Markov jump processes can be used to model the effective dynamics of observables in applications ranging from molecular dynamics to finance. In this paper we present a different method which allows the inverse modeling of Markov jump processes based on incomplete observations in time: We consider the case of a given time series of the discretely observed jump process. We show how to compute efficiently the maximum likelihood estimator of its infinitesimal generator and demonstrate in detail that the method allows us to handle observations nonequidistant in time. The method is based on the work of and Bladt and Sørensen [J. R. Stat. Soc. Ser. B (Stat. Methodol.) 67, 395 (2005)] but scales much more favorably than it with the length of the time series and the dimension and size of the state space of the jump process. We illustrate its performance on a toy problem as well as on data arising from simulations of biochemical kinetics of a genetic toggle switch.

Using the projection operator formalism we explore the decay form of the time correlation function $U_n\left(t\right)\equiv ⟨{\widehat{u}}_n\left(t\right){\widehat{u}}_n^{\ast }\left(0\right)⟩$ of the state variable ${\widehat{u}}_n\left(t\right)$ in the chaotic Kuramoto-Sivashinsky equation. The decay form turns out to be the algebraic decay $1∕\left[1+{\left({\gamma }_{na}t\right)}^2\right]$ in the initial regime $t<1∕{\gamma }_{ne}$ and the exponential decay $\text{exp}\left(-{\gamma }_{ne}t\right)$ in the final regime $t>1∕{\gamma }_{ne}$. The memory function ${\Gamma }_n\left(t\right)$ that represents the chaos-induced transport is found to obey the Gaussian decay $\text{exp}\left[-{\left({\beta }_{ng}t\right)}^2\right]$ in the case of large wave numbers, but the 3/2 power decay $\text{exp}\left[-{\left({\beta }_{n3}t\right)}^{3∕2}\right]$ in the case of small wave numbers. The power spectrum of ${\widehat{u}}_n\left(t\right)$ is given by the real part $U_n^{\prime }\left(\omega \right)$ of the Fourier-Laplace transform of $U_n\left(t\right)$ and has a dominant peak at $\omega =0$. This peak within the linewidth ${\overline{\gamma }}_{ne}\left(\approx {\gamma }_{ne}\right)$ is given by the Lorentzian spectrum ${\overline{\gamma }}_{ne}^2∕\left({\omega }^2+{\overline{\gamma }}_{ne}^2\right)$. However, the wings of the peak outside the width ${\overline{\gamma }}_{ne}$ turn out to take the exponential spectrum $\text{exp}\left(-\omega ∕{\gamma }_{na}\right)$. Thus it is found that the exponential decay $\text{exp}\left(-{\gamma }_{ne}t\right)$ appears to lead to the universal Lorentzian peak, while the algebraic decay $1∕\left[1+{\left({\gamma }_{na}t\right)}^2\right]$ arises to bring about the exponential wing.

A surface model on compartmentalized spheres is studied by using the Monte Carlo simulation technique with dynamical triangulations. We found that the model exhibits a variety of phases: The spherical phase, the tubular phase, the planar phase, the wormlike planar phase, the wormlike long phase, the wormlike short phase, and the collapsed phase. We also demonstrated that almost all phases are separated from their neighboring phases by first-order transitions. Mechanical strength of the surface is given only by elastic skeletons, which are the compartment boundaries, and therefore vertices diffuse freely inside the compartments. We confirm that the cytoskeletal structure and the lateral diffusion of vertices are origins of such a variety of phases.

In this paper the linear theory of nonequilibrium thermodynamics, developed by Onsager and others, is applied to random networks with arbitrary degree distribution. Using the well-known methods of nonequilibrium thermodynamics we identify thermodynamic forces and their conjugated flows induced in networks as a result of single node degree perturbation. The forces and the flows can be understood as a response of the system to events, such as random removal of nodes or intentional attacks on them. Finally, we show that cross effects (such as thermodiffusion, or thermoelectric phenomena), in which one force may not only give rise to its own conjugated flow, but to many other flows, can be observed also in complex networks.

We probe the dynamics of intermittent avalanches caused by steady addition of grains to a quasi-two-dimensional heap. To characterize the time-dependent average avalanche flow speed $v\left(t\right)$, we image the top free surface. To characterize the grain fluctuation speed $\delta v\left(t\right)$, we use speckle-visibility spectroscopy. During an avalanche, we find that the fluctuation speed is approximately one-tenth the average flow speed, $\delta v\approx 0.1v$, and that these speeds are largest near the beginning of an event. We also find that the distribution of event durations is peaked, and that event sizes are correlated with the time interval since the end of the previous event. At high rates of grain addition, where successive avalanches merge into smooth continuous flow, the relationship between average and fluctuation speeds changes to $\delta v\sim v^{1/2}$.

The mean-squared displacement, velocity autocorrelation function, and the non-Gaussian parameter, obtained by dynamic light scattering on suspensions of particles with hard-sphere interactions, are compared with the results of the idealized version of mode-coupling theory. Both leading order asymptotic and full numerical solutions of the mode-coupling equations are considered. Experiment and the full numerical results of the theory expose similar qualitative changes at the volume fraction of the first order freezing transition. In particular, the emergence of negative algebraic decays in the velocity autocorrelation function of the undercooled suspension suggest the emergence of clusters in which particles are trapped. Consistency of experiment, computer simulation, and theory in this regard suggests that, at particular strengths of the delayed, nonlinear feedback, contained in mode coupling theory, the latter predicts not only structural arrest which, as already established, is symptomatic of a glass transition, but also a more subtle change in dynamics that signals the onset of the first order transition.

The role of H bonds in the formation of the fragility and dielectric properties of highly viscous liquids is investigated. The heuristic supposition about the proportionality between the logarithm of the shear viscosity and oscillatory contributions to the mean-square displacement of a molecule is presented. Concrete calculations are carried out for the H-bond subsystem of the two-dimensional model lattice water. The conjecture on the interrelation between the phase transition in the subsystem of H bonds and the glassification point is formulated. It is shown that (i) the glassification temperature is proportional to the H-bonding energy and (ii) the fragilities of glycerol-like liquids differ from each other as a consequence of distinct interaction energies between H bonds. The existence of a close connection between the fragility parameter and dielectric permittivity is established.

In this paper, we investigate the dynamical properties of electroencephalogram (EEG) signals of humans in sleep. By using a modified random walk method, we demonstrate that scale-invariance is embedded in EEG signals after a detrending procedure is applied. Furthermore, we study the dynamical evolution of the probability density function (PDF) of the detrended EEG signals by nonextensive statistical modeling. It displays a scale-independent property, which is markedly different from the usual scale-dependent PDF evolution and cannot be described by the Fokker-Planck equation.

We investigate the effects of risk perception in a simple model of epidemic spreading. We assume that the perception of the risk of being infected depends on the fraction of neighbors that are ill. The effect of this factor is to decrease the infectivity, that therefore becomes a dynamical component of the model. We study the problem in the mean-field approximation and by numerical simulations for regular, random, and scale-free networks. We show that for homogeneous and random networks, there is always a value of perception that stops the epidemics. In the “worst-case” scenario of a scale-free network with diverging input connectivity, a linear perception cannot stop the epidemics; however, we show that a nonlinear increase of the perception risk may lead to the extinction of the disease. This transition is discontinuous, and is not predicted by the mean-field analysis.

We obtain the best upper bound for the ground-state energy of a system of chargeless fermions of mass $m$, spin $s=1∕2$, and magnetic moment $\mu \vec{s}$ as a function of its density in the fully spin-polarized Hartree-Fock determinantal state, specified by a prolate spheroidal plane-wave single-particle occupation function $n_{\uparrow }\left(\vec{k}\right)$, by minimizing the total energy $E$ at each density with respect to the variational spheroidal deformation parameter ${\beta }_2,0⩽{\beta }_2⩽1$. We find that at high densities, this spheroidal ferromagnetic state is the most likely ground state of the system, but it is still unstable towards the infinite-density collapse. This optimized ferromagnetic state is shown to be a stable ground state of the dipolar system at high densities, if one has an additional repulsive short-range hardcore interaction of sufficient strength and nonvanishing range.

We consider the problem of determining the proportion of edges that are discovered in an Erdős-Rényi graph when one constructs all shortest paths from a given source node to all other nodes. This problem is equivalent to the one of determining the proportion of edges connecting nodes that are at identical distance from the source node. The evolution of this quantity with the probability of existence of the edges exhibits intriguing oscillatory behavior. In order to perform our analysis, we introduce a different way of computing the distribution of distances between nodes. Our method outperforms previous similar analyses and leads to estimates that coincide remarkably well with numerical simulations. It allows us to characterize the phase transitions appearing when the connectivity probability varies.

The properties of one-particle and particle-pair diffusion in rotating and stratified turbulence are studied by applying the rapid distortion theory to a kinematic simulation of the Boussinesq equation with a Coriolis term. We discuss the simplified Corrsin hypothesis and restrict the validity of its predictions to pure rotation. We emphasize the existence of two $\tau$ regimes driven by very different physics when rotation is present. Particular attention is given to the locality-in-scale hypothesis for two-particle diffusion in both the horizontal and the vertical directions.

Complete and partial synchronization have been largely studied on networks of identical coupled oscillators. However, we study a network in which not all oscillators when uncoupled show the same dynamics and nonetheless the network shows partial synchronization. Our system is composed by four Rössler oscillators diffusively coupled in a ring. Oscillators 1 and 3 are identical, as 2 and 4 are also. In short, the network is said to be composed of different classes of oscillators (in our example, two classes with two oscillators each). Primary synchronization is defined as the case when all oscillators on the same class are identically synchronized, for all classes. Secondary synchronization is related to the other possible cases of partial synchronization. Both are achieved for the system we have chosen, shown by means of direct integration and transverse Lyapunov exponent computation. Furthermore, evidence of riddled basins of attraction is presented.

In this paper we seek an approximate expression for the time-dependent lift force, initially derived by Saffman in the steady case, by using the Asmolov and McLaughlin frequential results. The single-frequency expression derived by these authors can indeed be used to obtain a temporal expression of the lift force acting on a sphere with arbitrary motion, since the problem is linear. The major difficulty lies in the fact that their frequential results are given under a very complicated algebraic expression. Therefore, no analytical inverse Fourier transform can be carried out and the expression of the time-dependent lift force acting on a particle cannot be obtained in the general case. In the present paper, however, it is shown that a closed temporal expression for this force can be found, provided one makes additional approximations. This expression takes the form of a convolution product involving an empirical kernel as well as the slip velocity of the particle.

Continuous-time random walks have been developed as a straightforward generalization of classical random-walk processes. Some ten years ago, Fogedby introduced a continuous representation of these processes by means of a set of Langevin equations [H. C. Fogedby, Phys. Rev. E 50, 1657 (1994)]. The present work is devoted to a detailed discussion of Fogedby’s model and presents its application for the robust numerical generation of sample paths of continuous time random-walk processes.

I comment on the relation between two sampling methods for absorbing-state models. It is shown that a certain ensemble without external field conditional to activity coincides with the unconditional ensemble for sufficiently small external field. The actual physical processes involved are identical and the derivation of the identity of the scaling behavior relies on a single (established) scaling law. While the conditional ensemble by construction does not contain information about the system with large external field, it contains all the information about the limit of vanishing external field and about the vicinity of the critical point: finite size scaling as well as critical scaling in the temperature-like variable or in (small) external field.

The phase behavior of a 50% binary hard-disk mixture with diameter ratio ${\sigma }_B/{\sigma }_A=0.414$, which is exposed to a one-dimensional periodic potential, is examined via Monte Carlo simulations. We find an induced structural crossover in the modulated liquid. At higher densities, depending on the strength of the external potential, the system exhibits a tunable demixing transition, followed by fluid-solid coexistence of an equimolar mixture with the $S_1\left(AB\right)$ square lattice. We find a decoupled melting of the sublattices of the $S_1\left(AB\right)$ lattice. The melting of the small-component sublattice perpendicular to the external potential minima leads to fissuring in the large-component sublattice.

We study numerically finite-size corrections in scaling relations for roughness distributions of various interface growth models. The most common relation, which considers the average roughness $⟨w_2⟩$ as a scaling factor, is not obeyed in the steady states of a group of ballisticlike models in $2+1$ dimensions, even when very large system sizes are considered. On the other hand, good collapse of the same data is obtained with a scaling relation that involves the root mean square fluctuation of the roughness, which can be explained by finite-size effects on second moments of the scaling functions. We also obtain data collapse with an alternative scaling relation that accounts for the effect of the intrinsic width, which is a constant correction term previously proposed for the scaling of $⟨w_2⟩$. This illustrates how finite-size corrections can be obtained from roughness distributions scaling. However, we discard the usual interpretation that the intrinsic width is a consequence of high surface steps by analyzing data of restricted solid-on-solid models with various maximal height differences between neighboring columns. We also observe that large finite-size corrections in the roughness distributions are usually accompanied by huge corrections in height distributions and average local slopes, as well as in estimates of scaling exponents. The molecular-beam epitaxy model of Das Sarma and Tamborenea in $1+1$ dimensions is a case example in which none of the proposed scaling relations work properly, while the other measured quantities do not converge to the expected asymptotic values. Thus although roughness distributions are clearly better than other quantities to determine the universality class of a growing system, it is not the final solution for this task.

We describe the effect of hydrodynamic interactions in the sedimentation of a pair of inextensible semiflexible filaments under a uniform constant force at low Reynolds numbers. We have analyzed the different regimes and the morphology of such polymers in simple geometries, which allow us to highlight the peculiarities of the interplay between elastic and hydrodynamic stresses. Cooperative and symmetry breaking effects associated to the geometry of the fibers gives rise to characteristic motion which give them distinct properties from rigid and elastic filaments.