The time evolution of macroscopic quantities describing the relaxation of complex systems often contains a domain with logarithmic time dependence. This logarithmic behavior at the macroscopic level is often associated with strongly interacting elements at the microscopic level, whose interactions depend significantly on their history. In this paper we show that stress relaxation in the Burridge-Knopoff (BK) model of multicontact friction behaves logarithmically, when the model is in, or close to, the solitary state where the elements move independently. For this regime we present an automaton that allows us to follow the decay of stress relaxation over the entire range where it behaves logarithmically in time. We show that our model can be mapped onto a system of noninteracting elements subject to a uniform distribution of forces, for which logarithmic stress relaxation is derived analytically.

Tuning of the decay law of light in an array of tunneling-coupled optical waveguides with a defect is theoretically demonstrated. An analytical form for the decay law in terms of a Neumann series is obtained in case of a semi-infinite array with a boundary defect waveguide. Different decay regimes, ranging from a near-exponential decay to an oscillatory or nonoscillatory power-law decay, are found in the parameter range where the boundary defect waveguide does not support localized modes.

We describe the surprising phenomenon of near-perfect coupling from free space into uniform two-dimensional rod-type photonic crystals over a wide range of incident angles. This behavior is shown to be a generic feature of many rod-type photonic crystal structures that is related to strong forward scattering resonances of the individual cylinders. We explain these results using both semianalytic analysis and two-dimensional numerical calculations and identify the conditions under which efficient, wide-angle coupling can occur. The results may lead to more efficient designs for in-band photonic crystal devices such as superprisms and self-collimation based photonic circuits.

We study the statistics of the force felt by a particle in the class of a spatially correlated distribution of identical pointlike particles, interacting via a $1∕r^2$ pair force (i.e., gravitational or Coulomb), and obtained by randomly perturbing an infinite perfect lattice. We specify the conditions under which the force on a particle is a well-defined stochastic quantity. We then study the small displacements approximation, giving both the limitations of its validity and, when it is valid, an expression for the force variance. The method introduced by Chandrasekhar to find the force probability density function for the homogeneous Poisson particle distribution is extended to shuffled lattices of particles. In this way, we can derive an approximate expression for the probability distribution of the force over the full range of perturbations of the lattice, i.e., from very small (compared to the lattice spacing) to very large where the Poisson limit is recovered. We show in particular the qualitative change in the large-force tail of the force distribution between these two limits. Excellent accuracy of our analytic results is found on detailed comparison with results from numerical simulations. These results provide basic statistical information about the fluctuations of the interactions (i) of the masses in self-gravitating systems like those encountered in the context of cosmological $N$-body simulations, and (ii) of the charges in the ordered phase of the one-component plasma, the so-called Coulomb or Wigner crystal.

We identify arches in a bed of granular disks generated by a molecular dynamic-type simulation. We use the history of the deposition of the particles to identify the supporting contacts of each particle. Then, arches are defined as sets of mutually stable disks. Different packings generated through tapping are analyzed. The possibility of identifying arches from the static structure of a deposited bed, without any information on the history of the deposition, is discussed.

In order to provide a sound physical basis for the understanding of the formation of desiccation crack networks, an experimental study is presented addressing junction formation. Focusing on junctions, basic features of the network determining the final pattern, provides an elemental approach and imparts conceptual clarity to the rather complicated problem of the evolution of crack patterns. Using coffee-water mixtures a clear distinction between junction formation during nucleation and propagation is achieved. It is shown that for the same drying suspension, one can switch from the well-known symmetric triple junctions that are unique to the nucleation phase to propagation junctions that are purely dictated by the variations of the stress state. In the latter case, one can even manipulate the path of a propagating crack in a deterministic fashion by changing the stress state within the suspension. Clear microscopic evidence is provided for the formation of propagation junctions, and material inhomogeneity is observed to be reflected by a broad distribution of angles, in stark contrast to shrinkage cracks in homogeneous solid films.

Supercooled liquid and glassy acetylsalicylic acid was studied using dielectric spectroscopy and deuteron relaxometry in a wide temperature range. The supercooled liquid is characterized by major deviations from thermally activated behavior. In the glass the secondary relaxation exhibits the typical features of a Johari-Goldstein process. Via measurements of spin-lattice relaxation times the selectively deuterated methyl group was used as a sensitive probe of its local environments. There is a large difference in the mean activation energy in the glass with respect to that in crystalline acetylsalicylic acid. This can be understood by taking into account the broad energy barrier distribution in the glass.

We study the four-point dynamic susceptibility ${\chi }_4\left(t\right)$ obtained from Brownian dynamics computer simulations of the Kob-Andersen Lennard-Jones mixture. We compare the results of the simulations with qualitative predictions of the mode-coupling theory. In addition, we test an estimate of the four-point susceptibility recently proposed by Berthier et al. [Science 310, 1797 (2005)].

The morphology changes of linear diblock copolymer lamellar microdomains under uniform simple shear are studied via the dissipative particle dynamics technique. The parallel and perpendicular reorientations of the lamellae are observed in the simulations, and two different reorientation mechanisms, under small and large shear rates respectively, are proposed. The parallel-to-perpendicular transition is also observed and the kinetics is discussed. Sinusoidal and chevron instabilities due to the shear are found. After relaxation the peculiar “bidirectionally undulating” instability is obtained.

We investigate the macroscopic effects of the ingredients that drive the origin of species through sympatric speciation. In our model, sympatric speciation is obtained as we tune up the strength of competition between individuals with different phenotypes. As a function of this control parameter, we can characterize, through the behavior of a macroscopic order parameter, a phase transition from a nonspeciation to a speciation state of the system. The behavior of the first derivative of the order parameter with respect to the control parameter is consistent with a phase transition and exhibits a sharp peak at the transition point. For different resources distribution, the transition point is shifted, an effect similar to pressure in a PVT system. The inverse of the parameter related to a sexual selection strength behaves like an external field in the system and, as thus, is also a control parameter. The macroscopic effects of the biological parameters used in our model are a reminiscent of the behavior of thermodynamic quantities in a phase transition of an equilibrium physical system.

We compare and synthesize the results of two microrheological experiments on the cytoskeleton of single cells. In the first one, the creep function $J\left(t\right)$ of a cell stretched between two glass plates is measured after applying a constant force step. In the second one, a microbead specifically bound to transmembrane receptors is driven by an oscillating optical trap, and the viscoelastic coefficient $G_e\left(\omega \right)$ is retrieved. Both $J\left(t\right)$ and $G_e\left(\omega \right)$ exhibit power law behaviors: $J\left(t\right)=A_0{(t∕t_0)}^{\alpha }$ and $\mid G_e\left(\omega \right)\mid =G_0{(\omega ∕{\omega }_0)}^{\alpha }$, with the same exponent $\alpha \approx 0.2$. This power law behavior is very robust; $\alpha$ is distributed over a narrow range, and shows almost no dependence on the cell type, on the nature of the protein complex which transmits the mechanical stress, nor on the typical length scale of the experiment. On the contrary, the prefactors $A_0$ and $G_0$ appear very sensitive to these parameters. Whereas the exponents $\alpha$ are normally distributed over the cell population, the prefactors $A_0$ and $G_0$ follow a log-normal repartition. These results are compared with other data published in the literature. We propose a global interpretation, based on a semiphenomenological model, which involves a broad distribution of relaxation times in the system. The model predicts the power law behavior and the statistical repartition of the mechanical parameters, as experimentally observed for the cells. Moreover, it leads to an estimate of the largest response time in the cytoskeletal network: ${\tau }_m\sim 1000\mathrm{s}$.

Human chromosome 21 is the only chromosome in the human genome that exhibits oscillation of the $(\mathrm{G}+\mathrm{C})$ content of a cycle length of hundreds kilobases (kb) ($500\mathrm{kb}$ near the right telomere). We aim at establishing the existence of a similar periodicity in structure-related sequence features in order to relate this $(\mathrm{G}+\mathrm{C})\%$ oscillation to other biological phenomena. The following quantities are shown to oscillate with the same $500\mathrm{kb}$ periodicity in human chromosome 21: binding energy calculated by two sets of dinucleotide-based thermodynamic parameters, AA/TT and AAA/TTT bi- and tri-nucleotide density, $5^{\prime }\text{−}\mathrm{TA}\text{−}{3}^{\prime }$ dinucleotide density, and signal for 10- or 11-base periodicity of AA/TT or AAA/TTT. These intrinsic quantities are related to structural features of the double helix of DNA molecules, such as base-pair binding, untwisting or unwinding, stiffness, and a putative tendency for nucleosome formation.

This paper shows the essence of conservation forms when applying the weak solution theory to solve the traveling wave solution of a wide cluster in the Payne-Whitham (PW) model. The consideration of the conservation form for the acceleration equation is an important ingredient in the development of higher-order traffic flow models, but it is largely ignored in the research community. To fix the idea, we define two conservation forms for the same PW model, and consequently derive two solutions with different sets of characteristic parameters of the wide cluster. The analytical results are in good agreement with those that are obtained from numerical simulations. Moreover, these two solutions are also shown to be asymptotic to those of the well-known Kühne and Kerner-Konhaüser models with a viscosity term. More importantly, the careful treatment of the conservation form for the acceleration equation closes the important gap in the literature. Without the conservation form, the solution obtained depends very much on the design of numerical schemes, and can be quite arbitrary and may not adequately conform to the physically relevant properties.

We study a modified prisoner’s dilemma game taking place on two-dimensional disordered square lattices. The players are pure strategists and can either cooperate or defect with their immediate neighbors. In the generations each player updates its strategy by following one of the neighboring strategies with a probability dependent on the payoff difference. The neighbor selection obeys a dynamic preferential rule, i.e., the more frequently a neighbor’s strategy was adopted by the focal player in the previous rounds, the larger probability it will be chosen to refer to in the subsequent rounds. It is found that cooperation is substantially promoted due to this simple selection mechanism. Corresponding analysis is provided by the investigation of the distribution of the players’ impact weights, persistence, and correlation function.

We show that the dynamic approach to fractional Brownian motion (FBM) establishes a link between a non-Poisson renewal process with abrupt jumps resetting to zero the system’s memory and correlated dynamic processes, whose individual trajectories keep a nonvanishing memory of their past time evolution. It is well known that the recrossings of the origin by an ordinary one-dimensional diffusion trajectory generates a Lévy (and thus renewal) process of index $\theta =1∕2$. We prove with theoretical and numerical arguments that this is the special case of a more general condition, insofar as the recrossings produced by the dynamic FBM generates a Lévy process with $0<\theta <1$. This result is extended to produce a satisfactory model for the fluorescent signal of blinking quantum dots.

We investigate kinetics of $A+B\to 0$ reaction with long-range attractive interaction $V\left(r\right)\sim -r^{-2\sigma }$ between $A$ and $B$ or with drift velocity $v\sim r^{-\sigma }$ in one dimension, where $r$ is the closest distance between $A$ and $B$. It is analytically shown that dynamical exponents for density of particles $\left(\rho \right)$ and size of domains $\left(\ell \right)$ continuously vary with $\sigma$ when $\sigma <{\sigma }_c=1∕2$, while that for the distance between adjacent opposite species $\left({\ell }_{AB}\right)$ varies when $\sigma <{\sigma }_c^{AB}=7∕6$. For $\sigma >{\sigma }_c^{AB}$ diffusive motions dominate the kinetics. These anomalous behaviors with the two crossover values of $\sigma$ are supported by numerical simulations.

Molecular dynamics (MD) simulations are performed for six- and seven-dimensional hard-hypersphere fluids. The equation of state, velocity autocorrelation function, self-diffusion coefficient, shear viscosity, and thermal conductivity are determined as a function of density. The molecular dynamics results for the equation of state are found to be in excellent agreement with values obtained from theoretical approaches and previous MD simulations in seven dimensions. The short-time behavior of the velocity autocorrelation function is well described by the Enskog exponential approximation. The Enskog predictions for the self-diffusion coefficient and the viscosity agree fairly well with the simulation data at low densities, but underestimate these quantities at higher densities. Data for the thermal conductivity are in fine agreement with Enskog theory for all densities and dimensions studied.

We explore the role of gas viscosity in the behavior of gas-fluidized beds of fine powders by means of experimental measurements using nitrogen and neon as fluidizing gases, and theoretical considerations. The existence of a nonbubbling fluidlike regime has been recently observed in beds of fine powders fluidized with nitrogen. Our experiments with neon reveal a discontinuous transition from heterogeneous fluidization to a highly expanded homogeneous fluidization state. We point out that increasing gas viscosity enhances the coherence of agglomerate swarms, which promotes a local void-splitting mechanism, thus improving the uniformity of fluidization. Our theoretical analysis predicts that further increase of gas viscosity would produce a full suppression of the bubbling regime, i.e., the uniformly fluidized bed would undergo a direct transition to a turbulent regime as seen in beds of nanoparticles fluidized by nitrogen and in liquid-fluidized beds of moderate-density beads.

The motility of certain gram-negative bacteria is mediated by retraction of type IV pili surface filaments, which are essential for infectivity. The retraction is powered by a strong molecular motor protein, PilT, producing very high forces that can exceed $150\mathrm{pN}$. The molecular details of the motor mechanism are still largely unknown, while other features have been identified, such as the ring-shaped protein structure of the PilT motor. The surprisingly high forces generated by the PilT system motivate a model investigation of the generation of large forces in molecular motors. We propose a simple model, involving a small ensemble of motor subunits interacting through the deformations on a circular backbone with finite stiffness. The model describes the motor subunits in terms of diffusing particles in an asymmetric, time-dependent binding potential (flashing ratchet potential), roughly corresponding to the ATP hydrolysis cycle. We compute force-velocity relations in a subset of the parameter space and explore how the maximum force (stall force) is determined by stiffness, binding strength, ensemble size, and degree of asymmetry. We identify two qualitatively different regimes of operation depending on the relation between ensemble size and asymmetry. In the transition between these two regimes, the stall force depends nonlinearly on the number of motor subunits. Compared to its constituents without interactions, we find higher efficiency and qualitatively different force-velocity relations. The model captures several of the qualitative features obtained in experiments on pilus retraction forces, such as roughly constant velocity at low applied forces and insensitivity in the stall force to changes in the ATP concentration.