The long-time dynamics of particles interacting resonantly with large-amplitude coherent plasma wave is investigated in the kinetic regime of stimulated Raman scattering in which particle trapping plays a major role (and which corresponds to a high value of the parameter $k_{\text{EPW}}{\lambda }_D$, where $k_{\text{EPW}}$ is the plasma wave vector and ${\lambda }_D$ is the electron Debye length). Using Vlasov simulations, the dynamics of such particles become stochastic when repeated wave-particle interactions take place. For small values of the ratio ${\tau }_{\text{auto}}/{\tau }_b$ of the autocorrelation time to the bounce time of particle (condition usually met in backward propagation of the scattered wave) the turbulent regime results in the merging of phase-space trapping vortices according to a weak turbulencelike scenario. For high values of ${\tau }_{\text{auto}}/{\tau }_b$ (or narrow spectrum of longitudinal electric field as met when only one plasma wave is present), the stochasticity is now induced by particle trapping, detrapping, and retrapping in the adiabatically fluctuating field. The stochastic transitions performed by resonant particles above (or below) the separatrix limit in phase space determine now the long-time plasma evolution.

We reconsider both the global and local stability of solutions of continuously evolving dynamical systems from a geometric perspective. We clarify that an unambiguous definition of stability generally requires the choice of additional geometric structure that is not intrinsic to the dynamical system itself. While we explain that global Lyapunov stability is based on the choice of seminorms on the vector bundle of perturbations, we propose a definition of local stability based on the choice of a linear connection. We show how this definition reproduces known stability criteria for second-order dynamical systems. In contrast to the general case, we show that the special geometry of Lagrangian systems provides completely intrinsic notions of global and local stability. We demonstrate that these do not suffer from the limitations occurring in the analysis of the Maupertuis-Jacobi geodesics associated to natural Lagrangian systems.

Nonlinear ensemble state estimation offers a paradigm-shifting improvement in our ability to observe, predict, and control the state of spiking neuronal systems. We use an ensemble Kalman filter to predict hidden states and future trajectories in the Hodgkin-Huxley equations, reconstruct ion dynamics, control neuronal activity including a strategy for dynamic conductance clamping, and show the feasibility of controlling pathological cellular activity such as seizures.

We study the phase-ordering kinetics of the one-dimensional Heisenberg model with conserved order parameter by means of scaling arguments and numerical simulations. We find a rich dynamical pattern with a regime characterized by two distinct growing lengths. Spins are found to be coplanar over regions of a typical size $L_V\left(t\right)$, while inside these regions smooth rotations associated to a smaller length $L_C\left(t\right)$ are observed. Two different and coexisting ordering mechanisms are associated to these lengths, leading to different growth laws $L_V\left(t\right)\sim t^{1/3}$ and $L_C\left(t\right)\sim t^{1/4}$ violating dynamical scaling.

We re-examine the electrodynamic Casimir effect in a wedge defined by two perfect conductors making dihedral angle $\alpha =\pi /p$. This system is analogous to the system defined by a cosmic string. We consider the wedge region as filled with an azimuthally symmetric material, with permittivity and permeability ${\epsilon }_1$, ${\mu }_1$ for distance from the axis $r<a$, and ${\epsilon }_2$, ${\mu }_2$ for $r>a$. The results are closely related to those for a circular-cylindrical geometry, but with noninteger azimuthal quantum number $mp$. Apart from a zero-mode divergence, which may be removed by choosing periodic boundary conditions on the wedge, and may be made finite if dispersion is included, we obtain finite results for the free energy corresponding to changes in $a$ for the case when the speed of light is the same inside and outside the radius $a$, and for weak coupling, $\left|{\epsilon }_1-{\epsilon }_2\right|⪡1$, for purely dielectric media. We also consider the radiation produced by the sudden appearance of an infinite cosmic string, situated along the cusp line of the pre-existing wedge.

The manner in which signals propagate through dense granular systems in both space and time is not well understood. In order to probe this process, we carry out discrete element simulations of the system response to excitations where we control the driving frequency and wavelength independently. Fourier analysis shows that properties of the signal depend strongly on the space-time scales of the perturbation. The features of the response provide a test bed for models that predict statistical and continuum space-time properties. We illustrate this connection between microscale physics and macroscale behavior by comparing the system response to a simple elastic model with damping.

We study simple lattice systems to demonstrate the influence of interpenetrating bond networks on phase behavior. We promote interpenetration by using a Hamiltonian with a weakly repulsive interaction with nearest neighbors and an attractive interaction with second-nearest neighbors. In this way, bond networks will form between second-nearest neighbors, allowing for two (locally) distinct networks to form. We obtain the phase behavior from analytic solution in the mean-field approximation and exact solution on the Bethe lattice. We compare these results with exact numerical results for the phase behavior from grand canonical Monte Carlo simulations on square, cubic, and tetrahedral lattices. All results show that these simple systems exhibit rich phase diagrams with two fluid-fluid critical points and three thermodynamically distinct phases. We also consider including third-nearest-neighbor interactions, which give rise to a phase diagram with four critical points and five thermodynamically distinct phases. Thus the interpenetration mechanism provides a simple route to generate multiple liquid phases in single-component systems, such as hypothesized in water and observed in several model and experimental systems. Additionally, interpenetration of many such networks appears plausible in a recently considered material made from nanoparticles functionalized by single-strands of DNA.

We study the dynamic stability of low Reynolds number swimming near a plane wall from a control-theoretic viewpoint. We consider a special class of swimmers having a constant shape, focus on steady motion parallel to the wall, and derive conditions under which it is passively stable without sensing or feedback. We study the geometric structure of the swimming equation and highlight the relation between stability and reversing symmetry of the dynamical system. Finally, our numerical simulations reveal the existence of stable periodic motion. The results have implications for design of miniature robotic swimmers, as well as for explaining the attraction of micro-organisms to surfaces.

We present a multiscale algorithm to couple atomistic water models with continuum incompressible flow simulations via a Schwarz domain decomposition approach. The coupling introduces an inhomogeneity in the description of the atomistic domain and prevents the use of periodic boundary conditions. The use of a mass conserving specular wall results in turn to spurious oscillations in the density profile of the atomistic description of water. These oscillations can be eliminated by using an external boundary force that effectively accounts for the virial component of the pressure. In this Rapid Communication, we extend a control algorithm, previously introduced for monatomic molecules, to the case of atomistic water and demonstrate the effectiveness of this approach. The proposed computational method is validated for the cases of equilibrium and Couette flow of water.

Time series obtained from the emission of an erbium-doped fiber ring laser with sine-wave pump modulation have been analyzed in order to determine the topological structure of the underlying chaotic attractor. With appropriate modulation conditions, topological structures not often observed in experimental systems have been found: the reverse horseshoe and the spiral template. The method employed for template determination is not conventional as it takes profit of the high dissipation of the system, which allows one to simplify dramatically the general procedure of analysis.

We analyze numerically the magnetorotational instability of a Taylor-Couette flow in a helical magnetic field [helical magnetorotational instability (HMRI)] using the inductionless approximation defined by a zero magnetic Prandtl number $\left({\text{Pr}}_m=0\right)$. The Chebyshev collocation method is used to calculate the eigenvalue spectrum for small-amplitude perturbations. First, we carry out a detailed conventional linear stability analysis with respect to perturbations in the form of Fourier modes that corresponds to the convective instability which is not in general self-sustained. The helical magnetic field is found to extend the instability to a relatively narrow range beyond its purely hydrodynamic limit defined by the Rayleigh line. There is not only a lower critical threshold at which HMRI appears but also an upper one at which it disappears again. The latter distinguishes the HMRI from a magnetically modified Taylor vortex flow. Second, we find an absolute instability threshold as well. In the hydrodynamically unstable regime before the Rayleigh line, the threshold of absolute instability is just slightly above the convective one although the critical wavelength of the former is noticeably shorter than that of the latter. Beyond the Rayleigh line the lower threshold of absolute instability rises significantly above the corresponding convective one while the upper one descends significantly below its convective counterpart. As a result, the extension of the absolute HMRI beyond the Rayleigh line is considerably shorter than that of the convective instability. The absolute HMRI is supposed to be self-sustained and, thus, experimentally observable without any external excitation in a system of sufficiently large axial extension.

We compare nonlinear stresses and temperatures for adiabatic-shear flows, using up to 262 144 particles, with those from corresponding homogeneous and inhomogeneous flows. Two varieties of kinetic temperature tensors are compared to the configurational temperatures. This comparison of temperatures led us to two findings beyond our original goal of analyzing shear algorithms. First, we found an improved form for local instantaneous velocity fluctuations, as calculated with smooth-particle weighting functions. Second, we came upon the previously unrecognized contribution of rotation to the configurational temperature.

In this paper, we present a numerical scheme for the analysis of steady-state nonlinear diffusion in random heterogeneous media. The key idea is to iteratively solve the nonlinear stochastic governing equations via an inexact Picard iteration scheme, wherein the nonlinear constitutive law is linearized using the current guess of the solution. The linearized stochastic governing equations are then spatially discretized and approximately solved using stochastic reduced basis projection schemes. The approximation to the solution process thus obtained is used as the guess for the next iteration. This iterative procedure is repeated until an appropriate convergence criterion is met. Detailed numerical studies are presented for diffusion in a square domain for varying degrees of nonlinearity. The numerical results are compared against benchmark Monte Carlo simulations, and it is shown that the proposed approach provides good approximations for the response statistics at modest computational effort.

Investigating the evolutionary dynamics of game theoretical interactions in populations where individuals are arranged on a graph can be challenging in terms of computation time. Here, we propose an efficient method to study any type of game on arbitrary graph structures for weak selection. In this limit, evolutionary game dynamics represents a first-order correction to neutral evolution. Spatial correlations can be empirically determined under neutral evolution and provide the basis for formulating the game dynamics as a discrete Markov process by incorporating a detailed description of the microscopic dynamics based on the neutral correlations. This framework is then applied to one of the most intriguing questions in evolutionary biology: the evolution of cooperation. We demonstrate that the degree heterogeneity of a graph impedes cooperation and that the success of tit for tat depends not only on the number of rounds but also on the degree of the graph. Moreover, considering the mutation-selection equilibrium shows that the symmetry of the stationary distribution of states under weak selection is skewed in favor of defectors for larger selection strengths. In particular, degree heterogeneity—a prominent feature of scale-free networks—generally results in a more pronounced increase in the critical benefit-to-cost ratio required for evolution to favor cooperation as compared to regular graphs. This conclusion is corroborated by an analysis of the effects of population structures on the fixation probabilities of strategies in general $2\times 2$ games for different types of graphs. Computer simulations confirm the predictive power of our method and illustrate the improved accuracy as compared to previous studies.

We consider motion of an underdamped Brownian particle in a washboard potential that is subjected to an unbiased time-periodic external field. While in the limiting deterministic system in dependence of the strength and phase of the external field directed net motion can exist; for a finite temperature the net motion averages to zero. Strikingly, with the application of an additional time-delayed feedback term directed particle motion can be accomplished persisting up to fairly high levels of the thermal noise. In detail, there exist values of the feedback strength and delay time for which the feedback term performs oscillations that are phase locked to the time-periodic external field. This yields an effective biasing rocking force promoting periods of forward and backward motion of distinct duration, and thus directed motion. In terms of phase space dynamics we demonstrate that with applied feedback desymmetrization of coexisting attractors takes place leaving the ones supporting either positive or negative velocities as the only surviving ones. Moreover, we found parameter ranges for which in the presence of thermal noise the directed transport is enhanced compared to the noiseless case.

We compute the entropy reduction in feedback controlled systems due to the repeated operation of the controller. This was the lacking ingredient to establish the thermodynamics of these systems, and in particular of Maxwell’s demons. We illustrate some of the consequences of our general results by deriving the maximum work that can be extracted from isothermal feedback controlled systems. As a case example, we finally study a simple system that performs an isothermal information-fueled particle pumping.

Transport coefficients associated with the mass flux of impurities immersed in a moderately dense granular gas of hard disks or spheres described by the inelastic Enskog equation are obtained by means of the Chapman-Enskog expansion. The transport coefficients are determined as the solutions of a set of coupled linear integral equations recently derived for polydisperse granular mixtures [Garzó et al., Phys. Rev. E 76, 031304 (2007)]. With the objective of obtaining theoretical expressions for the transport coefficients that are sufficiently accurate for highly inelastic collisions, we solve the above integral equations by using the second Sonine approximation. As a complementary route, we numerically solve by means of the direct simulation Monte Carlo method (DSMC) the inelastic Enskog equation to get the kinetic diffusion coefficient $D_0$ for two and three dimensions. We have observed in all our simulations that the disagreement, for arbitrarily large inelasticity, in the values of both solutions (DSMC and second Sonine approximation) is less than 4%. Moreover, we show that the second Sonine approximation to $D_0$ yields a dramatic improvement (up to 50%) over the first Sonine approximation for impurity particles lighter than the surrounding gas and in the range of large inelasticity. The results reported in this paper are of direct application in important problems in granular flows, such as segregation driven by gravity and a thermal gradient. We analyze here the segregation criteria that result from our theoretical expressions of the transport coefficients.

We present an exact three-dimensional solitonic solution to a sine-Gordon-type Euler-Lagrange equation that describes a configuration of a three-dimensional vector field $\widehat{n}$ constrained to a surface $p$-vortex, with a prescribed polar tilt angle on a planar substrate and escaping into the third dimension in the bulk. The solution is relevant to characterization of a schlieren texture in nematic liquid-crystal films with tangential (in-plane) substrate alignment. The solution is identical to a section of a point defect discovered many years ago by Saupe [Mol. Cryst. Liq. Cryst. 21, 211 (1973)], when latter is restricted to a surface.

The driving force of density fluctuation of amorphous polymer films under annealing processes was evaluated synthetically in terms of thermodynamics on the basis of the logarithmic light intensity as a function of annealing time. The time dependence of $\mathcal{l}n\left(I\right)$ of polyethylene (terephthalate) (PET) as an example for characterizing an amorphous state was classified into three stages: the first stage (stage I), where $\mathcal{l}n\left(I\right)$ showed insignificant changes with time; the second stage (stage II), where $\mathcal{l}n\left(I\right)$ increased linearly; and the third stage (stage III), where the intensity deviated from the linear relationship and tended to level off. The density fluctuation by chain diffusion, termed quasi-spinodal decomposition, in stage II was analyzed in terms of an increase of trans-conformation of an amorphous chain in stage I. To provide conclusive evidence, the orientation function of chain segments was calculated by using a lattice model that accounts for entropic and energetic characters. The former character is associated with segmental orientation due to the effect of chain stiffness of Kuhn segments characterized by a rod with a relatively large length-to-width ratio $x$, whereas the latter is associated with thermotropic systems with anisotropic polarizabilities. By using the theoretical orientation function, Hv light scattering patterns were calculated by a statistical approach in which the optical axis of a PET chain segment was chosen along the direction perpendicular to the benzene ring. This selection was justified by comparison of the three principal refractive indexes of a PET chain. The calculated patterns provided a clear $X$-type lobe, when the correlation between optical elements concerning the rotational fluctuation became stronger. The calculated patterns were in good agreement with the patterns observed in stage III. The series of experimental and theoretical results indicated that the conversion from gauche- to trans-conformation plays an important role to derive the density fluctuation of amorphous polymer chains associated with the initiation of crystallization.