Acoustic gaps are normally observed in granular inhomogeneous structures made of composite materials. The modulation of the elastic properties in such media creates the coherent effects of scattering and interference that ultimately lead to frequency intervals where sound propagation is forbidden. Contrastingly, we report here an experimental observation of acoustic gaps in homogeneous media; specifically, in granular chains. The beads used in our study are magnetic. Therefore, instead of modulating the elastic properties of the chain, we modulate the magnetization (i.e., the contact forces). We also observe that the propagation speed of acoustic signals through the magnetic chains used in this study is at odds with the speed predicted by Hertz’s law.

It is well known that the dynamics of a quantum system is always nonadiabatic in passage through a quantum critical point and the defect density in the final state following a quench shows a power-law scaling with the rate of quenching. However, we propose here a possible situation where the dynamics of a quantum system in passage across quantum critical regions is adiabatic and the defect density decays exponentially. This is achieved by incorporating additional interactions which lead to quantum critical behavior and gapless phases but do not participate in the time evolution of the system. To illustrate the general argument, we study the defect generation in the quantum critical dynamics of a spin-1/2 anisotropic quantum $XY$ spin chain with three spin interactions and a linearly driven staggered magnetic field.

The role of double-humped states in spreading of wave packets for the nonlinear Schrödinger equation (NLSE) with a random potential is explored and the spreading mechanism is unraveled. Comparison to an NLSE with a double-well potential is made. There are two independent effects of the nonlinearity on the double-humped states for the NLSE: coupling to other states and destruction. The interplay between these effects is discussed.

The relationships among reversible Carnot cycles, the absence of perpetual motion machines, and the existence of a nondecreasing globally unique entropy function form the starting point of many textbook presentations of the foundations of thermodynamics. However, the thermal fluctuation phenomena associated with statistical mechanics has been argued to restrict the domain of validity of this basis of the second law of thermodynamics. Here we demonstrate that fluctuation phenomena can be incorporated into the traditional presentation, extending rather than restricting the domain of validity of the phenomenologically motivated second law. Consistency conditions lead to constraints upon the possible spectrum of thermal fluctuations. In a special case this uniquely selects the Gibbs canonical distribution and more generally incorporates the Tsallis distributions. No particular model of microscopic dynamics need be assumed.

Diffusion in a narrow two-dimensional channel with a midline that need not be straight and a width that may vary is reduced to an effective one-dimensional equation of motion. This equation takes the form of the Fick-Jacobs equation with a spatially varying effective diffusivity. The effective diffusivity includes a contribution that comes from the slope of the midline as well as the usual term stemming from variations in the channel width along the length of the channel. Our derivation of our equation of motion is completely rigorous and is based on an asymptotic expansion in a small dimensionless parameter that characterizes the channel width. For a channel that has a straight midline or wall, our equation of motion reduces to Zwanzig’s equation [R. Zwanzig, J. Phys. Chem. 96, 3926 (1992)]. Our derivation therefore provides a rigorous proof of the validity of the latter equation. Finally, the equation of motion is solved analytically for channels with curved midline and constant width.

If a fluctuating medium is confined, the ensuing perturbation of its fluctuation spectrum generates Casimir-like effective forces acting on its confining surfaces. Near a continuous phase transition of such a medium the corresponding order parameter fluctuations occur on all length scales and therefore close to the critical point this effect acquires a universal character, i.e., to a large extent it is independent of the microscopic details of the actual system. Accordingly it can be calculated theoretically by studying suitable representative model systems. We report on the direct measurement of critical Casimir forces by total internal reflection microscopy with femtonewton resolution. The corresponding potentials are determined for individual colloidal particles floating above a substrate under the action of the critical thermal noise in the solvent medium, constituted by a binary liquid mixture of water and 2,6-lutidine near its lower consolute point. Depending on the relative adsorption preferences of the colloid and substrate surfaces with respect to the two components of the binary liquid mixture, we observe that, upon approaching the critical point of the solvent, attractive or repulsive forces emerge and supersede those prevailing away from it. Based on the knowledge of the critical Casimir forces acting in film geometries within the Ising universality class and with equal or opposing boundary conditions, we provide the corresponding theoretical predictions for the sphere—planar wall geometry of the experiment. The experimental data for the effective potential can be interpreted consistently in terms of these predictions and a remarkable quantitative agreement is observed.

We discuss some interesting physical features stemming from our previous analytical study of a simple model of a fluid with dipolarlike interactions of very short range in addition to the usual isotropic Baxter potential for adhesive spheres. While the isotropic part is found to rule the global structural and thermodynamical equilibrium properties of the fluid, the weaker anisotropic part gives rise to an interesting short-range local ordering of nearly spherical condensation clusters, containing short portions of chains having nose-to-tail parallel alignment, which runs antiparallel to adjacent similar chains.

The bifurcation diagram of a model stochastic differential equation with delayed feedback is presented. We are motivated by recent research on stochastic effects in models of transcriptional gene regulation. We start from the normal form for a pitchfork bifurcation, and add multiplicative or parametric noise and linear delayed feedback. The latter is sufficient to originate a Hopf bifurcation in that region of parameters in which there is a sufficiently strong negative feedback. We find a sharp bifurcation in parameter space, and define the threshold as the point in which the stationary distribution function $p\left(x\right)$ changes from a delta function at the trivial state $x=0$ to $p\left(x\right)\sim x^{\alpha }$ at small $x$ (with $\alpha =-1$ exactly at threshold). We find that the bifurcation threshold is shifted by fluctuations relative to the deterministic limit by an amount that scales linearly with the noise intensity. Analytic calculations of the bifurcation threshold are also presented in the limit of small delay $\tau \to 0$ that compare quite favorably with the numerical solutions even for moderate values of $\tau$.

Friction force time series showing irregular fluctuations have been since long considered one of the possible stick-slip regimes in sliding friction. However, it has not been until recently that a $1/f$ power spectrum in friction force time series derived from sliding friction experiments under wear conditions has been identified. A variety of models, mostly inspired in the field of earthquakes, has been explored, without reaching a fully satisfactory explanation of that behavior. Recently, the present authors have reported results of sliding friction experiments on steel with alumina pins, carried out with and without debris blowing, that proved the role of loose debris in determining the $1/f$ character of the friction force. A damped-forced harmonic oscillator with two friction terms was proposed to describe the dynamics of friction under wear conditions: one purely random, which accounts for surface roughness, and another inversely proportional to the amount of loose debris that was calculated by means of a modified sand-pile model. This paper presents a full discussion of the experiments that allowed to reach that conclusion and of the model proposed to rationalize the results. In addition, the results of experiments devised to understand the transition from friction with debris to friction without debris (experiment initiated without blowing and after some time switching on blowing) and vice versa are reported. The results of further studies of the wear track are presented, namely, the variation in the track width with sliding distance and results of chemical analyses and surface roughness measurements of the track, for both with or without debris blowing experiments. These additional data give further support to the crucial role of debris in the $1/f$ character of the friction force.

We investigate analytically the random walk of magnetic field lines. In previous analytical treatments of field line wandering or random walk, it was assumed that the turbulent magnetic field is much weaker than the mean field. In the present paper, we develop an improved analytical method to describe the stochastic properties of turbulent magnetic fields. This approach is an extension of the standard theory of field line wandering and can be applied to weak as well as to strong magnetic turbulence.

We study rotation of a spheroidal dielectric particle immersed into a viscous dielectric fluid and subjected to a constant external electric field. The electrorotation is caused by the mechanical torque due to a fluid shear flow and by the electric moment due to the difference between electric conductivities and permeabilities of a particle and a host fluid. We consider effect of a shear flow on the orientation of the spheroid in a case of an ideal dielectric and for the finite electric conductivities of the spheroid and a host medium. We determined the critical magnitude of the shear flow velocity whereby spheroid cannot be held by the external electric field with a given strength and found the dependencies of the Euler angles of the spheroid vs the strength of the electric field. In a case of a system with a finite electric conductivity we considered two types of the nonideal dielectrics, namely, negative electroviscosity particles and positive electroviscosity particles. For a given magnitude of shear velocity and for two types of particles we determined the critical strengths of the electric field whereby rotation regime changes qualitatively in a case of rotation around the symmetry axis and in a case when the orientation of the axis of symmetry changes.

Dynamic features describing the collisions of the bound vector solitons and soliton complexes are investigated for the coupled nonlinear Schrödinger (CNLS) equations, which model the propagation of the multimode soliton pulses under some physical situations in nonlinear fiber optics. Equations of such type have also been seen in water waves and plasmas. By the appropriate choices of the arbitrary parameters for the multisoliton solutions derived through the Hirota bilinear method, the periodic structures along the propagation are classified according to the relative relations of the real wave numbers. Furthermore, parameters are shown to control the intensity distributions and interaction patterns for the bound vector solitons and soliton complexes. Transformations of the soliton types (shape changing with intensity redistribution) during the collisions of those stationary structures with the regular one soliton are discussed, in which a class of inelastic properties is involved. Discussions could be expected to be helpful in interpreting such structures in the multimode nonlinear fiber optics and equally applied to other systems governed by the CNLS equations, e.g., the plasma physics and Bose-Einstein condensates.

We report an experimental study of particle kinematics in a three-dimensional system of inelastic spheres fluidized by intense vibration. The motion of particles in the interior of the medium is tracked by high-speed video imaging, yielding a spatially resolved measurement of the velocity distribution. The distribution is wider than a Gaussian and broadens continuously with increasing volume fraction. The deviations from a Gaussian distribution for this boundary-driven system are different in sign and larger in magnitude than predictions for homogeneously driven systems. We also find correlations between velocity components which grow with increasing volume fraction.

The nonlinear dependence of cellular orientation on an external, time-varying stress field determines the distribution of orientations in the presence of noise and the characteristic time, ${\tau }_c$, for the cell to reach its steady-state orientation. The short, local cytoskeletal relaxation time distinguishes between high-frequency (nearly perpendicular) and low-frequency (random or parallel) orientations. However, ${\tau }_c$ is determined by the much longer, orientational relaxation time. This behavior is related to experiments for which we predict the angle and characteristic time as a function of frequency.

A driven Ising model with friction due to magnetic correlations was proposed by Kadau et al. [Phys. Rev. Lett. 101, 137205 (2008)]. The nonequilibrium phase transition present in this system is investigated in detail using analytical methods as well as Monte Carlo simulations. In the limit of high driving velocities $v$ the model shows mean-field behavior due to dimensional reduction and can be solved exactly for various geometries. The simulations are performed with three different single spin-flip rates: the common Metropolis and Glauber rates as well as a multiplicative rate. Due to the nonequilibrium nature of the model all rates lead to different critical temperatures at $v>0$, while the exact solution matches the multiplicative rate. Finally, the crossover from Ising to mean-field behavior as function of velocity and system size is analyzed in one and two dimensions.

An experimental evidence of the phenomenon of resonance activation (RA) in bistable semiconductor vertical-cavity surface-emitting laser (VCSEL) with a high level of internal noise under strong periodic excitation is presented. It is shown that the mean switching period (MSP) between polarization states passes through a minimum depending on the modulation frequency. From comparing frequency dependencies of the MSP and the coefficient of variation it is demonstrated for different conditions that resonance activation and stochastic resonance (SR) occur at different optimal values of the modulation frequency. The influence of the signal amplitude, the level of noise in VCSEL and asymmetry of bistable quasipotential are also experimentally studied. For large enough modulation amplitudes, RA and SR are accompanied by the phenomenon of the mean switching frequency locking.

The magnetic properties of a nonequilibrium mixed spin-2 and spin-5/2 Ising ferrimagnetic system with a crystal-field interaction (D) in the presence of a time-varying magnetic field on a hexagonal lattice are studied by using the Glauber-type stochastic dynamics. The model system consists of two interpenetrating sublattices with $\sigma =2$ and $S=5/2$. The Hamiltonian model includes intersublattice, intrasublattice, and crystal-field interactions. The intersublattice interaction is considered antiferromagnetic to have a simple but interesting model of a ferrimagnetic system. The set of mean-field dynamic equations is obtained by employing the Glauber transition rates. First, we investigate the time variations in average sublattice magnetizations to find the phases in the system, and the temperature dependence of the dynamic sublattice magnetizations to characterize the nature (continuous or discontinuous) of the phase transitions and to obtain the dynamic phase transition points. Then, we study the temperature dependence of the total magnetization to find the dynamic compensation points as well as to determine the type of behavior. We also investigate the effect of a crystal-field interaction and the exchange couplings between the nearest-neighbor pairs of spins on the compensation phenomenon and present the dynamic phase diagrams. According to values of Hamiltonian parameters, the paramagnetic, the nonmagnetic, and the four different ferrimagnetic fundamental phases, seven different mixed phases, and the compensation temperature, or the $N$-type behavior in the Néel classification nomenclature exist in the system. A comparison is made with the results of the available mixed spin Ising systems.

A new interfacial microrheology technique using atomic force microscope (AFM) as a force sensor is developed. The probe used for microrheology contains a long vertical glass fiber with one end glued onto a rectangular shaped cantilever beam and the other end immersed through a water-air interface. The motion of the modified cantilever can be accurately described by the Langevin equation for a damped harmonic oscillator, from which we obtain the friction coefficient $\xi$ of the glass fiber in contact with the water. It is found that $\xi$ contains two contributions. One is generated by the bulk fluid, which increases with the immersion length of the glass fiber. The other contribution comes from the contact line between the water-air interface and the glass fiber, which is obtained by an extrapolation of the measured $\xi$ at the limit of zero immersion length. The experiment thus demonstrates an application of AFM in the studies of interfacial microrheology and contact line dynamics.

We have performed simulations to study how increasing humidity affects the structure of Nafion-like ionomers under conditions of low sulfonate concentration and low humidity. At the onset of membrane hydration, the clusters split into smaller parts. These subsequently swell, but then maintain constant the number of sulfonates per cluster. We find that the distribution of water in low-sulfonate membranes depends strongly on the sulfonate concentration. For a relatively low sulfonate concentration, nearly all the side-chain terminal groups are within cluster formations, and the average water loading per cluster matches the water content of membrane. However, for a relatively higher sulfonate concentration the water-to-sulfonate ratio becomes nonuniform. The clusters become wetter, while the intercluster bridges become drier. We note the formation of unusual shells of water-rich material that surround the sulfonate clusters.

We have measured the response of shear stress to ac electric fields under steady shear flow in the droplet-dispersed phase of an immiscible polymer blend. A characteristic mode was found under steady shear flow, the relaxation frequency of which increased with increasing the shear rate. In the frequency dispersion, a scaling relation derived from dimensional analysis was confirmed to hold. The origin of the mode was investigated on the basis of the Maffettone-Minale (MM) model, in which the droplet shape is described by a second-rank tensor. The frequency dispersion of the response was also calculated using a modified MM model.