The flow of a simple glass forming system (a 80:20 binary Lennard-Jones mixture) through a planar channel is studied via molecular dynamics simulations. The flow is driven by an external body force similar to gravity. Previous studies show that the model exhibits both a static [F. Varnik et al., J. Chem. Phys. 120, 2788 (2004)] and a dynamic [F. Varnik and O. Henrich, Phys. Rev. B 73, 174209 (2006)] yield stress in the glassy phase. These observations are corroborated by the present work, where we investigate how the presence of a yield stress may affect the system behavior in a Poiseuille-type flow geometry. In particular, we observe a blunted velocity profile across the channel: A relatively wide region in the channel center flows with a constant velocity (zero shear rate) followed by a nonlinear change of the shear rate as the walls are approached. The observed velocity gradients are compared to those obtained from the knowledge of the shear stress across the channel and the flow curves (stress versus shear rate), the latter being determined in our previous simulations of homogeneous shear flow. Furthermore, using the value of the (dynamic) yield stress known from previous simulations, we estimate the threshold body force for a complete arrest of the flow. Indeed, a blockage is observed as the imposed force falls below this threshold value. Small but finite shear rates are observed at stresses above the dynamic but below the static yield stress. We discuss the possible role of the stick-slip-like motion for this observation.

We use orientational-bias Monte Carlo simulations to examine the phase behavior of two-dimensional hard rectangles in the bulk and under confinement by hard walls. For all of the rod aspect ratios and area fractions studied, we find that confinement increases the degree of nematic ordering over the bulk, as confined rods tend to align their long axes parallel to the confining walls. The extent of nematic ordering increases as the separation between the confining walls decreases. If the aspect ratio of the rectangles is sufficiently large, they exhibit nematic ordering in both the bulk and under confinement, where the nematic director is set by the walls. Rods with a small aspect ratio are isotropic in the bulk and exhibit weak tetratic tendencies for sufficiently high densities. From studies of density profiles, angular distributions, and orientational correlation functions for confined, low-aspect-ratio rods, it is apparent that they align their long axes parallel to the wall in the near-wall region, where layering occurs for sufficiently high rod densities. However, confined rods with low aspect ratios still exhibit weak tetratic (isotropic) tendencies near the center of the confined region for all but the smallest wall separations. We note that although our studies probe the ordering of hard rectangles, the entropic tendencies that we observe here will be present for rods with energetic interactions. Thus, these studies serve as a general starting point for understanding and controlling the assembly of rods in two-dimensional confining geometries.

We study the response properties of $d$-dimensional hypercubic excitable networks to a stochastic stimulus. Each site, modeled either by a three-state stochastic susceptible-infected-recovered-susceptible system or by the probabilistic Greenberg-Hastings cellular automaton, is continuously and independently stimulated by an external Poisson rate $h$. The response function (mean density of active sites $\rho$ versus $h$) is obtained via simulations (for $d=1,2,3,4$) and mean-field approximations at the single-site and pair levels $\left(\forall d\right)$. In any dimension, the dynamic range and sensitivity of the response function are maximized precisely at the nonequilibrium phase transition to self-sustained activity, in agreement with a reasoning recently proposed. Moreover, the maximum dynamic range attained at a given dimension $d$ is a decreasing function of $d$.

The dynamic motion of three-dimensional (3D) capsules in a shear flow is investigated by direct numerical simulation. The capsules are modeled as Newtonian liquid droplets enclosed by elastic membranes, with or without considering the membrane-area incompressibility. The internal liquid of the capsules is the same as that outside. The dynamic motion of capsules with initially spherical and oblate spheroidal unstressed shapes is studied under various shear rates. The results show that spherical capsules deform to stationary configurations and then the membranes rotate around the liquid inside (steady tank-treading motion). Such a steady mode is not observed for oblate spheroidal capsules. It is shown that with the shear rate decreasing, the motion of oblate spheroidal capsules changes from the swinging mode (a capsule undergoes periodic shape deformation and inclination oscillation while its membrane is rotating around the liquid inside) to tumbling mode.

Numerical simulations of bubble pulsations have been performed for a system of two bubble clouds in order to study the experimentally observed bubble motion under an ultrasonic horn by high-speed video camera. The comparison between the calculated results and the experimental observation of the bubble pulsation has indicated that the bubble pulsation is strongly influenced by the interaction with surrounding bubbles. The expansion of a bubble during the rarefaction phase of ultrasound is strongly reduced by the bubble-bubble interaction. Some bubbles move toward the horn tip due to the secondary Bjerknes force acting from the bubbles near the horn tip. It has also been shown that the acoustic amplitude in the liquid is strongly reduced by cavitation due to the decrease in acoustic radiation resistance.

By studying a modified (unbiased) quantum multibaker map, we were able to obtain a finite asymptotic quantum current without a classical analog. This result suggests a general method for the design of purely quantum ratchets and sheds light on the investigation of the mechanisms leading to net transport generation by breaking symmetries of quantum systems. Moreover, we propose the multibaker map as a resource to study directed transport phenomena in chaotic systems without bias. In fact, this is a paradigmatic model in classical and quantum chaos, but also in statistical mechanics.

The universality class, even the order of the transition, of the two-dimensional Ising model depends on the range and the symmetry of the interactions (Onsager model, Baxter-Wu model, Turban model, etc.), but the critical temperature is generally the same due to self-duality. Here we consider a sudden change in the form of the interaction and study the nonequilibrium critical dynamical properties of the nearest-neighbor model. The relaxation of the magnetization and the decay of the autocorrelation function are found to display a power law behavior with characteristic exponents that depend on the universality class of the initial state.

We consider a simple random walk on the T-fractal and we calculate the exact mean time ${\tau }^g$ to first reach the central node $i_0$. The mean is performed over the set of possible walks from a given origin and over the set of starting points uniformly distributed throughout the sites of the graph, except $i_0$. By means of analytic techniques based on decimation procedures, we find the explicit expression for ${\tau }^g$ as a function of the generation $g$ and of the volume $V$ of the underlying fractal. Our results agree with the asymptotic ones already known for diffusion on the T-fractal and, more generally, they are consistent with the standard laws describing diffusion on low-dimensional structures.

We study the fidelity approach to quantum phase transitions (QPTs) and apply it to general thermal phase transitions (PTs). We analyze two particular cases: The Stoner-Hubbard itinerant electron model of magnetism and the BCS theory of superconductivity. In both cases we show that the sudden drop of the mixed state fidelity marks the line of the phase transition. We conduct a detailed analysis of the general case of systems given by mutually commuting Hamiltonians, where the nonanalyticity of the fidelity is directly related to the nonanalyticity of the relevant response functions (susceptibility and heat capacity), for the case of symmetry-breaking transitions. Further, on the case of BCS theory of superconductivity, given by mutually noncommuting Hamiltonians, we analyze the structure of the system’s eigenvectors in the vicinity of the line of the phase transition showing that their sudden change is quantified by the emergence of a generically nontrivial Uhlmann mixed state geometric phase.

The evolution of a system of chemical reactions can be studied, in the eikonal approximation, by means of a Hamiltonian dynamical system. The fixed points of this dynamical system represent the different states in which the chemical system can be found, and the connections among them represent instantons or optimal paths linking these states. We study the relation between the phase portrait of the Hamiltonian system representing a set of chemical reactions with constant rates and the corresponding system when these rates vary in time. We show that the topology of the phase space is robust for small time-dependent perturbations in concrete examples and state general results when possible. This robustness allows us to apply some of the conclusions on the qualitative behavior of the autonomous system to the time-dependent situation.

The multifractal spectrum $f\left(\alpha \right)$ characterizing the scaling properties of the growth probability on the boundary of radial diffusion-limited aggregates is known to exhibit strong finite size effects. We demonstrate that there exists a correlation between these finite size effects and those present in measurements of the angular width of the fjords which lie between the principal cluster arms. We subsequently conclude that it is the evolution in the global structure of the clusters which is responsible for the slow convergence in $f\left(\alpha \right)$ and discuss how this global structure induces a phase transition in $f\left(\alpha \right)$.

We consider a capillary consisting of two coaxial cylinders whose core is filled with a nematic liquid crystal (LC) subjected to the simultaneous action of both a pressure gradient applied parallel to the axis of the cylinders and a radial low frequency electric field. We find the configuration of the director of the nematic, initially with an escaped-like configuration, for the flow aligning LC $4^{\prime }\text{−}n$-pentyl-4-cyanobiphenyl (5CB) by assuming hard anchoring hybrid boundary conditions. Also, we obtain the velocity profile parametrized by the electric field and the pressure gradient for nonslip boundary conditions. Finally, we calculate exactly the effective viscosity, the first normal stress difference, and the dragging forces on the cylinders. The results show an important electrorheological effect and a directional non-Newtonian response with regions of flow thinning and thickening.

We investigate a prototypical agent-based model, the naming game, on two-dimensional random geometric networks. The naming game [Baronchelli et al., J. Stat. Mech.: Theory Exp. (2006) P06014] is a minimal model, employing local communications that captures the emergence of shared communication schemes (languages) in a population of autonomous semiotic agents. Implementing the naming games with local broadcasts on random geometric graphs, serves as a model for agreement dynamics in large-scale, autonomously operating wireless sensor networks. Further, it captures essential features of the scaling properties of the agreement process for spatially embedded autonomous agents. Among the relevant observables capturing the temporal properties of the agreement process, we investigate the cluster-size distribution and the distribution of the agreement times, both exhibiting dynamic scaling. We also present results for the case when a small density of long-range communication links are added on top of the random geometric graph, resulting in a “small-world”-like network and yielding a significantly reduced time to reach global agreement. We construct a finite-size scaling analysis for the agreement times in this case.

We study the damage process of fiber bundles in a wedge-shape geometry which ensures a constant strain gradient. To obtain the wedge geometry we consider the three-point bending of a bar, which is modeled as two rigid blocks glued together by a thin elastic interface. The interface is discretized by parallel fibers with random failure thresholds, which become elongated when the bar is bent. Analyzing the progressive damage of the system we show that the strain gradient results in a rich spectrum of novel behavior of fiber bundles. We find that for weak disorder an interface crack is formed as a continuous region of failed fibers. Ahead of the crack a process zone develops which proved to shrink with increasing deformation, making the crack tip sharper as the crack advances. For strong disorder, failure of the system occurs as a spatially random sequence of breakings. Damage of the fiber bundle proceeds in bursts whose size distribution shows a power law behavior with a crossover from an exponent 2.5 to 2.0 as the disorder is weakened. The size of the largest burst increases as a power law of the strength of disorder with an exponent $2∕3$ and saturates for strongly disordered bundles.

We study a generalized isotropic $XY$ model which includes both two- and four-spin mean-field interactions. This model can be solved in the microcanonical ensemble. It is shown that in certain parameter regions the model exhibits gaps in the magnetization at fixed energy, resulting in ergodicity breaking. This phenomenon has previously been reported in anisotropic and discrete spin models. The entropy of the model is calculated and the microcanonical phase diagram is derived, showing the existence of first-order phase transitions from the ferromagnetic to a paramagnetic disordered phase. It is found that ergodicity breaking takes place in both the ferromagnetic and paramagnetic phases. As a consequence, the system can exhibit a stable ferromagnetic phase within the paramagnetic region, and conversely a disordered phase within the magnetically ordered region.

The phase diagram of the spin-1 Ising model in the presence of a biaxial crystal-field anisotropy is studied within the framework of a variational approach, based on the Bogolyubov inequality for the free energy. We have investigated the effects of a transverse crystal field $D_y$ on the phase diagram in the $T\text{−}{D}_x$ plane. Results obtained by using effective-field theory (EFT) on the honeycomb $\left(z=3\right)$, square $\left(z=4\right)$, and simple cubic $\left(z=6\right)$ lattices ($z$ is the coordination number) show only continuous phase transitions, while the variational approach presents first-order and continuous phase transitions for $D_y=0$. We have also used the EFT for larger values of $z$ and we observe the presence of tricritical points in the phase diagrams, for $z\ge 7$, in accordance with the variational approach results.

The distribution of the return intervals $\tau$ between price volatilities above a threshold height $q$ for financial records has been approximated by a scaling behavior. To explore how accurate is the scaling and therefore understand the underlined nonlinear mechanism, we investigate intraday data sets of 500 stocks which consist of Standard & Poor’s 500 index. We show that the cumulative distribution of return intervals has systematic deviations from scaling. We support this finding by studying the $m$-th moment ${\mu }_m\equiv {⟨{\left(\tau /⟨\tau ⟩\right)}^m⟩}^{1/m}$, which show a certain trend with the mean interval $⟨\tau ⟩$. We generate surrogate records using the Schreiber method, and find that their cumulative distributions almost collapse to a single curve and moments are almost constant for most ranges of $⟨\tau ⟩$. Those substantial differences suggest that nonlinear correlations in the original volatility sequence account for the deviations from a single scaling law. We also find that the original and surrogate records exhibit slight tendencies for short and long $⟨\tau ⟩$, due to the discreteness and finite size effects of the records, respectively. To avoid as possible those effects for testing the multiscaling behavior, we investigate the moments in the range $10<⟨\tau ⟩\le 100$, and find that the exponent $\alpha$ from the power law fitting ${\mu }_m\sim {⟨\tau ⟩}^{\alpha }$ has a narrow distribution around $\alpha \ne 0$ which depends on $m$ for the 500 stocks. The distribution of $\alpha$ for the surrogate records are very narrow and centered around $\alpha =0$. This suggests that the return interval distribution exhibits multiscaling behavior due to the nonlinear correlations in the original volatility.

We derive an analytic evolution equation for overlap parameters, including the effect of degree distribution on the transient dynamics of sequence processing neural networks. In the special case of globally coupled networks, the precisely retrieved critical loading ratio ${\alpha }_c=N^{-1∕2}$ is obtained, where $N$ is the network size. In the presence of random networks, our theoretical predictions agree quantitatively with the numerical experiments for delta, binomial, and power-law degree distributions.

Fast ions created in the fusion processes will provide up to 70% of the heating in ITER. To optimize heating and current drive in magnetically confined plasmas insight into fast-ion dynamics is important. First measurements of such dynamics by collective Thomson scattering (CTS) were recently reported [Bindslev et al., Phys. Rev. Lett. 97, 205005 2006]. Here we extend the discussion of these results which were obtained at the TEXTOR tokamak. The fast ions are generated by neutral-beam injection and ion-cyclotron resonance heating. The CTS system uses $100–150\mathrm{kW}$ of $110\text{−}\mathrm{GHz}$ gyrotron probing radiation which scatters off the collective plasma fluctuations driven by the fast-ion motion. The technique measures the projected one-dimensional velocity distribution of confined fast ions in the scattering volume where the probe and receiver beams cross. By shifting the scattering volume a number of scattering locations and different resolved velocity components can be measured. The temporal resolution is $4\mathrm{ms}$ while the spatial resolution is $\sim 10\mathrm{cm}$ depending on the scattering geometry. Fast-ion velocity distributions in a variety of scenarios are measured, including the evolution of the velocity distribution after turnoff of the ion heating. These results are in close agreement with numerical simulations.