The response behavior of strongly nonlinear binary fluid convection to temporal modulation of the heating is investigated for the case of a negative Soret coupling between temperature and concentration gradients. Finite difference numerical simulations are performed for ethanol-water parameters subject to realistic boundary conditions. Traveling waves with modulated amplitudes and phase velocities, subharmonic standing waves, and synchronously modulated patterns with fixed spatial phase are found as stable solutions. The hysteretic transitions between subcritical traveling and standing waves that coexist bistably with the quiescent fluid state are investigated. Various diagnostic analysis tools are used to elucidate the complex spatiotemporal and bifurcation properties that are ultimately caused by nonlinear advection and mixing of concentration being very strong.

Nanoparticles produced in low-temperature plasmas (LTPs) are often found with crystalline structure, which suggests rather high temperatures during synthesis. This even applies to particles of high-melting-point materials, which is surprising, because the gas temperature in LTPs is often close to room temperature and particles may reside in the plasma only for a few milliseconds. In this paper, we present a numerical study of nanoparticle heating in plasmas through energetic surface reactions. We find that, under realistic plasma conditions, particle temperatures can exceed the gas temperature by many hundreds of kelvins. However, as the particle temperature is highly unsteady, it is more reasonable to consider particle temperature distribution functions. The dependence of the particle temperature distribution on particle size and particle density in a dusty LTP is discussed.

Rotation of a single dust granule (spin) is investigated experimentally in a stratified glow discharge. We employ the technique of measurement of the angular velocity, which is based on coordinate tracing of the light scattered by a hollow transparent particle. The angular velocity measured in the experiment is about 1–2 orders of magnitude higher than observed in previous experiments. We found that the angular velocity depends linearly on the discharge current. The mechanism of rotation of the granule is also described.

We propose a method to retrieve the effective constitutive parameters of a slab of bianisotropic metamaterial from reflection and transmission coefficients (or scattering parameters). In our retrieval method, only the scattering parameters in one propagation direction are used. Analytical inversion equations are derived in order to retrieve the effective parameters of the permittivity, permeability, and magnetoelectric coupling coefficient of the bianisotropic metamaterial. To demonstrate the validity of the method, we used it to retrieve the parameters of four different metamaterials, among which two were normal media without bianisotropy and the other two were bianisotropic media. In using our retrieval method, including bianisotropy, the intrinsic differences between a normal medium and a bianisotropic medium were illustrated clearly. Our simulation and retrieval results also corroborate the conclusions of the previously published literature.

We evaluate the percolation threshold values for a realistic model of continuum segregated systems, where random spherical inclusions forbid the percolating objects, modeled by hardcore spherical particles surrounded by penetrable shells, to occupy large regions inside the composite. We find that the percolation threshold is generally a nonmonotonous function of segregation, and that an optimal (i.e., minimum) critical concentration exists well before maximum segregation is reached. We interpret this feature as originating from a competition between reduced available volume effects and enhanced concentrations needed to ensure percolation in the highly segregated regime. The relevance with existing segregated materials is discussed.

Single protein molecules are regarded as contact networks of amino-acid residues. Relationships between the shortest path lengths and the numbers of residues within single molecules in the native structures are examined for various sized proteins. A universal scaling among proteins is obtained, which shows that the residue networks are fractal networks. This universal fractal network is characterized with three kinds of dimensions: the network topological dimension $D_c\approx 1.9$, the fractal dimension $D_f\approx 2.5$, and the spectral dimension $D_s\approx 1.3$. These values are in surprisingly good coincidence with those of the three-dimensional critical percolation cluster. Hence the residue contact networks in the protein native structures belong to the universality class of the three-dimensional percolation cluster. The criticality is relevant to the ambivalence in the protein native structures, the coexistence of stability and instability, both of which are necessary for protein functions.

A physiologically based model of the mechanisms that control the human sleep-wake cycle is formulated in terms of an equivalent nonconservative mechanical potential. The potential is analytically simplified and reduced to a quartic two-well potential, matching the bifurcation structure of the original model. This yields a dynamics-based model that is analytically simpler and has fewer parameters than the original model, allowing easier fitting to experimental data. This model is first demonstrated to semiquantitatively match the dynamics of the physiologically based model from which it is derived, and is then fitted directly to a set of experimentally derived criteria. These criteria place rigorous constraints on the parameter values, and within these constraints the model is shown to reproduce normal sleep-wake dynamics and recovery from sleep deprivation. Furthermore, this approach enables insights into the dynamics by direct analogies to phenomena in well studied mechanical systems. These include the relation between friction in the mechanical system and the timecourse of neurotransmitter action, and the possible relation between stochastic resonance and napping behavior. The model derived here also serves as a platform for future investigations of sleep-wake phenomena from a dynamical perspective.

In classical mechanics the complexity of a dynamical system is characterized by the rate of local exponential instability which effaces the memory of initial conditions and leads to practical irreversibility. In striking contrast, quantum mechanics appears to exhibit strong memory of the initial state. Here we introduce a notion of complexity for a quantum system and relate it to its stability and reversibility properties.

This work deals with soliton solutions of the nonlinear Schrödinger equation with cubic and quintic nonlinearities. We extend the procedure put forward in a recent paper [J. Belmonte-Beitia et al., Phys. Rev. Lett. 100, 164102 (2008)], and we solve the equation in the presence of a linear background and cubic and quintic interactions which are modulated in space and time. As a result, we show how a simple parameter can be used to generate brightlike or darklike localized nonlinear waves which oscillate in several distinct ways, driven by the space and time dependence of the parameters that control the trapping potential and the cubic and quintic nonlinearities.

Random phase approximation (RPA) has become one of the most used methods to describe the energy loss of charged particles in plasmas. The RPA is usually valid for high-velocity projectiles and in the weak coupling limit of the electron gas. However, for partially coupled plasmas RPA is not sufficient and the electronic coupling must be taken into account. This coupling can be considered through local field corrections. In this work, we have constructed a dynamical local field correction (DLFC) function from Mermin dielectric function. This DLFC function has the advantage to describe plasmas at any degeneracy. Mermin DLFC function is compared with other DLFC functions from the literature in the energy loss calculation. We see important differences between them; they are significant at low velocities and very relevant around the maximum, almost 30%.

We investigate transport in a disordered reaction-diffusion model consisting of particles which are allowed to diffuse, compete with one another $(2A\to A)$, give birth in small areas called “oases” $(A\to 2A)$, and die in the “desert” outside the oases $(A\to 0)$. This model has previously been used to study bacterial populations in the laboratory and is related to a model of plankton populations in the oceans. We first consider the nature of transport between two oases: In the limit of high growth rate, this is effectively a first passage process, and we are able to determine the first passage time probability density function in the limit of large oasis separation. This result is then used along with the theory of hopping conduction in doped semiconductors to estimate the time taken by a population to cross a large system.

The paper is devoted to the theoretical investigation of the magnetodipolar interparticle interaction effect on magnetization dynamics in moderately concentrated ferrofluids. We consider a homogenous (without particle aggregates) ferrofluid consisting of identical spherical particles and employ a rigid dipole model, where the magnetic moment of a particle is fixed with respect to the particle itself. In particular, for the magnetization relaxation after the external field is instantly switched off, we show that the magnetodipolar interaction leads to the increase of the initial magnetization relaxation time. For the complex ac susceptibility $\chi \left(\omega \right)={\chi }^{\prime }\left(\omega \right)+i{\chi }^{″}\left(\omega \right)$ we find that this interaction leads to an overall increase of ${\chi }^{″}\left(\omega \right)$ and shifts the ${\chi }^{″}\left(\omega \right)$ peak towards lower frequencies. Comparing results obtained with our analytical approach (second order virial expansion) to numerical simulation data (Langevin dynamics method), we demonstrate that the employed virial expansion approximation gives a good qualitative description of the ferrofluid magnetization dynamics and provides a satisfactory quantitative agreement with numerical simulations for the dc magnetization relaxation, up to the particle volume fraction $\varphi \sim 10\%$, and for the ac susceptibility, up to $\varphi \approx 5\%$.

The new area of nematic colloidal systems (or nematic emulsions) has been greatly guided by the fruitful analogy between the colloidal nematostatics and electrostatics. The elastic charge density representation of the colloidal nematostatics [V. M. Pergamenshchik and V. O. Uzunova, Eur. Phys. J. E 23, 161 (2007); Phys. Rev. E 76, 011707 (2007)] develops this analogy at the level of charge density and Coulomb interaction. It shows, however, that the colloidal nematostatics in three dimensions substantially differs from the electrostatics both in its mathematical structure and physical implications: the elastic charge and multipoles are dyads; similar charges attract while opposite charges repel each other, and so on. In this paper we consider the interaction between an elastic charge and elastic dipole with a nematic surface (wall) at which the director alignment is fixed. Using the mirror image method of electrostatics as a guiding idea, we develop the mirror image method in the nematostatics for arbitrary director tilt at the wall. A wall is shown to induce a repulsive $1∕R^4$ force on the elastic dipole which, in general, is accompanied by its reorientation. External torque on the colloid induces an elastic charge therein and triggers switching to the $1∕R^2$ repulsion. The dyadic nature of an elastic dipole is shown to be essential: a particle-wall interaction potential cannot be obtained in phenomenological theories with a single component dipole. In the introductory sections we discuss connection between the director-mediated interaction in two and three dimensions and the electrostatic interaction and consider different symmetries of elastic dipoles. Conservation of the torque components exerted upon colloids is shown to play the role of Gauss’ theorem and determines the elastic charge dyad.

We investigate the effects of particle size and shape on the quadrupolar (Saturn-ring-like) defect structures formed by a nematic liquid crystal around nm-sized and $\mu \mathrm{m}$-sized particles with spherical and spherocylindrical shapes. We also report results for the potentials of mean force in our systems, calculated using a mesoscale theory for the tensor order parameter $\mathbf{Q}$ of the nematic. Our results indicate that for pairs of nm-sized particles in close proximity, the nematic forms “entangled hyperbolic” defect structures regardless of the shape of the nanoparticles. In our calculations with nanoparticles we did not observe any other entangled or unentangled defect structures, in contrast to what was reported for pairs of $\mu \mathrm{m}$-sized spherical particles. Such a finding suggests that the “entangled hyperbolic” defect structures are the most stable for pairs of nanoparticles in close proximity. For pairs of $\mu \mathrm{m}$-sized particles, our results indicate that the nematic forms entangled “figure-of-eight” defect structures around pairs of spheres and spherocylinders. Our results suggest that the transition between “entangled hyperbolic” and figure-of-eight defect structures takes place when the diameter of the particle is between $D=100\mathrm{nm}$ and $1\mu \mathrm{m}$. We have also calculated the torques that develop when pairs of spherocylindrical nanoparticles in a nematic approach each other. Our calculations suggest that the nematic-mediated interactions between the nm-sized particles are fairly strong, up to 5700 $k_{B}T$ for the case of pairs of spherocylindrical nanoparticles arranged with their long axis parallel to each other. Furthermore, these interactions can make the particles to bind together at specific locations, and thus could be used to assemble the particles into ordered structures with different morphologies.

The Navier-Stokes equations and boundary conditions for viscous fluids of capillary size are formulated in curvilinear coordinates associated with a geometry of the fluid-gas interface. As a result, the fluid dynamics of drops and menisci, which takes into account the influence of gravitational forces and flows on the surface shape, can be described. This gives a convenient basis for numerical studies. Estimations of the effects are presented for the case of an evaporating sessile drop.

Pattern formation in an excitable medium described by a three-component reaction-diffusion system is investigated. Our focus is on stable self-organized pacemakers which give rise to spatially extended target patterns. Bistability of pulse solutions in the excitable regime is also reported, and interactions of the different pulses with each other and the pacemaker are studied. Self-organized pacemakers are created by a suitable perturbation from the steady state or through interaction of pulses. Bound states of one-dimensional pacemakers and phase flips are also observed.

In this paper we make a thorough exploration of the technique of partial control of chaotic systems. This control technique allows one to keep the trajectories of a dynamical system close to a chaotic saddle even if the control applied is smaller than the effects of environmental noise in the system, provided that the chaotic saddle is due to the existence of a horseshoelike mapping in phase space. We state this here in a mathematically precise way using the Conley-Moser conditions, and we prove that they imply that our partial control strategy can be applied. We also give an upper bound of the control-noise ratio needed to achieve this goal, and we describe how this technique can be applied for large noise values. Finally, we study in detail the effect of imperfect targeting in our control technique. All these results are illustrated numerically with the paradigmatic Hénon map.

The unpinning of a spiral wave from an anatomic obstacle by the application of a single stimulus near the core of the rotating wave was studied experimentally in a cell culture of cardiomyocyte monolayers as well as by computer simulations. It is shown that, with suitable positioning and timing, a single stimulus is sufficient for the successful unpinning of a pinned spiral wave. Successful unpinning is achieved when two conditions are fulfilled: (1) The stimulus is delivered in the vulnerable window of the rotating wave, and (2) the stimulus is delivered in a spatial zone in proximity to the obstacle, where the shape of the zone is defined by the phase of the anchored spiral wave. Two different scenarios for successful unpinning are discussed, which are distinguished by the distance to the stimuli applied to the obstacle.

We study experimentally and theoretically mixing at the external boundary of a submerged turbulent jet. In the experimental study we use particle image velocimetry and an image processing technique based on the analysis of the intensity of the Mie scattering to determine the spatial distribution of tracer particles. An air jet is seeded with the incense smoke particles, which are characterized by a large Schmidt number and a small Stokes number. We determine the spatial distributions of the jet fluid characterized by a high concentration of the particles and of the ambient fluid characterized by a low concentration of the tracer particles. In the data analysis we use two approaches, whereby one approach is based on the measured phase function for the study of the mixed state of two fluids. The other approach is based on the analysis of the two-point second-order correlation function of the particle number density fluctuations generated by tangling of the gradient of the mean particle number density by the turbulent velocity field. This gradient is formed at the external boundary of a submerged turbulent jet. We demonstrate that probability density function of the phase function of a jet fluid penetrating into an external flow and the two-point second-order correlation function of the particle number density do not have universal scaling and cannot be described by a power-law function. The theoretical predictions made in this study are in qualitative agreement with the obtained experimental results.

A collective variable approach is used to map domains of existence for $(3+1)$-dimensional spatiotemporal soliton solutions of a complex cubic-quintic Ginzburg-Landau equation. A rich variety of evolution behaviors, which include stationary and pulsating dissipative soliton dynamics, is revealed. Comparisons between the results obtained by the semianalytical approach of collective variables, and those obtained by a purely numerical approach show good agreement for a wide range of equation parameters. This also demonstrates the relevance of the semianalytical method for a systematic search of stability domains for spatiotemporal solitons, leading to a dramatic reduction of the computation time.