The dynamic behavior of liquid metal drops submitted to a high-frequency magnetic field is investigated experimentally. The motivation for this study comes from the coating industry. In this industry, liquid metals showing a free surface held in a dome-type shape are evaporated by applying electromagnetic pressure. The Galinstan drops are placed on a curved glass plate. A ringlike inductor fed by an alternating electrical current generates the magnetic field. The surface contour of the drop is observed using a high-speed camera system. The data are analyzed by utilizing image processing methods. In the experiment, we vary the inductor current $I$ and the drop volume $V$ while the frequency is fixed at $20\mathrm{kHz}$. Upon increasing the inductor current within the range $0<I<I_C$, we first observe a static axisymmetric squeezing. However, when the inductor current exceeds a certain critical value, i.e., $I>I_C$, these symmetric states become unstable to capillary waves. The critical current (critical electromagnetic Bond number) as well as the critical mode number, the critical frequency, and the amplitudes of the waves depend strongly on the volume (Bond number).

We construct families of two-component spatial solitons in a one-dimensional lattice with saturable on-site nonlinearity (focusing or defocusing) in a photorefractive crystal. We identify 14 species of vector solitons, depending on their type (bright/dark), phase (in-phase/staggered), and location on the lattice (on/off-site). Two species of the bright/bright type form entirely stable soliton families, four species are partially stable (depending on the value of the propagation constant), while the remaining eight species are completely unstable. “Symbiotic” soliton pairs (of the bright/dark type), which contain components that cannot exist in isolation in the same model, are found as well.

In this paper we present lattice Boltzmann (LB) schemes for convection diffusion coupled to fluid flow on two-dimensional rectangular lattices. Via inverse Chapman-Enskog analysis of LB schemes including source terms, we show that for consistency with physics it is required that the moments of the equilibrium distributions equal those of the Maxwell-Boltzmann distribution. These constraints can be satisfied for the rectangular D2Q9 lattice for only fluid flow in the weakly compressible regime. The analysis of source terms shows that fluxes are really defined on the boundaries of the Wigner-Seitz cells, and not on the lattice sites where the densities are defined—which is quite similar to the staggered grid finite-volume schemes. Our theoretical findings are confirmed by numerical solutions of benchmark problems for convection diffusion and natural convection. The lattice Boltzmann scheme shows remarkably good performance for convection diffusion, showing little to non-numerical diffusion or numerical dispersion, even at high grid Peclet numbers.

We scrutinize the anomalies in diffusion observed in an extended long-range system of classical rotors, the HMF model. Under suitable preparation, the system falls into long-lived quasi-stationary states for which superdiffusion of rotor phases has been reported. In the present work, we investigate diffusive motion by monitoring the evolution of full distributions of unfolded phases. After a transient, numerical histograms can be fitted by the $q$-Gaussian form $P\left(x\right)\propto {\{1+(q-1){[x∕\beta ]}^2\}}^{1∕(1-q)}$, with parameter $q$ increasing with time before reaching a steady value $q\simeq 3∕2$ (squared Lorentzian). From the analysis of the second moment of numerical distributions, we also discuss the relaxation to equilibrium and show that diffusive motion in quasistationary trajectories depends strongly on system size.

The free self-diffusion of an assembly of interacting particles confined on a quasi-one-dimensional ring is investigated both numerically and analytically. The interparticle pairwise interaction can be either attractive or repulsive and the energy barrier opposing thermal hopping of two particles one past the other is finite. Thus, for sufficiently long times, self-diffusion becomes normal or conventional diffusion. However, depending on the particle density, subdiffusive transients with exponent $1∕2$ and suppression of normal diffusion are observed. Above a certain density threshold, a sudden drop to zero of the diffusion coefficient for attractive particles signals the transition to a jammed phase. Furthermore, a Gaussian cluster of attractive particles condenses, by shrinking in size, for densities larger than such density threshold; lower density clusters spread out, regardless of the interaction sign, through a diffusion mechanism that is anomalous at short times, and normal for sufficiently long times. These effects could be observed in systems with colloidal particles, vortices, electrons, among other interacting particle systems.

The Tsallis entropy, which is a generalization of the Boltzmann-Gibbs entropy, plays a central role in nonextensive statistical mechanics of complex systems. A lot of efforts have recently been made on establishing a dynamical foundation for the Tsallis entropy. They are primarily concerned with nonlinear dynamical systems at the edge of chaos. Here, it is shown by generalizing a formulation of thermostatistics based on time averages recently proposed by Carati [A. Carati, Physica A 348, 110 (2005)] that, whenever relevant, the Tsallis entropy indexed by $q$ is temporally extensive: linear growth in time, i.e., finite entropy production rate. Then, the universal bound on the entropy production rate is shown to be $1∕\mid 1-q\mid$. The property of the associated probabilistic process, i.e., the sojourn time distribution, determining randomness of motion in phase space is also analyzed.

We perform extensive Potts model simulations of three-dimensional dry foam coarsening. Starting with 2.25 million bubbles, we have enough statistics to fulfill the three constraints required for the study of statistical scale invariance: first, enough time for the transient to end and reach the scaling state; then, enough time in the scaling state itself to characterize its properties; and finally, enough bubbles at the end to avoid spurious finite size effects. In the scaling state, we find that the average surface area of the bubbles increases linearly with time. The geometry (bubble shape and size) and topology (number of faces and edges), as well as their correlations, become constant in time. Their distributions agree with the data of the literature. We present an analytical model (universal, up to parameters extracted from the simulations) for a disordered foam minimizing its free energy, which agrees with the simulations. We discuss the limitations of the simulations and of the model.

We investigate theoretically the elliptical shapes of soft colloids in freely standing smectic-$C$ films, that have been reported recently. The colloids favor parallel alignment of the liquid crystal molecules at their surfaces and, for sufficiently strong anchoring, will generate a pair of defects at the poles of the colloidal particles. The elastic free energy of the liquid crystal matrix will, in turn, affect the shape of the colloids. In this study we will focus on elliptical soft colloids and determine how their equilibrium shapes depend on the elastic constants of the liquid crystal, the anchoring strength, the surface tension, and the size of the colloids. A shape diagram is obtained analytically, by minimizing the Frank elastic free energy, in the limit of small eccentricities. The analytical results are verified, and generalized to arbitrary eccentricities, by numerical minimization of an appropriate Landau free energy. The latter is required for an adequate description of the topological defects when the liquid crystal correlation length is comparable to the size of the colloidal particles.

We present a kinetic model allowing one to classify likely scenarios of protein-mediated communication between attached cells of two distinct types. In our treatment, messenger proteins, synthesized in type-1 cells, are considered to penetrate the external membrane of these cells, diffuse in the extracellular medium, associate with the receptors in the external membrane of cells of both types, and induce intracellular signal transduction cascades, influencing the development of cells. Protein degradation inside and outside cells is taken into account as well.

To characterize the dynamical features of seismicity as a complex phenomenon, the seismic data are mapped to a growing random graph, which is a small-world scale-free network. Here, hierarchical and mixing properties of such a network are studied. The clustering coefficient is found to exhibit asymptotic power-law decay with respect to connectivity, showing hierarchical organization. This structure is supported by not only main shocks but also small shocks, and may have its origin in the combined effect of vertex fitness and deactivation by stress release at faults. The nearest-neighbor average connectivity and the Pearson correlation coefficient are also calculated. It is found that the earthquake network has assortative mixing. This is a main difference of the earthquake network from the Internet with disassortative mixing. Physical implications of these results are discussed.

The one-dimensional motion of a chain of $N$ beads is studied to determine its drift velocity when an external field is applied. The dependences of the drift velocity with the chain length and field strength are addressed. Two cases are considered, chains with all their beads charged and chains having an end bead charged. In the last case, an analytical expression for the drift velocity is proposed for all $N$. Results are tested with the help of Monte Carlo simulations.

The probability distribution of the entropy production for the effusion of an ideal gas between two compartments is calculated explicitly. The fluctuation theorem is verified. The analytic results are in good agreement with numerical data from hard disk molecular dynamics simulations.

Using a high resolution Monte Carlo simulation technique based on a multihistogram method and cluster algorithm, we have investigated the critical properties of a coupled XY model, consisting of a sixfold symmetric hexatic and a hidden order parameter of threefold symmetry in two dimensions. The simulation results demonstrate a series of continuous transitions in which both kinds of orderings are established simultaneously. It is found that the specific-heat anomaly exponents for some regions in coupling constants space are in excellent agreement with the experimentally measured exponents extracted from heat-capacity data near the smectic-$A$–hexatic-$B$ transition of two-layer free standing films.

We investigate theoretically the phase diagram of an insoluble charged surfactant monolayer in contact with a semidilute polyelectrolyte solution (of opposite charge). The polyelectrolytes are assumed to have long-range and attractive (electrostatic) interaction with the surfactant molecules. In addition, we introduce a short-range (chemical) interaction which is either attractive or repulsive. The surfactant monolayer can have a lateral phase separation between dilute and condensed phases. Three different regimes of the coupled system are investigated depending on system parameters. A regime where the polyelectrolyte is depleted due to short range repulsion from the surface, and two adsorption regimes, one being dominated by electrostatics, whereas the other by short range chemical attraction (similar to neutral polymers). When the polyelectrolyte is more attracted (or at least less repelled) by the surfactant molecules as compared with the bare water-air interface, it will shift upwards the surfactant critical temperature. For repulsive short-range interactions the effect is opposite. Finally, the addition of salt to the solution is found to increase the critical temperature for attractive surfaces, but does not show any significant effect for repulsive surfaces.

A simple phenomenological model for describing the conformational dynamics of biological macromolecules via the nonlinearity-induced instabilities is proposed. It is shown that the interaction between charges and bending degrees of freedom of closed molecular aggregates may act as drivers giving impetus to conformational dynamics of biopolymers. It is demonstrated that initially circular aggregates may undergo transformation to polygonal shapes and possible application to aggregates of bacteriochlorophyl $a$ molecules is considered.

The influence of visible light on the velocities of spiral waves in the $\left[\mathrm{Ru}\right(\mathrm{bpy}){]}_3^{2+}$-catalyzed Belousov-Zhabotinsky (BZ) reaction is well documented. However, there are only few reports showing the effect of the way a change in the applied intensity is made, or on “desensitization” or “memory” type phenomena. In this paper, we present observations showing significant changes in spiral tip dynamics without varying the light intensity during the course of the experiments. We produce further evidence showing that changes in wave velocity and inhibitory effects are depending on whether the increase in intensity is applied in one large step or in a number of smaller steps. Also, the tip trajectories before and after the spiral waves have been subjected to an increase and subsequent decrease in intensity levels are different, suggesting a change in excitation of the system. The experimental results are separated into two groups depending on the light sensitivity of the system and the behavior of the spiral tip. Simulation results demonstrate that the different tip trajectories observed in the experiments can be modeled by only varying the excitation threshold. Our observations indicate that there must be at least two different competing pathways for the reaction mechanism not only in the oscillatory BZ system but also in excitable media and that intermediates may also play an important part in determining the excitation of the system and not just the initial concentrations of the reactants.

We study the decay rate of the Loschmidt echo or fidelity in a chaotic system under a time-dependent perturbation $V(\mathbf{q},t)$ with typical strength $\hslash ∕{\tau }_V$. The perturbation represents the action of an uncontrolled environment interacting with the system, and is characterized by a correlation length ${\xi }_0$ and a correlation time ${\tau }_0$. For small perturbation strengths or rapid fluctuating perturbations, the Loschmidt echo decays exponentially with a rate predicted by the Fermi “golden rule,” $1∕\tilde{\tau }={\tau }_c∕{\tau }_V^2$, where ${\tau }_c\sim \min [{\tau }_0,{\xi }_0∕v]$ and $v$ is the typical particle velocity. Whenever the rate $1∕\tilde{\tau }$ is larger than the Lyapunov exponent of the system, a perturbation independent Lyapunov decay regime arises. We also find that by speeding up the fluctuations (while keeping the perturbation strength fixed) the fidelity decay becomes slower, and hence one can protect the system against decoherence.

Drag reduction by polymers is bounded between two universal asymptotes, the von Kármán log law of the law and the maximum drag reduction (MDR) asymptote. It is theoretically understood why the MDR asymptote is universal, independent of whether the polymers are flexible or rodlike. The crossover behavior from the Newtonian von Kármán log law to the MDR is, however, not universal, showing different characteristics for flexible and rodlike polymers. In this paper we provide a theory for this crossover phenomenology.

A system of hydrodynamic equations in the presence of large-scale inhomogeneities for a high plasma beta solar wind is derived. The theory is derived under the assumption of low turbulent Mach number and is developed for the flows where the usual incompressible description is not satisfactory and a full compressible treatment is too complex for any analytical studies. When the effects of compressibility are incorporated only weakly, a new description, referred to as “nearly incompressible hydrodynamics,” is obtained. The nearly incompressible theory, was originally applied to homogeneous flows. However, large-scale gradients in density, pressure, temperature, etc., are typical in the solar wind and it was unclear how inhomogeneities would affect the usual incompressible and nearly incompressible descriptions. In the homogeneous case, the lowest order expansion of the fully compressible equations leads to the usual incompressible equations, followed at higher orders by the nearly incompressible equations, as introduced by Zank and Matthaeus. With this work we show that the inclusion of large-scale inhomogeneities (in this case time-independent and radially symmetric background solar wind) modifies the leading-order incompressible description of solar wind flow. We find, for example, that the divergence of velocity fluctuations is nonsolenoidal and that density fluctuations can be described to leading order as a passive scalar. Locally (for small lengthscales), this system of equations converges to the usual incompressible equations and we therefore use the term “locally incompressible” to describe the equations. This term should be distinguished from the term “nearly incompressible,” which is reserved for higher-order corrections. Furthermore, we find that density fluctuations scale with Mach number linearly, in contrast to the original homogeneous nearly incompressible theory, in which density fluctuations scale with the square of Mach number. Inhomogeneous nearly incompressible equations for higher order fluctuation components are derived and it is shown that they converge to the usual homogeneous nearly incompressible equations in the limit of no large-scale background. We use a time and length scale separation procedure to obtain wave equations for the acoustic pressure and velocity perturbations propagating on fast-time–short-wavelength scales. On these scales, the pseudosound relation, used to relate density and pressure fluctuations, is also obtained. In both cases, the speed of propagation (sound speed) depends on background variables and therefore varies spatially. For slow-time scales, a simple pseudosound relation cannot be obtained and density and pressure fluctuations are implicitly related through a relation which can be solved only numerically. Subject to some simplifications, a generalized inhomogeneous pseudosound relation is derived. With this paper, we extend the theory of nearly incompressible hydrodynamics to flows, including the solar wind, which include large-scale inhomogeneities (in this case radially symmetric and in equilibrium).

In this paper, we present a method for the solution of those linear transport processes that may be described by a master equation, such as electron, neutron, and photon transport, and more exotic variants thereof. We base our algorithm on a Markov process on a Voronoi-Delaunay grid, a nonperiodic lattice which is derived from a random point process that is chosen to optimally represent certain properties of the medium through which the transport occurs. Our grid is locally translation and rotation invariant in the mean. We illustrate our approach by means of a particular example, in which the expectation value of the length of a grid line corresponds to the local mean free path. In this example, the lattice is a direct representation of the “free path space” of the medium. Subsequently, transport is defined as simply moving particles from one node to the next, interactions taking place at each point. We derive the statistical properties of such lattices, describe the limiting behavior, and show how interactions are incorporated as global coefficients. Two elementary linear transport problems are discussed: that of free ballistic transport, and the transport of particles through a scattering medium. We also mention a combination of these two. We discuss the efficiency of our method, showing that it is much faster than most other methods because the operation count does not scale with the number of sources. We test our method by focusing on the transport of ionizing radiation through a static medium, and show that the computed results for the classical test case of an ionization front expanding in a homogeneous medium agree perfectly with the analytic solution. We finish by illustrating the efficiency and flexibility of our method with the results of a simulation of the reionization of the large scale structure of the Universe.