Aging observed in soft glassy materials inherently affects the rheological properties of these systems and has been described by the soft glassy rheology (SGR) model [S. M. Fielding et al., J. Rheol. 44, 323 (2000)]. In this paper, we report the measured linear rheological behavior of thermosensitive microgel suspensions and compare it quantitatively with the predictions of the SGR model. The dynamic moduli [$G^{\prime }(\omega ,t)$ and $G^{″}(\omega ,t)$] obtained from oscillatory measurements are in good agreement with the model. The model also predicts quantitatively the creep compliance $J(t-t_w,t_w)$, obtained from step stress experiments, for the short time regime $\left[\right(t-t_w)<t_w]$. The relative effective temperature $\mathcal{X}∕{\mathcal{X}}_g$ obtained from both the oscillatory and the step stress experiments is indeed less than 1 $(\mathcal{X}∕{\mathcal{X}}_g<1)$ in agreement with the definition of aging. Moreover, the elasticity of the compressed particles $\left(G_p\right)$ increases with increased compression, i.e., the degree of hindrance and consequently also the bulk elasticity ($G^{\prime }$ and $1∕J$) increases with the degree of compression.

The long-range elastic model, which is believed to describe the evolution of a self-affine rough crack front, is analyzed to linear and nonlinear orders. It is shown that the nonlinear terms, while important in changing the front dynamics, do not change the scaling exponent which characterizes the roughness of the front. The scaling exponent thus predicted by the model is much smaller than the one observed experimentally. The inevitable conclusion is that the gap between the results of experiments and the model that is supposed to describe them is too large and some new physics has to be invoked for another model.

We present a theory of transport of magnetic flux and momentum in two fluid three-dimensional reduced magnetohydrodynamic (MHD) turbulence. By including the effects of shear flows and magnetic fields consistently, we show that kinetic Alfven waves can help weaken the quenching in turbulent transport of a strong magnetic field $B_0$ found in single fluid MHD turbulence, leading to turbulent magnetic diffusivity ${\eta }_T\propto {(\eta ∕\Omega )}^{1∕3}{B}_0^{-2}$. Here, $\eta$ and $\Omega$ are the Ohmic diffusivity and the shearing rate of the shear flow. Momentum transport is diffusive, with the value of eddy viscosity larger than that in single fluid MHD turbulence. The effects of drift waves are found to be weaker. Implications for the instability of shear flows are discussed.

We develop an athermal shear-transformation-zone (STZ) theory of plastic deformation in spatially inhomogeneous, amorphous solids. Our ultimate goal is to describe the dynamics of the boundaries of voids or cracks in such systems when they are subjected to remote, time-dependent tractions. The theory is illustrated here for the case of a circular hole in an infinite two-dimensional plate, a highly symmetric situation that allows us to solve much of the problem analytically. In spite of its special symmetry, this example contains many general features of systems in which stress is concentrated near free boundaries and deforms them irreversibly. We depart from conventional treatments of such problems in two ways. First, the STZ analysis allows us to keep track of spatially heterogeneous, internal state variables such as the effective disorder temperature, which determines plastic response to subsequent loading. Second, we subject the system to stress pulses of finite duration, and therefore are able to observe elastoplastic response during both loading and unloading. We compute the final deformations and residual stresses produced by these stress pulses. Looking toward more general applications of these results, we examine the possibility of constructing a boundary-layer theory that might be useful in less symmetric situations.

In many Hamiltonian systems subjected to a time (or space) -periodic perturbation with a broad spectrum an approach is widely used of replacing the system by periodically $\delta$-kicked dynamical systems, which allows us to reduce them to symplectic mappings. In this paper it is shown that this approach has a fundamental failure, and the corresponding mapping does not correctly describe the continuous original system. It is demonstrated on the example of the stochastic web map obtained by this approach to describe a periodically driven harmonic oscillator which exhibits non-Kolmogorov—Arnold—Moser chaos, particularly, the formation of stochastic webs. A correct canonical map corresponding to this system is obtained using a recently developed method based on the canonical transformation of variables [S. S. Abdullaev, J. Phys. A 35, 2811 (2002)]. Using a direct numerical integration of the system it is shown that the canonical map correctly describes the periodically driven harmonic oscillator with a finite number of spectrum modes.

We study a configuration for displacement detection consisting of a nanomechanical resonator coupled to both a radio frequency superconducting interference device and to a superconducting stripline resonator. We employ an adiabatic approximation and rotating wave approximation and calculate the displacement sensitivity. We study the performance of such a displacement detector when the stripline resonator is driven into a region of nonlinear oscillations. In this region the system exhibits noise squeezing in the output signal when homodyne detection is employed for readout. We show that displacement sensitivity of the device in this region may exceed the upper bound imposed upon the sensitivity when operating in the linear region. On the other hand, we find that the high displacement sensitivity is accompanied by a slowing down of the response of the system, resulting in a limited bandwidth.

We discuss the dynamics of approximate adiabatic invariants in several nonlinear models being related to the physics of Bose-Einstein condensates (BECs). We show that the nonadiabatic dynamics in Feshbach resonance passage, nonlinear Landau-Zener (NLZ) tunneling, and BEC tunneling oscillations in a double well can be considered within a unifying approach based on the theory of separatrix crossings. The separatrix crossing theory was applied previously to some problems of classical mechanics, plasma physics, and hydrodynamics, but has not been used in the rapidly growing BEC-related field yet. We derive explicit formulas for the change in the action in several models. Extensive numerical calculations support the theory and demonstrate its universal character. We also discovered a nonlinear phenomenon in the NLZ model which we propose to call separated adiabatic tunneling.

The influence of shock waves, driven by amplified spontaneous emission (ASE), on laser-accelerated proton beams is investigated. A local deformation, produced by a cold shock wave launched by the ablation pressure of the ASE pedestal, can under oblique laser irradiation significantly direct the proton beam toward the laser axis. This can be understood in the frame of target normal sheath acceleration as proton emission from an area of the target where the local target normal is shifted toward the laser axis. Hydrodynamic simulations and experimental data show that there exists a window in laser and target parameter space where the target can be significantly deformed and yet facilitate efficient proton acceleration. The dependence of the magnitude of the deflection on target material, foil thickness, and ASE pedestal intensity and duration is experimentally investigated. The deflection angle is found to increase with increasing ASE intensity and duration and decrease with increasing target thickness. In a comparison between aluminum and copper target foils, aluminum is found to yield a larger proton beam deflection. An analytic model is successfully used to predict the proton emission direction.

We consider diffusively coupled map lattices with $P$ neighbors (where $P$ is arbitrary) and study the stability of the synchronized state. We show that there exists a critical lattice size beyond which the synchronized state is unstable. This generalizes earlier results for nearest neighbor coupling. We confirm the analytical results by performing numerical simulations on coupled map lattices with logistic map at each node. The above analysis is also extended to two-dimensional $P$-neighbor diffusively coupled map lattices.

A Brownian motor is a nanoscale or molecular device that combines the effects of thermal noise, spatial or temporal asymmetry, and directionless input energy to drive directed motion. Because of the input energy, Brownian motors function away from thermodynamic equilibrium and concepts such as linear response theory, fluctuation dissipation relations, and detailed balance do not apply. The generalized fluctuation-dissipation relation, however, states that even under strongly thermodynamically nonequilibrium conditions the ratio of the probability of a transition to the probability of the time reverse of that transition is the exponential of the change in the internal energy of the system due to the transition. Here, we derive an extension of the generalized fluctuation dissipation theorem for a Brownian motor for the ratio between the probability for the motor to take a forward step and the probability to take a backward step.

Diamond is a promising material for wear-resistant medical coatings. Here we report a remarkable increase in the melting point of ice resting on a diamond $\left(111\right)$ surface modified with a submonolayer of ${\mathrm{Na}}^{+}$. Our molecular dynamics simulations show that the interfacial ice bilayer melts at a temperature $130\mathrm{K}$ higher than in free ice, and relatively thick ice films ($2.6\mathrm{nm}$ at $298\mathrm{K}$ and $2.2\mathrm{nm}$ at $310\mathrm{K}$) are stabilized by dipole interactions with the substrate. This unique physical effect may enable biocompatibility-enhancing ice overcoatings for diamond at human body temperature.

We discuss an analysis of constraint satisfaction problems, such as sphere packing, K-SAT, and graph coloring, in terms of an effective energy landscape. Several intriguing geometrical properties of the solution space become in this light familiar in terms of the well-studied ones of rugged (glassy) energy landscapes. A benchmark algorithm naturally suggested by this construction finds solutions in polynomial time up to a point beyond the clustering and in some cases even the thermodynamic transitions. This point has a simple geometric meaning and can be in principle determined with standard statistical mechanical methods, thus pushing the analytic bound up to which problems are guaranteed to be easy. We illustrate this for the graph 3- and 4-coloring problem. For packing problems the present discussion allows to better characterize the $J$-point, proposed as a systematic definition of random close packing, and to place it in the context of other theories of glasses.

The spontaneous motion of microbeads bound to the cytoskeleton of living cells is not an ordinary random walk. Unlike Brownian motion, the mean-square displacement undergoes a transition from subdiffusive to superdiffusive behavior with time. This transition is associated with characteristic changes of the turning angle distribution. Recent experimental data demonstrated that force fluctuations measured in an elastic hydrogel matrix beneath the cell correlate with the bead motion [C. Raupach et al., Phys. Rev. E 76, 011918 (2007)]. These data indicate that the bead trajectory is driven by motor forces originating from the actomyosin network and that cytoskeletal remodeling processes with short- and long-time dynamics are mainly responsible for the non-Brownian behavior. We show that the essential statistical properties of the spontaneous bead motion can be reproduced by a particle diffusing in a potential well with a slowly drifting minimum position. Based on this simple model, which can be solved analytically, we develop a biologically plausible numerical model of a tensed and continuously remodeling actomyosin network that accounts quantitatively for the measured data.

The configuration space network (CSN) of a dynamical system is an effective approach to represent the ensemble of configurations sampled during a simulation and their dynamic connectivity. To elucidate the connection between the CSN topology and the underlying free-energy landscape governing the system dynamics and thermodynamics, an analytical solution is provided to explain the heavy tail of the degree distribution, neighbor connectivity, and clustering coefficient. This derivation allows us to understand the universal CSN topology observed in systems ranging from a simple quadratic well to the native state of the beta3s peptide and a two-dimensional lattice heteropolymer. Moreover, CSNs are shown to fall in the general class of complex networks described by the fitness model.

The evolution of costly cooperation between selfish individuals seems to contradict Darwinian selection, as it reduces the fitness of a cooperating individual. However, several mechanisms such as repeated interactions or spatial structure can lead to the evolution of cooperation. One such mechanism for the evolution of cooperation, in particular among humans, is indirect reciprocity, in which individuals base their decision to cooperate on the reputation of the potential receiver, which has been established in previous interactions. Cooperation can evolve in these systems if individuals preferably cooperate with those that have shown to be cooperative in the past. We analyze the impact of fake reputations or fraud on the dynamics of reputation and on the success of the reputation system itself, using a mean-field description for evolutionary games given by the replicator equation. This allows us to classify the qualitative dynamics of our model analytically. Our results show that cooperation based on indirect reciprocity is robust with respect to fake reputations and can even be enhanced by them. We conclude that fraud per se does not necessarily have a detrimental effect on social systems.

A pair of complementary algorithms are presented. One of the pair is a fast method for connecting graphs with an edge. The other is a fast method for removing edges from a graph. Both algorithms employ the same tree-based graph representation and so, in concert, can arbitrarily modify any graph. Since the clusters of a percolation model may be described as simple connected graphs, an efficient Monte Carlo scheme can be constructed which uses the algorithms to sweep the occupation probability back and forth between two turning points. This approach concentrates computational sampling time within a region of interest. A high-precision value of $p_c=0.59274603\left(9\right)$ was thus obtained, by Mersenne twister, for the two-dimensional square site percolation threshold.

The present work examines the applicability and efficacy of recurrence plots and recurrence quantification analysis in interpreting statistical-mechanics-based simulations of classical fluids and solids. We analyze temperature time series obtained from molecular dynamics simulations of a Lennard-Jones system at various fluid and solid states. It turns out that the structure of the recurrence plots reflects the different regimes of atomic motion as well as the degree of atomic diffusivity as the system density and temperature are varied. Recurrence plots (RPs) can help to localize a region where a phase transition occurs, while recurrence quantitative analysis descriptors confirm in a more clear way the results of RPs. The trends identified in our results are in qualitative agreement with direct computation of Lyapunov exponents for liquid Lennard-Jones systems reported in the literature.

Synthetic biomolecular spiders with “legs” made of single-stranded segments of DNA can move on a surface which is also covered by single-stranded segments of DNA complementary to the leg DNA. In experimental realizations, when a leg detaches from a segment of the surface for the first time it alters that segment, and legs subsequently bind to these altered segments more weakly. Inspired by these experiments, we investigate spiders moving along a one-dimensional substrate, whose legs leave newly visited sites at a slower rate than revisited sites. For a random walk (one-leg spider), the slowdown does not affect the long time behavior. For a bipedal spider, however, the slowdown generates an effective bias toward unvisited sites, and the spider behaves similarly to the excited walk. Surprisingly, the slowing down of the spider at new sites increases the diffusion coefficient and accelerates the growth of the number of visited sites.

We generalize the formalism of dynamical density functional theory for translational Brownian dynamics toward that of anisotropic colloidal particles which perform both translational and rotational Brownian motion. Using a mean-field approximation for the density functional and a Gaussian-segment model for the rod interaction, the dynamical density functional theory is then applied to a concentrated rod suspension in a confined slab geometry made by two parallel soft walls. The walls are either expanded or compressed and the relaxation behavior is investigated for an equilibrated starting configuration. We find distinctly different orientational ordering during expansion and compression. During expansion we observe preferential parallel ordering of the rods relative to the wall while during compression there is homeotropic ordering perpendicular to the wall. We find a nonexponential relaxation behavior in time. Furthermore, an external field which aligns the rods perpendicular to the walls is turned on or switched off and similar differences in the relaxational dynamics are found. Comparing the theoretical predictions to Brownian dynamics computer simulation data, we find good agreement.