The ensemble averaged power scattered in and out of lossless chaotic cavities decays as a power law in time for large times. In the case of a pulse with a finite duration, the power scattered from a single realization of a cavity closely tracks the power-law ensemble decay initially, but eventually transitions to an exponential decay. In this paper, we explore the nature of this transition in the case of coupling to a single port. We find that for a given pulse shape, the properties of the transition are universal if time is properly normalized. We define the crossover time to be the time at which the deviations from the mean of the reflected power in individual realizations become comparable to the mean reflected power. We demonstrate numerically that, for randomly chosen cavity realizations and given pulse shapes, the probability distribution function of reflected power depends only on time, normalized to this crossover time.

We compare the dynamics of the periodically forced FitzHugh-Nagumo oscillator in its relaxation regime to that of a one-dimensional discrete map of the circle derived from the phase-resetting response of this oscillator (the “phase-resetting map”). The forcing is a periodic train of Gaussian-shaped pulses, with the width of the pulses much shorter than the intrinsic period of the oscillator. Using numerical continuation techniques, we compute bifurcation diagrams for the periodic solutions of the full differential equations, with the stimulation period being the bifurcation parameter. The period-1 solutions, which belong either to isolated loops or to an everywhere-unstable branch in the bifurcation diagram at sufficiently small stimulation amplitudes, merge together to form a single branch at larger stimulation amplitudes. As a consequence of the fast-slow nature of the oscillator, this merging occurs at virtually the same stimulation amplitude for all the period-1 loops. Again using continuation, we show that this stimulation amplitude corresponds, in the circle map, to a change of topological degree from one to zero. We explain the origin of this coincidence, and also discuss the translational symmetry properties of the bifurcation diagram.

We investigate the dynamics of $N$ moving point vortices, whose vorticity changes periodically between a finite value and zero. The dynamics of such blinking vortices is chaotic, but the degree of chaoticity, expressed in terms of finite size Lyapunov exponents, decreases monotonically with time. In contrast to traditional point vortices, the average diameter of the blinking vortex system increases in time. The average size follows a subdiffusive power law scaling $\sim t^{\sigma }$, with $\sigma <1∕2$. This expanding vortex system provides a flow which is in between closed and open flows. The advection dynamics generated by the blinking vortices is also studied, and leads to dye distribution patterns which are much more realistic than those of the classical point vortex problems, and can be characterized by a dimension less than 2.

We study the nonlinear dynamics of collective excitation in an $N$-site $XXZ$ quantum spin chain, which is manipulated by an oblique magnetic field. We show that, when the tilted field is applied along the magic angle, ${\theta }_0=\pm \text{arccos}\sqrt{1∕3}$, the anisotropic Heisenberg spin chain becomes isotropic and thus an freely propagating spin wave is stimulated. Also, in the regime of tilted angles larger and smaller than the magic angle, two types of nonlinear excitations appear: bright and dark solitons.

Telechelic star polymers are macromolecules with functionalized, mutually attractive end groups. We employ computer simulations on a lattice to investigate the phase behavior of trifunctional telechelic stars as a function of the fraction $\lambda$ of attractive terminal monomers. We find macrophase separation that disappears at some value $0.4<\lambda <0.5$, at which point it is replaced by self-organization into interconnected micelles. We supplement the thermodynamics with a morphometric analysis that provides insight into the mesostructure of the resulting aggregates.

We evaluate the azimuthal anchoring energy of a grooved surface by calculating numerically the Frank elastic energy of a nematic cell composed of the grooved surface and a flat one with rigid azimuthal anchoring, where the director is fixed along the $\varphi$ direction. We pay attention to the surface anchoring induced by elastic distortions of the director due to its contact with a nonflat surface, which impose local planar degenerate anchoring. Surface anchoring of this kind was analyzed analytically for shallow grooves by Berreman [Phys. Rev. Lett. 28, 1683 (1972)] and critically reexamined by the present authors [Phys. Rev. Lett. 98, 187803; 99, 139902(E) (2007)]. We consider two types of surface. one is a surface with one-dimensional sinusoidal parallel grooves, and the other is a surface with two-dimensional square patterns whose surface height is given by a sum of two sinusoidal functions with orthogonal wave vectors. The total energy is the sum of the anchoring energy and the twist energy in the bulk. For the calculation of the twist energy to be eliminated and the evaluation of the azimuthal-angle dependence of the anchoring energy, the “average” azimuthal angle at the bottom, $\phi \left(0\right)$, must be determined. We adopt two methods to determine $\phi \left(0\right)$. One is a simple extrapolation of the twist deformation in the bulk. The other relates $\phi \left(0\right)$ to the variation of the total Frank elastic energy with respect to $\varphi$. Our calculations indicate that both methods give essentially the same results, which indicates the consistency of those two methods. We also show that, for a surface with square patterns, the agreement between theory and numerical calculations is quite good even when the maximum of the surface slope is around 0.4, which theory assumes is much smaller than unity. When the surface slope is of order unity, the deviation of numerical results from theory crucially depends on the the surface elastic constant $K_{24}$.

In this paper, the response of single three-dimensional phantom and self-avoiding polymers to localized step strains are studied for two cases in the absence of hydrodynamic interactions: (i) Polymers tethered at one end with the strain created at the point of tether, and (ii) free polymers with the strain created in the middle of the polymer. The polymers are assumed to be in their equilibrium state before the step strain is created. It is shown that the strain relaxes as a power law in time $t$ as $t^{-\eta }$. While the strain relaxes as $1∕t$ for the phantom polymer in both cases; the self-avoiding polymer relaxes its strain differently in case (i) than in case (ii): As $t^{-(1+\nu )∕(1+2\nu )}$ and as $t^{-2∕(1+2\nu )}$, respectively. Here $\nu$ is the Flory exponent for the polymer, with value $\approx 0.588$ in three dimensions. Using the mode expansion method, exact derivations are provided for the $1∕t$ strain relaxation behavior for the phantom polymer. However, since the mode expansion method for self-avoiding polymers is nonlinear, similar theoretical derivations for the self-avoiding polymer proves difficult to provide. Only simulation data are therefore presented in support of the $t^{-(1+\nu )∕(1+2\nu )}$ and the $t^{-2∕(1+2\nu )}$ behavior. The relevance of these exponents for the anomalous dynamics of polymers is also discussed.

The low-frequency limit of the electrical conductivity (dc conductivity) of differently flexible polyions in aqueous solutions has been measured over an extended polyion concentration range, covering both the dilute and semidilute (entangled and unentangled) regime, up to the concentrated regime. The data have been analyzed taking into account the different flexibility of the polymer chains according to the scaling theory of polyion solutions, in the case of flexible polyions, and according to the Manning model, in the case of rigid polyions. In both cases, the fraction $f$ of free counterions, released into the aqueous phase from the ionizable polyion groups, has been evaluated and its dependence on the polyion concentration determined. Our results show that the counterion condensation follows at least three different regimes in dependence on the polyion concentration. The fraction $f$ of free counterions remains constant only in the semidilute regime (a region that we have named the Manning regime), while there is a marked dependence on the polyion concentration both in the dilute and in the concentrated regime. These results are briefly discussed in the light of the scaling theory of polyelectrolyte aqueous solutions.

We study the effect of delay on the synchronization of two nerve impulses traveling along two ephaptically coupled, unmyelinated nerve fibers. The system is modeled as a pair of delay-coupled Fitzhugh-Nagumo equations. A multiple-scale perturbation approach is used for the analysis of these equations in the limit of weak coupling. In the absence of delay, two pulses with identical speeds are shown to be entrained precisely. However, as the delay is increased beyond a critical value, we show that this precise entrainment becomes unstable. We make quantitative estimates for the actual values of delay at which this can occur in the case of squid giant axons and compare them with the relevant time scales involved.

The dynamics of lines composed of two monatomic steps of opposite sign and periodically spaced on a crystal surface has been investigated under electromigration. It is found that, when adatoms have a diffusion bias parallel to the step edges, lines may become unstable with respect to shape fluctuation, which may lead to the formation of a pattern composed of antiphase serpentinelike lines.

Frequency entrainment and nonlinear synchronization are commonly observed between simple oscillatory systems, but their occurrence and behavior in continuum fluid systems are much less well understood. Motivated by possible applications to geophysical fluid systems, such as in atmospheric circulation and climate dynamics, we have carried out an experimental study of the interaction of fully developed baroclinic instability in a differentially heated, rotating fluid annulus with an externally imposed periodic modulation of the thermal boundary conditions. In quasiperiodic and chaotic amplitude-modulated traveling wave regimes, the results demonstrate a strong interaction between the natural periodic modulation of the wave amplitude and the externally imposed forcing. This leads to partial or complete phase synchronization. Synchronization effects were observed even with very weak amplitudes of forcing, and were found with both 1:1 and 1:2 frequency ratios between forcing and natural oscillations.

In order to simulate observational and experimental situations, we consider a leak in the phase space of a chaotic dynamical system. We obtain an expression for the escape rate of the survival probability by applying the theory of transient chaos. This expression improves previous estimates based on the properties of the closed system and explains dependencies on the position and size of the leak and on the initial ensemble. With a subtle choice of the initial ensemble, we obtain an equivalence to the classical problem of Poincaré recurrences in closed systems, which is treated in the same framework. Finally, we show how our results apply to weakly chaotic systems and justify a split of the invariant saddle into hyperbolic and nonhyperbolic components, related, respectively, to the intermediate exponential and asymptotic power-law decays of the survival probability.

We introduce a system of linearly coupled parametrically driven damped nonlinear Schrödinger equations, which models a laser based on a nonlinear dual-core waveguide with parametric amplification symmetrically applied to both cores. The model may also be realized in terms of parallel ferromagnetic films, in which the parametric gain is provided by an external field. We analyze spontaneous symmetry breaking (SSB) of fundamental and multiple solitons in this system, which was not studied systematically before in linearly coupled dissipative systems with intrinsic nonlinearity. For fundamental solitons, the analysis reveals three distinct SSB scenarios. Unlike the standard dual-core-fiber model, the present system gives rise to a vast bistability region, which may be relevant to applications. Other noteworthy findings are restabilization of the symmetric soliton after it was destabilized by the SSB bifurcation, and the existence of a generic situation with all solitons unstable in the single-component (decoupled) model, while both symmetric and asymmetric solitons may be stable in the coupled system. The stability of the asymmetric solitons is identified via direct simulations, while for symmetric and antisymmetric ones the stability is verified too through the computation of stability eigenvalues, families of antisymmetric solitons being entirely unstable. In this way, full stability maps for the symmetric solitons are produced. We also investigate the SSB bifurcation of two-soliton bound states (it breaks the symmetry between the two components, while the two peaks in the shape of the soliton remain mutually symmetric). The family of the asymmetric double-peak states may decouple from its symmetric counterpart, being no longer connected to it by the bifurcation, with a large portion of the asymmetric family remaining stable.

A noninvasive optical technique combining digital interferometry in transmission and transparency measurement of concentration is developed to analyze spatiotemporal dynamics of physicochemical systems. This technique allows one to measure simultaneously the two-dimensional (2D) dynamics of concentration and temperature fields in both reactive and nonreactive systems contained inside a transparent cell. When used to experimentally analyze buoyancy-driven fingering of an exothermic autocatalytic chemical front, this method reveals in the 2D temperature field the presence of hot spots where the temperature locally exceeds the adiabatic one.

We consider coherent exciton transport modeled by continuous-time quantum walks on long-range interacting cycles (LRICs), which are constructed by connecting all the two nodes of distance $m$ in the cycle graph. LRIC has a symmetric structure and can be regarded as the extensions of the cycle graph (nearest-neighboring lattice). For small values of $m$, the classical and quantum return probabilities show power law behavior $p\left(t\right)\sim t^{-0.5}$ and $\pi \left(t\right)\sim t^{-1}$, respectively. However, for large values of $m$, the classical and quantum efficiency scales as $p\left(t\right)\sim t^{-1}$ and $\pi \left(t\right)\sim t^{-2}$. We give a theoretical explanation of this transition using the method of stationary phase approximation. In the long time limit, depending on the network size $N$ and parameter $m$, the limiting probability distributions of quantum transport show various patterns. When the network size $N$ is an even number, we find an asymmetric transition probability of quantum transport between the initial node and its opposite node. This asymmetry depends on the precise values of $N$ and $m$. Finally, we study the transport processes in the presence of traps and find that the survival probability decays faster on networks of large $m$.

The doubly deprotonated $[\mathrm{Asn},{\mathrm{Val}}^5]$ angiopeptide, in the gas phase, was irradiated with $266\mathrm{nm}$ photons. The time of flight (TOF) of the products formed following photoabsorption, namely, the monoanion and neutral fragments, was recorded with submicrosecond time resolution. Monte Carlo simulations of the TOF of the neutral fragments indicate that the dissociation occurs faster than $100\mathrm{ns}$. A similar experiment performed on the ${\mathrm{Val}}^5$ angiopeptide also yielded a dissociation time shorter than $100\mathrm{ns}$. We suggest dissociation mechanisms that account for the different number of photons required for the release of $\mathrm{C}{\mathrm{O}}_2$.

We propose a multiscale approach to understand the physics related to ion-beam cancer therapy. It allows the calculation of the probability of DNA damage as a result of irradiation of tissues with energetic ions, up to $430\mathrm{MeV}∕\mathrm{u}$. This approach covers different scales, starting from the large scale, defined by the ion stopping, followed by a smaller scale, defined by secondary electrons and radicals, and ending with the shortest scale, defined by interactions of secondaries with the DNA. We present calculations of the probabilities of single and double strand breaks of DNA, suggest a way to further expand such calculations, and also make some estimates for glial cells exposed to radiation.

We define a minimal model of traffic flows in complex networks in order to study the trade-off between topological-based and traffic-based routing strategies. The resulting collective behavior is obtained analytically for an ensemble of uncorrelated networks and summarized in a rich phase diagram presenting second-order as well as first-order phase transitions between a free-flow phase and a congested phase. We find that traffic control improves global performance, enlarging the free-flow region in parameter space only in heterogeneous networks. Traffic control introduces nonlinear effects and, beyond a critical strength, may trigger the appearance of a congested phase in a discontinuous manner. The model also reproduces the crossover in the scaling of traffic fluctuations empirically observed on the Internet.

We study synchronization of unidirectionally coupled optical bistable systems. In particular, we consider two semiconductor lasers with an external cavity, which exhibit, when isolated, coexistence of two different attractors: fixed point and chaos, fixed point and one periodic orbit, and two periodic orbits with different periods. The analysis is performed with a cross-correlation function between the master and slave laser oscillations calculated with model equations based on the Lang-Kobayashi approach. Depending on both the laser operating point and the coupling strength, different bifurcations (Hopf, period doubling, saddle node, torus, and crisis) and diverse dynamical regimes (steady state, periodicity, quasiperiodicity, bistability, and chaos) occur in the route from asynchronous motion to complete synchronization. We show some similarities and differences between synchronization of monostable and bistable lasers.

We present microwave measurements for the density and spatial correlation of current critical points in an open billiard system and compare them with new and previous predictions of the random-wave model (RWM). In particular, due to an improvement of the experimental setup, we determine experimentally the spatial correlation of saddle points of the current field. An asymptotic expression for the vortex-saddle and saddle-saddle correlation functions based on the RWM is derived, with experiment and theory agreeing well. We also derive an expression for the density of saddle points in the presence of a straight boundary with general mixed boundary conditions in the RWM and compare with experimental measurements of the vortex and saddle density in the vicinity of a straight wall satisfying Dirichlet conditions.