We analytically study a system of spinless fermions driven at the boundary with an oscillating chemical potential. Various transport regimes can be observed: At zero driving frequency the particle current through the system is independent of the system's length; at the phase-transition frequency, being equal to the bandwidth, the current decays as $\sim$$n^{-\alpha }$ with the chain length $n$, $\alpha$ being either 2 or 3; below the transition the scaling of the current is $\sim$$n^{-1/2}$, indicating anomalous transport, while it is exponentially small $\sim$$\exp (-\frac{n}{2\xi })$ above the transition. Therefore, by a simple change of frequency of the a.c. driving of the system one can vary transport from ballistic, anomalous to insulating.

Using molecular dynamics simulations we study, in two dimensions, the temperature-density phase diagram of a simple model with two internal states labeled 1 and $-1$. The particles interact with a modified Lennard-Jones potential, which depends on relative positions of the particles as well as on their state. Working in an ensemble where the system reduces to a $50:50$ binary mixture of two species of particles, we obtain a rich phase diagram showing many features of common network-forming liquids such as water and silica, including polymorphism and thermodynamic anomalies. We believe our model may be useful for studies concerning generic features of such complex liquids.

We present a quantitative analysis of grain morphology of self-organizing hexagonal patterns based on the phase-field crystal model to examine the effect of stochastic noise on grain coarsening. We show that the grain size increases with increasing noise strength, resulting in enhanced hexagonal orientation due to noise up to some critical noise level above which the system becomes disordered.

Randomly connected networks of neurons exhibit a transition from fixed-point to chaotic activity as the variance of their synaptic connection strengths is increased. In this study, we analytically evaluate how well a small external input can be reconstructed from a sparse linear readout of network activity. At the transition point, known as the edge of chaos, networks display a number of desirable features, including large gains and integration times. Away from this edge, in the nonchaotic regime that has been the focus of most models and studies, gains and integration times fall off dramatically, which implies that parameters must be fine tuned with considerable precision if high performance is required. Here we show that, near the edge, decoding performance is characterized by a critical exponent that takes a different value on the two sides. As a result, when the network units have an odd saturating nonlinear response function, the falloff in gains and integration times is much slower on the chaotic side of the transition. This means that, under appropriate conditions, good performance can be achieved with less fine tuning beyond the edge, within the chaotic regime.

Certain high-dimensional dynamical systems present two or more attractors characterized by different energy branches. For some parameter values the dynamics oscillates between these two branches in a seemingly random fashion, a phenomenon called two-state on-off intermittency. In this work we show that the dynamical mechanism underlying this intermittency involves the severe breakdown of hyperbolicity of the attractors through a mechanism known as unstable dimension variability. We characterize the parametric evolution of this variability using statistical properties of the finite-time Lyapunov exponents. As a model system that exhibits this behavior we consider periodically forced and damped drift waves. In this spatiotemporal example there is a low-dimensional chaotic attractor that is created by an interior crisis, already presenting unstable dimension variability.

Ferrofluids are colloidal suspensions of magnetic nanoparticles that exhibit normal liquid behavior in the absence of magnetic fields but respond to imposed magnetic fields by changing their viscosity without loss of fluidity. The response of ferrofluids to constant shear and magnetic fields has received a lot of attention, but the response of ferrofluids to oscillatory shear remains largely unexplored. In the present work we used rotational Brownian dynamics to study the dynamic properties of ferrofluids with thermally blocked nanoparticles under oscillatory shear and constant magnetic fields. Comparisons between simulations and modeling using the ferrohydrodynamics equations were also made. Simulation results show that, for small rotational Péclet number, the in-phase and out-of-phase components of the complex viscosity depend on the magnitude of the magnetic field and frequency of the shear, following a Maxwell-like model with field-dependent viscosity and characteristic time equal to the field-dependent transverse magnetic relaxation time of the nanoparticles. Comparison between simulations and the numerical solution of the ferrohydrodynamic equations shows that the oscillatory rotational magnetoviscosity for an oscillating shear field obtained using the kinetic magnetization relaxation equation quantitatively agrees with simulations for a wide range of Péclet number and Langevin parameter but has quantitative deviations from the simulations at high values of the Langevin parameter. These predictions indicate an apparent elastic character to the rheology of these suspensions, even though we are considering the infinitely dilute limit in which there are negligible particle-particle interactions and, as such, chains do not form. Additionally, an asymptotic analytical solution of the ferrohydrodynamics equations, valid for $\mathrm{Pe}\ll 2$, was used to demonstrate that the Cox-Merz rule applies for dilute ferrofluids under conditions of small shear rates. At higher shear rates the Cox-Merz rule ceases to apply.

We present an approximate description of the behavior of an elastic-plastic material processed by a cylindrically or spherically symmetric converging shock, following Whitham's shock dynamics theory. Originally applied with success to various gas dynamics problems, this theory is presently derived for solid media, in both elastic and plastic regimes. The exact solutions of the shock dynamics equations obtained reproduce well the results obtained by high-resolution numerical simulations. The examined constitutive laws share a compressible neo-Hookean structure for the internal energy $e=e_s\left(I_1\right)+e_h(\rho ,\varsigma )$, where $e_s$ accounts for shear through the first invariant of the Cauchy–Green tensor, and $e_h$ represents the hydrostatic contribution as a function of the density $\rho$ and entropy $\varsigma$. In the strong-shock limit, reached as the shock approaches the axis or origin $r=0$, we show that compression effects are dominant over shear deformations. For an isothermal constitutive law, i.e., $e_h=e_h\left(\rho \right)$, with a power-law dependence $e_h\propto {\rho }^{\alpha }$, shock dynamics predicts that for a converging shock located at $r=R\left(t\right)$ at time $t$, the Mach number increases as $M\propto {\left[\log (1/R)\right]}^{\alpha }$, independently of the space index $s$, where $s=2$ in cylindrical geometry and 3 in spherical geometry. An alternative isothermal constitutive law with $p\left(\rho \right)$ of the $\text{arctanh}$ type, which enforces a finite density in the strong-shock limit, leads to $M\propto R^{-(s-1)}$ for strong shocks. A nonisothermal constitutive law, whose hydrostatic part $e_h$ is that of an ideal gas, is also tested, recovering the strong-shock limit $M\propto R^{-(s-1)/n\left(\gamma \right)}$ originally derived by Whitham for perfect gases, where $\gamma$ is inherently related to the maximum compression ratio that the material can reach, $(\gamma +1)/(\gamma -1)$. From these strong-shock limits, we also estimate analytically the density, radial velocity, pressure, and sound speed immediately behind the shock. While the hydrostatic part of the energy essentially commands the strong-shock behavior, the shear modulus and yield stress modify the compression ratio and velocity of the shock far from the axis or origin. A characterization of the elastic-plastic transition in converging shocks, which involves an elastic precursor and a plastic compression region, is finally exposed.

The wake of a circular cylinder performing rotary oscillations is studied using hydrodynamic tunnel experiments at $\text{Re}=100$. Two-dimensional particle image velocimetry on the midplane perpendicular to the axis of a cylinder is used to characterize the spatial development of the flow and its stability properties. The lock-in phenomenon that determines the boundaries between regions of the forcing parameter space where the wake is globally unstable or convectively unstable [see  Thiria and Wesfreid, J. Fluids Struct. 25, 654 (2009) for a review] is scrutinized using the experimental data. A method based on the analysis of power density spectra of the flow allows us to give a detailed description of the forced wake, shedding light on the energy distribution in the different frequency components and in particular on a cascade-like mechanism evidenced for a high amplitude of the forcing oscillation. In addition, a calculation of the drag from the velocity field is performed, allowing us to relate the resulting force on the body to the wake properties.

We expand the Potts-percolation model of a solid to include stress and strain. Neighboring atoms are connected by bonds. We set the energy of a bond to be given by the Lennard-Jones potential. If the energy is larger than a threshold the bond is more likely to fail, whereas if the energy is lower than the threshold, the bond is more likely to be alive. In two dimensions we compute the equation of state: stress as a function of interatomic distance and temperature by using renormalization-group and Monte Carlo simulations. The phase diagram, the equation of state, and the isothermal modulus are determined. When the Potts heat capacity is divergent the continuous transition is replaced by a weak first-order transition through the van der Waals loop mechanism. When the Potts transition is first order the stress exhibits a large discontinuity as a function of the interatomic distance.

Various situations where a signal is enhanced by noise through stochastic resonance are now known. This paper contributes to determining general conditions under which improvement by noise can be a priori decided as feasible or not. We focus on the detection of a known signal in additive white noise. Under the assumptions of a weak signal and a sufficiently large sample size, it is proved, with an inequality based on the Fisher information, that improvement by adding noise is never possible, generically, in these conditions. However, under less restrictive conditions, an example of signal detection is shown with favorable action of adding noise.

Lévy flights with inertial term in various potentials are studied analytically and numerically in terms of the fractional Fokker-Planck equation. The probability density functions of the Lévy flight particle in the linear and harmonic potentials are exactly obtained and a transient contribution of inertial term is found in the case of linear potential, which can be neglected when evolution time is much longer than ${\gamma }^{-1}$ ($\gamma$ is the damping coefficient); for the harmonic potential, where the stationary state has still infinite variance of coordinate and its width is larger than that of the inertialess case for arbitrary Lévy index $\mu$ in the region of $0<\mu <2$, we still find that the distribution of velocity of the particle is also the Lévy-type one. Moreover, a crossover from bimodal to unimodal shape for the spatial distribution is shown in the anharmonic potential. Finally, we represent an analytical expression of the rate constant for the inertial Lévy flight particle escaping from a metastable potential by using the reactive flux method and show that the rate is a nonmonotonic function of the Lévy index.

We give a variational formulation of classical statistical mechanics where the one-body density and the local entropy distribution constitute the trial fields. Using Levy's constrained search method, it is shown that the grand potential is a functional of both distributions, that it is minimal in equilibrium, and that the minimizing fields are those at equilibrium. The functional splits into a sum of entropic, external energetic, and internal energetic contributions. Several common approximate Helmholtz free-energy density functionals, such as the Rosenfeld fundamental measure theory for hard-sphere mixtures, are transformed to internal-energy functionals. The variational derivatives of the internal-energy functional are used to generalize dynamical density-functional theory to include the dynamics of the microscopic entropy distribution, as is relevant for studying heat transport and thermal diffusion.

On the basis of discrete element numerical simulations of a Couette cell, we revisit the rheology of granular materials in the quasistatic and inertial regimes, and discuss the origin of the transition between these two regimes. We show that quasistatic zones are the seat of a creep process whose rate is directly related to the existence and magnitude of velocity fluctuations. The mechanical behavior in the quasistatic regime is characterized by a three-variable constitutive law relating the friction coefficient (normalized stress), the inertial number (normalized shear rate), and the normalized velocity fluctuations. Importantly, this constitutive law appears to remain also valid in the inertial regime, where it can account for the one-to-one relationship observed between the friction coefficient and the inertial number. The abrupt transition between the quasistatic and inertial regimes is then related to the mode of production of the fluctuations within the material, from nonlocal and artificially sustained by the boundary conditions in the quasistatic regime, to purely local and self-sustained in the inertial regime. This quasistatic-to-inertial transition occurs at a critical inertial number or, equivalently, at a critical level of fluctuations.

This paper presents full cross-section measurements of drift waves in the linear magnetized plasma of the Mirabelle device. Drift wave modes are studied in regimes of weakly developed turbulence. The drift wave modes develop azimuthal space-time structures of plasma density, plasma potential, and visible light fluctuations. A fast camera diagnostic is used to record visible light fluctuations of the plasma column in an azimuthal cross section with a temporal resolution of $10\mu \mathrm{s}$ corresponding approximately to $10\%$ of the typical drift wave period. Mode coupling and drift wave dispersion are studied by spatiotemporal Fourier decomposition of the camera frames. The observed coupling between modes is compared to calculations of nonlinearly coupled oscillators described by the Kuramoto model.

The slow passage problem through a resonance is considered. As a model problem, we consider a damped harmonically forced oscillator whose forcing frequency is slowly ramped linearly in time. The setup is similar to the familiar slow passage through a Hopf bifurcation problem, where for slow variations of the control parameter, oscillations are delayed until the parameter has exceeded the critical value of the static-parameter problem by an amount that is the difference between the Hopf value and the initial value of the parameter. In sharp contrast, in the resonance problem there is an early onset of resonance, setting in when the ramped forcing frequency is midway between its initial value and the natural frequency for resonance in the unforced problem; we term this value the jump frequency. Numerically, we find that the jump frequency is independent of the system's damping coefficient, and so we also consider the undamped problem, which is analytically tractable. The analysis of the undamped problem confirms the numerical results found in the damped problem that the maximal amplitude obtained at the jump frequency scales as $A\sim {\epsilon }^{-1/2}$, $\epsilon$ being the ramp rate, and that the jump frequency is midway between the initial frequency at the start of the ramp and the natural frequency of the unforced problem.

When the parameters of electron-extreme power laser interaction enter the regime of dominated radiation reaction, the electron dynamics changes qualitatively. The adequate theoretical description of this regime becomes crucially important with the use of the radiation friction force either in the Lorentz-Abraham-Dirac form, which possesses unphysical runaway solutions, or in the Landau-Lifshitz form, which is a perturbation valid for relatively low electromagnetic wave amplitude. The goal of the present paper is to find the limits of the Landau-Lifshitz radiation force applicability in terms of the electromagnetic wave amplitude and frequency. For this, a class of the exact solutions to the nonlinear problems of charged particle motion in the time-varying electromagnetic field is used.

We propose a general method (based on the Wang-Landau algorithm) to compute numerically free energies that are obtained from the logarithm of the ratio of suitable partition functions. As an application, we determine with high accuracy the order-order interface tension of the four-state Potts model in three dimensions on cubic lattices of linear extension up to $L=56$. The infinite volume interface tension is then extracted at each $\beta$ from a fit of the finite volume interface tension to a known universal behavior. A comparison of the order-order and order-disorder interface tension at ${\beta }_c$ provides a clear numerical evidence of perfect wetting.

We report experiments with very compressible fluids near the liquid-gas critical point. These experiments are performed (i) under microgravity in low Earth orbit by using SF${}_6$ at liquidlike density and (ii) under Earth's gravity with CO${}_2$ at gaslike density. The sample fluid is filled in an interferometer cell with its walls maintained at constant temperature. In situ thermistors measure the local fluid temperature. One of the thermistors is also used as a heat source to generate heat pulses. With no gravity-induced fluid convection, the evolution of fluid temperature is governed by the balance of heat flux between the thermal boundary layer of the heat source, which compresses the bulk fluid, and the thermal boundary layer at the wall, which expands it. When heat pulses are applied to the fluid under weak or Earth's gravity, a long thermal transient is observed at the end of the heat pulse where the bulk fluid temperature reaches significantly below the initial temperature. This unconventional cooling originates from the fast decompression of the fluid, which is induced by the rapid convectively disappearing hot boundary layer at the heat source, and the persistence of an anomalously thin cold boundary layer convectively induced at the cell wall. This striking phenomenon is observed in a large range of temperature, density, and various thermodynamic conditions. This anomalous cooling effect persists for an appreciable period of time corresponding to the diffusive destruction of the cold boundary layer. We found that the effect is also more pronounced when the free fall acceleration is large. We have analyzed the result by using a simple one-dimensional model with ad hoc convective heat losses.