We study numerically the dynamics of excitons on discrete rings in the presence of static disorder. Based on continuous-time quantum walks we compute the time evolution of the Wigner function (WF) both for pure diagonal (site) disorder, as well as for diagonal and off-diagonal (site and transfer) disorder. In both cases, large disorder leads to localization and destroys the characteristic phase space patterns of the WF found in the absence of disorder.

We apply the spectral method, recently developed by the authors, to calculate the statistics of a reaction-limited multistep birth-death process, or chemical reaction, that includes as elementary steps branching $A\to 2A$ and annihilation $2A\to 0$. The spectral method employs the generating function technique in conjunction with the Sturm-Liouville theory of linear differential operators. We focus on the limit when the branching rate is much higher than the annihilation rate and obtain accurate analytical results for the complete probability distribution (including large deviations) of the metastable long-lived state and for the extinction time statistics. The analytical results are in very good agreement with numerical calculations. Furthermore, we use this example to settle the issue of the “lacking” boundary condition in the spectral formulation.

Computing Granger causal relations among bivariate experimentally observed time series has received increasing attention over the past few years. Such causal relations, if correctly estimated, can yield significant insights into the dynamical organization of the system being investigated. Since experimental measurements are inevitably contaminated by noise, it is thus important to understand the effects of such noise on Granger causality estimation. The first goal of this paper is to provide an analytical and numerical analysis of this problem. Specifically, we show that, due to noise contamination, (1) spurious causality between two measured variables can arise and (2) true causality can be suppressed. The second goal of the paper is to provide a denoising strategy to mitigate this problem. Specifically, we propose a denoising algorithm based on the combined use of the Kalman filter theory and the expectation-maximization algorithm. Numerical examples are used to demonstrate the effectiveness of the denoising approach.

We study the ordering dynamics of polymer crystallization using molecular dynamics simulations, in which the polymers are confined to small nanodomains surrounded by a noncrystalline medium. Although the adsorption process and surface diffusion of polymer chains play a major role in the case of the crystalline interface, the domain interface which consists of noncrystalline medium does not have such a crystal substrate to induce the growth of a crystal layer, which may lead to different ordering dynamics. We found that existence of a noncrystalline domain interface has two opposite effects. In the case of semiflexible polymer systems, the domain interface accelerates crystallization in the initial period, whereas it suppresses crystallization in the intermediate or late period. When the rigidity of polymer chains increases, the acceleration effect of the initial crystallization induced by the domain interface is sometimes hidden by spontaneous homogeneous nucleation. These ordering behaviors can be explained by the restriction on the local chain direction near the domain surface in the crystal nucleation stage and the restriction of large orientation relaxation and coalescence in the crystal growth stage. Simulation results reveal that the confinement by the noncrystalline medium does not have a simple effect on the polymer crystallization dynamics, but has various conflicting effects combined with the time stage, the rigidity of polymer chains, and the strength of the surrounding domain interface.

The present experiments concern electron interactions with a film of short single strands of DNA covered by 3 monolayers of water, which corresponds to 5.25 water molecules per nucleotide. We report on the desorption of ${\mathrm{H}}^{-}$, ${\mathrm{O}}^{-}$, $\mathrm{O}{\mathrm{H}}^{-}$ from this target induced by $3–20\mathrm{eV}$ electrons. Below $15\mathrm{eV}$, these anions emanate principally from a new type of dissociative core-excited transient anions formed via electron capture by a DNA-${\mathrm{H}}_2\mathrm{O}$ complex. A smaller portion of the ${\mathrm{H}}^{-}$ desorption signal arises from weakly bonded ${\mathrm{H}}_2\mathrm{O}$ molecules. The overall anion yield from DNA is increased by a factor of 1.6 owing to the presence of water.

Properties of a quantum mushroom billiard in the form of a superconducting microwave resonator have been investigated. They reveal unexpected nonuniversal features such as, e.g., a supershell effect in the level density and a dip in the nearest-neighbor spacing distribution. Theoretical predictions for the quantum properties of mixed systems rely on the sharp separability of phase space—an unusual property met by mushroom billiards. We however find deviations which are ascribed to the presence of dynamic tunneling.

The entropy production rate for an open quantum system with a classically chaotic limit has been previously argued to be independent of $\hslash$ and $D$, the parameter denoting coupling to the environment, and to be equal to the sum of generalized Lyapunov exponents, with these results applying in the near-classical regime. We present results for a specific system going well beyond earlier work, considering how these dynamics are altered for the Duffing problem by changing $\hslash$,$D$ and show that the entropy dynamics have a transition from classical to quantum behavior that scales, at least for a finite time, as a function of ${\hslash }^2∕D$.

We present methods to detect the transitions from quasiperiodic to chaotic motion via strange nonchaotic attractors (SNAs). These procedures are based on the time needed by the system to recur to a previously visited state and a quantification of the synchronization of trajectories on SNAs. The applicability of these techniques is demonstrated by detecting the transition to SNAs or the transition from SNAs to chaos in representative quasiperiodically forced discrete maps. The fractalization transition to SNAs—for which most existing diagnostics are inadequate—is clearly detected by recurrence analysis. These methods are robust to additive noise, and thus can be used in analyzing experimental time series.

The phase fluctuations of arbitrarily nonlinearity- and dispersion-managed solitons propagating in a noisy fiber channel are studied both analytically and numerically. We begin by discussing the stability problem of such linearly chirped solitons with a full linear stability analysis. It is shown that these sophisticated solitons possess an enhanced stability against perturbations and therefore hold promise for applications in optical telecommunications. We then make an approach to the phase statistics of these solitons, which stems from an inevitable random walk in phase evolutions due to amplified spontaneous emission noise. By using the variational approach together with impulse-response (Green) functions, an elegant closed-form expression for the phase variance is derived based on an unconstrained self-similar soliton ansatz in which the effect of chirp fluctuations has been critically taken into account as well as the dispersive and nonlinear effects. An inspection of the intriguing subtleties of the interplay among these effects reveals that the chirp fluctuations effect does play an important role in the control of nonlinear phase noise via fiber dispersion, independently of whether the input solitons are initially chirped or not. Our analytical result also offers many possibilities of optimally manipulating nonlinear phase noise with engineered fiber parameters that may lead to the steady pulse propagation, broadening, or compression under favorable parametric conditions. Last, we demonstrate our result by several convincible examples and show an excellent agreement between analytical predictions and numerical simulations.

We revisit the classical stability versus accuracy dilemma for the lattice Boltzmann methods (LBM). Our goal is a stable method of second-order accuracy for fluid dynamics based on the lattice Bhatnager-Gross-Krook method (LBGK). The LBGK scheme can be recognized as a discrete dynamical system generated by free flight and entropic involution. In this framework the stability and accuracy analysis are more natural. We find the necessary and sufficient conditions for second-order accurate fluid dynamics modeling. In particular, it is proven that in order to guarantee second-order accuracy the distribution should belong to a distinguished surface—the invariant film (up to second order in the time step). This surface is the trajectory of the (quasi)equilibrium distribution surface under free flight. The main instability mechanisms are identified. The simplest recipes for stabilization add no artificial dissipation (up to second order) and provide second-order accuracy of the method. Two other prescriptions add some artificial dissipation locally and prevent the system from loss of positivity and local blowup. Demonstration of the proposed stable LBGK schemes are provided by the numerical simulation of a one-dimensional (1D) shock tube and the unsteady 2D flow around a square cylinder up to Reynolds number $\mathrm{Re}\sim 20000$.

There are two disparate formulations of the entropic lattice Boltzmann scheme: one of these theories revolves around the analog of the discrete Boltzmann $H$ function of standard extensive statistical mechanics, while the other revolves around the nonextensive Tsallis entropy. It is shown here that it is the nonenforcement of the pressure tensor moment constraints that lead to extremizations of entropy resulting in Tsallis-like forms. However, with the imposition of the pressure tensor moment constraint, as is fundamentally necessary for the recovery of the Navier-Stokes equations, it is proved that the entropy function must be of the discrete Boltzmann form. Three-dimensional simulations are performed which illustrate some of the differences between standard lattice Boltzmann and entropic lattice Boltzmann schemes, as well as the role played by the number of phase-space velocities used in the discretization.

We investigate an idealized model for the size reduction and smoothing of a polygonal rock due to repeated chipping at corners. Each chip is sufficiently small so that only a single corner and a fraction of its two adjacent sides are cut from the object in a single chipping event. After many chips have been cut away, the resulting shape of the rock is generally anisotropic, with facet lengths and corner angles distributed over a broad range. Although a well-defined shape is quickly reached for each realization, there are large fluctuations between realizations.

The analysis of transitions in stochastic neurodynamical systems is essential to understand the computational principles that underlie those perceptual and cognitive processes involving multistable phenomena, like decision making and bistable perception. To investigate the role of noise in a multistable neurodynamical system described by coupled differential equations, one usually considers numerical simulations, which are time consuming because of the need for sufficiently many trials to capture the statistics of the influence of the fluctuations on that system. An alternative analytical approach involves the derivation of deterministic differential equations for the moments of the distribution of the activity of the neuronal populations. However, the application of the method of moments is restricted by the assumption that the distribution of the state variables of the system takes on a unimodal Gaussian shape. We extend in this paper the classical moments method to the case of bimodal distribution of the state variables, such that a reduced system of deterministic coupled differential equations can be derived for the desired regime of multistability.

Recent experimental and theoretical studies suggest that, although topology is the determinant factor in protein folding, especially for small single-domain proteins, energetic factors also play an important role in the folding process. The ribosomal protein S6 has been subjected to intensive studies. A radical change of the transition state in its circular permutants has been observed, which is believed to be caused by a biased distribution of contact energies. Since the simplistic topology-only $\mathrm{G}\overline{\mathrm{o}}$-like model is not able to reproduce such an observation, we modify the model by introducing variable contact energies between residues based on their physicochemical properties. The modified $\mathrm{G}\overline{\mathrm{o}}$-like model can successfully reproduce the $\Phi$-value distributions, folding nucleus, and folding pathways of both the wild-type and circular permutants of S6. Furthermore, by comparing the results of the modified and the simplistic models, we find that the hydrophobic effect constructs the major force that balances the loop entropies. This may indicate that nature maintains the folding cooperativity of this protein by carefully arranging the location of hydrophobic residues in the sequence. Our study reveals a strategy or mechanism used by nature to get out of the dilemma when the native structure, possibly required by biological function, conflicts with folding cooperativity. Finally, the possible relationship between such a design of nature and amyloidosis is also discussed.

We consider the impact of the effective gravitational acceleration $g_{eff}$ on gravity-driven granular shear flow utilizing a tumbler of radius $R$ rotating at angular velocity $\omega$ when $g_{eff}$ is varied up to 25 times the gravitational level on Earth in a large centrifuge. The Froude number $\mathrm{Fr}={\omega }^{2}R∕g_{eff}$ is shown to be the proper scaling to characterize the effect of gravity on the angle of repose of the flowing layer. Likewise, transitions between flow regimes depend on $\mathrm{Fr}$. Furthermore, the thickness of the flowing layer is independent of the $g$ level. These results provide a starting point for understanding granular flows on planetary bodies with $g_{eff}$ different than on Earth for application to planetary exploration and formation of geologic features.

Vortexlike swarming behavior is observed in a wide range of biological systems. In the work reported here a discrete particle model is used to investigate the onset of such vortexlike behavior in a swarm of interacting particles. A constrained minimization of the total effective energy of the swarm of particles is performed, with the total angular momentum of the swarm conserved. It is shown that the emergence of vortexlike behavior can then be viewed as a constrained minimum energy configuration which the swarm relaxes into.

Two species involved in a simple, fast reaction tend to become segregated in patches composed of a single of these reactants. These patches are separated by a boundary where the stoichiometric condition is satisfied and the reaction occurs, fed by diffusion. Stirred by advection, this boundary and the concentration fields within the patches may tend to present multiple-scale characteristics. Based on this segregated state, this paper aims at evaluating the temporal evolutions of the length of the boundary and diffusive flux of reactants across it, when concentrations presenting initial self-similar fluctuations are advected by a singular vortex. First the two sources of singularity, i.e., the self-similar initial conditions and the singular vortex, are considered isolatedly. On the one hand, self-similar initial conditions are imposed to a diffusion-reaction system, for one- and two-dimensional cases. On the other hand, an imposed singular vortex advects initially on/off concentration fields, in combination with diffusion and reaction. This problem is addressed analytically, by characterizing the boundary by a box-counting dimension and the concentration fields by a Hölder exponent, and numerically, by direct numerical simulations of the advection-diffusion-reaction equations. Second, the way the two sources hang together shows that, depending on the self-similar properties of the initial concentration fields, the vortex promotes the chemical activity close to its inner smoothed-out core or close to the outer region where the boundary starts to spiral. For all the considered situations, the length of the boundary and the global reaction speed are found to evolve algebraically with time after a short transient and a good agreement is found between the analytical and numerical scaling laws.

We address the breakup (splitting) of multisoliton solutions of the nonlinear Schrödinger equation (NLSE), occurring due to linear loss. Two different approaches are used for the study of the splitting process. The first one is based on the direct numerical solution of the linearly damped NLSE and the subsequent analysis of the eigenvalue drift for the associated Zakharov-Shabat spectral problem. The second one involves the multisoliton adiabatic perturbation theory applied for studying the evolution of the solution parameters, with the linear loss taken as a small perturbation. We demonstrate that in the case of strong nonadiabatic loss the evolution of the Zakharov-Shabat eigenvalues can be quite nontrivial. We also demonstrate that the multisoliton breakup can be correctly described within the framework of the adiabatic perturbation theory and can take place even due to small linear loss. Eventually we elucidate the occurrence of the splitting and its dependence on the phase mismatch between the solitons forming a two-soliton bound state.

Contact detection is a general problem of many physical simulations. This work presents a $O\left(N\right)$ multigrid method for general contact detection problems (MGCD). The multigrid idea is integrated with contact detection problems. Both the time complexity and memory consumption of the MGCD are $O\left(N\right)$. Unlike other methods, whose efficiencies are influenced strongly by the object size distribution, the performance of MGCD is insensitive to the object size distribution. We compare the MGCD with the no binary search (NBS) method and the multilevel boxing method in three dimensions for both time complexity and memory consumption. For objects with similar size, the MGCD is as good as the NBS method, both of which outperform the multilevel boxing method regarding memory consumption. For objects with diverse size, the MGCD outperform both the NBS method and the multilevel boxing method. We use the MGCD to solve the contact detection problem for a granular simulation system based on the discrete element method. From this granular simulation, we get the density property of monosize packing and binary packing with size ratio equal to 10. The packing density for monosize particles is 0.636. For binary packing with size ratio equal to 10, when the number of small particles is 300 times as the number of big particles, the maximal packing density 0.824 is achieved.

We provide a perturbative analytical treatment of the soliton self-frequency-shift (SSFS) in optical fibers including the main physical mechanisms limiting the SSFS, such as the high-order dispersion, the wavelength dependence of the effective mode area, and optical loss. We use this approach to estimate the frequency shift of a soliton with adiabatically varying local parameters and compare this estimate with the results of numerical simulations for SSFS in photonic-crystal fibers. This comparison shows that, in many situations of practical interest, the proposed approach can adequately predict important tendencies of SSFS, and allows a fair estimation of characteristic length scales for the mechanisms limiting the SSFS.