We demonstrate analytically and numerically the possibility that the fractal property of a scale-free network cannot be characterized by a unique fractal dimension and the network takes a multifractal structure. It is found that the mass exponents $\tau \left(q\right)$ for several deterministic, stochastic, and real-world fractal scale-free networks are nonlinear functions of $q$, which implies that structural measures of these networks obey the multifractal scaling. In addition, we give a general expression of $\tau \left(q\right)$ for some class of fractal scale-free networks by a mean-field approximation. The multifractal property of network structures is a consequence of large fluctuations of local node density in scale-free networks.

Diseases emerge, persist, and vanish in an ongoing battle for available hosts. Hosts, on the other hand, defend themselves by developing immunity that limits the ability of pathogens to reinfect them. We here explore a multidisease system with emphasis on mutual exclusion. We demonstrate that such a system develops toward a steady state, where the spread of individual diseases self-organizes to a state close to that of critical percolation, without any global control mechanism or separation of time scale. For a broad range of introduction rates of new diseases, the likelihood of transmitting diseases remains approximately constant.

We investigate the scaling behavior of the relaxation process for an unstable state near a subcritical Hopf bifurcation point. When the parametric modulation is applied to a magneto-optical trap, the atomic cloud becomes unstable and decays to the dynamic bistable states. Near the subcritical Hopf bifurcation point, we experimentally show that the relaxation process exhibits the scaling behavior; the relaxation time shows a scaling exponent of $-1.002$ ($\pm$0.024). We also present the passage time distribution for the statistical interpretation of the escape process associated with the relaxation of the unstable state. We compare the experimental results to the numerical and analytic results, demonstrating the good agreement between them.

Tortuosity ($T$) is a parameter describing an average elongation of fluid streamlines in a porous medium as compared to free flow. In this paper several methods of calculating this quantity from lengths of individual streamlines are compared and their weak and strong features are discussed. An alternative method is proposed, which enables one to calculate $T$ directly from the fluid velocity field, without the need of determining streamlines, which greatly simplifies determination of tortuosity in complex geometries, including those found in experiments or three-dimensional computer models. Based on numerical results obtained with this method, (a) a relation between the hydraulic tortuosity of an isotropic fibrous medium and the porosity is proposed, (b) a relation between the divergence rate of $T$ with the system size at percolation porosity and the scaling of the most probable traveling length at bond percolation is found, and (c) a range of porosities for which the shape factor is constant is identified.

Simulations of a silicon oil Taylor drop rising in a tube filled with a glycerol-water mixture are performed to investigate the viscosity ratio effects on the rise velocity of the Taylor drop. By varying the viscosity ratio $\lambda$ between the drop and the suspending liquid from $O\left(0.1\right)$ to $O\left(10\right)$, a simple relationship of the nondimensional terminal velocity, the Froude number (Fr), is revealed as $\text{Fr}\propto {\lambda }^{-0.27}$. This scaling is further confirmed by recently published experimental data [Hayashi, Kurimoto, and Tomiyama, Int. J. Multiphase Flow 37, 241 (2011)]. The simulated drop shapes also compare well with the experiments. Increasing the viscosity ratio elongates the drop and tends to make the tail bulge out. The correlation applies to small Reynolds numbers and finite viscosity ratios.

The nature of dynamo action in shear flows prone to magnetohydrodynamc instabilities is investigated using the magnetorotational dynamo in Keplerian shear flow as a prototype problem. Using direct numerical simulations and Newton’s method, we compute an exact time-periodic magnetorotational dynamo solution to three-dimensional dissipative incompressible magnetohydrodynamic equations with rotation and shear. We discuss the physical mechanism behind the cycle and show that it results from a combination of linear and nonlinear interactions between a large-scale axisymmetric toroidal magnetic field and nonaxisymmetric perturbations amplified by the magnetorotational instability. We demonstrate that this large-scale dynamo mechanism is overall intrinsically nonlinear and not reducible to the standard mean-field dynamo formalism. Our results therefore provide clear evidence for a generic nonlinear generation mechanism of time-dependent coherent large-scale magnetic fields in shear flows and call for new theoretical dynamo models. These findings may offer important clues to understanding the transitional and statistical properties of subcritical magnetorotational turbulence.

We study the dynamics and structure of clusters in the inhomogeneous clustered regime of a freely cooling granular gas of point particles in one dimension. The coefficient of restitution is modeled as $r_0<1$ or 1, depending on whether the relative speed is greater or smaller than a velocity scale $\delta$. The effective fragmentation rate of a cluster is shown to rise sharply beyond a $\delta$-dependent time scale. This crossover is coincident with the velocity fluctuations within a cluster becoming order $\delta$. Beyond this crossover time, the cluster-size distribution develops a nontrivial power-law distribution, whose scaling properties are related to those of the velocity fluctuations. We argue that these underlying features are responsible for the recently observed nontrivial coarsening behavior in the one-dimensional freely cooling granular gas.

The temperature evolution of the primary relaxation time in the isotropic phase of 4-cyano-4′-tetradecylbiphenyl (14CB) above the isotropic-smectic A (I-SmA) transition is discussed. Based on the enthalpy space and distortion-sensitive analysis, the prevalence of the mode coupling theory (MCT) “critical” and “glassy” dynamics is shown. The obtained singular dependence is related to the MCT critical temperature located approximately 48 K below the clearing (I-SmA) temperature. However, a weak but detectable distortion in the immediate vicinity of the transition occurs. It is also shown that the value of the fragile strength coefficient $D_T$ is characteristic of a very fragile glassy liquid whereas the steepness index m is typical of a strong one. Both magnitudes anomalously change on approaching the I-SmA phase transition. The static permittivity shows the pretransitional effect linked to the temperature of the hypothetical continuous phase transition located approximately 10.2 K below the I-SmA transition.

We study the effect of a linear shear flow on a collection of interacting active, self-propelled particles modeled via the Vicsek model. The imposed flow has a dramatic effect on the behavior of the model. We find that in the presence of shear there is no order-disorder transition, and that coarsening of the domains is arrested. Shear also suppresses the so-called giant density fluctuations that are observed in the quiescent limit.

Concentration fluctuations are always present in solutions; it has been noticed that, in chemical systems, they can lead to deviations from what is expected from mass-action equations. I recently described the class of the “marginally stable” chemical systems; namely, a system that have an infinity of stationary states forming a continuous curve, and I showed that they present such deviations, which appear as a drift along the stationary-state curve [Phys. Rev. Lett. 105, 058102 (2010)]. Here I describe various marginally stable chemical reaction networks, including replicating molecules, and I present numerical calculations based on reaction-diffusion master equations, showing that the thermodynamic fluctuations induce a drift. This drift can be interpreted in terms of evolution toward a more efficiently replicating system and is analogous to a Darwinian evolution. The concentration fluctuations observed during the drift are scale invariant. Relevance of this phenomenon to the origin of life is discussed. I propose that marginal stability is the mathematical property defining chemical reaction networks potentially involved in the origin of life.

As an alternative to the paradigmatic fragmentation problem of a single object crushed into a great number of pieces, we survey a large collection of identical bodies, each one randomly split into two fragments only. While some key features of usual fragmentation are preserved, this minimal approach allows for closed analytical results on both shape abundances and mass distributions for the fragments, with robust power-law regimes. All the results are compared to numerical simulations.

We show that directed percolation (DP) simulations in a pipe geometry in $3+1$ dimensions capture the observed complex phenomenology of the transition to turbulence. At low Reynolds numbers (Re), turbulent puffs form and spontaneously relaminarize. At high Re, turbulent slugs expand uniformly into the laminar regions. In a spatiotemporally intermittent state between these two regimes of Re, puffs split and turbulent regions exhibit laminar patches. DP also captures some of the quantitative features of the transition, with a superexponentially diverging characteristic lifetime below the transition. Above the percolation threshold, active (turbulent) clusters expand into the inactive (laminar) phase with a well-defined velocity whose scaling with control parameter (Reynolds number or percolation probability) is consistent with experimental results. Our results provide strong evidence in favor of a conjecture of Pomeau.

It is well known that biological and social interaction networks have a varying degree of redundancy, though a consensus of the precise cause of this is so far lacking. In this paper, we introduce a topological redundancy measure for labeled directed networks that is formal, computationally efficient, and applicable to a variety of directed networks such as cellular signaling, and metabolic and social interaction networks. We demonstrate the computational efficiency of our measure by computing its value and statistical significance on a number of biological and social networks with up to several thousands of nodes and edges. Our results suggest a number of interesting observations: (1) Social networks are more redundant that their biological counterparts, (2) transcriptional networks are less redundant than signaling networks, (3) the topological redundancy of the C. elegans metabolic network is largely due to its inclusion of currency metabolites, and (4) the redundancy of signaling networks is highly (negatively) correlated with the monotonicity of their dynamics.

We show the existence of a type of excitation, which we term as “gap compactonlike,” within the gap of the linear spectrum of a system of coupled Kortweg–de Vries equations with linear and nonlinear dispersions. Since the solutions lie in the gap region of the spectra, they avoid resonance with the linear oscillatory wave and, therefore, do not decay into radiations. These types of solutions are important in energy localization and transport in polymers and biopolymers, optical systems, etc.

Zhang and Chen proposed a lattice Boltzmann method for simulations of liquid-vapor thermal flows [Zhang and Chen, Phys. Rev. E 67, 066711 (2003)]. In their numerical test, the authors show simulation results with a temperature ratio of approximately 1.2 for a thermal two-phase flow with $T<0.8T_c$. However, we believe this to be erroneous and demonstrate the error to originate from a wrong choice of a parameter of critical importance in the Carnahan-Starling equation of state used in their work. Our numerical tests show that using the correct parameter choice, the scheme is only valid and robust to simulate temperature ratios below 1.10 and the lowest temperature in the flow field should be $0.85T_c$.

In this reply to the Comment by Huang and Krafczyk [Phys. Rev. E 84, 038701 (2011)], we clarify that a correct set of parameter values was used in our original work, and that the simulation was performed in a proper water-vapor two phase flow regime [R. Zhang and H. Chen, Phys. Rev. E 67, 066711 (2003)].

Porous media with a wide distribution of pore sizes are quite common. We show that variable-step-size random walk simulations can be used to model the time-dependent diffusion coefficient $D\left(t\right)$ in such porous media. The issue to be overcome is that, in variable-step-size walks, each walker carries its own “clock,” and its position is known only at a random set of times. Thus, a direct ensemble-average calculation of $\langle \Delta r^2\left(t\right)\rangle$ (the mean-square distance traveled at time $t$) is problematic. We introduce a sequence of approximations that overcome this apparent difficulty. Calculations are carried out on periodic systems that contain pores of quite different sizes. Where possible, our results are compared to those obtained using fixed-step-size random walks.

A two-segment Fermi-Pasta-Ulam lattice has been investigated by using nonequilibrium molecular dynamics. Here we present an anomalous negative differential thermal resistance (NDTR) that has not been reported in Frenkel-Kontorova and ${\phi }_4$ lattices up to the present. The NDTR disappears in the low-temperature region. The region of NDTR shifts from the large to the small temperature difference region as the system size increases. The anomalous dependence of NDTR on the temperature can be explained as the negative effect induced by the nonlinear coupling. The explanation can also cover the phenomenon of NDTR in momentum-nonconserved lattices.

The dynamics of fluctuating radially growing interfaces is approached using the formalism of stochastic growth equations on growing domains. This framework reveals a number of dynamic features arising during surface growth. For fast growth, dilution, which spatially reorders the incoming matter, is responsible for the transmission of correlations. Its effects include the erasing of memory with respect to the initial condition, a partial attenuation of geometrically originated instabilities, and the restoration of universality in some special cases in which the critical exponents depend on the parameters of the equation of motion. In this sense, dilution rends the dynamics more similar to the usual one of planar systems. This fast growth regime is also characterized by the spatial decorrelation of the interface, which, in the case of radially growing interfaces, naturally originates rapid roughening and scale-dependent fractality, and suggests the advent of a self-similar fractal dimension. The center-of-mass fluctuations of growing clusters are also studied, and our analysis suggests the possible nonapplicability of usual scalings to the long-range surface fluctuations of the radial Eden model. In fact, our study points to the fact that this model belongs to a dilution-free universality class.

We investigated the effects of particle shape on shear thickening in densely packed suspensions. Rods of different aspect ratios and nonconvex hooked rods were fabricated. Viscosity curves and normal stresses were measured using a rheometer for a wide range of packing fractions for each shape. Suspensions of each shape exhibit qualitatively similar discontinuous shear thickening. The logarithmic slope of the stress vs shear rate increases dramatically with packing fraction and diverges at a critical packing fraction ${\phi }_c$ which depends on particle shape. The packing fraction dependence of the viscosity curves for different convex shapes can be collapsed when the packing fraction is normalized by ${\phi }_c$. Intriguingly, viscosity curves for nonconvex particles do not collapse on the same set as convex particles, showing strong shear thickening over a wider range of packing fraction. The value of ${\phi }_c$ is found to coincide with the onset of a yield stress at the jamming transition, suggesting the jamming transition also controls shear thickening. The yield stress is found to correspond with trapped air in the suspensions, and the scale of the stress can be attributed to interfacial tension forces which dramatically increase above ${\phi }_c$ due to the geometric constraints of jamming. Using this connection we show that the jamming transition can be identified by simply looking at the surface of suspensions. The relationship between shear and normal stresses is found to be linear in both the shear thickening and jammed regimes, indicating that the shear stresses come from friction. In the limit of zero shear rate, normal stresses pull the rheometer plates together due to the surface tension of the liquid below ${\phi }_c$, but push the rheometer plates apart due to jamming above ${\phi }_c$.