We generalize the Kuramoto model of globally coupled oscillators to multifrequency communities. A situation when mean frequencies of two subpopulations are close to the resonance $2:1$ is considered in detail. We construct uniformly rotating solutions describing synchronization inside communities and between them. Remarkably, cross coupling across the frequencies can promote synchrony even when ensembles are separately asynchronous. We also show that the transition to synchrony due to the cross coupling is accompanied by a huge multiplicity of distinct synchronous solutions, which is directly related to a multibranch entrainment. On the other hand, for synchronous populations, the cross-frequency coupling can destroy phase locking and lead to chaos of mean fields.

Some exact interactions between vibrational modes in systems with discrete symmetry can be described by the theory of the bushes of nonlinear normal modes (NNMs) [G. M. Chechin and V. P. Sakhnenko, Phys. D (Amsterdam, Neth.) 117, 43 (1998)]. Each bush represents a dynamical object conserving the energy of the initial excitation. The existence of bushes of NNMs is ensured by some group-theoretical selection rules. In G. M. Chechin et al. [Int. J. Nonlinear Mech. 38, 1451 (2003)], existence and stability of the bushes of vibrational modes in the simple octahedral model of mass points interacting via Lennard-Jones potential were investigated. In the present paper, we study these dynamical objects by the density functional theory in the ${\text{SF}}_6$ molecule, which possesses the same symmetry and structure. We have fully confirmed the results previously obtained in the framework of the group-theoretical approach and have found some properties of the bushes of NNMs.

We present a study of single-mode Rayleigh-Taylor instabilities with a modified direct simulation Monte Carlo (MDSMC) code in two dimensions. The MDSMC code is aimed to capture the dynamics of matter for a large range of Knudsen numbers within one approach. Our method combines the traditional Monte Carlo technique to efficiently propagate particles and the point-of-closest-approach method for high spatial resolution. Simulations are performed using different particle mean free paths and we compare the results to linear theory predictions for the growth rate including diffusion and viscosity. We find good agreement between theoretical predictions and simulations and, at late times, observe the development of secondary instabilities, similar to hydrodynamic simulations and experiments. Large mean free paths favor particle diffusion, reduce the occurrence of secondary instabilities, and approach the noninteracting gas limit.

In a recent paper Gamayun et al. [O. Gamayun, O. Lychkovskiy, and V. Cheianov, Phys. Rev. E 90, 032132 (2014)] studied the dynamics of a mobile impurity weakly coupled to a one-dimensional Tonks-Girardeau gas of strongly interacting bosons. Employing the Boltzmann equation approach, they, in particular, arrived at the following conclusions: (i) a light impurity, being accelerated by a constant force $F$, does not exhibit Bloch oscillations, which were predicted and studied by Gangardt and co-workers [D. M. Gangardt and A. Kamenev, Phys. Rev. Lett. 102, 070402 (2009); M. Schecter, D. M. Gangardt, and A. Kamanev, Ann. Phys. (N.Y.) 327, 639 (2012)]; (ii) a heavy impurity does undergo Bloch oscillations, accompanied by a drift with the velocity $v_D\propto \sqrt{F}$. In this Comment we argue that result (i) is an artifact of the classical Boltzmann approximation. The latter misses the formation of the quasibound state between the impurity and a hole. Its dispersion relation $E_b(P,\rho )$ is a smooth periodic function of momentum $P$ with the period $2k_F=2\pi \hslash \rho$, where $\rho$ is a density of the host gas. Being accelerated by a small force, such a bound-state exhibits Bloch oscillations superimposed with the drift velocity $v_D=\mu F$. The mobility $\mu$ may be expressed exactly [M. Schecter et al., Ann. Phys. (N.Y.) 327, 639 (2012)] in terms of $E_b(P,\rho )$. Result (ii), while not valid at exponentially small forces, indeed reflects an interesting intermediate-force behavior.

In our recent paper [O. Gamayun, O. Lychkovskiy, and V. Cheianov, Phys. Rev. E 90, 032132 (2014)] we studied the dynamics of a mobile impurity particle weakly interacting with the Tonks-Girardeau gas and pulled by a small external force $F$. Working in the regime when the thermodynamic limit is taken prior to the small force limit, we found that the Bloch oscillations of the impurity velocity are absent in the case of a light impurity. Further, we argued that for a light impurity the steady-state drift velocity $V_D$ remains finite in the limit $F\to 0$. These results are in contradiction with earlier works by Gangardt and co-workers [D. M. Gangardt and A. Kamenev, Phys. Rev. Lett. 102, 070402 (2009); M. Schecter, D. M. Gangardt, and A. Kamenev, Ann. Phys. (NY) 327, 639 (2012)]. One of us has conjectured [O. Lychkovskiy, Phys. Rev. A 91, 040101 (2015)] that the central assumption of these works, the adiabaticity of the dynamics, can break down in the thermodynamic limit. In the preceding Comment [M. Schecter, D. M. Gangardt, and A. Kamenev, Phys. Rev. E 92, 016101 (2015)], Schecter et al. have argued against this conjecture and in support of the existence of Bloch oscillations and the linearity of $V_D\left(F\right)$. They have suggested that the ground state of the impurity-fluid system is a quasibound state and that this is sufficient to ensure adiabaticity in the thermodynamic limit. Their analytical argument is based on a certain truncation of the Hilbert space of the system. We argue that extending the results and intuition based on their truncated model on the original many-body problem lacks justification.

We have studied the $A+A\to \varnothing$ reaction-diffusion model on a ring, with a bias $\epsilon (0\le \epsilon \le 0.5)$ of the random walkers $A$ to hop towards their nearest neighbor. Though the bias is local in space and time, we show that it alters the universality class of the problem. The $z$ exponent, which describes the growth of average spacings between the walkers with time, changes from the value 2 at $\epsilon =0$ to the mean-field value of unity for any nonzero $\epsilon$. We study the problem analytically using independent interval approximation and compare the scaling results with those obtained from simulation. The distribution $P(k,t)$ (per site) of the spacing between two walkers is given by $t^{-2/z}f(k/t^{1/z})$ and is obtained both analytically and numerically. We also obtain the result that $\epsilon t$ becomes the new time scale for $\epsilon \ne 0$.

We study the role of quantum statistics in the performance of Otto cycles. First, we show analytically that the work distributions for bosonic and fermionic working fluids are identical for cycles driven by harmonic trapping potentials. Subsequently, in the case of nonharmonic potentials, we find that the interplay between different energy level spacings and particle statistics strongly affects the performances of the engine cycle. To demonstrate this, we examine three trapping potentials which induce different (single-particle) energy level spacings: monotonically decreasing with the level number, monotonically increasing, and the case in which the level spacing does not vary monotonically.

We consider partially directed walk models of polymers undergoing inhomogeneous adsorption. The inhomogeneity can be in the polymer, in the surface, or in both. For the cases where the polymer is either a homopolymer or a strictly alternating copolymer and where the surface is either homogeneous or has stripes of width 1, we calculate detailed order parameters and show that these provide important information about the ways in which the polymer adsorbs.

Percolation of carbon nanotubes (CNTs) in liquid crystals (LCs) opens the way for a unique class of anisotropic hybrid materials with a complex dielectric constant widely controlled by CNT concentration. Percolation in such systems is commonly described as a one-step process starting at a very low loading of CNTs. In the present study the two-step percolation was observed in the samples of thickness 250 $\mu \mathrm{m}$ obtained by pressing the suspension between two substrates. The first threshold concentration, $C_n^{p_1}\sim {10}^{-4}$ wt.%, was sensitive to temperature and phase state of LC, while the second one, $C_n^{p_2}\sim {10}^{-1}$ wt.%, remained practically unchanged in the temperature tests. The two-stage nature of percolation was explained on a base of mean-field theory assuming core-shell structure of CNTs.

The $p\text{H}$-induced conformational changes of proteins are systematically studied in the framework of a hydrophobic-polar (HP) model, in which proteins are dramatically simplified as chains of hydrophobic (H) and polar (P) beads on a lattice. We express the electrostatic interaction, the principal driving force of $p\text{H}$-induced unfolding that is not included in the conventional HP model, as the repulsive energy term between P monomers. As a result of the exact enumeration of all of the 14- to 18-mers, it is found that lowest-energy states in many sequences change from single “native” conformations to multiple sets of “denatured” conformations with an increase in the electrostatic repulsion. The switching of the lowest-energy states occurs in quite a similar way to real proteins: it is almost always between two states, while in a small fraction of $\ge 16$-mers it is between three states. We also calculate the structural fluctuations for all of the denatured states and find that the denatured states contain a broad range of incompletely unfolded conformations, similar to “molten globule” states referred to in acid or alkaline denatured real proteins. These results show that the proposed model provides a simple physical picture of $p\text{H}$-induced protein denaturation.

The emission pattern from a classical dipole located above and oriented perpendicular to a metallic or dielectric half space is calculated for a dipole driven at constant amplitude. Emphasis is placed on the fields in the metal or dielectric. It is shown that the radial Poynting vector in the metal points inwards when the frequency of the dipole is below the surface plasmon resonance frequency. In this case, energy actually flows out of the interface at small radii and the power entering the metal can actually oscillate as a function of radius. The Joule heating in the metal is also calculated for a cylindrical volume in the metal. When the metal is replaced by a dielectric having permittivity less than that of the medium in which the dipole is immersed, it is found that energy flows out of the interface for sufficiently large radii, a result reminiscent of the Goos-Hänchen effect.

Accurate determination of geometrical and physical properties of natural porous materials is notoriously difficult. Continuum multiscale modeling has provided carefully calibrated realistic microstructure models of reservoir rocks with floating point accuracy. Previous measurements using synthetic microcomputed tomography ($\mu$-CT) were based on extrapolation of resolution-dependent properties for discrete digitized approximations of the continuum microstructure. This paper reports continuum measurements of volume and specific surface with full floating point precision. It also corrects an incomplete description of rotations in earlier publications. More importantly, the methods of differential permeametry and differential porosimetry are introduced as precision tools. The continuum microstructure chosen to exemplify the methods is a homogeneous, carefully calibrated and characterized model for Fontainebleau sandstone. The sample has been publicly available since 2010 on the worldwide web as a benchmark for methodical studies of correlated random media. High-precision porosimetry gives the volume and internal surface area of the sample with floating point accuracy. Continuum results with floating point precision are compared to discrete approximations. Differential porosities and differential surface area densities allow geometrical fluctuations to be discriminated from discretization effects and numerical noise. Differential porosimetry and Fourier analysis reveal subtle periodic correlations. The findings uncover small oscillatory correlations with a period of roughly $850\mu \mathrm{m}$, thus implying that the sample is not strictly stationary. The correlations are attributed to the deposition algorithm that was used to ensure the grain overlap constraint. Differential permeabilities are introduced and studied. Differential porosities and permeabilities provide scale-dependent information on geometry fluctuations, thereby allowing quantitative error estimates.

A thin-interface phase-field model of electrochemical interfaces is developed based on Marcus kinetics for concentrated solutions, and used to simulate dendrite growth during electrodeposition of metals. The model is derived in the grand electrochemical potential to permit the interface to be widened to reach experimental length and time scales, and electroneutrality is formulated to eliminate the Debye length. Quantitative agreement is achieved with zinc Faradaic reaction kinetics, fractal growth dimension, tip velocity, and radius of curvature. Reducing the exchange current density is found to suppress the growth of dendrites, and screening electrolytes by their exchange currents is suggested as a strategy for controlling dendrite growth in batteries.

The Ehrenfest urn model is extended to a complex directed network, over which a conserved quantity is transported in a random fashion. The evolution of the conserved number of packets in each urn, or node of the network, is illustrated by means of a stochastic simulation. Using mean-field theory we were able to compute an approximation to the ensemble-average evolution of the number of packets in each node which, in the thermodynamic limit, agrees quite well with the results of the stochastic simulation. Using this analytic approximation we are able to find the asymptotic dynamical state of the system and the time scale to approach the equilibrium state, for different networks. The study is extended to large scale-free and small-world networks, in which the relevance of the connectivity distribution and the topology of the network for the distribution of time scales of the system is apparent. This analysis may contribute to the understanding of the transport properties in real networks subject to a perturbation, e.g., the asymptotic state and the time scale required to approach it.

We study the statistics of the work distribution $P\left(w\right)$ in a $d$-dimensional closed quantum system with linear dimension $L$ subjected to a periodic drive with frequency ${\omega }_0$. We show that the corresponding rate function $I\left(w\right)=-ln[P\left(w\right)/{\mathrm{\Lambda }}_0]/L^d$ after a drive period satisfies a universal lower bound $I\left(0\right)\ge n_d$ and has a zero at $w=Q{L}^d/N$, where $n_d$ and $Q$ are the excitation and the residual energy densities generated during the drive, ${\mathrm{\Lambda }}_0$ is a constant fixed by the normalization of $P\left(w\right)$, and $N$ is the total number of constituent particles or spins in the system. We supplement our results by calculating $I\left(w\right)$ for a class of $d$-dimensional integrable models and show that $I\left(w\right)$ has an oscillatory dependence on ${\omega }_0$ originating from Stuckelberg interference generated due to double passage through the critical point or region during the drive. We suggest experiments to test our theory.

An improved method for driving a system into a desired distribution, for example, the Gibbs-Boltzmann distribution, is proposed, which makes use of an artificial relaxation process. The standard techniques for achieving the Gibbs-Boltzmann distribution involve numerical simulations under the detailed balance condition. In contrast, in the present study we formulate the Langevin dynamics, for which the corresponding Fokker-Planck operator includes an asymmetric component violating the detailed balance condition. This leads to shifts in the eigenvalues and results in the acceleration of the relaxation toward the steady state. The numerical implementation demonstrates faster convergence and shorter correlation time, and the technique of biased event sampling, Nemoto-Sasa theory, further highlights the efficacy of our method.

Scaling analysis, in which one infers scaling exponents and a scaling function in a scaling law from given data, is a powerful tool for determining universal properties of critical phenomena in many fields of science. However, there are corrections to scaling in many cases, and then the inference problem becomes ill-posed by an uncontrollable irrelevant scaling variable. We propose a new kernel method based on Gaussian process regression to fix this problem generally. We test the performance of the new kernel method for some example cases. In all cases, when the precision of the example data increases, inference results of the new kernel method correctly converge. Because there is no limitation in the new kernel method for the scaling function even with corrections to scaling, unlike in the conventional method, the new kernel method can be widely applied to real data in critical phenomena.

Stochastic thermodynamics and the associated fluctuation relations provide the means to extend the fundamental laws of thermodynamics to small scales and systems out of equilibrium. The fluctuating thermodynamic variables are usually treated in the context of either isolated Hamiltonian evolution, or Markovian dynamics in open systems. However, there is no reason a priori why the Markovian approximation should be valid in driven systems under nonequilibrium conditions. In this work, we introduce an explicitly non-Markovian model of dynamics of an open system, where the correlations between the system and the environment drive a subset of the environment out of equilibrium. Such an environment gives rise to a new type of non-Markovian entropy production term. Such non-Markovian components must be taken into account in order to recover the fluctuation relations for entropy. As a concrete example, we explicitly derive such modified fluctuation relations for the case of an overheated single electron box.