Scaling analysis of negative differential thermal resistance.

Negative differential thermal resistance (NDTR) can be generated for any one-dimensional heat flow with a temperature-dependent thermal conductivity. In a system-independent scaling analysis, the general condition for the occurrence of NDTR is found to be an inequality with three scaling exponents: n(1)n(2) < -(1+n(3)), where n(1) ∈ (-∞,+∞) describes a particular way of varying the temperature difference, and n(2) and n(3) describe, respectively, the dependence of the thermal conductivity on an average temperature and on the temperature difference. For cases with a temperature-dependent thermal conductivity, i.e. n(2) ≠ 0, NDTR can always be generated with a suitable choice of n(1) such that this inequality is satisfied. The results explain the illusory absence of a NDTR regime in certain lattices and predict new ways of generating NDTR, where such predictions have been verified numerically. The analysis will provide insights for a designing of thermal devices, and for a manipulation of heat flow in experimental systems, such as nanotubes.

Validity of Fourier's law in one-dimensional momentum-conserving lattices with asymmetric interparticle interactions.

We have numerically studied heat conduction in a few one-dimensional momentum-conserving lattices with asymmetric interparticle interactions by the nonequilibrium heat bath method, the equilibrium Green-Kubo method, and the heat current power spectra analysis. Very strong finite-size effects are clearly observed. Such effects make the heat conduction obey a Fourier-like law in a wide range of lattice lengths. However, in yet longer lattice lengths, the heat conductivity regains its power-law divergence. Therefore, the power-law divergence of the heat conductivity in the thermodynamic limit is verified, as is expected by many existing theories.

Logarithmic divergent thermal conductivity in two-dimensional nonlinear lattices.

Heat conduction in three two-dimensional (2D) momentum-conserving nonlinear lattices are numerically calculated via both nonequilibrium heat-bath and equilibrium Green-Kubo algorithms. It is expected by mainstream theories that heat conduction in such 2D lattices is divergent and the thermal conductivity κ increases with lattice length N logarithmically. Our simulations for the purely quartic lattice firmly confirm it. However, very robust finite-size effects are observed in the calculations for the other two lattices, which well explain some existing studies and imply the extreme difficulties in observing their true asymptotic behaviors with affordable computation resources.

Thermal control in graphene nanoribbons: thermal valve, thermal switch and thermal amplifier.

We study the thermal transport in graphene nanoribbons by using nonequilibrium molecular dynamics simulations. It is reported that the three-terminal graphene nanoribbons can perform some functions of thermal devices such as thermal valve, thermal switch and thermal amplifier. Electronic devices have transformed almost all aspects of our lives. It has not escaped our attention that the graphene nanoribbons we have presented here may have similar surprising applications in devices that allow the flow of heat to be controlled in a short future.

Anomalous negative differential thermal resistance in a momentum-conserving lattice.

A two-segment Fermi-Pasta-Ulam lattice has been investigated by using nonequilibrium molecular dynamics. Here we present an anomalous negative differential thermal resistance (NDTR) that has not been reported in Frenkel-Kontorova and φ(4) lattices up to the present. The NDTR disappears in the low-temperature region. The region of NDTR shifts from the large to the small temperature difference region as the system size increases. The anomalous dependence of NDTR on the temperature can be explained as the negative effect induced by the nonlinear coupling. The explanation can also cover the phenomenon of NDTR in momentum-nonconserved lattices.

Double negative differential thermal resistance induced by nonlinear on-site potentials.

We study heat conduction through one-dimensional homogeneous lattices in the presence of the nonlinear on-site potentials containing the bounded and unbounded parts, and the harmonic interaction potential. We observe the occurrence of double negative differential thermal resistance (NDTR); namely, there exist two regions of temperature difference, where the heat flux decreases as the applied temperature difference increases. The nonlinearity of the bounded part contributes to NDTR at low temperatures and NDTR at high temperatures is induced by the nonlinearity of the unbounded part. The nonlinearity of the on-site potentials is necessary to obtain NDTR for the harmonic interaction homogeneous lattices. However, for the anharmonic homogeneous lattices, NDTR even occurs in the absence of the on-site potentials, for example, the rotator model.

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.

Heat conduction in deformable Frenkel-Kontorova lattices: thermal conductivity and negative differential thermal resistance.

Heat conduction through the Frenkel-Kontorova lattices is numerically investigated in the presence of a deformable substrate potential. It is found that the deformation of the substrate potential has a strong influence on heat conduction. The thermal conductivity as a function of the shape parameter is nonmonotonic. The deformation can enhance thermal conductivity greatly, and there exists an optimal deformable value at which thermal conductivity takes its maximum. Remarkably, we also find that the deformation can facilitate the appearance of the negative differential thermal resistance.

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.

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.

Heat conduction in the nonlinear response regime: scaling, boundary jumps, and negative differential thermal resistance.

We report a numerical study on heat conduction in one-dimensional homogeneous lattices in both the linear and the nonlinear response regime, with a comparison among three prototypical nonlinear lattice models. In the nonlinear response regime, negative differential thermal resistance (NDTR) can occur in both the Frenkel-Kontorova model and the phi4 model. In the Fermi-Pasta-Ulam- beta model, however, only positive differential thermal resistance can be observed, as shown by a monotonous power-law dependence of the heat flux on the applied temperature difference. In general, it was found that NDTR can occur if there is nonlinearity in the onsite potential of the lattice model. It was also found that the regime of NDTR becomes smaller as the system size increases, and eventually vanishes in the thermodynamic limit. For the phi4 model, a phenomenological description of the size-induced crossover from the existence to the nonexistence of a NDTR regime is provided.

Heat conduction in driven Frenkel-Kontorova lattices: thermal pumping and resonance.

Heat conduction through the Frenkel-Kontorova chain under the influence of an ac driving force applied locally at one boundary is studied by nonequilibrium molecular dynamics simulations. We observe the occurrence of thermal resonance, namely, there exists a value of the driving frequency at which the heat flux takes its maximum value. The resonance frequency is determined by the dynamical parameters of the model, which has been numerically explored. Remarkably, the heat can be pumped from the low-temperature heat bath to the high temperature one by suitably adjusting the frequency of the ac driving force. By examining effects of the driving amplitude on heat conduction, we show that the amplitude threshold for nonlinear supratransmission is absent when the system is in contact with heat baths, namely, the heat flux smoothly increases with the increasing of amplitude.

Properties of the Shapiro steps in the ac driven Frenkel-Kontorova model with deformable substrate potential.

Properties of the dynamical-mode-locking phenomena are studied in the ac driven overdamped Frenkel-Kontorova model with deformable substrate potential. Appearance of very large subharmonic steps due to deformation of the substrate potential significantly influences the stability and existence of harmonic steps. Strong correlation among harmonic and subharmonic steps has been observed in which the larger the width of half-integer steps, the smaller that of harmonic steps. Amplitude dependence of harmonic steps significantly changes with the deformation of the potential where deviation from the well-known Bessel-like oscillations appears. Strong influence of the frequency of the ac driving force on the appearance and size of subharmonic steps has been observed.

Optimizing transport efficiency on scale-free networks through assortative or dissortative topology.

We find that transport on scale-free random networks depends strongly on degree-correlated network topologies whereas transport on Erdös-Rényi networks is insensitive to the degree correlation. An approach for the tuning of scale-free network transport efficiency through assortative or dissortative topology is proposed. We elucidate that the unique transport behavior for scale-free networks results from the heterogeneous distribution of degrees.

Spatial shift of lattice soliton scattering in the Fermi-Pasta-Ulam model.

Spatial shift produced in scattering process of lattice soliton is studied in the Fermi-Pasta-Ulam model with anharmonic-limit potential. Kink-shaped and antikink-shaped lattice solitons are excited by kicking one single particle. Different behaviors are discovered in two types of head-on collision: kink-kink-shaped collision and kink-antikink-shaped collision. In both cases, the spatial shift not only depends on the scattering pair of lattice solitons but also depends on their collision configuration, i.e., their phase difference. To make a comparison between integrable and nonintegrable lattices, and also to check our method, the Toda model is revisited.

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.

Complexity versus modularity and heterogeneity in oscillatory networks: combining segregation and integration in neural systems.

Normal functioning in many realistic complex dynamical systems, such as neural networks, requires coherence and synchronization for collective actions of network components. However, strong synchronization of the whole network is often related to pathological situations. A regime in between enabling both segregation in subsystems and integration as a whole is thus desirable. Here, we characterize this regime by complexity of synchronization patterns and study its relationship to heterogeneous and modular architecture in complex network of oscillators. We show that these networks possess a broad range of high complexity associated with the formation of dynamical clusters and the coordination between the clusters. In realistic networks of C. elegans and cat cortex, the complexity is reduced when the original network is rewired in various ways, reflecting that the neural systems are organized to provide a combination of segregation and integration with the coexistence of various complex network features, especially modularity and heterogeneity. Our work can stimulate further studies on structure-function relationships in neural systems through the inquiry of the specific functional roles of the intermediate dynamical regime.

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.

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.

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.