A liquid in Cassie-Baxter state above a structured superhydrophobic surface is ideally suited for surface driven transport due to its large free surface fraction in close contact to a solid. We investigate thermal Marangoni flow over a superhydrophobic array of fins oriented parallel or perpendicular to an applied temperature gradient. In the Stokes limit we derive an analytical expression for the bulk flow velocity above the surface and compare it with numerical solutions of the Navier-Stokes equation. Even for moderate temperature gradients comparatively large flow velocities are induced, suggesting to utilize this principle for microfluidic pumping.

Stochastic point processes with refractoriness appear frequently in the quantitative analysis of physical and biological systems, such as the generation of action potentials by nerve cells, the release and reuptake of vesicles at a synapse, and the counting of particles by detector devices. Here we present an extension of renewal theory to describe ensembles of point processes with time varying input. This is made possible by a representation in terms of occupation numbers of two states: active and refractory. The dynamics of these occupation numbers follows a distributed delay differential equation. In particular, our theory enables us to uncover the effect of refractoriness on the time-dependent rate of an ensemble of encoding point processes in response to modulation of the input. We present exact solutions that demonstrate generic features, such as stochastic transients and oscillations in the step response as well as resonances, phase jumps and frequency doubling in the transfer of periodic signals. We show that a large class of renewal processes can indeed be regarded as special cases of the model we analyze. Hence our approach represents a widely applicable framework to define and analyze nonstationary renewal processes.

We show in this paper that the sample (time average) mean-squared displacement (MSD) of the fractional Lévy $\alpha$-stable motion behaves very differently from the corresponding ensemble average (second moment). While the ensemble average MSD diverges for $\alpha <2$, the sample MSD may exhibit either subdiffusion, normal diffusion, or superdiffusion. Thus, $H$-self-similar Lévy stable processes can model either a subdiffusive, diffusive or superdiffusive dynamics in the sense of sample MSD. We show that the character of the process is controlled by a sign of the memory parameter $d=H-1/\alpha$. We also introduce a sample $p$-variation dynamics test which allows to distinguish between two models of subdiffusive dynamics. Finally, we illustrate a subdiffusive behavior of the fractional Lévy stable motion on biological data describing the motion of individual fluorescently labeled mRNA molecules inside live E. coli cells, but it may concern many other fields of contemporary experimental physics.

Cardiac arrhythmias, a precursor of fibrillationlike states in the beating heart, are associated with spiral waves, which are likely to become pinned to heterogeneities. Far-field pacing (FFP) is a promising method for terminating such waves by using heterogeneities in the tissue as internal pacing sites. In this study we investigated the role of multiple obstacles and their interaction during FFP. We show that a secondary nearby obstacle can significantly modulate the minimum electrical field in FFP. Further, we show that essentially the same effect can be observed in cardiac tissue culture, which is a powerful experimental model to simulate heart activity. Here, an isotropic cell distribution leads to domain formation of locally distributed depolarization sites. Both secondary obstacles and domain formation of local depolarization sites can modulate energy requirements to originate wave propagation on obstacles. Our theoretical result was confirmed by experiments with cardiomyocyte monolayers. This result may be useful for the future application of FFP to a real beating heart.

The transition from the behavior of a single dislocation interacting with a field of fixed obstacles to the collective motion of multiple dislocations is studied below the depinning transition (thermally activated glide). In absence of interactions, a truncated power law distribution of jump amplitudes (avalanches) with a diverging cutoff toward the critical point, and intermittency are observed. Interactions lead to a modification of the correlation length exponent below the critical point and to more pronounced intermittency, a dynamics more compatible to acoustic emission experimental data.

A purely kinetic instability of the dust acoustic mode in inhomogeneous plasmas is discussed. In the presence of a magnetic field, electrons and ions may be magnetized while at the same time dust grains may remain unmagnetized. Although the dynamics of the light species is strongly affected by the magnetic field, the dust acoustic mode may still propagate in practically any direction. The inhomogeneity implies a source of free energy for an instability that develops through the diamagnetic drift effects of the magnetized species. It is shown that this may be a powerful mechanism for the excitation of dust acoustic waves. The analysis presented in the work is also directly applicable to plasmas containing both positive and negative ions and electrons, provided that at least one of the two ion species is unmagnetized.

We present an equation for the heat-flux vector that goes beyond Fourier’s Law of heat conduction, in order to model shockwave propagation in gases. Our approach is motivated by the observation of a disequilibrium among the three components of temperature, namely, the difference between the temperature component in the direction of a planar shock wave, versus those in the transverse directions. This difference is most prominent near the shock front. We test our heat-flow equation for the case of strong shock waves in the ideal gas, which has been studied in the past and compared to Navier-Stokes solutions. The new heat-flow treatment improves the agreement with nonequilibrium molecular-dynamics simulations of hard spheres under strong shockwave conditions.

We study the steady state of a phase-separated driven Ising lattice gas in three dimensions using computer simulations with Kawasaki dynamics. An external force field $\mathbf{F}\left(z\right)$ acts in the $x$ direction parallel to the interface, creating a lateral order parameter current $j^x\left(z\right)$ which varies with distance $z$ from the interface. Above the roughening temperature, our data for “shearlike” linear variation of $\mathbf{F}\left(z\right)$ are in agreement with the picture wherein shear acts as effective confinement in this system, thus suppressing the interfacial capillary-wave fluctuations. We find sharper magnetization profiles and reduced interfacial width as compared to equilibrium. Pair correlations are more suppressed in the vorticity direction $y$ than in the driving direction; the opposite holds for the structure factor. Lateral transport of capillary waves occurs for those forms of $\mathbf{F}\left(z\right)$ for which the current $j^x\left(z\right)$ is an odd function of $z$, for example the shearlike drive, and a “steplike” driving field. For a V-shaped driving force no such motion occurs, but capillary waves are suppressed more strongly than for the shearlike drive. These findings are in agreement with our previous simulation studies in two dimensions. Near and below the (equilibrium) roughening temperature the effective-confinement picture ceases to work, but the lateral motion of the interface persists.

We investigate the Lévy glass, a mean-field spin-glass model with power-law distributed couplings characterized by a divergent second moment. By combining extensively many small couplings with a spare random backbone of strong bonds the model is intermediate between the Sherrington-Kirkpatrick and the Viana-Bray models. A truncated version where couplings smaller than some threshold $\epsilon$ are neglected can be studied within the cavity method developed for spin glasses on locally treelike random graphs. By performing the limit $\epsilon \to 0$ in a well-defined way we calculate the thermodynamic functions within replica symmetry and determine the de Almeida-Thouless line in the presence of an external magnetic field. Contrary to previous findings we show that there is no replica-symmetric spin-glass phase. Moreover we determine the leading corrections to the ground-state energy within one-step replica symmetry breaking. The effects due to the breaking of replica symmetry appear to be small in accordance with the intuitive picture that a few strong bonds per spin reduce the degree of frustration in the system.

We present a procedure for the determination of the interaction potential from the knowledge of the radial pair distribution function. The method, realized inside an inverse Monte Carlo simulation scheme, is based on the application of the maximum entropy principle of information theory and the interaction potential emerges as the asymptotic expression of the transition probability. Results obtained for high density monoatomic fluids are very satisfactory and provide an accurate extraction of the potential, despite a modest computational effort.

We introduce a multispecies lattice-gas model for motor protein driven collective cargo transport on cellular filaments. We use this model to describe and analyze the collective motion of interacting vesicle cargos being carried by oppositely directed molecular motors, moving on a single biofilament. Building on a totally asymmetric exclusion process to characterize the motion of the interacting cargos, we allow for mass exchange with the environment, input, and output at filament boundaries and focus on the role of interconversion rates and how they affect the directionality of the net cargo transport. We quantify the effect of the various different competing processes in terms of nonequilibrium phase diagrams. The interplay of interconversion rates, which allow for flux reversal and evaporation-deposition processes, introduces qualitatively unique features in the phase diagrams. We observe regimes of three-phase coexistence, the possibility of phase re-entrance, and a significant flexibility in how the different phase boundaries shift in response to changes in control parameters. The moving steady-state solutions of this model allows for different possibilities for the spatial distribution of cargo vesicles, ranging from homogeneous distribution of vesicles to polarized distributions, characterized by inhomogeneities or shocks. Current reversals due to internal regulation emerge naturally within the framework of this model. We believe that this minimal model will clarify the understanding of many features of collective vesicle transport, apart from serving as the basis for building more exact quantitative models for vesicle transport relevant to various in vivo situations.

We study the instability development during a viscous liquid drop impacting a smooth substrate, using high-speed photography. The onset time of the instability highly depends on the surrounding air pressure and the liquid viscosity: it decreases with air pressure with the power of minus two, and increases linearly with the liquid viscosity. From the real-time dynamics measurements, we construct a model which compares the destabilizing stress from air with the stabilizing stress from liquid viscosity. Under this model, our experimental results indicate that at the instability onset time, the two stresses balance each other. This model also illustrates the different mechanisms for the inviscid and viscous regimes previously observed: the inviscid regime is stabilized by the surface tension and the viscous regime is stabilized by the liquid viscosity.

An air bubble driven by ultrasound can become shape-unstable through a parametric instability. We report time-resolved optical observations of shape oscillations (mode $n=2$ to 6) of micron-sized single air bubbles. The observed mode number $n$ was found to be linearly related to the ambient radius of the bubble. Above the critical driving pressure threshold for shape oscillations, which is minimal at the resonance of the volumetric radial mode, the observed mode number $n$ is independent of the forcing pressure amplitude. The microbubble shape oscillations were also analyzed numerically by introducing a small nonspherical linear perturbation to a Rayleigh-Plesset-type equation, capturing the experimental observations in detail.

We develop a Monte Carlo wave function algorithm for the quantum linear Boltzmann equation, a Markovian master equation describing the quantum motion of a test particle interacting with the particles of an environmental background gas. The algorithm leads to a numerically efficient stochastic simulation procedure for the most general form of this integrodifferential equation, which involves a five-dimensional integral over microscopically defined scattering amplitudes that account for the gas interactions in a nonperturbative fashion. The simulation technique is used to assess various limiting forms of the quantum linear Boltzmann equation, such as the limits of pure collisional decoherence and quantum Brownian motion, the Born approximation, and the classical limit. Moreover, we extend the method to allow for the simulation of the dissipative and decohering dynamics of superpositions of spatially localized wave packets, which enables the study of many physically relevant quantum phenomena, occurring e.g., in the interferometry of massive particles.

We study the regression to the origin of a walker driven by dynamically generated fractional Brownian motion (FBM) and we prove that when the FBM scaling, i.e., the Hurst exponent $H<1/3$, the emerging inverse power law is characterized by a power index that is a compelling signature of the infinitely extended memory of the system. Strong memory effects leads to the relation $H=\theta /2$ between the Hurst exponent and the persistent exponent $\theta$, which is different from the widely used relation $H=1-\theta$. The latter is valid for $1/3<H<1$ and is known to be compatible with the renewal assumption.

We study the dynamical response to an external force $F$ for a particle performing a random walk in a two-dimensional quenched random potential of Hurst exponent $H=1/2$. We present numerical results on the statistics of first-passage times that satisfy closed backward master equations. We find that there exists a zero-velocity phase in a finite region of the external force $0<F<F_c$, where the dynamics follows the anomalous diffusion law $x\left(t\right)\sim \xi \left(F\right)t^{\mu \left(F\right)}$. The anomalous exponent $0<\mu \left(F\right)<1$ and the correlation length $\xi \left(F\right)$ vary continuously with $F$. In the limit of vanishing force $F\to 0$, we measure the following power laws: the anomalous exponent vanishes as $\mu \left(F\right)\propto F^a$ with $a\simeq 0.6$ (instead of $a=1$ in dimension $d=1$), and the correlation length diverges as $\xi \left(F\right)\propto F^{-\nu }$ with $\nu \simeq 1.29$ (instead of $\nu =2$ in dimension $d=1$). Our main conclusion is thus that the dynamics renormalizes onto an effective directed trap model, where the traps are characterized by a typical length $\xi \left(F\right)$ along the direction of the force, and by a typical barrier $1/\mu \left(F\right)$. The fact that these traps are “smaller” in linear size and in depth than in dimension $d=1$, means that the particle uses the transverse direction to find lower barriers.

We calculate non-Brownian fluid particle diffusion in a semidilute suspension of swimming micro-organisms. Each micro-organism is modeled as a spherical squirmer, and their motions in an infinite suspension otherwise at rest are computed by the Stokesian-dynamics method. In calculating the fluid particle motions, we propose a numerical method based on a combination of the boundary element technique and Stokesian dynamics. We present details of the numerical method and examine its accuracy. The limitation of semidiluteness is required to ensure accuracy of the fluid particle velocity calculation. In the case of a suspension of non-bottom-heavy squirmers the spreading of fluid particles becomes diffusive in a shorter time than that of the squirmers, and the diffusivity of fluid particles is smaller than that of squirmers. It is confirmed that the probability density distribution of fluid particles also shows diffusive properties. The effect of tracer particle size is investigated by inserting some inert spheres of the same radius as the squirmers, instead of fluid particles, into the suspension. The diffusivity for inert spheres is not less than one tenth of that for fluid particles, even though the particle size is totally different. Scaling analysis indicates that the diffusivity of fluid particles and inert spheres becomes proportional to the volume fraction of squirmers in the semidilute regime provided that there is no more than a small recirculation region around a squirmer, which is confirmed numerically. In the case of a suspension of bottom-heavy squirmers, horizontal diffusivity decreases considerably even with small values of the bottom heaviness, which indicates the importance of bottom heaviness in the diffusion phenomena. We believe that these fundamental findings will enhance our understanding of the basic mechanics of a suspension of swimming micro-organisms.

We have studied the effect of an external acoustic wave on bubble displacements inside an aqueous foam. The signature of the acoustic-induced bubble displacements is found using a multiple light scattering technique, and occurs as a modulation on the photon correlation curve. Measurements for various sound frequencies and amplitudes are compared to analytical predictions and numerical simulations. These comparisons finally allow us to elucidate the nontrivial acoustic displacement profile inside the foam; in particular, we find that the acoustic wave creates a localized shear in the vicinity of the solid walls holding the foam, as a consequence of inertial contributions. This study of how bubbles “dance” inside a foam as a response to sound turns out to provide new insights on foam acoustics and sound transmission into a foam, foam deformation at high frequencies, and analysis of light scattering data in samples undergoing nonhomogeneous deformations.