A model of three-disk micromachine swimming in a quasi-two-dimensional supported membrane is proposed. We calculate the average swimming velocity as a function of the disk size and the arm length. Due to the presence of the hydrodynamic screening length in the quasi-two-dimensional fluid, the geometric factor appearing in the average velocity exhibits three different asymptotic behaviors depending on the microswimmer size and the hydrodynamic screening length. This is in sharp contrast with a microswimmer in a three-dimensional bulk fluid that shows only a single scaling behavior. We also find that the maximum velocity is obtained when the disks are equal-sized, whereas it is minimized when the average arm lengths are identical. The intrinsic drag of the disks on the substrate does not alter the scaling behaviors of the geometric factor.

Nematogenic liquids are materials that are in high demand for many application purposes. Field-induced nematic order in isotropic liquids can be observed by the enhancement of electric permittivity during dielectric spectroscopy measurements under the bias electric field. For this reason, dielectric measurements were done on a nematogenic mixture of highly polar compounds. This paper presents a discussion on the influence of the bias electric field on the dielectric response. We observed a decrease of electric permittivity in the isotropic phase under the bias electric field. This effect is most likely caused by the field-induced creation of some complex molecular objects. In the paper, relaxation parameters of the molecular modes were analyzed. The field-induced orientational order was determined using a dichroic ratio in a guest-host system. The measurements show the significant order parameter in the isotropic phase under an electric field.

We investigate the dynamics of classical spins mapped as walkers in a virtual “spin” space using a generalized two-parameter family of spin models characterized by parameters $y$ and $z$ [de Oliveira et al., J. Phys. A 26, 2317 (1993)]. The behavior of $S(x,t)$, the probability that the walker is at position $x$ at time $t$, is studied in detail. In general $S(x,t)\sim t^{-\alpha }f(x/t^{\alpha })$ with $\alpha \simeq 1$ or 0.5 at large times depending on the parameters. In particular, $S(x,t)$ for the point $y=1,z=0.5$ corresponding to the Voter model shows a crossover in time; associated with this crossover, two timescales can be defined which vary with the system size $L$ as $L^{2}logL$. We also show that as the Voter model point is approached from the disordered regions along different directions, the width of the Gaussian distribution $S(x,t)$ diverges in a power law manner with different exponents. For the majority Voter case, the results indicate that the the virtual walk can detect the phase transition perhaps more efficiently compared to other nonequilibrium methods.

Fractional transport equations are used to build an effective model for transport across the running sandpile cellular automaton [Hwa et al., Phys. Rev. A 45, 7002 (1992)]. It is shown that both temporal and spatial fractional derivatives must be considered to properly reproduce the sandpile transport features, which are governed by self-organized criticality, at least over sufficiently long or large scales. In contrast to previous applications of fractional transport equations to other systems, the specifics of sand motion require in this case that the spatial fractional derivatives used for the running sandpile must be of the completely asymmetrical Riesz-Feller type. Appropriate values for the fractional exponents that define these derivatives in the case of the running sandpile are obtained numerically.

We revisit the well-known problem of multiscaling in substances passively advected by homogeneous and isotropic turbulent flows or passive scalar turbulence. To that end we propose a two-parameter continuum hydrodynamic model for an advected substance concentration $\theta$, parametrized jointly by $y$ and $\overline{y}$, that characterize the spatial scaling behavior of the variances of the advecting stochastic velocity and the stochastic additive driving force, respectively. We analyze it within a one-loop dynamic renormalization group method to calculate the multiscaling exponents of the equal-time structure functions of $\theta$. We show how the interplay between the advective velocity and the additive force may lead to simple scaling or multiscaling. In one limit, our results reduce to the well-known results from the Kraichnan model for passive scalar. Our framework of analysis should be of help for analytical approaches for the still intractable problem of fluid turbulence itself.

Quantum-classical correspondence in chaotic systems is a long-standing problem. We describe a method to quantify Bohr's correspondence principle and calculate the size of quantum numbers for which we can expect to observe quantum-classical correspondence near periodic orbits of Floquet systems. Our method shows how the stability of classical periodic orbits affects quantum dynamics. We demonstrate our method by analyzing quantum-classical correspondence in the quantum kicked top (QKT), which exhibits both regular and chaotic behavior. We use our correspondence conditions to identify signatures of classical bifurcations even in a deep quantum regime. Our method can be used to explain the breakdown of quantum-classical correspondence in chaotic systems.

Speech requires programming the sequence of vocal gestures that produce the sounds of words. Here we explored the timing of this program by asking our participants to pronounce, as quickly as possible, a sequence of consonant-consonant-vowel (CCV) structures appearing on screen. We measured the delay between visual presentation and voice onset. In the case of plosive consonants, produced by sharp and well defined movements of the vocal tract, we found that delays are positively correlated with the duration of the transition between consonants. We then used a battery of statistical tests and mathematical vocal models to show that delays reflect the motor planning of CCVs and transitions are proxy indicators of the vocal effort needed to produce them. These results support that the effort required to produce the sequence of movements of a vocal gesture modulates the onset of the motor plan.

The present paper is devoted to studying the thermophoresis of a nonspherical convex particle suspended in a gas with nonuniform temperature distribution in the free-molecule regime. Based on the gas kinetic theory and the assumption of a rigid-body collision for the gas-particle interaction, analytical expressions for the thermophoretic forces are obtained for several typical nonspherical bodies, including cylinders, spheroids, needles, disks, and cuboids. The orientation dependences of the thermophoretic forces and thermophoretic velocities are evaluated based on these expressions. It is found that the influence of the pitching effect of the nonspheres can be significant. The expressions for the orientation-averaged thermophoretic forces are also obtained under the assumption of a uniform particle orientation distribution.

A direct observation of the stratified electrothermal instability on the surface of thick metal is reported. Aluminum rods coated with $70\mu \mathrm{m}$ Parylene-N were driven to 1 MA in $100\mathrm{ns}$, with the metal thicker than the skin depth. The dielectric coating suppressed plasma formation, enabling persistent observation of discrete azimuthally correlated stratified thermal perturbations perpendicular to the current whose wave numbers, $k$, grew exponentially with rate $\gamma \left(k\right)=0.06\mathrm{n}{\mathrm{s}}^{-1}-\left(0.4\mathrm{n}{\mathrm{s}}^{-1}\mu {\mathrm{m}}^2\mathrm{ra}{\mathrm{d}}^{-2}\right)k^2$ in $\sim 1\mathrm{g}/\mathrm{c}{\mathrm{m}}^3$, $\sim 7000\mathrm{K}$ aluminum.

Analytic relations are derived for finite-volume integrals over the pair correlation function of a fluid, the so-called Kirkwood-Buff integrals. Closed-form expressions are obtained for cubes and cuboids, the system shapes commonly employed in molecular simulations. When finite-volume Kirkwood-Buff integrals are expanded over an inverse system size, the leading term depends on shape only through the surface area-to-volume ratio. This conjecture is proved for arbitrary shapes and a general expression for the leading term is derived. From this, an extrapolation to the infinite-volume limit is proposed, which converges much faster with system size than previous approximations and thus significantly simplifies the numerical computations.

We consider the two-dimensional motion of a particle in a confining potential, subject to Brownian orthogonal forces associated with two different temperatures. Exact solutions are obtained for an asymmetric harmonic potential in the overdamped and underdamped regimes. For more general confining potentials, a perturbative approach shows that the stationary state exhibits some universal properties. The nonequilibrium stationary state is characterized with a nonzero orthoradial mean current, corresponding to a global rotation of the particle around the center. The rotation is due to two broken symmetries: two different temperatures and a mismatch between the principal axes of the confining asymmetric potential and the temperature axes. We confirm our predictions by performing a Brownian dynamics simulation. Finally, we propose to observe this effect on a laser-cooled atomic gas.

Ferrofluid heating by an external alternating field is studied based on the rigid dipole model, where the magnetization of each particle in a fluid is supposed to be firmly fixed in the crystal lattice. Equations of motion, employing Newton's second law for rotational motion, the condition of rigid body rotation, and the assumption that the friction torque is proportional to angular velocity are used. This oversimplification permits us to expand the model easily: to take into account the thermal noise and interparticle interaction that allows us to estimate from unified positions the role of thermal activation and dipole interaction in the heating process. Our studies are conducted in three stages. The exact expressions for the average power loss of a single particle are obtained within the dynamical approximation. Then, in the stochastic case, the power loss of a single particle is estimated analytically using the Fokker-Planck equation and numerically using the effective Langevin equation. Finally, the power loss for the particle ensemble is obtained using the molecular dynamics method. Here, the local dipole fields are calculated approximately based on the Barnes-Hut algorithm. The revealed trends in the behavior of both a single particle and the particle ensemble suggest the way of choosing the conditions for obtaining the maximum heating efficiency. The competitiveness character of the interparticle interaction and thermal noise is investigated in detail. Two situations, when the thermal noise rectifies the power loss reduction caused by the interaction, are described. The first of them is related to the complete destruction of dense clusters at high noise intensity. The second one originates from the rare switching of the particles in clusters due to thermal activation, when the noise intensity is relatively weak. In this way, the constructive role of noise appears in the system.

Acoustophoresis is a form of contact-free particle manipulation in microfluidic devices. The precision of manipulation can be enhanced with better understanding of the acoustic radiation force. In this paper we present the measurements of interparticle radiation force between a pair of polystyrene beads in the Rayleigh limit. The study is conducted for three different sizes of beads and the experimental results are of the same order of magnitude when compared with theoretical predictions. However, the experimental values are larger than the theoretical values. The trend of a decrease in the magnitude of the interparticle radiation force with decreasing particle size and increasing center-to-center distance between the particles is also observed experimentally. The experiments are conducted in the specific scenario where the pair of beads are in close proximity, but not in contact with each other, and the beads are approaching the pressure nodal plane with the center-to-center line aligned perpendicular to the incident wave. This scenario minimizes the presence of the primary radiation force, allowing accurate measurement of the interparticle force. The attractive nature of the interparticle force is observed, consistent with theoretical predictions.

The Dzyaloshinskii-Moriya (DM) interaction in magnetic models is the result of a combination of superexchange and spin-orbital coupling, and it can give rise to rich phase-transition behavior. In this paper, we study ferromagnetic $XY$ models with the DM interaction on two-dimensional $L\times L$ square lattices using a hybrid Monte Carlo algorithm. To match the incommensurability between the resultant spin structure and the lattice due to the DM interaction, a fluctuating boundary condition is adopted. We also define a different kind of order parameter and use finite-size scaling to study the critical properties of this system. We find that a Kosterlitz-Thouless-like phase transition appears in this system and that the phase-transition temperature shifts toward higher temperature with increasing DM interaction strength.

High-density (HD) percolation describes the percolation of specific $\kappa$-clusters, which are the compact sets of sites each connected to $\kappa$ nearest filled sites at least. It takes place in the classical patterns of independently distributed sites or bonds in which the ordinary percolation transition also exists. Hence, the study of series of $\kappa$-type HD percolations amounts to the description of classical clusters’ structure for which $\kappa$-clusters constitute $\kappa$-cores nested one into another. Such data are needed for description of a number of physical, biological, and information properties of complex systems on random lattices, graphs, and networks. They range from magnetic properties of semiconductor alloys to anomalies in supercooled water and clustering in biological and social networks. Here we present the statistical mechanics approach to study HD bond percolation on an arbitrary graph. It is shown that the generating function for $\kappa$-clusters’ size distribution can be obtained from the partition function of the specific $q$-state Potts-Ising model in the $q\to 1$ limit. Using this approach we find exact $\kappa$-clusters’ size distributions for the Bethe lattice and Erdos-Renyi graph. The application of the method to Euclidean lattices is also discussed.

Thermal-equilibrated finite classical lattices are considered as a minimal model of the systems showing an interplay between low-energy collective fluctuations and single-site degrees of freedom. Standard local field approach, as well as classical limit of the bosonic DMFT method, do not provide a satisfactory description of Ising and Heisenberg small lattices subjected to an external polarizing field. We show that a dramatic improvement can be achieved within a simple approach, in which the local field appears to be a fluctuating quantity related to the low-energy degree(s) of freedom.

The modulational instability of nonlinear plane waves and the existence of periodic and localized dissipative solitons and waves of the discrete Ginzburg-Landau equation with saturable nonlinearity are investigated. Explicit analytic expressions for periodic solutions with a zero and a finite background are derived and their stability properties investigated by means of direct numerical simulations. We find that while discrete periodic waves and solitons on a zero background are stable under time evolution, they may become modulationally unstable on finite backgrounds. The effects of a linear ramp potential on stable localized dissipative solitons are also briefly discussed.

Stimulus-related brain activity is considered using wavelet-based analysis of neural interactions between occipital and parietal brain areas in alpha (8–12 Hz) and beta (15–30 Hz) frequency bands. We show that human sensory processing related to the visual stimuli perception induces brain response resulted in different ways of parieto-occipital interactions in these bands. In the alpha frequency band the parieto-occipital neuronal network is characterized by homogeneous increase of the interaction between all interconnected areas both within occipital and parietal lobes and between them. In the beta frequency band the occipital lobe starts to play a leading role in the dynamics of the occipital-parietal network: The perception of visual stimuli excites the visual center in the occipital area and then, due to the increase of parieto-occipital interactions, such excitation is transferred to the parietal area, where the attentional center takes place. In the case when stimuli are characterized by a high degree of ambiguity, we find greater increase of the interaction between interconnected areas in the parietal lobe due to the increase of human attention. Based on revealed mechanisms, we describe the complex response of the parieto-occipital brain neuronal network during the perception and primary processing of the visual stimuli. The results can serve as an essential complement to the existing theory of neural aspects of visual stimuli processing.

Random impedance networks are widely used as a model to describe plasmon resonances in disordered metal-dielectric and other two-component nanocomposites. In the present work, the spectral properties of resonances in random networks are studied within the framework of the random matrix theory. We have shown that the appropriate ensemble of random matrices for the considered problem is the Jacobi ensemble (the MANOVA ensemble). The obtained analytical expressions for the density of states in such resonant networks show a good agreement with the results of numerical simulations in a wide range of metal filling fractions $0<p<1$. A correspondence with the effective medium approximation is observed.