Subwavelength vortical plasmonic lattice solitons.

We present a theoretical study of vortical plasmonic lattice solitons, which form in two-dimensional arrays of metallic nanowires embedded into nonlinear media with both focusing and defocusing Kerr nonlinearities. Their existence, stability, and subwavelength spatial confinement are investigated in detail.

Soliton drift, rebound, penetration, and trapping at the interface between media with uniform and spatially modulated nonlinearities.

We numerically study soliton dynamics at the interface between media with uniform and periodically modulated self-focusing nonlinearities. We find that the soliton can spontaneously laterally drift if its power is large enough. The drift direction can be controlled by changing the sign of the nonlinear modulation coefficient. We also study the dynamics of soliton launched with a tilt angle toward the nonlinear interface and reveal unique features, such as soliton rebound, penetration, and trapping.

Twin-vortex solitons in nonlocal nonlinear media.

We consider soliton formation in thermal nonlinear media bounded by rectangular cross sections and uncover what we believe to be a new class of nonlinear stationary topological state. Specifically, we find that stationary higher-order vortex states in standard shapes do not exist, but rather they take the form of multiple spatially separated single-charge singularities nested in an elliptical beam. Double-charge states are found to be remarkably robust despite their shape asymmetry and phase-singularity splitting. States with higher topological charges are found to be unstable.

Heat conduction in a three-dimensional momentum-conserving anharmonic lattice.

Heat conduction in three-dimensional anharmonic lattices was numerically studied by the Green-Kubo theory. For a given lattice width W, a dimensional crossover is generally observed to occur at a W-dependent threshold of the lattice length. Lattices shorter than W will display a 3D behavior while lattices longer than W will display a 1D behavior. In the 3D regime, the heat current autocorrelation function was found to show a power-law decay as a function of the time lag τ as τ^{ß} with ß=-1.2. This indicates normal heat conduction. However, the decay exponent deviates significantly from the conventional theoretical value of ß=-1.5. A flat power spectrum S(ω) of the global heat current in the low-frequency limit was also observed in the 3D regime. This provides not only an alternative verification of normal heat conduction but also a clear physical insight into its origin.

Pattern formation controlled by time-delayed feedback in bistable media.

Effects of time-delayed feedback on pattern formation are studied both numerically and theoretically in a bistable reaction-diffusion model. The time-delayed feedback applied to the activator and/or the inhibitor alters the behavior of the nonequilibrium Ising-Bloch (NIB) bifurcation. If the intensities of the feedbacks applied to the two species are identical, only the velocities of Bloch fronts are changed. If the intensities are different, both the critical point of the NIB bifurcation and the threshold of stability of front to transverse perturbations are changed. The effect of time-delayed feedback on the activator opposes the effect of time-delayed feedback on the inhibitor. When the time-delayed feedback is applied individually to one of the species, positive and negative feedbacks make the bifurcation point shift to different directions. The time-delayed feedback provides a flexible way to control the NIB bifurcation and the pattern formation.

Light bullets in Bessel optical lattices with spatially modulated nonlinearity.

We address the stability of light bullets supported by Bessel optical lattices with out-of-phase modulation of the linear and nonlinear refractive indices. We show that spatial modulation of the nonlinearity significantly modifies the shapes and stability domains of the light bullets. The addressed bullets can be stable, provided that the peak intensity does not exceed a critical value. We show that the width of the stability domain in terms of the propagation constant may be controlled by varying the nonlinearity modulation depth. In particular, we show that the maximum energy of the stable bullets grows with increasing nonlinearity modulation depth.

Power-dependent soliton steering in thermal nonlinear media.

We address the existence and properties of optical solitons excited in thermal nonlinear media with a transverse refractive index gradient. The interplay between the nonlocality of the thermal nonlinearity and the linear refractive index enables generating controllable switching from surface soliton propagating near the sample edges to bulk solitons. Beam steering associated with the different soliton output locations can be achieved by varying the input light intensity.

Role of ionization in orientation dependence of molecular high-order harmonic generation.

We investigate the orientation dependence of high-order harmonic generation (HHG) from O(2) and CO(2) molecules using the strong-field approximation (SFA). Our simulations reveal the important modulation of the ionization to the HHG orientation dependence, especially at larger orientation angles. By virtue of a simplified model arising from the SFA, we show that this modulation can be read from the harmonic order where the HHG spectra at different orientation angles intersect. These results give suggestions on probing the molecular structure and dynamics using HHG.

Reading molecular messages from high-order harmonic spectra at different orientation angles.

We investigate the orientation dependence of high-order harmonic generation (HHG) from H(2) (+) with different internuclear distances irradiated by intense laser fields both numerically and analytically. The calculated molecular HHG spectra are found to be sensitive to the molecular axis orientation relative to incident laser field polarization and internuclear separation. In particular, our simulations demonstrate that at certain harmonic orders the envelopes of the HHG spectra taken at different orientation angles intersect. Moreover, the position of intersection is largely independent of the laser intensity while strongly dependent on the internuclear separation. This striking "intersection" phenomenon is identified as arising due to intramolecular two-center interference in the HHG and can be used to probe the molecular instantaneous structure.

Noise effects in the ac-driven Frenkel-Kontorova model.

The noise effects on dynamical-mode-locking phenomena in the ac-driven dissipative Frenkel-Kontorova model are studied by molecular-dynamics simulations. It was found that the noise strongly influences the properties of the Shapiro steps and the way they respond to the changing of system parameters. The increase of temperature produces the melting of the Shapiro steps, while the critical depinning force is significantly reduced. The oscillatory form of the amplitude dependence is strongly affected where the Bessel-like form changes as the temperature increases. In the frequency dependence of the Shapiro steps, due to the decrease of the dc threshold value, noise may transfer the system to the high-amplitude regime where oscillations of the step width with frequency or period of the ac force appear. These phenomena will additionally destabilize the steps in real systems and significantly limit the region of parameters where dynamical-mode-locking phenomena could be observed.

Transition from the exhibition to the nonexhibition of negative differential thermal resistance in the two-segment Frenkel-Kontorova model.

An extensive study of the one-dimensional two-segment Frenkel-Kontorova (FK) model reveals a transition from the counterintuitive existence to the ordinary nonexistence of a negative-differential-thermal-resistance (NDTR) regime, when the system size or the intersegment coupling constant increases to a critical value. A "phase" diagram which depicts the relevant conditions for the exhibition of NDTR was obtained. In the existence of a NDTR regime, the link at the segment interface is weak and therefore the corresponding exhibition of NDTR can be explained in terms of effective phonon-band shifts. In the case where such a regime does not exist, the theory of phonon-band mismatch is not applicable due to sufficiently strong coupling between the FK segments. The findings suggest that the behavior of a thermal transistor will depend critically on the properties of the interface and the system size.

Spontaneously periodic wave generation in coupled excitable media.

We studied a modified reaction-diffusion model theoretically by coupling two ideal excitable media systems. In the simulated homogeneous system, we observed the propagation of reaction-diffusion wave trains that required no external force after the initial stimulation. We investigated the dependence of the system's oscillation patterns on model parameters, and we discussed the influence of the different dynamic constants of the individual coupled systems on the dynamics of the coupled systems. Some complex two-dimensional patterns generated by our model are shown. We also found similar phenomena in the models for catalytic CO oxidation on Pt(110), and for cardiac tissue.

Negative differential thermal resistance induced by ballistic transport.

Using nonequilibrium molecular-dynamics simulations, we study the temperature dependence of the negative differential thermal resistance that appears in two-segment Frenkel-Kontorova lattices. We apply the theoretical method based on Landauer equation to obtain the relationship between the heat current and the temperature, which states a fundamental interpretation about the underlying physical mechanism of the negative differential thermal resistance. The temperature profiles and transport coefficients are demonstrated to explain the crossover from diffusive to ballistic transport. The finite-size effect is also discussed.

Suppression of spirals and turbulence in inhomogeneous excitable media.

Suppression of spiral and turbulence in inhomogeneous media due to local heterogeneity with higher excitability is investigated numerically. When the inhomogeneity is small, control tactics by boundary periodic forcing (BPF) is effective against the existing spiral and turbulence. When the inhomogeneity of excitability is large, a rotating electric field (REF) is utilized to "smooth" regional heterogeneity based on driven synchronization. Consequently, a control approach combining BPF with REF is proposed to suppress the spiral and turbulence. The underlying mechanism of successful suppression is discussed in terms of dispersion relation.

Thermal conductivity of anharmonic lattices: effective phonons and quantum corrections.

We compare two effective phonon theories, which have both been applied recently to study heat conduction in anharmonic lattices. In particular, we study the temperature dependence of the thermal conductivity of the Fermi-Pasta-Ulam beta model via the Debye formula, showing the equivalence of both approaches. The temperature for the minimum of the thermal conductivity and the corresponding scaling behavior are analytically calculated, which agree well with the result obtained from nonequilibrium simulations. We also give quantum corrections for the thermal conductivity from quantum self-consistent phonon theory. The vanishing behavior at the low temperature regime and the existence of an umklapp peak are qualitatively consistent with experimental studies.

Computation of the temperature dependence of the heat capacity of complex molecular systems using random color noise.

We propose a method for computing the temperature dependence of the heat capacity in complex molecular systems. The proposed scheme is based on the use of the Langevin equation with low-frequency color noise. We obtain the temperature dependence of the correlation time of random noises, which enables us to model the partial thermalization of high-frequency vibrations. This purely quantum effect is responsible for the decreasing behavior of the specific heat c(T) in the low-temperature regime. By applying the method to carbon nanotubes and polyethylene molecules, we show that the consideration of the color noise in the Langevin equation allows us to reproduce the temperature evolution of the specific heat with a good accuracy.

Active and passive control of spiral turbulence in excitable media.

The influence of a spatially localized heterogeneity defect, defined by failure of the diffusion effect, on spiral turbulence suppression in two-dimensional excitable media is studied numerically, based on the Bär model. It is shown that in certain parameter regions spiral turbulence without the defect can be suppressed by a boundary periodic forcing (called active control) if the forcing frequency is properly chosen. However, with a sufficiently large defect this active control method no longer works due to the wake turbulence following the defect. We suggest an auxiliary method of enclosing the defect with a thin layer of material of high excitability (called passive control) to screen the interaction between the defect and the turbulence and to restore the global control effect of the periodic forcing. The possible application of the method in cardiac defibrillation is discussed.

Scaling and the thermal conductivity of the Frenkel-Kontorova model.

We have studied the dependence of the thermal conductivity kappa on the strength of the interparticle potential lambda and the strength of the external potential beta in the Frenkel-Kontorova model. We found that the functional relation can be expressed in a scaling form, kappa proportional, variantlambda;{32}/beta;{2} . This result is first obtained by nonequilibrium molecular dynamics. It is then confirmed by two analytical methods, the self-consistent phonon theory and the self-consistent stochastic reservoirs method. The thermal conductivity kappa is therefore a decreasing functon of beta and an increasing function of lambda.

Amplitude and frequency dependence of the Shapiro steps in the dc- and ac-driven overdamped Frenkel-Kontorova model.

The amplitude and frequency dependence of dynamical mode locking phenomena in the dc- and ac-driven overdamped Frenkel-Kontorova model is studied by molecular-dynamics simulations. It was found that the Shapiro steps and the critical depinning force exhibit very complex behavior. The form of amplitude dependence is determined by the frequency of ac force, where the Bessel-type oscillations appear at the high frequencies. With a changing of frequency, after initial increase, the critical depinning force saturates, while the step width remains strongly frequency dependent even at the high frequencies. The dependence of frequency is strongly influenced by the amplitude of ac force where, in the large amplitude regime, the oscillations of the step width and the critical depinning force have been observed at the low frequencies. In the physical processes that stay behind amplitude and frequency oscillations of the step size, an analogy between the influence of amplitude and the period of the ac force is revealed. These oscillations are directly related to the existence and the stability of the interference phenomena in the real systems.

Dynamical mode locking in commensurate structures with an asymmetric deformable substrate potential.

The overdamped dynamics in the commensurate structures of the one-dimensional Frenkel-Kontorova model subjected to a parametrized deformable periodic substrate potential and driven by a periodic force is examined. It was found that when the shape of the substrate potential starts to deviate from the standard one, new subharmonic steps appear in the response function even in the structures with an integer value of average interparticle distance while the critical depinning force can even decrease for some values of system parameters. These novel phenomena could be particularly relevant for the charge-density wave systems, vortex lattices, and systems of Josephson-junction arrays.