Distributed-order fractional Langevin-like equations are introduced and applied to describe anomalous diffusion without unique diffusion or scaling exponent. It is shown that these fractional Langevin equations of distributed order can be used to model the kinetics of retarding subdiffusion whose scaling exponent decreases with time and the strongly anomalous ultraslow diffusion with mean square displacement which varies asymptotically as a power of logarithm of time.

In the present work, we study the dynamics of thermally excited fluctuations on the surface of non-Newtonian viscoelastic liquids, which shows complex behaviors such as crossover between the capillary wave and the elastic wave, and the coexistence of several modes. We show that the power spectrum is separated into surface localized modes and the bulk shear modes, and they are decomposed further into several modes using the partial fraction expansion. The peak positions of these modes are characterized by roots of a polynomial equation. We calculate the decomposition of the surface wave spectra numerically, and discuss evolution of constituent peaks with liquid parameters.

We consider emergent collective behavior of a multicellular biological system. Specifically, we investigate the role of hypoxia (lack of oxygen) in migration of brain tumor cells. We performed two series of cell migration experiments. In the first set of experiments, cell migration away from a tumor spheroid was investigated. The second set of experiments was performed in a typical wound-healing geometry: Cells were placed on a substrate, a scratch was made, and cell migration into the gap was investigated. Experiments show a surprising result: Cells under normal and hypoxic conditions have migrated the same distance in the “spheroid” experiment, while in the “scratch” experiment cells under normal conditions migrated much faster than under hypoxic conditions. To explain this paradox, we formulate a discrete stochastic model for cell dynamics. The theoretical model explains our experimental observations and suggests that hypoxia decreases both the motility of cells and the strength of cell-cell adhesion. The theoretical predictions were further verified in independent experiments.

By use of Boltzmann’s equation to describe an ensemble of particles under the influence of a friction force, Boltzmann’s $H$ theorem is refined to explicitly include frictional dissipation, the accompanying fluctuations being modeled via an added diffusive, Fokker-Planck term. If the friction force per particle mass is proportional to velocity, as is the case with viscous drag with a friction coefficient $\gamma$, Boltzmann’s $H$ theorem for the time rate of change of the quantity $H$ reads $\mathit{dH}/\mathit{dt}⩽\gamma$. The classical formulation stating that $H$ can never increase is thus replaced by the statement that $H$ cannot increase at a rate higher than $\gamma$, a general result but of particular relevance when fluctuations are negligible and the system is far from equilibrium. When the particles are not far from thermal equilibrium, an alternative, more suitable expression emerges which can be written in the form of a Clausius inequality.

We study, both analytically and numerically, the cascade of failures in two coupled network systems A and B, where multiple support-dependence relations are randomly built between nodes of networks A and B. In our model we assume that each node in one network can function only if it has at least a single support link connecting it to a functional node in the other network. We assume that networks A and B have (i) sizes $N^A$ and $N^B$, (ii) degree distributions of connectivity links $P^A(k)$ and $P^B(k)$, (iii) degree distributions of support links ${\mathrm{P̃}}^A(k)$ and ${\mathrm{P̃}}^B(k)$, and (iv) random attack removes $(1-R^A)N^A$ and $(1-R^B)N^B$ nodes form the networks A and B, respectively. We find the fractions of nodes ${\mu }_{\infty }^A$ and ${\mu }_{\infty }^B$ which remain functional (giant component) at the end of the cascade process in networks A and B in terms of the generating functions of the degree distributions of their connectivity and support links. In a special case of Erdős-Rényi networks with average degrees $a$ and $b$ in networks A and B, respectively, and Poisson distributions of support links with average degrees $\mathrm{ã}$ and $\mathrm{b̃}$ in networks A and B, respectively, ${\mu }_{\infty }^A=R^A[1-\exp (-\mathrm{ã}{\mu }_{\infty }^B)][1-\exp (-a{\mu }_{\infty }^A)]$ and ${\mu }_{\infty }^B=R^B[1-\exp (-\mathrm{b̃}{\mu }_{\infty }^A)][1-\exp (-b{\mu }_{\infty }^B)]$. In the limit of $\mathrm{ã}\to \infty$ and $\mathrm{b̃}\to \infty$, both networks become independent, and our model becomes equivalent to a random attack on a single Erdős-Rényi network. We also test our theory on two coupled scale-free networks, and find good agreement with the simulations.

Pumping of a compressible viscous fluid through a planar duct or a circular tube due to running waves on the surface of the duct or tube is studied on the basis of the Navier-Stokes equations. The flux is calculated to second order in the amplitude of the exciting surface waves. It is shown that the flux exhibits a resonance as a function of frequency, leading to a high pumping velocity near resonance.

The spectral emission of atoms in a dusty radio frequence (rf) discharge plasma in argon and helium has been measured with a gated ICCD camera. The spatially and temporally resolved emission/excitation of the argon and helium atoms during the rf cycle in the dusty discharge was compared to the dust-free case. In the bulk plasma above the dust cloud, the emission is clearly enhanced in the dusty discharge with respect to the pure discharge, whereas in the sheath the emission is reduced. In addition, the emission of a dusty argon plasma is studied via particle-particle particle-mesh (P${}^3\mathrm{M}$) simulations. The rf dynamics with a single dust particle trapped in the sheath was calculated. Like in the experiment the dust modifies the atomic emission. The spatiotemporal excitation pattern of the experiment is reproduced and a detailed understanding of the difference in excitation of the discharge with and without dust is presented.

A weakly magnetized expanding hydrogen plasma, created by a cascaded arc, was investigated using optical emission spectroscopy. The emission of the expanding plasma is dominated by ${\mathrm{H}}_{\alpha }$ emission in the first part of the plasma expansion, after which a sharp transition to a blue afterglow is observed. The position of this sharp transition along the expansion axis depends on the magnetic field strength. The blue afterglow emission is associated with population inversion of the electronically excited atomic hydrogen states $n=4-6$ with respect to $n=3$. By comparing the measured densities with the densities using an atomic collisional radiative model, we conclude that atomic recombination processes cannot account for the large population densities observed. Therefore, molecular processes must be important for the formation of excited states and for the occurrence of population inversion. This is further corroborated at the transition from red to blue, where a hollow profile of the excited states $n=4-6$ in the radial direction is observed. This hollow profile is explained by the molecular mutual neutralization process of $\mathrm{H}{{}_2}^{+}$ with ${\mathrm{H}}^{-}$, which has a maximum production for excited atomic hydrogen $1-2$ cm outside the plasma center.

We revisit the problem of the spontaneous symmetry breaking (SSB) of solitons in two-component linearly coupled nonlinear systems, adding the nonlinear interaction between the components. With this feature, the system may be realized in new physical settings, in terms of optics and the Bose-Einstein condensate (BEC). SSB bifurcation points are found analytically, for both symmetric and antisymmetric solitons (the symmetry between the two components is meant here). Asymmetric solitons, generated by the bifurcations, are described by means of the variational approximation (VA) and numerical methods, demonstrating good accuracy of the variational results. In the space of the self-phase-modulation (SPM) parameter and soliton’s norm, a border separating stable symmetric and asymmetric solitons is identified. The nonlinear coupling may change the character of the SSB bifurcation, from subcritical to supercritical. Collisions between moving asymmetric and symmetric solitons are investigated too. Antisymmetric solitons are destabilized by a supercritical bifurcation, which gives rise to self-confined modes featuring Josephson oscillations, instead of stationary states with broken antisymmetry. An additional instability against delocalized perturbations is also found for the antisymmetric solitons.

Random networks of symmetrically coupled, excitable elements can self-organize into coherently oscillating states if the networks contain loops (indeed loops are abundant in random networks) and if the initial conditions are sufficiently random. In the oscillating state, signals propagate in a single direction and one or a few network loops are selected as driving loops in which the excitation periodically circulates. We analyze the mechanism, describe the oscillating states, identify the pacemaker loops, and explain key features of their distribution.

We carry out a finite-size scaling analysis of the jamming transition in frictionless bidisperse soft core disks in two dimensions. We consider two different jamming protocols: (i) quench from random initial positions and (ii) quasistatic shearing. By considering the fraction of jammed states as a function of packing fraction for systems with different numbers of particles, we determine the spatial correlation length critical exponent $\nu \approx 1$ and show that corrections to scaling are crucial for analyzing the data. We show that earlier numerical results yielding $\nu <1$ are due to the improper neglect of these corrections.

The modification of the glass transition in confined domains, particularly the length scales associated with cooperative motion, remains a mystery. Hard-sphere suspensions are confined between two surfaces to progressively smaller dimensions to probe the confinement effect on the growth of dynamic heterogeneities via confocal microscopy. The confinement length scale is defined as the critical spacing where deviations from bulk behaviors begin and is observed to occur at progressively larger gap spacings as the volume fraction is increased. However, dynamic length scales extracted from the four-point correlation function are on average smaller than the confinement length scale.

We investigate the condensation phenomena of the generalized symmetric conserved-mass aggregation (GSCA) model on scale-free networks (SFNs) with degree distribution $P(k)~k^{-\gamma }$. In the GSCA model the whole mass of a node with mass $m$ isotropically diffuses to one of directly linked nodes with rate $D(m)=m^{-\alpha }$. With rate $\omega$, a mass $\delta m=m^{-\lambda }$ is fragmented from the mass $m$ and also isotropically diffuses. From a mean-field analysis we map out the full $\alpha$-$\lambda$ phase diagram for a given $\gamma (⩾$2). We also numerically confirm the mean-field phase diagram.

We propose a simple generalization of the explosive percolation process [Achlioptas et al., Science 323, 1453 (2009)], and investigate its structural and transport properties. In this model, at each step, a set of $q$ unoccupied bonds is randomly chosen. Each of these bonds is then associated with a weight given by the product of the cluster sizes that they would potentially connect, and only that bond among the $q$ set which has the smallest weight becomes occupied. Our results indicate that, at criticality, all finite-size scaling exponents for the spanning cluster, the conducting backbone, the cutting bonds, and the global conductance of the system, change continuously and significantly with $q$. Surprisingly, we also observe that systems with intermediate values of $q$ display the worst conductive performance. This is explained by the strong inhibition of loops in the spanning cluster, resulting in a substantially smaller associated conducting backbone.

We analyze diffusion in a finite domain with a position-dependent diffusion coefficient in terms of a stochastic hopping process. Via a coordinate transformation, we map the original system onto a problem with constant diffusion but nontrivial potential. In this way we show that a regime with enhanced diffusion acts as a potential barrier. We compute first-passage time distributions, hopping rates, and eigenvalues of the Fokker-Planck operator, and thereby verify that diffusion with a heat barrier is equivalent to a hopping process between metastable states.

Granular temperature underpins the kinetic theory of granular flows as well as models for heat transfer, segregation, erosion, attrition, and aggregation in various granular systems. It is generally thought that granular temperature in vibrated granular systems scales with the square of the peak vibrational velocity. However, careful diffusing wave spectroscopy experiments and statistical analysis of data obtained from these for a three-dimensional vibrated bed of monodisperse glass particles reveals that the granular temperature is also significantly correlated with other vibrational parameters. Reexamination of previously published data obtained by others using alternative methods further supports our thus far unremarked upon observation reported here.

An energy landscape view of phase separation and nonideality in binary mixtures is developed by exploring their potential energy landscape (PEL) as functions of temperature and composition. We employ molecular dynamics simulations to study a model that promotes structure breaking in the solute-solvent parent binary liquid, at low temperatures. The PEL of the system captures the potential energy distribution of the inherent structures (IS) of the system and is obtained by removing the kinetic energy (including that of intermolecular vibrations). The broader distribution of the inherent structure energy for structure breaking liquid than that of the structure making liquid demonstrates the larger role of entropy in stabilizing the parent liquid of the structure breaking type of binary mixtures. At high temperature, although the parent structure of the structure breaking binary mixture is homogenous, the corresponding inherent structure is found to be always phase separated, with a density pattern that exhibits marked correlation with the energy of its inherent structure. Over a broad range of intermediate inherent structure energy, bicontinuous phase separation prevails with interpenetrating stripes as signatures of spinodal decomposition. At low inherent structure energy, the structure is largely phase separated with one interface where as at high inherent structure energy we find nucleation type growth. Interestingly, at low temperature, the average inherent structure energy ($\langle E_{\mathrm{IS}}\rangle$) exhibits a drop with temperature which signals the onset of crystallization in one of the phases while the other remains in the liquid state. The nonideal composition dependence of viscosity is anticorrelated with average inherent structure energy.

We consider control of reaction and population systems by imposing transitions between states with different numbers of particles or individuals. The transitions take place at predetermined instants of time. Even where they are significantly less frequent than spontaneous transitions, they can exponentially strongly modify the rates of rare events, including switching between metastable states or population extinction. We also study optimal control of rare events. Specifically, we are interested in the optimal control of disease extinction for a limited vaccine supply. A comparison is made with control of rare events by modulating the rates of elementary transitions rather than imposing transitions deterministically. It is found that, unexpectedly, for the same mean control parameters, controlling the transitions rates can be more efficient.

Zipf’s law seems to be ubiquitous in human languages and appears to be a universal property of complex communicating systems. Following the early proposal made by Zipf concerning the presence of a tension between the efforts of speaker and hearer in a communication system, we introduce evolution by means of a variational approach to the problem based on Kullback’s Minimum Discrimination of Information Principle. Therefore, using a formalism fully embedded in the framework of information theory, we demonstrate that Zipf’s law is the only expected outcome of an evolving communicative system under a rigorous definition of the communicative tension described by Zipf.

In this paper we calculate the contribution to the ponderomotive force in a plasma from the electron spin using a recently developed model. The spin-fluid model used in the present paper contains spin-velocity correlations, in contrast to previous models used for the same purpose. Is its then found that previous terms for the spin-ponderomotive force are recovered, but also that additional terms appear. Furthermore, the results due to the spin-velocity correlations are confirmed using the spin-kinetic theory. The significance of our results is discussed.