Plasma-based parametric amplification using stimulated Brillouin scattering offers a route to coherent x-ray pulses orders of magnitude more intense than those of the brightest available sources. Brillouin amplification permits amplification of shorter wavelengths with lower pump intensities than Raman amplification, which Landau and collisional damping limit in the x-ray regime. Analytic predictions, numerical solutions of the three-wave-coupling equations, and particle-in-cell simulations suggest that Brillouin amplification in solid-density plasmas will allow compression of current x-ray free-electron laser pulses to subfemtosecond durations and unprecedented intensities.

Description of long-term (over years) ion diffusion at the pore scale is a huge challenge since the characteristic time of diffusion in a typical representative elementary volume is around microseconds, generally ten orders of magnitude lower than the time we were concerned with. This paper presents a numerical upscaling scheme for ion diffusion with electrical double-layer effects (electrodiffusion) considered in charged porous media. After a scaling analysis for the nondimensional governing equations of ion transport at the pore scale, we identify the conditions for decoupling of electrical effect and diffusion, and therefore are able to choose apposite temporal and spatial scales for corresponding directions of the electrodiffusion process. The upscaling scheme is therefore proposed based on a numerical framework for governing equations using a lattice Boltzmann method. The electrical potential or concentration profiles from steady- or unsteady-state electrodiffusion in the long, straight channel, calculated by this upscaling scheme, are compared with the well-meshed full-sized simulations with good agreement. Furthermore, this scheme is used to predict tracer-ion throughdiffusion and outdiffusion in hardened cement pastes. All numerical results show good agreement with the full-sized simulations or experiment data without any fitting parameters. This upscaling scheme bridges the ion diffusion behaviors in different time scales, and may help to improve the understanding of long-term ion transport mechanisms in charged porous media.

Rooted from the gas kinetics, the lattice Boltzmann method (LBM) is a powerful tool in modeling hydrodynamics. In the past decade, it has been extended to simulate rarefied gas flows beyond the Navier-Stokes level, either by using the high-order Gauss-Hermite quadrature, or by introducing the relaxation time that is a function of the gas-wall distance. While the former method, with a limited number of discrete velocities (e.g., D2Q36), is accurate up to the early transition flow regime, the latter method (especially the multiple relaxation time (MRT) LBM), with the same discrete velocities as those used in simulating hydrodynamics (i.e., D2Q9), is accurate up to the free-molecular flow regime in the planar Poiseuille flow. This is quite astonishing in the sense that less discrete velocities are more accurate. In this paper, by solving the Bhatnagar-Gross-Krook kinetic equation accurately via the discrete velocity method, we find that the high-order Gauss-Hermite quadrature cannot describe the large variation in the velocity distribution function when the rarefaction effect is strong, but the MRT-LBM can capture the flow velocity well because it is equivalent to solving the Navier-Stokes equations with an effective shear viscosity. Since the MRT-LBM has only been validated in simple channel flows, and for complex geometries it is difficult to find the effective viscosity, it is necessary to assess its performance for the simulation of rarefied gas flows. Our numerical simulations based on the accurate discrete velocity method suggest that the accuracy of the MRT-LBM is reduced significantly in the simulation of rarefied gas flows through the rough surface and porous media. Our simulation results could serve as benchmarking cases for future development of the LBM for modeling and simulation of rarefied gas flows in complex geometries.

In this work we construct individual-based models that give rise to the generalized logistic model at the mean-field deterministic level and that allow us to interpret the parameters of these models in terms of individual interactions. We also study the effect of internal fluctuations on the long-time dynamics for the different models that have been widely used in the literature, such as the theta-logistic and Savageau models. In particular, we determine the conditions for population extinction and calculate the mean time to extinction. If the population does not become extinct, we obtain analytical expressions for the population abundance distribution. Our theoretical results are based on WKB theory and the probability generating function formalism and are verified by numerical simulations.

We consider forces acting on objects immersed in, or attached to, long fluctuating polymers. The confinement of the polymer by the obstacles results in polymer-mediated forces that can be repulsive (due to loss of entropy) or attractive (if some or all surfaces are covered by adsorbing layers). The strength and sign of the force in general depends on the detailed shape and adsorption properties of the obstacles but assumes simple universal forms if characteristic length scales associated with the objects are large. This occurs for scale-free shapes (such as a flat plate, straight wire, or cone) when the polymer is repelled by the obstacles or is marginally attracted to it (close to the depinning transition where the absorption length is infinite). In such cases, the separation $h$ between obstacles is the only relevant macroscopic length scale, and the polymer-mediated force equals $\mathcal{A}{k}_{B}T/h$, where $T$ is temperature. The amplitude $\mathcal{A}$ is akin to a critical exponent, depending only on geometry and universality of the polymer system. The value of $\mathcal{A}$, which we compute for simple geometries and ideal polymers, can be positive or negative. Remarkably, we find $\mathcal{A}=0$ for ideal polymers at the adsorption transition point, irrespective of shapes of the obstacles, i.e., at this special point there is no polymer-mediated force between obstacles (scale free or not).

We consider the response of a memoryless nonlinear device that acts instantaneously, converting an input signal $\xi \left(t\right)$ into an output $\eta \left(t\right)$ at the same time $t$. For input Gaussian noise with power-spectrum $1/f^{\alpha }$, the nonlinearity can modify the spectral index of the output to give a spectrum that varies as $1/f^{{\alpha }^{\prime }}$ with ${\alpha }^{\prime }\ne \alpha$. We show that the value of ${\alpha }^{\prime }$ depends on the nonlinear transformation and can be tuned continuously. This provides a general mechanism for the ubiquitous $1/f$ noise found in nature.

Energy or quasienergy (QE) band spectra depending on two parameters may have a nontrivial topological characterization by Chern integers. Band spectra of one-dimensional (1D) systems that are spanned by just one parameter, a Bloch phase, are topologically trivial. Recently, an ensemble of 1D Floquet (time-periodic) systems, double-kicked rotors (DKRs) that are classically nonintegrable and depend on an external parameter, has been studied. It was shown that a QE band spanned by both the Bloch phase and the external parameter is characterized by a Chern integer. The latter determines the change in the mean angular momentum of a state in the band when the external parameter is adiabatically varied by a natural period. We show here, under conditions much more general than in previous works, that the ensemble of DKRs for all values of the external parameter corresponds to a 1D double-kicked particle (DKP) having translational invariance in the position-momentum phase plane. This DKP can be characterized by a second Chern integer, which is shown to be connected with the integer above for the DKR ensemble. This connection is expressed by a Diophantine equation (DE), which we derive. The DE, involving the band degeneracies of the DKR ensemble and of the DKP system, determines the allowed values of the DKR-ensemble integer. In particular, this integer is generically nonzero, showing the general topological nontriviality of the DKR ensemble.

Dynamical intermittency is known to generate anomalous statistical behavior of dynamical systems, a prominent example being the Pomeau-Manneville map. We present a nonlinear oscillator, i.e., a physical model in continuous time, whose properties in terms of weak ergodity breaking and aging have a one-to-one correspondence to the properties of the Pomeau-Manneville map. So for both systems in a wide range of parameters no physical invariant density exists. We show how this regime can be characterized quantitatively using the techniques of infinite invariant densities and the Thaler-Dynkin limit theorem. We see how expectation values exhibit aging in terms of scaling in time.

We numerically study jamming transitions in pedestrian flow interacting with an attraction, mostly based on the social force model for pedestrians who can join the attraction. We formulate the joining probability as a function of social influence from others, reflecting that individual choice behavior is likely influenced by others. By controlling pedestrian influx and the social influence parameter, we identify various pedestrian flow patterns. For the bidirectional flow scenario, we observe a transition from the free flow phase to the freezing phase, in which oppositely walking pedestrians reach a complete stop and block each other. On the other hand, a different transition behavior appears in the unidirectional flow scenario, i.e., from the free flow phase to the localized jam phase and then to the extended jam phase. It is also observed that the extended jam phase can end up in freezing phenomena with a certain probability when pedestrian flux is high with strong social influence. This study highlights that attractive interactions between pedestrians and an attraction can trigger jamming transitions by increasing the number of conflicts among pedestrians near the attraction. In order to avoid excessive pedestrian jams, we suggest suppressing the number of conflicts under a certain level by moderating pedestrian influx especially when the social influence is strong.

The role of photoresponse of $\pi$ electrons in light-driven DNA dissociations is theoretically studied. A new model combining the Peyrard-Bishop-Dauxois model and the charge ladder model is first proposed. Then the evolutions of $\pi$-electronic states and H-bond stretching in the light-driven DNA dissociations are studied. The results show that light irradiation will induce ultrafast charge redistribution among bases, leading to the precursory insulator-to-metallic transition. This electronic transition will assist DNA to dissociate. Effects of screened Coulomb interactions on dissociation dynamics is emphatically discussed. Finally, it is also found that light-driven DNA dissociation preferentially occurs in the adenine-thymine–rich region rather than the guanine-cytosine–rich region.

Suspensions of hydrodynamical active particles exhibit interesting rheological properties. For a dilute suspension of microswimmers, it has been shown that the effective viscosity of the suspension depends on the volume fraction of swimmers, and it behaves differently for pushers and pullers. Here we develop a theoretical framework to study the rheological properties of an interacting suspension. Taking into account the hydrodynamic interaction between swimmers and considering the small Péclet number condition, we calculate the effective viscosity of a two-dimensional suspension. For a dilute suspension, a perturbative result is obtained up to the second order of the surface fraction of swimmers. Our results show that the effective viscosity for the suspension can be very different for pushers and pullers.

In elastic-wave turbulence, strong turbulence appears in small wave numbers while weak turbulence does in large wave numbers. Energy transfers in the coexistence of these turbulent states are numerically investigated in both the Fourier space and the real space. An analytical expression of a detailed energy balance reveals from which mode to which mode energy is transferred in the triad interaction. Stretching energy excited by external force is transferred nonlocally and intermittently to large wave numbers as the kinetic energy in the strong turbulence. In the weak turbulence, the resonant interactions according to the weak turbulence theory produce cascading net energy transfer to large wave numbers. Because the system's nonlinearity shows strong temporal intermittency, the energy transfers are investigated at active and moderate phases separately. The nonlocal interactions in the Fourier space are characterized by the intermittent bundles of fibrous structures in the real space.

In a recent molecular dynamics simulation work it has been shown that glasses composed of hard spheres crystallize via cooperative, stochastic particle displacements called avalanches [E. Sanz et al., Proc. Natl. Acad. Sci. USA 111, 75 (2014)]. In this Rapid Communication we investigate if such a devitrification mechanism is also present when the dynamics is Brownian rather than Newtonian. The research is motivated in part by the fact that colloidal suspensions, an experimental realization of hard-sphere systems, undergo Brownian motion. We find that Brownian hard-sphere glasses do crystallize via avalanches with very similar characteristics to those found in the Newtonian case. We briefly discuss the implications of these findings for experiments on colloids.

We use Newtonian and overdamped Langevin dynamics to study long flexible polymers dragged by an external force at a constant velocity $v$. The work $W$ performed by that force depends on the initial state of the polymer and the details of the process. The Jarzynski equality can be used to relate the nonequilibrium work distribution $P\left(W\right)$ obtained from repeated experiments to the equilibrium free energy difference $\mathrm{\Delta }F$ between the initial and final states. We use the power law dependence of the geometrical and dynamical characteristics of the polymer on the number of monomers $N$ to suggest the existence of a critical velocity $v_c\left(N\right)$, such that for $v<v_c$ the reconstruction of $\mathrm{\Delta }F$ is an easy task, while for $v$ significantly exceeding $v_c$ it becomes practically impossible. We demonstrate the existence of such $v_c$ analytically for an ideal polymer in free space and numerically for a polymer which is being dragged away from a repulsive wall. Our results suggest that the distribution of the dissipated work $W_{\mathrm{d}}=W-\mathrm{\Delta }F$ in properly scaled variables approaches a limiting shape for large $N$.

We investigate a two-dimensional spatially extended system that has a weak sense of excitability, where an excitation wave has a uniform profile and propagates only within a finite range. Using a cellular automaton model of such a weakly excitable system, we show that three kinds of sustained dynamics emerge when nonlocal spatial interactions are provided, where a chain of local wave propagation and nonlocal activation forms an elementary oscillatory cycle. Transition between different oscillation regimes can be understood as different ways of interactions among these cycles. Analytical expressions are given for the oscillation probability near the onset of oscillations.

We study analytically and numerically envelope solitons (bright and gap solitons) in a one-dimensional, nonlinear acoustic metamaterial, composed of an air-filled waveguide periodically loaded by clamped elastic plates. Based on the transmission line approach, we derive a nonlinear dynamical lattice model which, in the continuum approximation, leads to a nonlinear, dispersive, and dissipative wave equation. Applying the multiple scales perturbation method, we derive an effective lossy nonlinear Schrödinger equation and obtain analytical expressions for bright and gap solitons. We also perform direct numerical simulations to study the dissipation-induced dynamics of the bright and gap solitons. Numerical and analytical results, relying on the analytical approximations and perturbation theory for solions, are found to be in good agreement.

Rapid experimental advances now enable simultaneous electrophysiological recording of neural activity at single-cell resolution across large regions of the nervous system. Models of this neural network activity will necessarily increase in size and complexity, thus increasing the computational cost of simulating them and the challenge of analyzing them. Here we present a method to approximate the activity and firing statistics of a general firing rate network model (of the Wilson-Cowan type) subject to noisy correlated background inputs. The method requires solving a system of transcendental equations and is fast compared to Monte Carlo simulations of coupled stochastic differential equations. We implement the method with several examples of coupled neural networks and show that the results are quantitatively accurate even with moderate coupling strengths and an appreciable amount of heterogeneity in many parameters. This work should be useful for investigating how various neural attributes qualitatively affect the spiking statistics of coupled neural networks.