It has been reported recently that the equipartition theorem is violated in molecular dynamics simulations with periodic boundary condition [R. B. Shirts et al., J. Chem. Phys. 125, 164102 (2006)]. This effect is associated with the conservation of the total momentum. Here, we propose a fluctuating center of mass molecular dynamics approach to solve this problem. Using the analogy to a system exchanging momentum with its surroundings, we work out—and validate via simulations—an expression for the rate at which fluctuations shall be added to the system. It is shown that the proposed method maintains equipartition both at equilibrium and beyond equilibrium in the linear response regime.

Exploiting previous results on Markovian dynamics and fluctuation theorems, we study the consequences of memory effects on single realizations of nonequilibrium processes within an open system approach. The entropy production along single trajectories for forward and backward processes is obtained with the help of a recently proposed classical-like non-Markovian stochastic unravelling, which is demonstrated to lead to a correction of the standard entropic fluctuation theorem. This correction is interpreted as resulting from the interplay between the information extracted from the system through measurements and the flow of information from the environment to the open system: Due to memory effects, single realizations of a dynamical process are no longer independent and their correlations fundamentally affect the behavior of entropy fluctuations.

In this paper we present an algorithm for exact generation of multivariate samples with prespecified marginal distributions and a given correlation matrix, based on a mixture of Fréchet-Hoeffding bounds and marginal products. In the bivariate case, the algorithm can accommodate any among the theoretically possible correlation coefficients, and explicitly provides a connection between simulation and the minimum correlation attainable for different distribution families. We calculate the minimum correlations in several common distributional examples, including in some that have not been looked at before. As an illustration, we provide the details and results of implementing the algorithm for generating three-dimensional negatively and positively correlated Beta random variables, making it the only noncopula algorithm for correlated Beta simulation in dimensions greater than two. This work has potential for impact in a variety of fields where simulation of multivariate stochastic components is desired.

We consider fluctuations of the time-averaged current in the one-dimensional weakly asymmetric exclusion process on a ring. The optimal density profile which sustains a given fluctuation exhibits an instability for low enough currents, where it becomes time dependent. This instability corresponds to a dynamical phase transition in the system fluctuation behavior: while typical current fluctuations result from the sum of weakly correlated local events and are still associated with the flat, steady-state density profile, for currents below a critical threshold, the system self-organizes into a macroscopic jammed state in the form of a coherent traveling wave, which hinders transport of particles and thus facilitates a time-averaged current fluctuation well below the average current. We analyze in detail this phenomenon using advanced Monte Carlo simulations, and work out macroscopic fluctuation theory predictions, finding very good agreement in all cases. In particular, we study not only the current large-deviation function, but also the critical current threshold, the associated optimal density profiles, and the traveling-wave velocity, analyzing in depth finite-size effects and hence providing a detailed characterization of the dynamical transition.

We consider the stochastic dynamics of escape in an excitable system, the FitzHugh-Nagumo (FHN) neuronal model, for different classes of excitability. We discuss, first, the threshold structure of the FHN model as an example of a system without a saddle state. We then develop a nonlinear (nonlocal) stability approach based on the theory of large fluctuations, including a finite-noise correction, to describe noise-induced escape in the excitable regime. We show that the threshold structure is revealed via patterns of most probable (optimal) fluctuational paths. The approach allows us to estimate the escape rate and the exit location distribution. We compare the responses of a monostable resonator and monostable integrator to stochastic input signals and to a mixture of periodic and stochastic stimuli. Unlike the commonly used local analysis of the stable state, our nonlocal approach based on optimal paths yields results that are in good agreement with direct numerical simulations of the Langevin equation.

In previous papers analytical equations were derived and validated for the packing fraction of crystalline structures consisting of bimodal randomly placed hard spheres [Phys. Rev. E 76, 041304 (2007); Phys. Rev. E 78, 011303 (2008)]. In this article it will be demonstrated that the bimodal random packing fraction of spheres with small size ratio can be described by the same type of closed-form equation. This equation contains the volume of the spheres and of the elementary cluster formed by these spheres. The obtained compact analytical expression appears to be in good agreement with a large collection of empirical and computer-generated packing data, taken from literature. By following a statistical approach of the number of uneven pairs in a binary packing, and the associated packing reduction (compared to the monosized limit), the number fraction of hypostatic spheres is estimated to be 0.548.

The electroporation process in response to a high-intensity, ultrashort (∼ns) electric pulse is probed based on molecular-dynamics simulations and shown to be a very rapid, twofold process. The electric driving force produces a Maxwell stress at the membrane and works to rearrange lipid dipoles and cause openings. However, water entry, which is essential for useful transport, is facilitated by electrowetting, which is an important component of the overall process. The molecular system can thus function as an electrically driven hydrophobic toggle switch that changes the water permeability. Furthermore, our results show that once they are fully formed, the nanopores do not close rapidly after cessation of the external electric field, in keeping with recent experiments. Finally, it is suggested that multiple pore formation in close proximity, as in situations involving high driving electric fields, is likely to be a rapid sequential process.

We report experiments on the full space- and time-resolved statistics of capillary wave turbulence at the air-water interface. The three-dimensional shape of the free interface is measured as a function of time by using the optical method of diffusing light photography associated with a fast camera. Linear and nonlinear dispersion relations are extracted from the spatiotemporal power spectrum of wave amplitude. When wave turbulence regime is reached, we observe power-law spectra both in frequency and in wave number whose exponents are found to agree with the predictions of capillary wave turbulence theory. Finally, the temporal dynamics of the spatial energy spectrum highlight the occurrence of stochastic bursts transferring wave energy through the spatial scales.

The emergence of group structure of cooperative relations is studied in an agent-based model. It is proved that specific types of reciprocity norms lead individuals to split into two groups only inside of which they are cooperative. The condition for the evolutionary stability of the norms is also obtained. This result suggests reciprocity norms, which usually promote cooperation, can cause society's separation into multiple groups.

The hydrostatic primitive equations (HPEs) form the basis of most numerical weather, climate, and global ocean circulation models. Analytical (not statistical) methods are used to find a scaling proportional to ${\left(\mathrm{Nu}\mathrm{Ra}\mathrm{Re}\right)}^{1/4}$ for the range of horizontal spatial sizes in HPE solutions, which is much broader than is currently achievable computationally. The range of scales for the HPE is determined from an analytical bound on the time-averaged enstrophy of the horizontal circulation. This bound allows the formation of very small spatial scales, whose existence would excite unphysically large linear oscillation frequencies and gravity wave speeds.

We study anomalous diffusion governed by the $n$-tuple order time-fractional Fokker-Planck equation of Riemann-Liouville type. We find a stochastic representation of this anomalous diffusion; that is, the stochastic process with probability density function evolving according to the considered diffusion equation. The stochastic representation, given in the form of the Brownian motion subordinated by a Lévy process defined in terms of the Lévy exponent, is shown to be an accelerating subdiffusion process. Taking advantage of the stochastic representation, we construct an algorithm for computer simulations of the accelerating-subdiffusion sample paths. Moreover, we obtain a stochastic representation and the simulation algorithm for the case of the anomalous diffusion influenced by an external space-dependent force field.

We study self-propelled motion of an active Brownian particle moving in a periodic, ratchet-type potential and subject to energy support distributed in quantized portions according to a Poisson spiking process. The motor features of such a system are examined by analyzing its ability to perform work against additional external load. The control parameter of the system is a mean duration time between subsequent energy pulses. Our analysis indicates that directionality of the motion depends strongly on the correlation time between events of energy supply and can be adjusted to maintain optimal functionality of the motor.

We consider a stochastic model for the directed motion of a solid object due to the rectification of asymmetric surface vibrations with Poissonian shot-noise statistics. The friction between the object and the surface is given by a piecewise-linear friction force. This models the combined effect of dynamic friction and singular dry friction. We derive an exact solution of the stationary Kolmogorov-Feller (KF) equation in the case of two-sided exponentially distributed amplitudes. The stationary density of the velocity exhibits singular features such as a discontinuity and a delta-peak singularity at zero velocity, and also contains contributions from nonintegrable solutions of the KF equation. The mean velocity in our model generally varies nonmonotonically as the strength of the dry friction is increased, indicating that transport improves for increased dissipation.

Linear response theory (LRT) can be used to compute spectral properties of single and populations of stochastic leaky integrate-and-fire neurons. The effects of inputs, both external and from delayed feedback, can be modeled within that theory when the neural function is sufficiently linearized by noise. It has been used to explain experiments where gamma oscillations are induced by spatially correlated stochastic inputs to a network with delayed inhibitory feedback. Here we expand this theory to include two distinct population types. We first show how to deal with homogeneous networks where both types of neurons have identical intrinsic properties. We further tackle the asymmetric case, where noise or bias differ. We also analyze the case where the membrane time constants differ, based on experimental evidence, which requires delicate alterations of the theory. We directly apply the theory to networks of ON and OFF cells in the electrosensory system, which together provide global delayed negative feedback to all cells; however, ON and OFF cells receive external inputs of opposite polarities. Theoretical results are in excellent agreement with numerical simulations of the two population network. In contrast to the case of a single ON cell population with feedback, the more realistic presence of both cell types can significantly reduce the propensity of the delayed feedback network to oscillate for spatially correlated inputs. Our results are further linked to recent predictions from deterministic neural field theory. Among other findings, our work suggests that the observed gamma oscillations could be explained only if the ON and OFF cell feedback pathways are anatomically segregated. Thus our two population LRT can make specific predictions about network topography in specific systems.

Many real networks are embedded in space, and often the distribution of the link lengths $r$ follows a power law, $p\left(r\right)\sim r^{-\delta }$. Indications that such systems can be characterized by the concept of dimension were found recently. Here, we present further support for this claim, based on extensive numerical simulations of model networks with a narrow degree distribution, embedded in lattices of dimensions $d_e=1$ and $d_e=2$. For networks with $\delta <d_e$, $d$ is infinity, while for $\delta >2d_e$, $d$ has the value of the embedding dimension $d_e$. In the intermediate regime of interest $d_e\le \delta <2d_e$, our numerical results suggest that $d$ decreases continuously from $d=\infty$ to $d_e$, with $d-d_e\propto (2-{\delta }^{\prime })/\left[{\delta }^{\prime }({\delta }^{\prime }-1)\right]$ and ${\delta }^{\prime }=\delta /d_e$. We also analyze how the mass $M$ and the Euclidean distance $r$ increase with the topological distance $\ell$ (minimum number of links between two sites in the network). Our results suggest that in the intermediate regime $d_e\le \delta <2d_e$, $M\left(\ell \right)$ and $r\left(\ell \right)$ increase with $\ell$ as a stretched exponential, $M\left(\ell \right)\sim \exp \left[Ad{\ell }^{{\delta }^{\prime }(2-{\delta }^{\prime })}\right]$ and $r\left(\ell \right)\sim \exp \left[A{\ell }^{{\delta }^{\prime }(2-{\delta }^{\prime })}\right]$, such that $M\left(\ell \right)\sim r{\left(\ell \right)}^d$. For $\delta <d_e$, $M$ increases exponentially with $\ell$ (as known for $\delta =0$), while $r$ is constant and independent of $\ell$. For $\delta \ge 2d_e$, we find the expected power-law scaling, $M\left(\ell \right)\sim {\ell }^{d_{\ell }}$ and $r\left(\ell \right)\sim {\ell }^{1/d_{\min }}$, with $d_{\ell }{d}_{\min }=d$. In $d_e=1$, we find the expected result, $d_{\ell }=d_{\min }=1$, while in $d_e=2$ we find surprisingly that although $d=2$, $d_{\ell }>2$ and $d_{\min }<1$, in contrast to regular lattices.

Well-known rigorous methods have been elaborated long ago to exactly solve conservative soliton equations. Mainly, there are the inverse scattering transform, Hirota's direct method, and Sato's formalism. These methods are fully satisfactory: analytical expressions for solitons are obtained in any spatial dimension as well as multisoliton solutions. Therefore, there is no need for an additional approach, especially if it is an approximate one, restricted to a one-dimensional situation and to a single soliton solution. Except, our approach is really elementary, straightforward, and unexpectedly accurate. It provides a physical background to the newfound exp-function method and, most importantly, it furnishes an analytical description of front solution in a nonconservative equation for which no other rigorous methods exist.

We perform a detailed numerical study of the distribution of conductances $P\left(T\right)$ for quasi-one-dimensional corrugated waveguides as a function of the corrugation complexity (from rough to smooth). We verify the universality of $P\left(T\right)$ in both the diffusive ($〈T〉>1$) and the localized ($〈T〉\ll 1$) transport regimes. However, at the crossover regime ($〈T〉\sim 1$), we observe that $P\left(T\right)$ evolves from the surface-disorder to the bulk-disorder theoretical predictions for decreasing complexity in the waveguide boundaries. We explain this behavior as a transition from disorder to deterministic chaos since in the limit of smooth boundaries the corrugated waveguides are, effectively, linear chains of chaotic cavities.

We present results from an ensemble of 50 runs of two-dimensional hydrodynamic turbulence with spatial resolution of ${2048}^2$ grid points and from an ensemble of 10 runs with ${4096}^2$ grid points. All runs in each ensemble have random initial conditions with the same initial integral scale, energy, enstrophy, and Reynolds number. When both ensemble and time averaged, an inverse energy cascade behavior is observed, even in the absence of external mechanical forcing: The energy spectrum at scales larger than the characteristic scale of the flow follows a $k^{-5/3}$ law, with negative flux, together with a $k^{-3}$ law at smaller scales, and a positive flux of enstrophy. The source of energy for this behavior comes from the modal energy around the energy-containing scale at $t=0$. The results shed some light on the connections between decaying and forced turbulence and recent controversies in experimental studies of two-dimensional and magnetohydrodynamic turbulent flows.

We show that strong coupling between ions in an ultracold neutral plasma is limited by electron screening. While electron screening reduces the quasiequilibrium ion temperature, it also reduces the ion-ion electrical potential energy. The net result is that the ratio of nearest-neighbor potential energy to kinetic energy in quasiequilibrium is constant and limited to approximately 1 unless the electrons are heated by some external source. We support these conclusions by reporting measurements of the ion velocity distribution in an ultracold neutral calcium plasma. These results match previously reported simulations of Yukawa systems. Theoretical considerations are used to determine the screened nearest-neighbor potential energy in the plasma.

The Vlasov-Maxwell statistical treatment of relativistic charged particles subject to electromagnetic (EM) radiation reaction (RR) represents an unsolved conceptual challenge. In fact, as shown here, the customary point-particle treatment based on the Landau-Lifschitz (LL) equation leads to a generally nonconstant Boltzmann-Shannon (BS) entropy even in the absence of binary collisions. This conclusion appears to be in contradiction with the intrinsic microscopic reversibility of the underlying physical system. In this paper the issue is addressed in the framework of a Hamiltonian treatment for extended charged particles in the presence of EM RR. It is shown that such a behavior actually has no physical ground, being a consequence of the asymptotic approximations involved in the construction of the LL equation. In particular, it is proved that the Hamiltonian structure of the underlying particle dynamics actually restores the conservation of the BS entropy. The connection between the two approaches is analyzed. As a result, it is pointed out that the fulfillment of the entropy law can still be warranted even in the framework of an asymptotic theory by introducing a suitable Hamiltonian approximation for the EM RR equation.