In this paper, the multipole expansion method is used to determine effective interaction potentials between particles in both classical dusty plasma and dense quantum plasma. In particular, formulas for interactions of dipole-dipole and charge-dipole pairs in a classical nondegenerate plasma as well as in degenerate quantum and semiclassical plasmas were derived. The potentials describe interactions between atoms, atoms and charged particles, dust particles in the complex plasma, atoms and electrons in the degenerate plasma, and metals. Correctness of the results obtained from the multipole expansion is confirmed by their agreement with the results based on other methods of statistical physics and dielectric response function. It is shown that the method of multipole expansion can be used to derive effective interaction potentials of compound particles, if the effect of the medium on the potential of individual particles comprising compound particles is known.

The von Neumann-Mullins law for the area evolution of a cell in the plane describes how a dry foam coarsens in time. Recent theory and experiment suggest that the dynamics are different on the surface of a three-dimensional object such as a sphere. This work considers the dynamics of dry foams on the surface of a sphere. Starting from first principles, we use computer simulation to show that curvature-driven motion of the cell boundaries leads to exponential growth and decay of the areas of cells, in contrast to the planar case where the growth is linear. We describe the evolution and distribution of cells to the final stationary state.

The relation between seismic moment and fractured area is crucial to earthquake hazard analysis. Experimental catalogs show multiple scaling behaviors, with some controversy concerning the exponent value in the large earthquake regime. Here, we show that the original Olami, Feder, and Christensen model does not capture experimental findings. Taking into account heterogeneous friction, the viscoelastic nature of faults, together with finite size effects, we are able to reproduce the different scaling regimes of field observations. We provide an explanation for the origin of the two crossovers between scaling regimes, which are shown to be controlled both by the geometry and the bulk dynamics.

Driven diffusive systems such as the zero-range process (ZRP) and the pair-factorized steady states (PFSS) stochastic transport process are versatile tools that lend themselves to the study of transport phenomena on a generic level. While their mathematical structure is simple enough to allow significant analytical treatment, they offer a variety of interesting phenomena. With appropriate dynamics, the ZRP and PFSS models feature a condensation transition where, for a supercritical density, the translational symmetry breaks spontaneously and excess particles form a single-site or spatially extended condensate, respectively. In this paper we numerically study the typical time scales of the two stages of this condensation process: Nucleation and coarsening. Nucleation is the first stage of condensation where the bulk system relaxes to its stationary distribution and droplet nuclei form in the system. These droplets then gradually grow or evaporate in the coarsening regime to coalesce in a single condensate when the system finally relaxes to the stationary state. We use the ZRP condensation model to discuss the choice of the estimation method for the nucleation time scale and present scaling exponents for the ZRP and PFSS condensation models with respect to the choice of the typical droplet nuclei mass. We then proceed to present scaling exponents in the coarsening regime of the ZRP for partially asymmetric dynamics and the PFSS model for symmetric and asymmetric dynamics.

We investigate the dynamical behavior of the Ising model under a zero-temperature quench with the initial fraction of up spins $0\le x\le 1$. In one dimension, the known results for persistence probability are verified; it shows algebraic decay for both up and down spins asymptotically with different exponents. It is found that the conventional finite-size scaling is valid here. In two dimensions, however, the persistence probabilities are no longer algebraic; in particular for $x\le 0.5$, persistence for the up (minority) spins shows the behavior $P_{\text{min}}\left(t\right)\sim t^{-\gamma }exp[-{(t/\tau )}^{\delta }]$ with time $t$, while for the down (majority) spins, $P_{\text{maj}}\left(t\right)$ approaches a finite value. We find that the timescale $\tau$ diverges as ${(x_c-x)}^{-\lambda }$, where $x_c=0.5$ and $\lambda \simeq 2.31$. The exponent $\gamma$ varies as ${\theta }_{2d}+c_0{(x_c-x)}^{\beta }$ where ${\theta }_{2d}\simeq 0.215$ is very close to the persistence exponent in two dimensions; $\beta \simeq 1$. The results in two dimensions can be understood qualitatively by studying the exit probability, which for different system size is found to have the form $E\left(x\right)=f\left[\left(\frac{x-x_c}{x_c}\right)L^{1/\nu }\right]$, with $\nu \approx 1.47$. This result suggests that $\tau \sim L^{\tilde{z}}$, where $\tilde{z}=\frac{\lambda }{\nu }=1.57\pm 0.11$ is an exponent not explored earlier.

Time-reversal methods are widely used to achieve wave focusing in acoustics and electromagnetics. Past time-reversal experiments typically require that a transmitter be initially present at the target focusing point, which limits the application of this technique. In this paper, we propose a method to focus waves at an arbitrary location inside a complex enclosure using a numerically calculated wave excitation signal. We use a semiclassical ray algorithm to calculate the signal that would be received at a transceiver port resulting from the injection of a short pulse at the desired target location. The time-reversed version of this signal is then injected into the transceiver port, and an approximate reconstruction of the short pulse is created at the target. The quality of the pulse reconstruction is quantified in three different ways, and the values of these metrics are shown to be predicted by the statistics of the scattering parameter $|S_{21}{|}^2$ between the transceiver and target points in the enclosure over the bandwidth of the pulse. We demonstrate the method experimentally using a flat microwave billiard, and we quantify the reconstruction quality as a function of enclosure loss, port coupling, and other considerations.

Inelastic collapse of stochastic trajectories of a randomly accelerated particle moving in half-space $z>0$ has been discovered by McKean [J. Math. Kyoto Univ. 2, 227 (1963)] and then independently rediscovered by Cornell et al. [Phys. Rev. Lett. 81, 1142 (1998)]. The essence of this phenomenon is that the particle arrives at the wall at $z=0$ with zero velocity after an infinite number of inelastic collisions if the restitution coefficient $\beta$ of particle velocity is smaller than the critical value ${\beta }_c=exp(-\pi /\sqrt{3})$. We demonstrate that inelastic collapse takes place also in a wide class of models with spatially inhomogeneous random forcing and, what is more, that the critical value ${\beta }_c$ is universal. That class includes an important case of inertial particles in wall-bounded random flows. To establish how inelastic collapse influences the particle distribution, we derive the exact equilibrium probability density function $\rho (z,v)$ for the particle position and velocity. The equilibrium distribution exists only at $\beta <{\beta }_c$ and indicates that inelastic collapse does not necessarily imply near-wall localization.

We present a self-contained discussion of the universality classes of the generalized epidemic process (GEP) on Poisson random networks, which is a simple model of social contagions with cooperative effects. These effects lead to rich phase transitional behaviors that include continuous and discontinuous transitions with tricriticality in between. With the help of a comprehensive finite-size scaling theory, we numerically confirm static and dynamic scaling behaviors of the GEP near continuous phase transitions and at tricriticality, which verifies the field-theoretical results of previous studies. We also propose a proper criterion for the discontinuous transition line, which is shown to coincide with the bond percolation threshold.

We introduce a variant of continuous random cascade models that extends former constructions introduced by Barral-Mandelbrot and Bacry-Muzy in the sense that they can be supported by sets of arbitrary fractal dimension. The so-introduced sets are exactly self-similar stationary versions of random Cantor sets formerly introduced by Mandelbrot as “random cutouts.” We discuss the main mathematical properties of our construction and compute its scaling properties. We then illustrate our purpose on several numerical examples and we consider a possible application to rainfall data. We notably show that our model allows us to reproduce remarkably the distribution of dry period durations.

Fluctuation scaling relates trial-to-trial variability to the average response by a power function in many physical processes. Here we address whether fluctuation scaling holds in sensory psychophysics and its functional role in visual processing. We report experimental evidence of fluctuation scaling in human color vision and form perception at threshold. Subjects detected thresholds in a psychophysical masking experiment that is considered a standard reference for studying suppression between neurons in the visual cortex. For all subjects, the analysis of threshold variability that results from the masking task indicates that fluctuation scaling is a global property that modulates detection thresholds with a scaling exponent that departs from 2, $\beta =2.48\pm 0.07$. We also examine a generalized version of fluctuation scaling between the sample kurtosis $K$ and the sample skewness $S$ of threshold distributions. We find that $K$ and $S$ are related and follow a unique quadratic form $K=\left(1.19\pm 0.04\right)S^2+\left(2.68\pm 0.06\right)$ that departs from the expected 4/3 power function regime. A random multiplicative process with weak additive noise is proposed based on a Langevin-type equation. The multiplicative process provides a unifying description of fluctuation scaling and the quadratic $S-K$ relation and is related to on-off intermittency in sensory perception. Our findings provide an insight into how the human visual system interacts with the external environment. The theoretical methods open perspectives for investigating fluctuation scaling and intermittency effects in a wide variety of natural, economic, and cognitive phenomena.

The nature of the $\theta$ point for a polymer in two dimensions has long been debated, with a variety of candidates put forward for the critical exponents. This includes those derived by Duplantier and Saleur for an exactly solvable model. We use a representation of the problem via the ${\mathrm{CP}}^{N-1}\sigma$ model in the limit $N\to 1$ to determine the stability of this critical point. First we prove that the Duplantier-Saleur (DS) critical exponents are robust, so long as the polymer does not cross itself: They can arise in a generic lattice model and do not require fine-tuning. This resolves a longstanding theoretical question. We also address an apparent paradox: Two different lattice models, apparently both in the DS universality class, show different numbers of relevant perturbations, apparently leading to contradictory conclusions about the stability of the DS exponents. We explain this in terms of subtle differences between the two models, one of which is fine-tuned (and not strictly in the DS universality class). Next we allow the polymer to cross itself, as appropriate, e.g., to the quasi-two-dimensional case. This introduces an additional independent relevant perturbation, so we do not expect the DS exponents to apply. The exponents in the case with crossings will be those of the generic tricritical $\mathrm{O}\left(n\right)$ model at $n=0$ and different from the case without crossings. We also discuss interesting features of the operator content of the ${\mathrm{CP}}^{N-1}$ model. Simple geometrical arguments show that two operators in this field theory, with very different symmetry properties, have the same scaling dimension for any value of $N$ (or, equivalently, any value of the loop fugacity). Also we argue that for any value of $N$ the ${\mathrm{CP}}^{N-1}$ model has a marginal odd-parity operator that is related to the winding angle.

Electrowetting (EW) enables facile manipulation of a liquid droplet on a hydrophobic surface. In this study, manipulation of an electrolyte droplet having a small floating object on it was investigated on a solid hydrophobic substrate under the EW process. Herein, the floating object exhibited a vertical motion under an applied electric field owing to the spreading and contraction of the droplet on its connecting substrates. The field-induced height variation of the floating object was significantly influenced by the thicknesses of the dielectric and hydrophobic materials. A small mass was also placed on the top floating object and its effect on the spreading of the droplet was observed. In this system, the height of the top floating object is precisely controllable under the application of an electric voltage. The proposed system is expected to be highly useful in the design of nano- and micro-oscillatory systems for microengineering.

We study Lévy flights with arbitrary index $0<\mu \le 2$ inside a potential well of infinite depth. Such a problem appears in many physical systems ranging from stochastic interfaces to fracture dynamics and multifractality in disordered quantum systems. The major technical tool is a transformation of the eigenvalue problem for initial fractional Schrödinger equation into that for Fredholm integral equation with hypersingular kernel. The latter equation is then solved by means of expansion over the complete set of orthogonal functions in the domain $D$, reducing the problem to the spectrum of a matrix of infinite dimensions. The eigenvalues and eigenfunctions are then obtained numerically with some analytical results regarding the structure of the spectrum.

Encounters between walkers performing a random motion on an appropriate structure can describe a wide variety of natural phenomena ranging from pharmacokinetics to foraging. On homogeneous structures the asymptotic encounter probability between two walkers is (qualitatively) independent of whether both walkers are moving or one is kept fixed. On infinite comblike structures this is no longer the case and here we deepen the mechanisms underlying the emergence of a finite probability that two random walkers will never meet, while one single random walker is certain to visit any site. In particular, we introduce an analytical approach to address this problem and even more general problems such as the case of two walkers with different diffusivity, particles walking on a finite comb and on arbitrary bundled structures, possibly in the presence of loops. Our investigations are both analytical and numerical and highlight that, in general, the outcome of a reaction involving two reactants on a comblike architecture can strongly differ according to whether both reactants are moving (no matter their relative diffusivities) or only one is moving and according to the density of shortcuts among the branches.

This article explores the excitation of different vibrational states in a spatially extended dynamical system through theory and experiment. As a prototypical example, we consider a one-dimensional packing of spherical particles (a so-called granular chain) that is subject to harmonic boundary excitation. The combination of the multimodal nature of the system and the strong coupling between the particles due to the nonlinear Hertzian contact force leads to broad regions in frequency where different vibrational states are possible. In certain parametric regions, we demonstrate that the nonlinear Schrödinger equation predicts the corresponding modes fairly well. The electromechanical model we apply predicts accurately the conversion from the obtained mechanical energy to the electrical energy observed in experiments.

Coupled oscillators can exhibit complex self-organization behavior such as phase turbulence, spatiotemporal intermittency, and chimera states. The latter corresponds to a coexistence of coherent and incoherent states apparently promoted by nonlocal or global coupling. Here we investigate the existence, stability properties, and bifurcation diagram of chimera-type states in a system with local coupling without different time scales. Based on a model of a chain of nonlinear oscillators coupled to adjacent neighbors, we identify the required attributes to observe these states: local coupling and bistability between a stationary and an oscillatory state close to a homoclinic bifurcation. The local coupling prevents the incoherent state from invading the coherent one, allowing concurrently the existence of a family of chimera states, which are organized by a homoclinic snaking bifurcation diagram.

Understanding why strains with different metabolic pathways that compete for a single limiting resource coexist is a challenging issue within a theoretical perspective. Previous investigations rely on mechanisms such as group or spatial structuring to achieve a stable coexistence between competing metabolic strategies. Nevertheless, coexistence has been experimentally reported even in situations where it cannot be attributed to spatial effects [Heredity 100, 471 (2008)]. According to that study a toxin expelled by one of the strains can be responsible for the stable maintenance of the two strain types. We propose a resource-based model in which an efficient strain with a slow metabolic rate competes with a second strain type which presents a fast but inefficient metabolism. Moreover, the model assumes that the inefficient strain produces a toxin as a by-product. This toxin affects the growth rate of both strains with different strength. Through an extensive exploration of the parameter space we determine the situations at which the coexistence of the two strains is possible. Interestingly, we observe that the resource influx rate plays a key role in the maintenance of the two strain types. In a scenario of resource scarcity the inefficient is favored, though as the resource influx rate is augmented the coexistence becomes possible and its domain is enlarged.

We merge the Kessler-Levine simple discrete model for Dictyostelium cyclic adenosine monophosphate (cAMP) production and diffusion with the Dilão-Hauser directional sensing aggregation mechanism. The resulting compound model describes all the known transient patterns that emerge during Dictyostelium aggregation, which include the spontaneous formation of cAMP self-sustained target and spiral waves and streaming. We show that the streaming patterns depend on the speed of the amoebae, on the relaxation time for the production of cAMP, on the cAMP degradation rate, and on directional sensing. Moreover, we show that different signaling centers emerge during Dictyostelium aggregation.

Mass fractal scaling, reflected in the mass fractal dimension $d_f$, is independently impacted by topology, reflected in the connectivity dimension $c$, and by tortuosity, reflected in the minimum dimension $d_{min}$. The mass fractal dimension is related to these other dimensions by $d_f=c{d}_{min}$. Branched fractal structures have a higher mass fractal dimension compared to linear structures due to a higher $c$, and extended structures have a lower dimension compared to convoluted self-avoiding and Gaussian walks due to a lower $d_{min}$. It is found, in this work, that macromolecules in thermodynamic equilibrium display a fixed mass fractal dimension $d_f$ under good solvent conditions, regardless of chain topology.  These equilibrium structures accommodate changes in chain topology such as branching $c$ by a decrease in chain tortuosity $d_{min}$. Symmetric star polymers are used to understand the structure of complex macromolecular topologies. A recently published hybrid Unified scattering function accounts for interarm correlations in symmetric star polymers along with polymer-solvent interaction for chains of arbitrary scaling dimension. Dilute solutions of linear, three-arm and six-arm polyisoprene stars are studied under good solvent conditions in deuterated $p$-xylene. Reduced chain tortuosity can be viewed as steric straightening of the arms. Steric effects for star topologies are quantified, and it is found that steric straightening of arms is more significant for lower-molecular-weight arms. The observation of constant $d_f$ is explained through a modification of Flory-Krigbaum theory for branched polymers.