Weak selection is an important assumption in theoretical evolutionary biology, but its biological significance remains unclear. In this study, we investigate the effect of weak selection on stochastic evolutionary stability in a two-phenotype evolutionary game dynamics with a random payoff matrix assuming an infinite, well-mixed population undergoing discrete, nonoverlapping generations. We show that, under weak selection, both stochastic local stability and stochastic evolutionary stability in this system depend on the means of the random payoffs but not on their variances. Moreover, although stochastic local stability or instability of an equilibrium may not depend on environmental noise if selection is weak enough, the growth rate near an equilibrium not only depends on environmental noise, but can even be enhanced by environmental noise if selection is weak. This is the case, for instance, when the variances of the random payoffs as well as the covariances are equal. These results suggest that natural selection could be able to filter (or resist) the effect of environmental noise on the evolution of animal behavior if selection is weak.

We use coarse-grained Langevin dynamics simulations to study packing of semiflexible polymers into a spherical capsid, with and without a tail, inside a crowded cell. We use neutral and charged, but highly screened, polymers and compare packing rates of the two. Such packing conditions are relevant, for example, to $\lambda$ DNA packing inside Escherichia coli bacterial cells, where the crowd particles are proteins, bacterial DNA, and salts. For a neutral polymer packing into a capsid with a tail, attractive interactions with the crowd particles make packing slightly harder at higher crowd densities, but repulsive interactions make it easier. Our results indicate that packing into a tailless capsid is less efficient at low crowd densities than into one with a long tail. However, this trend becomes opposite at higher densities. In addition, packing into a capsid with a long tail shows a highly variable waiting time before packing initiates, a feature absent for a tailless capsid. Electrical interactions at physiological conditions do not have much effect. Some bacterial cells, such as Pseudomonas chlororaphis, form a nucleuslike structure encapsulating the phage $201\varphi 2-1$ DNA. We also study here the packing dynamics with the nucleus present. We find packing is faster compared to the case of no-nucleus packing. We also observe knot formations but these knots untangle quickly while the polymer translocates. This knot formation is independent of polymer charge and presence of crowd particles.

A mechanism for the cyclic generation of bursts of magnetic fields by nonlinear torsional flows of complex time dependence but very simple spatial structure is described. These flows were obtained numerically as axisymmetric solutions of convection in internally heated rotating fluid spheres in the Boussinesq approximation. They behave as repeated transients, which start with nearly periodic oscillations of the velocity field of slowly increasing amplitude. This regime is followed by a chaotic fast increase and a final decrease of the amplitude of, at least, one order of magnitude. The magnetic field decays due to the magnetic diffusion during the regular oscillations, but it grows in the form of bursts during the intervals of irregular time dependence of the velocity. The magnetic field is strongly localized in spirals, with spatial- and temporal-dependent intensity.

A temporal analysis of the evolution of Gaussian wave packets in cylindrical capillary jets is presented through both a linear two-mode formulation and a one-dimensional nonlinear numerical scheme. These analyses are normally applicable to arbitrary initial conditions but our study focuses on pure-impulsive ones. Linear and nonlinear findings give consistent results in the stages for which the linear theory is valid. The inverse Fourier transforms representing the formal linear solution for the jet shape is both numerically evaluated and approximated by closed formulas. After a transient, these formulas predict an almost Gaussian-shape deformation with (i) a progressive drift of the carrier wave number to that given by the maximum of the Rayleigh dispersion relation, (ii) a progressive increase of its bell width, and (iii) a quasiexponential growth of its amplitude. These parameters agree with those extracted from the fittings of Gaussian wave packets to the numerical simulations. Experimental results are also reported on near-Gaussian pulses perturbing the exit velocity of a 2-mm diameter water jet. The possibility of controlling the breakup location along the jet and other features, such as pinch-off simultaneity, are demonstrated.

Efficient energy transfer from electromagnetic waves to ions has been demanded to control laboratory plasmas for various applications and could be useful to understand the nature of space and astrophysical plasmas. However, there exists the severe unsolved problem that most of the wave energy is converted quickly to electrons but not to ions. Here, an energy-to-ion conversion process in overdense plasmas associated with whistler waves is investigated by numerical simulations and a theoretical model. Whistler waves propagating along a magnetic field in space and laboratories often form standing waves by the collision of counter-propagating waves or through the reflection. We find that ions in standing whistler waves acquire a large amount of energy directly from the waves over a short time scale comparable to the wave oscillation period. The thermalized ion temperature increases in proportion to the square of the wave amplitude and becomes much higher than the electron temperature in a wide range of wave-plasma conditions. This efficient ion-heating mechanism applies to various plasma phenomena in space physics and fusion energy sciences.

Work in isolated quantum systems is a random variable and its probability distribution function obeys the celebrated fluctuation theorems of Crooks and Jarzynski. In this study, we provide a simple way to describe the work probability distribution function for sudden quench processes in quantum systems with large Hilbert spaces. This description can be constructed from two elements: the level density of the initial Hamiltonian, and a smoothed strength function that provides information about the influence of the perturbation over the eigenvectors in the quench process, and is especially suited to describe quantum many-body interacting systems. We also show how random models can be used to find such smoothed work probability distribution and apply this approach to different one-dimensional spin-$1/2$ chain models. Our findings provide an accurate description of the work distribution of such systems in the cases of intermediate and high temperatures in both chaotic and integrable regimes.

Thermodynamic uncertainty relations quantify how the signal-to-noise ratio of a given observable is constrained by dissipation. Fluctuation relations generalize the second law of thermodynamics to stochastic processes. We show that any fluctuation relation directly implies a thermodynamic uncertainty relation, considerably increasing their range of applicability. In particular, we extend thermodynamic uncertainty relations to scenarios which include measurement and feedback. Since feedback generally breaks time-reversal invariance, the uncertainty relations involve quantities averaged over the forward and the backward experiment defined by the associated fluctuation relation. This implies that the signal-to-noise ratio of a given experiment can in principle become arbitrarily large as long as the corresponding backward experiment compensates, e.g., by being sufficiently noisy. We illustrate our results with the Szilard engine as well as work extraction by free energy reduction in a quantum dot.

Evidence of critical dynamics has been found recently in both experiments and models of large-scale brain dynamics. The understanding of the nature and features of such a critical regime is hampered by the relatively small size of the available connectome, which prevents, among other things, the determination of its associated universality class. To circumvent that, here we study a neural model defined on a class of small-world networks that share some topological features with the human connectome. We find that varying the topological parameters can give rise to a scale-invariant behavior either belonging to the mean-field percolation universality class or having nonuniversal critical exponents. In addition, we find certain regions of the topological parameter space where the system presents a discontinuous, i.e., noncritical, dynamical phase transition into a percolated state. Overall, these results shed light on the interplay of dynamical and topological roots of the complex brain dynamics.

We discuss the structure of the equation of motion that governs nucleation processes at first order phase transitions. From the underlying microscopic dynamics of a nucleating system, we derive by means of a nonequilibrium projection operator formalism the equation of motion for the size distribution of the nuclei. The equation is exact, i.e., the derivation does not contain approximations. To assess the impact of memory, we express the equation of motion in a form that allows for direct comparison to the Markovian limit. As a numerical test, we have simulated crystal nucleation from a supersaturated melt of particles interacting via a Lennard-Jones potential. The simulation data show effects of non-Markovian dynamics.

The dynamics of $A+B\to C$ reaction fronts is studied both analytically and numerically in three-dimensional systems when $A$ is injected radially into $B$ at a constant flow rate. The front dynamics is characterized in terms of the temporal evolution of the reaction front position, $r_f$, of its width, $w$, of the maximum local production rate, $R^{\text{max}}$, and of the total amount of product generated by the reaction, $n_C$. We show that $r_f, w$, and $R^{\text{max}}$ exhibit the same temporal scalings as observed in rectilinear and two-dimensional radial geometries both in the early-time limit controlled by diffusion, and in the longer time reaction-diffusion-advection regime. However, unlike the two-dimensional cases, the three-dimensional problem admits an asymptotic stationary solution for the reactant concentration profiles where $n_C$ grows linearly in time. The timescales at which the transition between the regimes arise, as well as the properties of each regime, are determined in terms of the injection flow rate and reactant initial concentration ratio.

In an earlier work, we presented an experimental study wherein reaction-transport processes were forged in a real rock medium. Zonation of ${\mathrm{CaSO}}_4$-rich and ${\mathrm{CaSO}}_4$-depleted domains were obtained and characterized. In the present study, we present a theoretical model to simulate the reaction-diffusion processes underlying the dynamics of the system. An ${\mathrm{H}}_2{\mathrm{SO}}_4$-acidization front propagating radially from a central source into a ${\mathrm{CaCO}}_3$ rock bed causes dissolution of the calcite mineral and precipitation of ${\mathrm{CaSO}}_4$ as either gypsum (${\mathrm{CaSO}}_4·2{\mathrm{H}}_2\mathrm{O}$) or anhydrite (anhydrous ${\mathrm{CaSO}}_4$). The deposition of ${\mathrm{CaSO}}_4$ is shown to exhibit a banded texture (irregular concentric rings in two dimensions). The model involves reaction-diffusion evolution equations for three aqueous species (${\mathrm{H}}^{+}, {\mathrm{Ca}}^{2+}$, and ${\mathrm{SO}}_4{}^{2-}$), the ${\mathrm{CaCO}}_3$ dissolution, and the deposition of ${\mathrm{CaSO}}_4$, which is taken to obey a scaled Cahn-Hilliard equation. The output captures the zonation observed experimentally. Fractal analysis of the experimental contour shapes of the deposits reveals an oscillation in the fractal dimension over successive band numbers. Such oscillation is interpreted in terms of the precipitation-depletion tug scenario, not observable in regular two-dimensional Liesegang systems with high circular symmetry.

Rössler and Chen systems with time delay are shown to be hyperchaotic, which exhibits a more complex dynamics, including multiple positive Lyapunov exponents and infinite dimension. The hyperchaos has better application potential where hyperchaos synchronization is concerned. Univariate impulse control requires smaller perturbation to the response system, thus promising better performance. However, synchronization of two hyperchaotic systems using this control method is a challenging task due to the difficulty to guarantee synchronization stability using a minimum number of manipulated variables. In this paper, a univariate impulse control method is proposed for the synchronization of two hyperchaotic dynamics generated by time delay. A theorem is developed and proved to provide the sufficient conditions for the synchronization of time delay systems using the univariate impulse control. The upper bound of the impulse interval is proved to guarantee the asymptotic synchronization. Simulation and circuit experiment show the correctness of the analysis and the feasibility of the proposed method.

The long-wave–short-wave (LWSW) model of Newell type is an integrable model describing the interaction between the gravity wave (long wave) and the capillary wave (short wave) for the surface wave of deep water under certain resonance conditions. In the present paper, we are concerned with rogue-wave solutions to the LWSW model of Newell type. By combining the Hirota's bilinear method and the KP hierarchy reduction, we construct its general rational solution expressed by the determinant. It is found that the fundamental rogue wave for the short wave can be classified into three different patterns: bright, intermediate, and dark states, whereas the one for the long wave is always a bright state. The higher-order rogue wave corresponds to the superposition of fundamental ones. The modulation instability analysis shows that the condition of the baseband modulation instability where an unstable continuous-wave background corresponds to perturbations with infinitesimally small frequencies, coincides with the condition for the existence of rogue-wave solutions.

For decades, the description and characterization of nonstationary coherent states in coupled oscillators have not been available. We here consider the Kuramoto model consisting of conformist and contrarian oscillators. In the model, contrarians are chosen from a bimodal Lorentzian frequency distribution and flipped into conformists at random. A complete and systematic analytical treatment of the model is provided based on the Ott-Antonsen ansatz. In particular, we predict and analyze not only the stability of all stationary states (such as the incoherent, the $\pi$, and the traveling-wave states), but also that of the two nonstationary states: the Bellerophon and the oscillating-$\pi$ state. The theoretical predictions are fully supported by extensive numerical simulations.

In contemporary society, understanding how information, such as trends and viruses, spreads in various social networks is an important topic in many areas. However, it is difficult to mathematically measure how widespread the information is, especially for a general network structure. There have been studies on opinion spreading, but many studies are limited to specific spreading models such as the susceptible-infected-recovered model and the independent cascade model, and it is difficult to apply these studies to various situations. In this paper, we first suggest a general opinion spreading model (GOSM) that generalizes a large class of popular spreading models. In this model, each node has one of several states, and the state changes through interaction with neighboring nodes at discrete time intervals. Next, we show that many GOSMs have a stable property that is a GOSM version of a uniform equicontinuity. Then, we provide an approximation method to approximate the expected spread size for stable GOSMs. For the approximation method, we propose a concentration theorem that guarantees that a generalized mean-field theorem calculates the expected spreading size within small error bounds for finite time steps for a slightly dense network structure. Furthermore, we prove that a “single simulation” of running the Monte Carlo simulation is sufficient to approximate the expected spreading size. We conduct experiments on both synthetic and real-world networks and show that our generalized approximation method well predicts the state density of the various models, especially in graphs with a large number of nodes. Experimental results show that the generalized mean-field approximation and a single Monte Carlo simulation converge as shown in the concentration theorem.

Natural enzymes often have enormous catalytic power developed by evolution. Revealing the underlying physical strategy used by enzymes to achieve high catalysis efficiency is one of the central focuses in the field of biological physics. Our recent work demonstrated that multisubstrate enzymes can utilize steric frustration encountered in the substrate-product cobound complex to overcome the bottleneck of the enzymatic cycle [W. Li et al., Phys. Rev. Lett. 122, 238102 (2019)]. However, the key atomic-level interactions by which the steric frustration contributes to the enzymatic cycle remain elusive. In this work we study the microscopic mechanism for the role of the substrate-product frustration on the key physical steps in the enzymatic cycle of adenylate kinase (AdK), a multisubstrate enzyme catalyzing the reversible phosphoryl transfer reaction $\mathrm{ATP}+\mathrm{AMP}\leftrightharpoons \mathrm{ADP}+\mathrm{ADP}$. By using atomistic molecular dynamics simulations with enhanced sampling, we showed that the competitive interactions from the phosphate groups of the substrate ATP and product ADP in the ATP-ADP cobound complex of the AdK lead to local frustration in the binding pockets. Such local frustration disrupts the hydrogen bond network around the binding pockets, which causes lowered barrier height for the opening of the enzyme conformations and expedited release of the bottleneck product ADP. Our results directly demonstrated from the atomistic level that the local frustration in the active sites of the enzyme can be utilized to facilitate the key physical steps of the enzymatic cycle, providing numerical evidence to the predictions of the previous theoretical work.

We present a Monte Carlo simulation study of chiral nematic liquid crystals confined in torus-shaped and cylindrical cavities. For an achiral nematic with planar degenerate anchoring confined to a toroidal or cylindrical cavity, the ground state is defect free, with an untwisted director field. As chirality is introduced, the ground state remains defect free but the director field becomes twisted within the cavity. For homeotropic anchoring, the ground state for an achiral nematic within a toroidal cavity consists of two disclination rings, one large and one small, that follow the major circumference of the torus. As chirality is introduced and increased, this ground state becomes unstable with respect to twisted configurations. The closed nature of the toroidal cavity requires that only a half integer number of twists can be formed and this leads to the ground state being either a single disclination line that encircles the torus twice or a pair of intertwined disclination rings forming stable, knotted defect structures.

We study hidden scale invariance in the glassy phase of the Kob-Andersen binary Lennard-Jones system. After cooling below the glass transition, we generate a so-called isomorph from the fluctuations of potential energy and virial in the $NVT$ ensemble: a set of density, temperature pairs for which structure and dynamics are identical when expressed in appropriate reduced units. To access dynamical features, we shear the system using the SLLOD algorithm coupled with Lees-Edwards boundary conditions and study the statistics of stress fluctuations and the particle displacements transverse to the shearing direction. We find good collapse of the statistical data, showing that isomorph theory works well in this regime. The analysis of stress fluctuations, in particular the distribution of stress changes over a given strain interval, allows us to identify a clear signature of avalanche behavior in the form of an exponential tail on the negative side. This feature is also isomorph invariant. The implications of isomorphs for theories of plasticity are discussed briefly.

A direction adaptive approach for the reduction of drag and the suppression of lift fluctuation in flow passing a circular cylinder is developed. Flexible filaments are attached to the surface of the cylinder, and different configurations, including the number, lengths, and angles of attachment of the filaments, as well as their tension and bending features, are investigated. In this comprehensive numerical study, the configuration with two filaments ${180}^{\text{o}}$ apart is found to be optimal for drag reduction and lift fluctuation suppression and is adaptive to the direction of the incoming flow. A drag reduction of $10.8\%$ and a lift fluctuation suppression of $34.6\%$ can be achieved as one filament is attached to the rear stagnation point and the other to the front stagnation point. The hairy coating resembled by 12 evenly attached filaments is also considered. Though marked drag reduction has not been found for this configuration, we leave it an open question for future studies to explore various properties of the filaments in turbulent flow, whose interaction with the filaments would be significant.