The deterministic Landau-Lifshitz-Gilbert equation has been used to investigate the nonlinear dynamics of magnetization and the specific loss power in magnetic nanoparticles with uniaxial anisotropy driven by a rotating magnetic field. We propose a new type of applied field, which is “simultaneously rotating and alternating,” i.e., the direction of the rotating external field changes periodically. We show that a more efficient heat generation by magnetic nanoparticles is possible with this new type of applied field and we suggest its possible experimental realization in cancer therapy which requires the enhancement of loss energies.

The appearance, evolution, and disappearance of periodic and quasiperiodic dynamics of fluid flows in a cylindrical annulus locally heated from below are analyzed using nonlinear simulations. The results reveal a route of the transition from a steady axisymmetric vertical vortex to a chaotic flow. The chaotic flow regime is reached after a sequence of successive supercritical Hopf bifurcations to periodic, quasiperiodic, and chaotic flow regimes. A scenario similar to the Ruelle-Takens-Newhouse scenario is verified in this convective flow. In the transition to chaos we find the appearance of subvortices embedded in the primary axisymmetric vortex, flows where the subvortical structure strengthens and weakens, that almost disappears before reforming again, leading to a more disorganized flow to a final chaotic regime. Results are remarkable as they connect to observations describing formation, weakening, and virtual disappearance before revival of subvortices in some atmospheric swirls such as dust devils.

The long wavelength limit of a recent microscopic phase-field crystal (PFC) theory of a binary alloy mixture is used to derive an analytical approximation for the segregation coefficient as a function of the interface velocity, and relate it to the two-point correlation function of the liquid and the thermodynamic properties of solid and liquid phases. Our results offer the first analytical derivation of solute segregation from a microscopic model, and support recent molecular dynamics and numerical PFC simulations. Our results also provide an independent framework, motivated from classical density functional theory, from which to elucidate the fundamental nature of solute drag, which is still highly contested in the literature.

We study the nonstationary Feller process with time varying coefficients. We obtain the exact probability distribution exemplified by its characteristic function and cumulants. In some particular cases we exactly invert the distribution and achieve the probability density function. We show that for sufficiently long times this density approaches a $\mathrm{\Gamma }$ distribution with time-varying shape and scale parameters. Not far from the origin the process obeys a power law with an exponent dependent of time, thereby concluding that accessibility to the origin is not static but dynamic. We finally discuss some possible applications of the process.

We study the dynamics of networks with inhibitory and excitatory leak-integrate-and-fire neurons with short-term synaptic plasticity in the presence of depressive and facilitating mechanisms. The dynamics is analyzed by a heterogeneous mean-field approximation, which allows us to keep track of the effects of structural disorder in the network. We describe the complex behavior of different classes of excitatory and inhibitory components, which give rise to a rich dynamical phase diagram as a function of the fraction of inhibitory neurons. Using the same mean-field approach, we study and solve a global inverse problem: reconstructing the degree probability distributions of the inhibitory and excitatory components and the fraction of inhibitory neurons from the knowledge of the average synaptic activity field. This approach unveils new perspectives on the numerical study of neural network dynamics and the possibility of using these models as a test bed for the analysis of experimental data.

Polymer translocation through a nanometer-scale pore assisted by chaperones binding to the polymer is a process encountered in vivo for proteins. Studying the relevant models by computer simulations is computationally demanding. Accordingly, previous studies are either for stiff polymers in three dimensions or flexible polymers in two dimensions. Here, we study chaperone-assisted translocation of flexible polymers in three dimensions using Langevin dynamics. We show that differences in binding mechanisms, more specifically, whether a chaperone can bind to a single site or multiple sites on the polymer, lead to substantial differences in translocation dynamics in three dimensions. We show that the single-binding mode leads to dynamics that is very much like that in the constant-force driven translocation and accordingly mainly determined by tension propagation on the cis side. We obtain $\beta \approx 1.26$ for the exponent for the scaling of the translocation time with polymer length. This fairly low value can be explained by the additional friction due to binding particles. The multiple-site binding leads to translocation the dynamics of which is mainly determined by the trans side. For this process we obtain $\beta \approx 1.36$. This value can be explained by our derivation of $\beta =4/3$ for constant-bias translocation, where translocated polymer segments form a globule on the trans side. Our results pave the way for understanding and utilizing chaperone-assisted translocation where variations in microscopic details lead to rich variations in the emerging dynamics.

A sled is a stylized mechanical model of a system which is constrained to move in space in a specific orientation, i.e., in the direction of the runners of the sled or a blade. The negation of motion transverse to the runners renders the sled a nonholonomic mechanical system. In this paper we report on the unexpected and fascinating richness of the dynamics of such a sled if it is subject to random forces. Specifically we show that the ensuing random dynamics is characterized by relatively smooth sections of motion interspersed by episodes of persistent tumbling (change of orientation) and sharp reversals resembling the random walks of bacterial cells. In the presence of self-propulsion, the diffusivity of the sled can be enhanced and suppressed depending on the directionality and strength of the propulsive force.

This study focuses on the geometrical properties of turbulent flame fronts and other interfaces. Toward that end, we use an original tool based on proper orthogonal decomposition (POD), which is applied to the interface spatial coordinates. The focus is mainly on the degree of roughness of the flame front, which is quantified through the scale dependence of its coverage arclength. POD is first validated by comparing with the caliper technique. Fractal characteristics are extracted in an unambiguous fashion using a parametric expression which appears to be impressively well suited for representing Richardson plots. Then it is shown that, for the range of Reynolds numbers investigated here, the scale-by-scale contribution to the arclength does not comply with scale similarity, irrespectively of the type of similarity which is invoked. The finite ratios between large and small scales, referred to as finite Reynolds number effects, are likely to explain this observation. In this context, the Reynolds number that ought to be achieved for a proper inertial range to be discernible, and for scale similarity to be likely to apply, is calculated. Fractal characteristics of flame folding are compared to available predictions. It is confirmed that the inner cutoff satisfactorily correlates with the Kolmogorov scale while the outer cutoff appears to be proportional to the integral length scale. However, the scaling for the fractal dimension is much less obvious. It is argued that much higher Reynolds numbers have to be reached for drawing firm statements about the evolution (or constancy) of the fractal dimension with respect to flame and flow parameters. Finally, a heuristic phenomenology of corrugated interfaces is highlighted. The degree of generality of the latter phenomenology is confirmed by comparing the folding of different interfaces including a turbulent-nonturbulent interface, a liquid jet destabilized by a surrounding air jet, a cavitating flow, and an isoscalar evolving in a turbulent medium. The latter outcome is likely to have strong implications for modeling the corrugation of turbulent interfaces occurring in many physical situations.

The incremental stiffness characterizes the variation of a material's force response to a small deformation change. In lattices with noninteracting vibrational modes, the excitation of localized states does not have any effect on material properties, such as the incremental stiffness. We report that, in nonlinear lattices, driving a defect mode introduces changes in the static force-displacement relation of the material. By varying the defect excitation frequency and amplitude, the incremental stiffness can be tuned continuously to arbitrarily large positive or negative values. Furthermore, the defect excitation parameters also determine the displacement region at which the force-displacement relation is being tuned. We demonstrate this phenomenon experimentally in a compressed array of spheres tuning its incremental stiffness from a finite positive value to zero and continuously down to negative infinity.

We extend an earlier study [W. A. M. Morgado and S. M. Duarte Queirós, Phys. Rev. E 90, 022110 (2014)] to the case of a small system subject to nonlinear interaction and in contact with an athermal shot-noise reservoir. We first focus on steady state properties, namely, on the impact of the singular measure of the reservoir in the steady state energy. We introduce the concept of temperatures of higher order, which aim to represent the effect produced by the cumulants of the noise of order larger than 2 in the form of sources of energy of higher order and new response functions such as high-order specific heats that zero out when the system is thermal or linear. Afterwards, we study the effect of the nature of the noise in the heat and energy fluxes and determine asymptotic expressions for its large deviation functions. Finally, by analyzing the probabilistics of the injected power, we verify that the exponential form of its fluctuation relation is only asymptotically valid, whereas in the thermal case it is valid for the injected power at all times.

We study the dynamics of nonlocally coupled phase oscillators in a modular network. The interactions include a phase lag, $\alpha$. Depending on the various parameters the system exhibits a number of different dynamical states. In addition to global synchrony there can also be modular synchrony when each module can synchronize separately to a different frequency. There can also be multicluster frequency chimeras, namely coherent domains consisting of modules that are separately synchronized to different frequencies, coexisting with modules within which the dynamics is desynchronized. We apply the Ott-Antonsen ansatz in order to reduce the effective dimensionality and thereby carry out a detailed analysis of the different dynamical states.

Despite the ubiquitous character and relevance of the electric double layer in the entire realm of interface and colloid science, very little is known of the effect that surface heterogeneity exerts on the underlying mechanisms of ion adsorption. Herein, computer simulations offer a perspective that, in sharp contrast to the homogeneously charged surface, discrete groups promote multivalent counterion binding, leading to charge reversal but possibly having not a sign change of the electrophoretic mobility. Counterintuitively, the introduction of dielectric images yields a significantly greater accumulation of counterions, which further facilitates the magnitude of charge reversal. The reported results are very sensitive to both the degree of ion hydration and the representation of surface charges. Our findings shed light on the mechanism for charge reversal over a broad range of coupling regimes operating the adsorption of counterions through surface group bridging attraction with their own images and provide opportunities for experimental studies and theoretical development.

Using numerical simulations, we studied the grouping behaviors of particles settling along their line of centers in narrow channels having a Reynolds number range of 5 $\le$ Re $\le$ 50. The calculations are based on our previously developed lattice Boltzmann direct-forcing–fictitious-domain method. We report the grouping behavior and investigate the dependence on the number of particles $n$, the initial interparticle separation $h_0$, and the Reynolds number Re. In particular, the mode of grouping is found to be independent of the number of particles when the Reynolds numbers is small. The two lowermost particles always come together first and form a vertical doublet and then the next two lowest particles form another doublet, and so on. Therefore, we observe $n$/2 doublets or $(n-1)/2$ doublets when $n$ is even or odd, respectively. The uppermost particle is always left behind when $n$ is odd. Furthermore, the separation between these doublets remains constant, displaying a power-law dependence decreasing from top to bottom.

We have investigated the $J_1-J_2$ Heisenberg model with exchange anisotropy on a square lattice and focused on possible AF1-AF2 phase transition below the Néel point and its dependence on the exchange anisotropy, where AF1 and AF2 represent Néel state and collinear state, respectively. We use the double-time Green's-function method and adopt the random-phase approximation. The less the exchange anisotropy, the stronger the quantum fluctuation of the system will be. Both the Néel state and collinear state can exist and have the same Néel temperature for arbitrary anisotropy and spin quantum number $S$ when $J_2/J_1=0.5$. Under such parameters, the calculated free energies show that there may occur a first-order phase transition between the Néel state and collinear state for an arbitrary $S$ when anisotropy is not strong.

A quantum field model that incorporates Bose-condensed systems near their phase transition into a superfluid phase and velocity fluctuations is proposed. The stochastic Navier-Stokes equation is used for a generation of the velocity fluctuations. As such this model generalizes model F of critical dynamics. The field-theoretic action is derived using the Martin-Siggia-Rose formalism and path integral approach. The regime of equilibrium fluctuations is analyzed within the perturbative renormalization group method. The double $(\epsilon ,\delta )$-expansion scheme is employed, where $\epsilon$ is a deviation from space dimension 4 and $\delta$ describes scaling of velocity fluctuations. The renormalization procedure is performed to the leading order. The main corollary gained from the analysis of the thermal equilibrium regime suggests that one-loop calculations of the presented models are not sufficient to make a definite conclusion about the stability of fixed points. We also show that critical exponents are drastically changed as a result of the turbulent background and critical fluctuations are in fact destroyed by the developed turbulence fluctuations. The scaling exponent of effective viscosity is calculated and agrees with expected value $4/3$.

We study absorbing-state phase transitions (APTs) in two-dimensional Voronoi-Delaunay (VD) random lattices with quenched coordination disorder. Quenched randomness usually changes the criticality and destroys discontinuous transitions in low-dimensional nonequilibrium systems. We performed extensive simulations of the Ziff-Gulari-Barshad model, and verified that the VD disorder does not change the nature of its discontinuous transition. Our results corroborate recent findings of Barghathi and Vojta [H. Barghathi and T. Vojta, Phys. Rev. Lett. 113, 120602 (2014)], stating the irrelevance of topological disorder in a class of random lattices that includes VD, and raise the interesting possibility that disorder in nonequilibrium APT may, under certain conditions, be irrelevant for the phase coexistence. We also verify that the VD disorder is irrelevant for the critical behavior of models belonging to the directed percolation and Manna universality classes.

We connect the rare fluctuations of an equilibrium (EQ) process and the typical fluctuations of a nonequilibrium (NE) stationary process. In the framework of large deviation theory, this observation allows us to introduce NE thermodynamic potentials. For continuous-time Markov chains, we identify the relevant pairs of conjugated variables and propose two NE ensembles: one with fixed dynamics and fluctuating time-averaged variables, and another with fixed time-averaged variables, but a fluctuating dynamics. Accordingly, we show that NE processes are equivalent to conditioned EQ processes ensuring that NE potentials are Legendre dual. We find a variational principle satisfied by the NE potentials that reach their maximum in the NE stationary state and whose first derivatives produce the NE equations of state and second derivatives produce the NE Maxwell relations generalizing the Onsager reciprocity relations.

Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but are unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Stochastic theories that treat semi-Markov age-dependent processes using, e.g., the Bellman-Harris equation do not resolve a population's age structure and are unable to quantify population-size dependencies. Conversely, current theories that include size-dependent population dynamics (e.g., mathematical models that include carrying capacity such as the logistic equation) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new, fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a Bogoliubov-–Born–-Green–-Kirkwood-–Yvon-like hierarchy. Explicit solutions are derived in three limits: no birth, no death, and steady state. These are then compared with their corresponding mean-field results. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution.

We study the entropy production in a globally coupled Brownian particles system that undergoes an order-disorder phase transition. Entropy production is a characteristic feature of nonequilibrium dynamics with broken detailed balance. We find that the entropy production rate is subextensive in the disordered phase and extensive in the ordered phase. It is found that the entropy production rate per particle vanishes in the disordered phase and becomes positive in the ordered phase following critical scaling laws. We derive the scaling relations for associated critical exponents. The disordered phase exemplifies a case where the entropy production is subextensive with the broken detailed balance.