In this paper we attack the challenging problem of modeling subdiffusion with an arbitrary space-time-dependent driving. Our method is based on a combination of the Langevin-type dynamics with subordination techniques. For the case of a purely time-dependent force, we recover the death of linear response and field-induced dispersion—two significant physical properties well-known from the studies based on the fractional Fokker-Planck equation. However, our approach allows us to study subdiffusive dynamics without referring to this equation.

The effects of midrange repulsion in lattice Boltzmann models on the coalescence and/or breakup behavior of single-component, nonideal fluids are investigated. It is found that midrange repulsive interactions allow the formation of spraylike, multidroplet configurations, with droplet size directly related to the strength of the repulsive interaction. The simulations show that just a tiny 10% of midrange repulsive pseudoenergy can boost the surface:volume ratio of the phase-separated fluid by nearly two orders of magnitude. Drawing upon a formal analogy with magnetic Ising systems, a pseudopotential energy is defined, which is found to behave similar to a quasiconserved quantity for most of the time evolution. This offers a useful quantitative indicator of the stability of the various configurations, thus helping the task of their interpretation and classification. The present approach appears to be a promising tool for the computational modeling of complex flow phenomena, such as atomization, spray formation, microemulsions, breakup phenomena, and possibly glassylike systems as well.

The existence of a special periodic window in the two-dimensional parameter space of an experimental Chua’s circuit is reported. One of the main reasons that makes such a window special is that the observation of one implies that other similar periodic windows must exist for other parameter values. However, such a window has never been experimentally observed, since its size in parameter space decreases exponentially with the period of the periodic attractor. This property imposes clear limitations for its experimental detection.

The flow properties in a granular system confined by a rapidly rotated bottom surface and fixed walls are investigated. Above sufficiently high rotation rates the system enters a state in which the flow is independent of the driving rate. Further, a nearly constant shear-strain rate is measured throughout the entire system. Optical and particle imaging velocimetry methods are used to measure the surface flows, and large-scale molecular dynamics simulations are performed to model the flows both at the surface and in the interior of the material. The analysis shows a regime of granular flow in which shear banding is absent.

We consider a general model of self-propelling particles interacting through a pairwise attractive force in the presence of noise and communication time delay. Previous work by Erdmann et al. [Phys. Rev. E 71, 051904 (2005)] has shown that a large enough noise intensity will cause a translating swarm of individuals to transition to a rotating swarm with a stationary center of mass. We show that with the addition of a time delay, the model possesses a transition that depends on the size of the coupling amplitude. This transition is independent of the initial swarm state (traveling or rotating) and is characterized by the alignment of all of the individuals along with a swarm oscillation. By considering the mean field equations without noise, we show that the time-delay-induced transition is associated with a Hopf bifurcation. The analytical result yields good agreement with numerical computations of the value of the coupling parameter at the Hopf point.

We study near-wall streaks that form herringbonelike patterns in Taylor-Couette turbulence and in counter-rotating Taylor-Couette turbulence through three-dimensional direct numerical simulations. The orientation, axial distribution, onset, and tilting angle of these streaks are characterized.

The effects of spatiotemporally correlated noise on the regularity of spiking oscillations are studied in a network composed of Fitz-Hugh-Nagumo neurons. The spiking regularity of the neural network becomes the best at a moderate noise intensity, indicating the occurrence of coherence resonance (CR). The CR in a Watts-Strogatz small-world network is further improved by adding a small fraction of long-range connections. Given a set of temporal correlation constant $\tau$ and spatial correlation length $\lambda$ of the noise, there exists an optimal network topology randomness, at which the spiking oscillations show the best regularity. The optimal randomness of the network topology at different $\tau$ and $\lambda$ varies in a narrow range. Changing $\lambda$ does not affect the optimal $\tau$ for achieving the most regular spike train, whereas varying $\tau$, the best spiking regularity emerges at different optimal $\lambda$.

A dynamic memory model is proposed in which an agent “learns” a new agent by means of recommendation. The agents can also “remember” and “forget.” The memory size is decreased while the population size is kept constant. “Fame” emerged as a few agents become very well known in expense of the majority being completely forgotten. The minimum and the maximum of fame change linearly with the relative memory size. The network properties of the who-knows-who graph, which represents the state of the system, are investigated.

We investigate analytically and numerically the critical line in undirected random Boolean networks with arbitrary degree distributions, including the scale-free topology of connections $P\left(k\right)\sim k^{-\gamma }$. We explain that the unattainability of the critical line in numerical simulations of classical random graphs is due to percolation phenomena. We suggest that recent findings of discrepancy between simulations and theory in directed random Boolean networks might have the same reason. We also show that in infinite scale-free networks the transition between frozen and chaotic phases occurs for $3<\gamma <3.5$. Since most critical phenomena in scale-free networks reveal their nontrivial character for $\gamma <3$, the position of the critical line in the Kauffman model seems to be an important exception to the rule.

A technique is introduced for identifying uncertain and/or unknown parameters of chaotic dynamical systems via using simple state feedback. The proposed technique is based on bringing the system into a stable steady state and then solving for the unknown parameters using a simple algebraic method that requires access to the complete or partial states of the system depending on the dynamical model of the chaotic system. The choice of the state feedback is optimized in terms of practicality and causality via employing a single feedback signal and tuning the feedback gain to ensure both stability and identifiability. The case when only a single scalar time series of one of the states is available is also considered and it is demonstrated that a synchronization-based state observer can be augmented to the state feedback to address this problem. A detailed case study using the Lorenz system is used to exemplify the suggested technique. In addition, both the Rössler and Chua systems are examined as possible candidates for utilizing the proposed methodology when partial identification of the unknown parameters is considered. Finally, the dependence of the proposed technique on the structure of the chaotic dynamical model and the operating conditions is discussed and its advantages and limitations are highlighted via comparing it with other methods reported in the literature.

We examine the validity of the power-law tails of the distributions of stock returns $P\left\{R>x\right\}\sim x^{-{\zeta }_R}$ using trade-by-trade data from three distinct markets. We find that both the negative as well as the positive tails of the distributions of returns display power-law tails, with mutually consistent values of ${\zeta }_R\approx 3$ for all three markets. We perform similar analyses of the related microstructural variable, the number of trades $N\equiv N_{\Delta t}$ over time interval $\Delta t$, and find a power-law tail for the cumulative distribution $P\left\{N>x\right\}\sim x^{-{\zeta }_N}$, with values of ${\zeta }_N$ that are consistent across all three markets analyzed. Our analysis of U.S. stocks shows that the exponent values ${\zeta }_R$ and ${\zeta }_N$ do not display systematic variations with market capitalization or industry sector. Moreover, since ${\zeta }_R$ and ${\zeta }_N$ are remarkably similar for all three markets, our results support the possibility that the exponents ${\zeta }_R$ and ${\zeta }_N$ are universal.

Diffusion on lattices with random mixed bonds in two and three dimensions is reconsidered using a random walk (RW) algorithm, which is equivalent to the master equation. In this numerical study the main focus is on the simple case of two different transition rates $W_1,W_2$ along bonds between sites. Although analysis of diffusion and transport on this type of disordered medium, especially for the case of one-bond pure percolation (i.e., $W_1=0$), comprises a sizable subliterature, we exhibit additional basic results for the two-bond case: When the probability $p$ of $W_2$ replacing $W_1$ in a lattice of $W_1$ bonds is below the percolation threshold $p_c$, the mean square displacement $⟨r^2⟩$ is a nonlinear function of time $t$. A best fit to the $\text{ln}⟨r^2⟩$ vs $\text{ln}t$ plot is a straight line with the value of the slope varying with $p,\Delta ,d$, where $\Delta \equiv W_2/W_1$ and $d$ is the dimension, i.e., $⟨r^2⟩\propto t^{1+\eta \left(p,\Delta ,d\right)}$ with $\eta >0$ for $\Delta >1$. In other terms, all the diffusion $\left(\mathcal{D}\equiv ⟨r^2⟩/2t\propto t^{\eta }\right)$ is anomalous superdiffusion for $p<p_c$ and $\Delta >1$ for $d=2,3$. Previous work in the literature for $d=2$ with a different RW algorithm established an effective diffusion constant ${\mathcal{D}}_{\text{eff}}$, which was shown to scale as ${\left(p_c-p\right)}^{1/2}$. However, the anomalous nature (time dependence) of $\mathcal{D}\left(t\right)$ becomes manifest with an expanded regime of $t$, increased range of $\Delta$, and the use of our algorithm. The nature of the superdiffusion is related to the percolation cluster geometry and Lévy walks.

The derivation of equations of state for fluid phases of a partially ionized gas or plasma is addressed from a fundamental point of view. The results of the Thomas-Fermi model always yield pressures which are less than or equal to that of an ideal Fermi gas. On the other hand, the spherical cellular model shows significant “overpressure” relative to the ideal Fermi gas in certain regions of low density and low temperature. This effect is studied in considerable detail. A nonthermodynamic region, more or less overlapping the regions of overpressure, is found. It is characterized by a negative specific heat at constant volume. An independent electron model within a $Z$-electron cell is employed. The inadequacy of the wave function in the low-density, low-temperature nonthermodynamic region is shown to be the cause of this overpressure. Numerical examples of the theory for several elements (Li, N, Al, K, and Er) are reported. These results reduce in various limits of temperature and density to the expected behavior, except in the aforementioned region.

We use a Markov method to study the efficiency of trapping processes involving both a random walker and a deep trap in regular and disordered networks. The efficiency is gauged by the mean absorption time (average of the mean number of steps performed by the random walker before being absorbed by the trap). We compute this quantity in terms of different control parameters, namely, the length of the walker jumps, the mobility of the trap, and the degree of spatial disorder of the network. For a proper choice of the system size, we find in all cases a nonmonotonic behavior of the efficiency in terms of the corresponding control parameter. We thus arrive at the conclusion that, despite the decrease of the effective system size underlying the increase of the control parameter, the efficiency is reduced as a result of an increase of the escape probability of the walker once it finds itself in the interaction zone of the trap. This somewhat anti-intuitive effect is very robust in the sense that it is observed regardless of the specific choice of the control parameter. For the case of a ring lattice, results for the mean absorption time in systems of arbitrary size are given in terms of a two-parameter scaling function. For the case of a mobile trap, we deal with both trapping via a single channel (walker-trap overlap) and via two channels (walker-trap overlap and walker-trap crossing), thereby generalizing previous work. As for the disordered case, our analysis concerns small world networks, for which we see several crossovers of the absorption time as a function of the control parameter and the system size. The methodology used may be well suited to exploring characteristic time scales of encounter-controlled phenomena in networks with a few interacting elements and the effect of geometric constraints in nanoscale systems with a very small number of particles.

For a linear medium, it is shown that the ratio of average relaxation to retardation time is given by the ratio of the high- to the low-frequency limit of the dielectric constants, ${\tau }_M/{\tau }_{\epsilon }={\epsilon }_{\infty }/{\epsilon }_s$. This statement holds for dispersive dynamics, i.e., it is not limited to the special case of exponential responses. A second general relation is found for the relative relaxation-time dispersions, which implies that the relaxation is always more stretched than its retardation counterpart. A difference equation for the charge buildup is established which provides a rationale for why retardation requires more time than its relaxation counterpart. According to the equation, the slowness of the charge buildup is due to a renewal process of continuous re-investment of potential made redundant by relaxation. The relevance of the results to experimental situations is also discussed.

This article introduces a type of stochastic model, which we call a multiphase stochastic model, for the particle transport in bubbling fluidized beds, making it possible to take into account the finite velocity of fluidization bubbles and also extra particle transport due to “gulf streaming.” An extended analysis of experimental results for particle transport in fluidized beds with gulf streaming is given, and results from the model are compared with the experimental results, showing that the model accounts for the effects seen.

We study the effect of both adhesion and friction on the geometry of monosized packings of spheres by means of discrete element simulations. We use elastic properties that are characteristic of materials typically used for particulate processing (Young’s modulus in the range 20–200 GPa). The geometrical features, both global and local, of the packings are studied using a variety of approaches in order to investigate their ability to quantify the effect of adhesion and/or friction. We show that both adhesion and friction interaction decrease the packing fraction. The very localized ordering that adhesion triggers is particularly investigated by use of the radial distribution function, the ordering parameter $Q_6$, and four triclinic cells that allow a description of the microstructure at the local level. We show that the probability of occurrence of these triclinic cells is approximately proportional to their degree of freedom when neither adhesion nor friction plays a role. We find that the introduction of adhesive interactions increases the probability of occurrence of those cells that have the lowest degree of freedom.

Liquid Lennard-Jones clusters of 14 different sizes from $N=55–923$ atoms were cooled down in Monte Carlo simulations (40 runs for each size) to the reduced temperature $T^{*}=0.05$. Structural analysis and visualization were applied for classification of the internal structure of all 560 final clusters. Small clusters revealed the presence of the multishell icosahedra or regular polyicosahedra. In larger clusters, beginning from $N=309$, the noncrystalline atom ordering is often replaced by the formation of defected crystalline clusters in the form of layered face-centered cubic–hexagonal close-packed (fcc-hcp) clusters or defected layered clusters with some additional nonparallel hcp overlayers. The presence of regular polyicosahedral clusters, relatively numerous even at the largest analyzed sizes, is attributed to kinetic effects in structure formation.

The transformation of a chiral antiferroelectric liquid crystal in an electric field was calculated. Minimization of the free energy was performed with respect to both the phase and the modulus of the two-component order parameter. Competition between the electric field, which favors a planar structure, and chirality and the anticlinic ordering leads to frustration and sequential formation of a distorted helix, a soliton state, transition to an unwound distorted antiferroelectric, and finally the planar synclinic state. In the soliton and distorted antiferroelectric states an anomalous electroclinic effect (the decrease of the tilt angle and layer polarization) was found. The antiferroelectric soliton can be removed by a large electric field only via the transition to the synclinic state.

Single-DNA stretching and twisting experiments provide a sensitive means to detect binding of proteins, via detection of their modification of DNA mechanical properties. However, it is often difficult or impossible to determine the numbers of proteins bound in such experiments, especially when the proteins interact nonspecifically (bind stably at any sequence position) with DNA. Here we discuss how analogs of the Maxwell relations of classical thermodynamics may be defined and used to determine changes in numbers of bound proteins, from measurements of extension as a function of bulk protein concentration. We include DNA twisting in our analysis, which allows us to show how changes in torque along single DNA molecules may be determined from measurements of extension as a function of DNA linking number. We focus on relations relevant to common experimental situations (e.g., magnetic and optical tweezers with or without controlled torque or linking number). The relation of our results to Gibbs adsorption is discussed.