Some of the studies on the dynamics of cavitating bubbles often consider simplified submodels assuming uniform fluid properties within the gas bubbles, ignoring chemical reactions, or suppressing fluid transport phenomena across the bubble interface. Another group of works, to which the present contribution belongs, includes the radial dependence of the fluid variables. Important fluid processes that occur inside the gas bubble, such as chemical reactions, and across the bubble interface, such as heat and mass transfer phenomena, are here considered also. As a consequence, this model should yield more realistic results. In particular, it is found that water evaporation and condensation are fundamental transport phenomena in estimating the dissociation reactions of water into OH. The thermal and mass boundary layers and the radial variation of the chemical concentrations also seem essential for accurate predictions.

We predict the existence of gap solitons in a nonlinear, quadratic Fabry-Pérot negative index cavity. A peculiarity of a single negative index layer is that if magnetic and electric plasma frequencies are different it forms a photonic band structure similar to that of a multilayer stack composed of ordinary, positive index materials. This similarity also results in comparable field localization and enhancement properties that under appropriate conditions may be used to either dynamically shift the band edge, or for efficient energy conversion. We thus report that an intense, fundamental pump pulse is able to shift the band edge of a negative index cavity, and make it possible for a weak second harmonic pulse initially tuned inside the gap to be transmitted, giving rise to a gap soliton. The process is due to cascading, a well-known phenomenon that occurs far from phase matching conditions that limits energy conversion rates, it resembles a nonlinear third-order process, and causes pulse compression due to self-phase modulation. The symmetry of the equations of motion under the action of either an electric or a magnetic nonlinearity suggests that both nonlinear polarization and magnetization, or a combination of both, can lead to solitonlike pulses. More specifically, the antisymmetric localization properties of the electric and magnetic fields cause a nonlinear polarization to generate a dark soliton, while a nonlinear magnetization spawns a bright soliton.

We derive classes of exact solitonic solutions of the time-dependent Gross-Pitaevskii equation with repulsive and attractive interatomic interactions. The solutions correspond to a string of bright solitons with phase difference between adjacent solitons equal to $\pi$. While the relative phase, width, and distance between adjacent solitons turn out to be a constant of the motion, the center of mass of the string moves with a constant acceleration arising from the inhomogeneity of the background.

We describe a general method for analyzing a nonstationary stochastic process $X\left(t\right)$ which, unlike many of the previous analysis methods, does not require $X\left(t\right)$ to have any scaling feature. The method is used to study the fluctuations in the daily price of oil. It is shown that the returns time series, $y\left(t\right)=\ln [X(t+1)∕X\left(t\right)]$, is a stationary and Markov process, characterized by a Markov time scale $t_M$. The coefficients of the Kramers-Moyal expansion for the probability density function $P(y,t\mid y_0,t_0)$ are computed. $P(y,t\mid ,y_0,t_0)$ satisfies a Fokker-Planck equation, which is equivalent to a Langevin equation for $y\left(t\right)$ that provides quantitative predictions for the oil price over times that are of the order of $t_M$. Also studied is the average frequency of positive-slope crossings, ${\nu }_{\alpha }^{+}=P(y_i>\alpha ,y_{i-1}<\alpha )$, for the returns, where $T\left(\alpha \right)=1∕{\nu }_{\alpha }^{+}$ is the average waiting time for observing $y\left(t\right)=\alpha$ again.

We consider two basic types of Brownian motors which generate directed motion in a periodic asymmetric piecewise-linear potential as a result of random half-period shifts of the potential relief (flashing ratchets) or due to a temporally asymmetric unbiased force applied to the system (rocking ratchets). Analytical relationships have been derived which enable the comparison of the upper limits for the conventional and generalized energy conversion efficiencies in these motors. As found, the increasing amplitude of a sawtooth potential (or the decreasing temperature) makes the conventional efficiency tend to the unity limit faster for a rocking ratchet (in the absence of temporal asymmetry) than for a flashing ratchet. The inverse is true for the generalized efficiency. The potential amplitude being the same, the generalized efficiency is always less than the conventional efficiency. A decreased asymmetry of the potential always results in the reduction of both efficiencies. The temporal asymmetry of an unbiased force has an opposite effect on the conventional and generalized efficiencies: the former rises and the latter drops as the positive signal component becomes shorter in time and larger in amplitude.

We have studied the dynamics of a trimer of vinyl acetate (3VAc) using broadband dielectric spectroscopy over a wide temperature range to cover its primary and secondary relaxations. The dielectric spectra for the primary process over the entire temperature range have been described in terms of the Kohlraush-Williams-Watts approach [Williams and Watts, Trans. Faraday Soc. 66, 80 (1970)]. The dielectric relaxation is found to show a characteristic crossover in the dynamics at $261\mathrm{K}$ through the temperature dependence of different dielectric parameters, viz., the relaxation time, shape parameter, and dielectric strength. Unlike in the polymer counterpart, this crossover temperature has been found to be different from the apparent merging temperature of the primary and secondary processes. Moreover, a direct comparison between the shape parameters in the case of 3VAc and poly(vinyl acetate) (PVAc) reflected a near absence of chain connectivity effects on the relaxation shape at the high-temperature side, which is interpreted as the decoupling of side group (containing the dipolar entity) motions from the main chain in the case of PVAc. A secondary relaxation for 3VAc was observed below its glass transition temperature, which is found to show the same activation energy as the $\beta$ process in PVAc, for which new measurements have been made. However, their shapes showed different temperature dependences, which are discussed in terms of the molecular structure.

Star patterns, reminiscent of a wide range of diffusively controlled growth forms from snowflakes to Saffman-Taylor fingers, are ubiquitous features of ice-covered lakes. Despite the commonality and beauty of these “lake stars,” the underlying physical processes that produce them have not been explained in a coherent theoretical framework. Here we describe a simple mathematical model that captures the principal features of lake-star formation; radial fingers of (relatively warm) water-rich regions grow from a central source and evolve through a competition between thermal and porous media flow effects in a saturated snow layer covering the lake. The number of star arms emerges from a stability analysis of this competition and the qualitative features of this meter-scale natural phenomenon are captured in laboratory experiments.

We examine the influence of a thermal gradient on a classical reaction-diffusion system. The different instability regions in the appropriate parameter space are examined. We show how the imposed temperature gradient destabilizes a chemical front via the Soret effect, giving rise to both absolute and convective instability.

We present a simplified phase model for neuronal dynamics with spike timing-dependent plasticity (STDP). For asymmetric, experimentally observed STDP we find multistability: a coexistence of a fully synchronized, a fully desynchronized, and a variety of cluster states in a wide enough range of the parameter space. We show that multistability can occur only for asymmetric STDP, and we study how the coexistence of synchronization and desynchronization and clustering depends on the distribution of the eigenfrequencies. We test the efficacy of the proposed method on the Kuramoto model which is, de facto, one of the sample models for a description of the phase dynamics in neuronal ensembles.

We report some observations concerning the statistics of longest increasing subsequences (LIS). We argue that the expectation of LIS, its variance, and apparently the full distribution function appears in statistical analysis of some simple nonlinear stochastic partial differential equation in the limit of very low noise intensity.

We investigate the properties of a deterministic walk, whose locomotion rule is always to travel to the nearest site. Initially the sites are randomly distributed in a closed rectangular $(A∕L\times L)$ landscape and, once reached, they become unavailable for future visits. As expected, the walker step lengths present characteristic scales in one $(L\to 0)$ and two $(A∕L\sim L)$ dimensions. However, we find scale invariance for an intermediate geometry, when the landscape is a thin striplike region. This result is induced geometrically by a dynamical trapping mechanism, leading to a power-law distribution for the step lengths. The relevance of our findings in broader contexts—of both deterministic and random walks—is also briefly discussed.

The fluid phase behavior of charge-stabilized colloidal suspensions is explored by applying a variant of the Gibbs ensemble Monte Carlo simulation method to a coarse-grained one-component model with implicit microions and solvent. The simulations take as input linear-response approximations for the effective electrostatic interactions—a hard-sphere-Yukawa pair potential and a one-body volume energy. The conventional Gibbs ensemble trial moves are supplemented by exchange of (implicit) salt between coexisting phases, with acceptance probabilities influenced by the state dependence of the effective interactions. Compared with large-scale simulations of the primitive model, with explicit microions, our computationally practical simulations of the one-component model closely match the pressures and pair distribution functions at moderate electrostatic couplings. For macroion valences and couplings within the linear-response regime, deionized aqueous suspensions with monovalent microions exhibit separation into macroion-rich and macroion-poor fluid phases below a critical salt concentration. The resulting pressures and phase diagrams are in excellent agreement with predictions of a variational free energy theory based on the same model.

We study both theoretically and experimentally switching dynamics in asymmetric surface stabilized ferroelectric liquid crystal cells where the bounding surfaces are treated differently to produce asymmetry in their anchoring properties. Our electro-optic measurements of the switching voltage thresholds, $V_{+}$ and $-V_{-}$, that are determined by the peaks of the reversal polarization current reveal the frequency dependent shift of the hysteresis loop, $V_{+}-V_{-}$. We examine the predictions of the uniform dynamic model with the anchoring energy taken into account. It is found that the asymmetry effects are dominated by the polar contribution to the anchoring energy. Frequency dependence of the voltage thresholds is studied by analyzing the properties of time-periodic solutions to the dynamic equation (cycles). For this purpose, we apply the method linking the cycles and the fixed points of the composition of two parametrized half-period mappings for the approximate model. It is found that the cycles are unstable and can only be formed if the driving frequency is lower than its critical value. The polar anchoring parameter is estimated by making a comparison between the results of modeling and the experimental data for the shift vs frequency curve.

We have formulated a generalization of the energy boundary condition for fluid-fluid interfaces that includes the transport of the Gibbs excess internal energy. A newly measured surface property—the surface thermal capacity $c_{\sigma }$—appears in the result, and couples the temperature and velocity fields. If this term is not included in the energy boundary condition at liquid-vapor interfaces, the energy-conservation principle cannot be satisfied during steady-state evaporation of ${\mathrm{H}}_2\mathrm{O}\left(l\right)$ or ${\mathrm{D}}_2\mathrm{O}\left(l\right)$. The $c_{\sigma }$ term is possibly important in a number of other circumstances, and its importance can be determined from the magnitude of two nondimensional numbers.

The multidimensional formulation of the quantum lattice Boltzmann (QLB) scheme is validated against analytical solutions of the time-dependent nonrelativistic Schrödinger equation in two and three spatial dimensions. As a result, we demonstrate the viability of the quantum lattice Boltzmann scheme for the numerical solution of the time-dependent Schrödinger equation in multiple spatial dimensions. In addition, the links between the QLB scheme and sequential splitting methods for partial differential equations are also clarified.

In order to understand the nature of friction in dense granular materials, a discrete element simulation on granular layers subjected to isobaric plain shear is performed. It is found that the friction coefficient increases as the power of the shear rate, the exponent of which does not depend on the material constants. Using a nondimensional parameter that is known as the inertial number, the power law can be cast in a generalized form so that the friction coefficients at different confining pressures collapse on the same curve. We show that the volume fraction also obeys a power law.

We report on experimental studies of the collision process between an incident bead and a three-dimensional granular packing (made of particles identical to the impacting one). The understanding of such a process and the resulting ejection of particles is, in particular, crucial to describe eolian sand transport. We present here an extensive experimental analysis of the collision and ejection process. The analysis is two dimensional in the sense that we determined only the vertical component $V_z$ of the ejection velocity of the splashed particles and the horizontal component $V_x$ lying in the incident plane. We extracted in particular the distribution of the ejection velocities for a wide range of impact angles ${\theta }_i$ and incident velocity $V_i$. We show that the mean quadratic horizontal velocity of the splashed particles is almost insensitive to changes in the impact angle and velocity, while the mean quadratic vertical velocity slightly increases with increasing impact velocity (as $V_i^{1∕2}$). Moreover, the mean number of splashed particles per collision is found to be dependent on both the impact angle and velocity, and to scale with the impact speed as $V_i^{3∕2}$. A consequence of these outcomes is that the sum of the kinetic energy of the splashed particles is directly proportional to the kinetic energy of the incident particle. Finally, we provide the bivariate probability distribution function $P(V_x,V_z)$ of the ejection velocities and show that it can be approximated by the product of a log-normal distribution and a circular normal one.

The shear flow of a triblock copolymer micellar solution (PEO-PPO-PEO Pluronic P84 in brine) is investigated using simultaneous rheological and velocity profile measurements in the concentric cylinder geometry. We focus on two different temperatures below and above the transition temperature $T_c$ which was previously associated with the apparition of a stress plateau in the flow curve. (i) At $T=37.0°\mathrm{C}<T_c$, the bulk flow remains homogeneous and Newtonian-like, although significant wall slip is measured at the rotor that can be linked to an inflexion point in the flow curve. (ii) At $T=39.4°\mathrm{C}>T_c$, the stress plateau is shown to correspond to stationary shear-banded states characterized by two high shear rate bands close to the walls and a very weakly sheared central band, together with large slip velocities at the rotor. In both cases, the high shear branch of the flow curve is characterized by flow instability. Interpretations of wall slip, three-band structure, and instability are proposed in light of recent theoretical models and experiments.

Using high-resolution x-ray scattering, the effect of quenched random disorder (QRD) on the second-order nematic–smectic-$A$ $\left(N\text{−}\mathrm{Sm}A\right)$ phase transition in butyloxybenzilidene-octylaniline (4O.8) has been studied. 4O.8 is a nonpolar liquid crystal (LC) with a monomeric smectic-$A$ phase. The QRD is created by aerosil nanoparticles which gelate to form a three-dimensional network, confining the LC. The QRD caused by the aerosil gel generates quenched random fields acting on both the nematic and smectic-$A$ order parameters. This results in the destruction of the quasi-long-range order of the smectic-$A$ phase. The x-ray scattering data are modeled with a structure factor composed of two terms, one thermal and one static, corresponding to the connected and disconnected susceptibilities, respectively. Unlike previous studies, the two parts of the structure factor are decoupled by allowing different thermal and static correlation lengths. Our fitting procedure involves temperature-dependent and temperature-independent (global) variables. The amplitude and the parallel correlation length for the thermal part of the line-shape show critical-like behavior both above and below the transition temperature. Detailed analysis reveals that the thermal correlation length does not truly diverge at the phase transition. This effect is discussed on the basis of a cutoff for the divergence caused by the random fields generated by the aerosil network confining the liquid crystal. The intensity of the static term in the line-shape behaves like the order parameter squared at a conventional second-order phase transition. The effective order parameter critical exponent shows an evolution with increasing aerosil gel density ranging from the Gaussian tricritical value to the 3D-$XY$ value. The results of a pseudocritical scaling analysis are compared to an analysis of $4\mathrm{O}.8+\text{aerosil}$ heat capacity data and discussed using a phenomenological correlation between the nematic range of pure liquid crystals and the aerosil mass density, ${\rho }_s$.

We study the dynamics of populations of predators and preys using a mean field approach and a spatial model. The mean field description assumes that the individuals are homogeneously mixed and interact with one another with equal probability, so that space can be ignored. In the spatial model, on the other hand, predators can prey only in a certain neighborhood of their spatial location. We show that the size of these predation neighborhoods has dramatic effects on the dynamics and on the organization of the species in space. In the case of a three species food chain, in particular, the populations of predators display a sequence of apparently irregular outbreaks when the predation neighborhood has intermediate values, as compared to the size of the available space. Nonetheless, further increasing their size makes the outbreaks disappear and the dynamics approach that of the mean field model. Our study of synchronization also shows that the periodic behavior displayed by the average populations in a spatially extended system may hide the existence of patches that oscillate out of phase in a highly coordinated fashion.