We investigate transition to synchrony in degree-frequency correlated Sakaguchi-Kuramoto (SK) model on complex networks both analytically and numerically. We analytically derive self-consistent equations for group angular velocity and order parameter for the model in the thermodynamic limit. Using the self-consistent equations we investigate transition to synchronization in SK model on uncorrelated scale-free (SF) and Erdős-Rényi (ER) networks in detail. Depending on the degree distribution exponent ($\gamma$) of SF networks and phase-frustration parameter, the population undergoes from first-order transition [explosive synchronization (ES)] to second-order transition and vice versa. In ER networks transition is always second order irrespective of the values of the phase-lag parameter. We observe that the critical coupling strength for the onset of synchronization is decreased by phase-frustration parameter in case of SF network where as in ER network, the phase-frustration delays the onset of synchronization. Extensive numerical simulations using SF and ER networks are performed to validate the analytical results. An analytical expression of critical coupling strength for the onset of synchronization is also derived from the self-consistent equations considering the vanishing order parameter limit.

Until now only for specific crossovers between Poissonian statistics (P), the statistics of a Gaussian orthogonal ensemble (GOE), or the statistics of a Gaussian unitary ensemble (GUE) have analytical formulas for the level spacing distribution function been derived within random matrix theory. We investigate arbitrary crossovers in the triangle between all three statistics. To this aim we propose an according formula for the level spacing distribution function depending on two parameters. Comparing the behavior of our formula for the special cases of $\mathrm{P}\to \mathrm{GUE}$, $\mathrm{P}\to \mathrm{GOE}$, and $\mathrm{GOE}\to \mathrm{GUE}$ with the results from random matrix theory, we prove that these crossovers are described reasonably. Recent investigations by F. Schweiner et al. [Phys. Rev. E 95, 062205 (2017)] have shown that the Hamiltonian of magnetoexcitons in cubic semiconductors can exhibit all three statistics in dependence on the system parameters. Evaluating the numerical results for magnetoexcitons in dependence on the excitation energy and on a parameter connected with the cubic valence band structure and comparing the results with the formula proposed allows us to distinguish between regular and chaotic behavior as well as between existent or broken antiunitary symmetries. Increasing one of the two parameters, transitions between different crossovers, e.g., from the $\mathrm{P}\to \mathrm{GOE}$ to the $\mathrm{P}\to \mathrm{GUE}$ crossover, are observed and discussed.

We analyze a one-dimensional extended discrete nonlinear Schrödinger (DNLS) dimer model for nonreciprocal wave transmission. The extension corresponds to the addition of a nonlocal or intersite nonlinear response in addition to a purely cubic local (on-site) nonlinear response, which refines the purely cubic model and aligns to more realistic situations. We observe that a diodelike action persists in the extended case; however, the inclusion of nonlocal response tends to reduce the diode action. We show that this extension results in achieving the diode effect at lower incoming intensities as compared to the purely cubic case. We also report that a nearly perfect diode action is possible in the extended case for a higher level of asymmetry between on-site potentials than its cubic counterpart. Moreover, we vary different site-dependent parameters to probe for regimes of a better diode effect within this extended model. We also present the corresponding stability analysis for the exact stationary solutions to the extended DNLS equation, we discuss the bifurcation behavior in detail, and we explicitly give the regions of stability.

Corticothalamic neural field theory is applied to a spherical geometry to better model neural activity in the human brain and is also compared with planar approximations. The frequency power spectrum, correlation, and coherence functions are computed analytically and numerically. The effects of cortical boundary conditions and resulting modal aspects of spherical corticothalamic dynamics are explored, showing that the results of spherical and finite planar geometries converge to those for the infinite planar geometry in the limit of large brain size. Estimates are made of the point at which modal series can be truncated and it is found that for physiologically plausible parameters only the lowest few spatial eigenmodes are needed for an accurate representation of macroscopic brain activity. A difference between the geometries is that there is a low-frequency $1/f$ spectrum in the infinite planar geometry, whereas in the spherical geometry it is $1/f^2$. Another difference is that the alpha peak in the spherical geometry is sharper and stronger than in the planar geometry. Cortical modal effects can lead to a double alpha peak structure in the power spectrum, although the main determinant of the alpha peak is corticothalamic feedback. In the spherical geometry, the cross spectrum between two points is found to only depend on their relative distance apart. At small spatial separations the low-frequency cross spectrum is stronger than for an infinite planar geometry and the alpha peak is sharper and stronger due to the partitioning of the energy into discrete modes. In the spherical geometry, the coherence function between points decays monotonically as their separation increases at a fixed frequency, but persists further at resonant frequencies. The correlation between two points is found to be positive, regardless of the time lag and spatial separation, but decays monotonically as the separation increases at fixed time lag. At fixed distance the correlation has peaks at multiples of the period of the dominant frequency of system activity.

We provide improved understanding of acoustophoretic focusing of a dense suspension (volume fraction $\phi >10\%$) in a microchannel subjected to an acoustic standing wave using a proposed theoretical model and experiments. The model is based on the theory of interacting continua and utilizes a momentum transport equation for the mixture, continuity equation, and transport equation for the solid phase. The model demonstrates the interplay between acoustic radiation and shear-induced diffusion (SID) forces that is critical in the focusing of dense suspensions. The shear-induced particle migration model of Leighton and Acrivos, coupled with the acoustic radiation force, is employed to simulate the continuum behavior of particles. In the literature, various closures for the diffusion coefficient $D_{\phi }^{*}$ are available for rigid spheres at high concentrations and nonspherical deformable particles [e.g., red blood cells (RBCs)] at low concentrations. Here we propose a closure for $D_{\phi }^{*}$ for dense suspension of RBCs and validate the proposed model with experimental data. While the available closures for $D_{\phi }^{*}$ fail to predict the acoustic focusing of a dense suspension of nonspherical deformable particles like RBCs, the predictions of the proposed model match experimental data within 15%. Both the model and experiments reveal a competition between acoustic radiation and SID forces that gives rise to an equilibrium width $w^{*}$ of a focused stream of particles at some distance $L_{\mathrm{eq}}^{*}$ along the flow direction. Using different shear rates, acoustic energy densities, and particle concentrations, we show that the equilibrium width is governed by Péclet number $\text{Pe}$ and Strouhal number $\text{St}\mathrm{as}{w}^{*}={1.4\left(\text{Pe}\text{St}\right)}^{-0.5}$ while the length required to obtain the equilibrium-focused width depends on $\text{St}$ as $L_{\mathrm{eq}}^{*}=3.8{/\left(\text{St}\right)}^{0.6}$. The proposed model and correlations would find significance in the design of microchannels for acoustic focusing of dense suspensions such as undiluted blood.

We investigate in detail the process of adiabatic cooling in the framework of the exactly solvable antiferromagnetic spin-$\frac{1}{2}$ Ising model in the presence of the external magnetic field on an approximate lattice with pyrochlore structure. The behavior of the entropy of the model is studied and exact values of the residual entropies of all ground states are found. The temperature variation of the system under adiabatic (de)magnetization is investigated and the central role of the macroscopically degenerated ground states in cooling processes is explicitly demonstrated. It is shown that the model parameter space of the studied geometrically frustrated system is divided into five disjunct regions with qualitatively different processes of the adiabatic cooling. The effectiveness of the adiabatic (de)magnetization cooling in the studied model is compared to the corresponding processes in paramagnetic salts. It is shown that the processes of the adiabatic cooling in the antiferromagnetic frustrated systems are much more effective especially in nonzero external magnetic fields. It means that the frustrated magnetic materials with pyrochlore structure can be considered as very promising refrigerants mainly in the situations with nonzero final values of the magnetic field.

By periodically driving the temperature of reservoirs in a quantum heat engine, geometric or Pancharatnam-Berry phaselike (PBp) effects in the thermodynamics can be observed. The PBp can be identified from a generating function (GF) method within an adiabatic quantum Markovian master equation formalism. The GF is shown not to lead to a standard open quantum system's fluctuation theorem in the presence of phase-different modulations with an inapplicability in the use of large deviation theory. Effect of quantum coherences in optimizing the flux is nullified due to PBp contributions. The linear coefficient, $1/2$, which is universal in the expansion of the efficiency at maximum power in terms of Carnot efficiency no longer holds true in the presence of PBp effects.

We address the degree of universality of the Fermi-Pasta-Ulam recurrence induced by multisoliton fission from a harmonic excitation by analyzing the case of the semiclassical defocusing nonlinear Schrödinger equation, which models nonlinear wave propagation in a variety of physical settings. Using a suitable Wentzel-Kramers-Brillouin approach to the solution of the associated scattering problem we accurately predict, in a fully analytical way, the number and the features (amplitude and velocity) of solitonlike excitations emerging post-breaking, as a function of the dispersion smallness parameter. This also permits us to predict and analyze the near-recurrences, thereby inferring the universal character of the mechanism originally discovered for the Korteweg-deVries equation. We show, however, that important differences exist between the two models, arising from the different scaling rules obeyed by the soliton velocities.

Inspired by the recent interest in collective dynamics of biological neural networks immersed in the glial cell medium, we investigate the frequency and phase order, i.e., Kuramoto type of synchronization in a multiplex two-layer network of phase oscillators of different time scales and topologies. One of them has a long-range connectivity, exemplified by the Erdős-Rényi random network, and supports both kinds of synchrony. The other is a locally coupled two-dimensional lattice that can reach frequency synchronization but lacks phase order. Drastically different layer frequencies disentangle intra- and interlayer synchronization. We find that an indirect but sufficiently strong coupling through the regular layer can induce both phase order in the originally nonsynchronized random layer and global order, even when an isolated regular layer does not manifest it in principle. At the same time, the route to global synchronization is complex: an initial onset of (partial) synchrony in the regular layer, when its intra- and interlayer coupling is increased, provokes the loss of synchrony even in the originally synchronized random layer. Ultimately, a developed asynchronous dynamics in both layers is abruptly taken over by the global synchrony of both kinds.

The permutation entropy and the statistical complexity are employed to study the boundary-layer transition induced by the surface roughness. The velocity signals measured in the transition process are analyzed with these symbolic quantifiers, as well as the complexity-entropy causality plane, and the chaotic nature of the instability fluctuations is identified. The frequency of the dominant fluctuations has been found according to the time scales corresponding to the extreme values of the symbolic quantifiers. The laminar-turbulent transition process is accompanied by the evolution in the degree of organization of the complex eddy motions, which is also characterized with the growing smaller and flatter circles in the complexity-entropy causality plane. With the help of the permutation entropy and the statistical complexity, the differences between the chaotic fluctuations detected in the experiments and the classical Tollmien-Schlichting wave are shown and discussed. It is also found that the chaotic features of the instability fluctuations can be approximated with a number of regular sine waves superimposed on the fluctuations of the undisturbed laminar boundary layer. This result is related to the physical mechanism in the generation of the instability fluctuations, which is the noise-induced chaos.

We study the force that noninteracting pointlike active particles apply to a symmetric inert object in the presence of a gradient of activity and particle sources and sinks. We consider two simple patterns of sources and sinks that are common in biological systems. We analytically solve a one-dimensional model designed to emulate higher-dimensional systems, and study a two-dimensional model by numerical simulations. We specify when the particle flux due to the creation and annihilation of particles can act to smooth the density profile that is induced by a gradient in the velocity of the active particles, and find the net resultant force due to both the gradient in activity and the particle flux. These results are compared qualitatively to observations of nuclear motion inside the oocyte, that is driven by a gradient in activity of actin-coated vesicles.

We study the influence of particle-size asymmetry on structural evolution of randomly jammed binary sphere mixtures with varying large-sphere and small-sphere composition. Simulations of jammed packings are used to assess the transition from large-sphere dominant to small-sphere dominant mixtures. For weakly asymmetric particle sizes, packing properties evolve smoothly, but not monotonically, with increasing small-sphere composition, $f$. Our simulations reveal that at high values of ratio $\alpha$ of large- to small-sphere radii ($\alpha \ge {\alpha }_c\approx 5.75$), evolution of structural properties, such as packing density, fraction of jammed spheres, and contact statistics with $f$, exhibit features that suggest a sharp transition, either through discontinuities in structural measures or their derivatives. We argue that this behavior is related to the singular, composition dependence of close-packing fraction predicted in infinite aspect ratio mixtures $\alpha \to \infty$ by the Furnas model, but occurring for finite valued range of $\alpha$ above a critical value, ${\alpha }_c\approx 5.75$. The existence of a sharp transition from small- to large-$f$ values for $\alpha \ge {\alpha }_c$ can be attributed to the existence of a subjamming transition of small spheres within the interstices of jammed large spheres along the line of compositions $f_{\text{sub}}\left(\alpha \right)$. We argue that the critical value of finite-size asymmetry ${\alpha }_c\simeq 5.75$ is consistent with the geometric criterion for the transmission of small-sphere contacts between neighboring tetrahedrally close-packed interstices of large spheres, facilitating a cooperative subjamming transition of small spheres confined within the disjoint volumes.

Disordered spring networks that are undercoordinated may abruptly rigidify when sufficient strain is applied. Since the deformation in response to applied strain does not change the generic quantifiers of network architecture, the number of nodes and the number of bonds between them, this rigidity transition must have a geometric origin. Naive, degree-of-freedom-based mechanical analyses such as the Maxwell-Calladine count or the pebble game algorithm overlook such geometric rigidity transitions and offer no means of predicting or characterizing them. We apply tools that were developed for the topological analysis of zero modes and states of self-stress on regular lattices to two-dimensional random spring networks and demonstrate that the onset of rigidity, at a finite simple shear strain ${\gamma }^{★}$, coincides with the appearance of a single state of self-stress, accompanied by a single floppy mode. The process conserves the topologically invariant difference between the number of zero modes and the number of states of self-stress but imparts a finite shear modulus to the spring network. Beyond the critical shear, the network acquires a highly anisotropic elastic modulus, resisting further deformation most strongly in the direction of the rigidifying shear. We confirm previously reported critical scaling of the corresponding differential shear modulus. In the subcritical regime, a singular value decomposition of the network's compatibility matrix foreshadows the onset of rigidity by way of a continuously vanishing singular value corresponding to the nascent state of self-stress.

We investigate the dependence on the vortex structure of the propagation of fronts in stirred flows. For this, we consider a regular set of vortices whose structure is changed by varying both their boundary conditions and their aspect ratios. These configurations are investigated experimentally in autocatalytic solutions stirred by electroconvective flows and numerically from kinematic simulations based on the determination of the dominant Fourier mode of the vortex stream function in each of them. For free lateral boundary conditions, i.e., in an extended vortex lattice, it is found that both the flow structure and the front propagation negligibly depend on vortex aspect ratios. For rigid lateral boundary conditions, i.e., in a vortex chain, vortices involve a slight dependence on their aspect ratios which surprisingly yields a noticeable decrease of the enhancement of front velocity by flow advection. These different behaviors reveal a sensitivity of the mean front velocity on the flow subscales. It emphasizes the intrinsic multiscale nature of front propagation in stirred flows and the need to take into account not only the intensity of vortex flows but also their inner structure to determine front propagation at a large scale. Differences between experiments and simulations suggest the occurrence of secondary flows in vortex chains at large velocity and large aspect ratios.

We derive a general integro-differential equation for the transient behavior of small-amplitude capillary waves on the planar surface of a viscous fluid in the presence of the Marangoni effect. The equation is solved for an insoluble surfactant solution in concentration below the critical micelle concentration undergoing convective-diffusive surface transport. The special case of a diffusion-driven surfactant is considered near the the critical damping wavelength. The Marangoni effect is shown to contribute to the overall damping mechanism, and a first-order term correction to the critical wavelength with respect to the surfactant concentration difference and the Schmidt number is proposed.

In a recent paper, M. R. Edwards, N. J. Fisch, and J. M. Mikhailova [Phys. Rev. Lett. 116, 015004 (2016)] reported that in electron-positron plasma stimulated Brillouin scattering is drastically enhanced, while stimulated Raman scattering is completely absent. However, when theory was compared to particle-in-cell (PIC) simulations, a discrepancy by at least a factor four appeared. Authors correctly argued that the disparity might be due to the fluid approximation of the low-frequency mode. They noted that a more precise analytic description of the acoustic resonance requires a kinetic approach, which was beyond the scope of the mentioned paper. Here we deliver the so-far-missing kinetic calculation. It shows quite good agreement with the PIC simulations presented in the above-mentioned paper by Edwards et al. The principal result of enhancement of Brillouin scattering and absence of Raman scattering remains valid. The Brillouin enhancement factors depend on electron temperature and background particle density. These dependencies as well as the transition to the well-known behavior of electron-ion plasma are discussed. It is also shown that pulse amplification in electron-positron plasma crosses over to the strong-coupling regime when the pump amplitude becomes large. Then, the fluid approximation becomes acceptable again.

The exact law for fully developed homogeneous compressible magnetohydrodynamics (CMHD) turbulence is derived. For an isothermal plasma, without the assumption of isotropy, the exact law is expressed as a function of the plasma velocity field, the compressible Alfvén velocity, and the scalar density, instead of the Elsasser variables used in previous works. The theoretical results show four different types of terms that are involved in the nonlinear cascade of the total energy in the inertial range. Each category is examined in detail, in particular, those that can be written either as source or flux terms. Finally, the role of the background magnetic field ${\mathbf{B}}_0$ is highlighted and a comparison with the incompressible MHD (IMHD) model is discussed. This point is particularly important when testing this exact law on numerical simulations and in situ observations in space plasmas.

Coarse-grained potentials are ubiquitous in mesoscale simulations. While various methods to compute effective interactions for spherically symmetric particles exist, anisotropic interactions are seldom used, due to their complexity. Here we describe a general formulation, based on a spatial decomposition of the density fields around the particles, akin to atomic orbitals. We show that anisotropic potentials can be efficiently computed in numerical simulations using Fourier-based methods. We validate the field formulation and characterize its computational efficiency with a system of colloids that have Gaussian surface charge distributions. We also investigate the phase behavior of charged Janus colloids immersed in screened media, with screening lengths comparable to the colloid size. The system shows rich behaviors, exhibiting vapor, liquid, gel, and crystalline morphologies, depending on temperature and screening length. The crystalline phase only appears for symmetric Janus particles. For very short screening lengths, the system undergoes a direct transition from a vapor to a crystal on cooling; while, for longer screening lengths, a vapor-liquid-crystal transition is observed. The proposed formulation can be extended to model force fields that are time or orientation dependent, such as those in systems of polymer-grafted particles and magnetic colloids.

Plastino et al. [Plastino et al., Phys. Rev. E 94, 012145 (2016)] recently stated that the Rényi entropy is not suitable for thermodynamics by using functional calculus, since it leads to anomalous results unlike the Tsallis entropy. We first show that the Tsallis entropy also leads to such anomalous behaviors if one adopts the same functional calculus approach. Second, we note that one of the Lagrange multipliers is set in an ad hoc manner in the functional calculus approach of Plastino et al. Finally, the explanation for these anomalous behaviors is provided by observing that the generalized distributions obtained by Plastino et al. do not yield the ordinary canonical partition function in the appropriate limit and therefore cannot be considered as genuine generalized distributions.

This Reply is intended as a refutation of the preceding Comment [Oikonomou and Bagci, Phys. Rev. E 96, 056101 (2017)] on our paper [Plastino et al., Phys. Rev. E 94, 012145 (2016).]. We show that the Tsallis probability distribution of our paper does not coincide with the Tsallis distribution studied by Oikonomou and Bagci. Consequently, their findings do not apply to our paper.