA molecules. Due to it, DNA molecules undergo a localization transition causing them to stretch by binding to highly curved sections (edges) of the supported membranes. This effect provides a new venue for controlling conformations of semiflexible polymers such as DNA by employing their interactions with specially designed biocompatible surfaces. We report the first experimental observation of semiflexible polymers unbinding transition in which DNA molecules unbind from one-dimensional manifolds (edges) while remaining bound to two-dimensional manifolds (cationic membranes).

Many ribosomes simultaneously move on the same messenger RNA (mRNA), each synthesizing separately a copy of the same protein. In contrast to the earlier models, here we develop a “unified” theoretical model that not only incorporates the mutual exclusions of the interacting ribosomes, but also describes explicitly the mechanochemistry of each of these macromolecular machines during protein synthesis. Using analytical and numerical techniques of nonequilibrium statistical mechanics, we analyze the rates of protein synthesis and the spatiotemporal organization of the ribosomes in this model. We also predict how these properties would change with the changes in the rates of the various chemomechanical processes in each ribosome. Finally, we illustrate the power of this model by making experimentally testable predictions on the rates of protein synthesis and the density profiles of the ribosomes on some mRNAs in E-coli.

A new polarization spectroscopy model has been developed to analyze energetic electrons distributed in a three-dimensional phase space. This model calculates the polarization degrees for a given line of sight. Time-dependent polarization degrees of $\mathrm{He}\alpha$ line emitted from heliumlike chlorine ions was obtained for two different lines of sight by using three-dimensional electron velocity distributions provided with two-dimensional particle-in-cell simulations. These results demonstrate that the polarization degrees are sensitively dependent on the profile of the electron velocity distributions which are affected by the polarization of the laser pulse.

We show that in slowly generated two-dimensional packings of frictional spheres, a significant fraction of the friction forces lie at the Coulomb threshold—for small pressure $p$ and friction coefficient $\mu$, about half of the contacts. Interpreting these contacts as constrained leads to a generalized concept of isostaticity, which relates the maximal fraction of fully mobilized contacts and contact number. For $p\to 0$, our frictional packings approximately satisfy this relation over the full range of $\mu$. This is in agreement with a previous conjecture that gently built packings should be marginal solids at jamming. In addition, the contact numbers and packing densities scale with both $p$ and $\mu$.

We develop a technique for probing the harmonic measure of a diffusion-limited-aggregation (DLA) cluster surface with variable-size particles and generate 1000 clusters with $50\times {10}^6$ particles using an original off-lattice killing-free algorithm. Taking, in sequence, the limit of the vanishing size of the probing particles and then sending the growing cluster size to infinity, we achieve unprecedented accuracy in determining the fractal dimension $D=1.7100\left(2\right)$ crucial to the characterization of the geometric properties of DLA clusters.

The one-dimensional expanding ideal gas model is used to compute the exact nonequilibrium distribution function. The state of the system during the expansion is defined in terms of local thermodynamics quantities. The final equilibrium free energy, obtained a long time after the expansion, is compared against the free energy that appears in the Jarzynski equality. Within this model, where the Jarzynski equality holds rigorously, the free energy change that appears in the equality does not equal the actual free energy change of the system at any time of the process. More generally, the work bound that is obtained from the Jarzynski equality is an upper bound to the upper bound that is obtained from the first and second laws of thermodynamics. The cancellation of the dissipative (nonequilibrium) terms that result in the Jarzynski equality is shown in the framework of response theory. This is used to show that the intuitive assumption that the Jarzynski work bound becomes equal to the average work done when the system evolves quasistatically is incorrect under some conditions.