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At least 1,243 records · Page 69Linked to original sources

Limitation on stabilizing plane waves via time-delay feedback.

Previous work has demonstrated the possibility of stabilizing plane wave solutions of one-dimensional systems using a spatially local form of time-delayed feedback. We show that the natural extension of this method to two-dimensional systems fails due to the presence of torsion-free unstable perturbations. Linear stability analysis of the complex Ginzburg-Landau equation reveals that long wavelength, transverse wave instabilities cannot be suppressed by the method of extended time-delay autosynchronization. The conclusion follows from symmetry considerations and therefore applies to a wide class of models with simple plane wave solutions.

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Spatial optical solitons in nonlinear photonic crystals.

We study spatial optical solitons in a one-dimensional nonlinear photonic crystal created by an array of thin-film nonlinear waveguides, the so-called Dirac-comb nonlinear lattice. We analyze modulational instability of the extended Bloch-wave modes and also investigate the existence and stability of bright, dark, and "twisted" spatially localized modes in such periodic structures. Additionally, we discuss both similarities and differences of our general results with the simplified models of nonlinear periodic media described by the discrete nonlinear Schrödinger equation, derived in the tight-binding approximation, and the coupled-mode theory, valid for shallow periodic modulations of the optical refractive index.

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Targeted transfer of solitons in continua and lattices.

We propose a robust mechanism of targeted energy transfer along a line, as well as on a surface, in the form of transport of coherent solitary-wave structures, driven by a moving, spatially localized external ac field ("arm") in a lossy medium. The efficiency and robustness of the mechanism are demonstrated analytically and numerically in terms of the nonlinear Schrödinger (NLS) equation, and broad regions of stable operation are identified in the model's parameter space. Direct simulations show that the driving arm can manipulate solitons equally well in a lattice NLS model. A salient feature, which is revealed by simulations and explained analytically, is a resonant character of the operation of the driving arm in the lattice medium, both integer and fractional resonances being identified. Numerical experiments also demonstrate that the same solitary-wave-transport mechanism works well in two-dimensional lattice media.

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Numerical approximation of breathers in lattices with nearest-neighbor interactions.

A numerical method is presented for accurately approximating time-periodic and spatially localized solutions known as (discrete) breathers, of the equations of motion describing lattices with one degree-of-freedom per lattice site and nearest-neighbor interactions. Our method is an extension of an approximation suggested by Tsironis [J. Phys. A 35, 951 (2002)], gives more accurate results than the rotating wave approximation and is more universally applicable for these lattices. As an illustration, the method is applied here to several one- and two-dimensional lattices.

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Scattering of dipole-mode vector solitons: theory and experiment.

We study, both theoretically and experimentally, the scattering properties of optical dipole-mode vector solitons-radially asymmetric composite self-trapped optical beams. First, we analyze the soliton collisions in an isotropic two-component model with a saturable nonlinearity, and demonstrate that in many cases the scattering dynamics of the dipole-mode solitons allows us to classify them as "molecules of light"-extremely robust spatially localized objects which survive a wide range of interactions and display many properties of composite states with a rotational degree of freedom. Next, we study the composite solitons in an anisotropic nonlinear model that describes photorefractive nonlinearities, and also present a number of experimental verifications of our analysis.

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Sparks and waves in a stochastic fire-diffuse-fire model of Ca2+ release.

Calcium ions are an important second messenger in living cells. Indeed, calcium signals in the form of waves have been the subject of much recent experimental interest. It is now well established that these waves are composed of elementary stochastic release events (calcium puffs or sparks) from spatially localized calcium stores. Here we develop a computationally inexpensive model of calcium release, based upon a stochastic generalization of the fire-diffuse-fire threshold model. Our model retains the discrete nature of calcium stores, but also incorporates a notion of release probability via the introduction of threshold noise. Numerical simulations of the model illustrate that stochastic calcium release leads to the spontaneous production of calcium sparks that may merge to form saltatory waves. In the parameter regime where deterministic waves exist, it is possible to identify a critical level of noise, defining a nonequilibrium phase transition between propagating and abortive structures. A statistical analysis shows that this transition is the same as for models in the directed percolation universality class. Moreover, in the regime where no initial structure can survive deterministically, threshold noise is shown to generate a form of array enhanced coherence resonance, whereby all calcium stores release periodically and simultaneously.

Biophysical Phenomena↗

Time-delay autosynchronization of the spatiotemporal dynamics in resonant tunneling diodes.

The double barrier resonant tunneling diode exhibits complex spatiotemporal patterns including low-dimensional chaos when operated in an active external circuit. We demonstrate how autosynchronization by time-delayed feedback control can be used to select and stabilize specific current density patterns in a noninvasive way. We compare the efficiency of different control schemes involving feedback in either local spatial or global degrees of freedom. The numerically obtained Floquet exponents are explained by analytical results from linear stability analysis.

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Spatiotemporal chaos control with a target wave in the complex Ginzburg-Landau equation system.

An effective method for controlling spiral turbulence in spatially extended systems is realized by introducing a spatially localized inhomogeneity into a two-dimensional system described by the complex Ginzburg-Landau equation. Our numerical simulations show that with the introduction of the inhomogeneity, a target wave can be produced, which will sweep all spiral defects out of the boundary of the system. The effects exist in certain parameter regions where the spiral waves are absolutely unstable. A theoretical explanation is given to reveal the underlying mechanism.

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Epidemic spreading in a hierarchical social network.

A model of epidemic spreading in a population with a hierarchical structure of interpersonal interactions is described and investigated numerically. The structure of interpersonal connections is based on a scale-free network. Spatial localization of individuals belonging to different social groups, and the mobility of a contemporary community, as well as the effectiveness of different interpersonal interactions, are taken into account. Typical relations characterizing the spreading process, like a range of epidemic and epidemic curves, are discussed. The influence of preventive vaccinations on the spreading process is investigated. The critical value of preventively vaccinated individuals that is sufficient for the suppression of an epidemic is calculated. Our results are compared with solutions of the master equation for the spreading process and good agreement of the character of this process is found.

Animals↗

Frozen water waves over rough topographical bottoms.

The propagation of surface water waves over rough topographical bottoms is investigated by the multiple scattering theory. It is shown that the waves can be localized spatially through the process of multiple scattering and wave interference, a peculiar wave phenomenon which has been previously discussed for frozen light in optical systems [Nature 390, 661 (1997)]]. This paper demonstrates that when frozen, the transmission of the waves falls off exponentially, and a cooperative behavior appears, fully supporting previous predictions. A graphic method is used to illustrate this distinct phase state in the wave propagation.

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Postionization regimes of femtosecond laser pulses self-channeling in air.

An optical self-guiding of femtosecond filaments in air is identified in a regime where plasma generation ceases to support the self-channeling process. Group-velocity dispersion is shown to keep the beam temporally and spatially localized upon a few meters by taking over the ionization of air molecules, once the pulse peak power becomes close to the self-focusing threshold. In this regime, the pulse undergoes slow splitting events that maintain a residual self-guiding with light intensities as high as 10 TW/cm2, as soon as the electron plasma density has fallen down below 10(15) cm(-3).

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Jamming transition in emulsions and granular materials.

We investigate the jamming transition in packings of emulsions and granular materials via molecular dynamics simulations. The emulsion model is composed of frictionless droplets interacting via nonlinear normal forces obtained using experimental data acquired by confocal microscopy of compressed emulsions systems. Granular materials are modeled by Hertz-Mindlin deformable spherical grains with Coulomb friction. In both cases, we find power-law scaling for the vanishing of pressure and excess number of contacts as the system approaches the jamming transition from high volume fractions. We find that the construction history parametrized by the compression rate during the preparation protocol has a strong effect on the micromechanical properties of granular materials but not on emulsions. This leads the granular system to jam at different volume fractions depending on the histories. Isostaticity is found in the packings close to the jamming transition in emulsions and in granular materials at slow compression rates and infinite friction. Heterogeneity of interparticle forces increases as the packings approach the jamming transition which is demonstrated by the exponential tail in force distributions and the small values of the participation number measuring spatial localization of the forces. However, no signatures of the jamming transition are observed in structural properties, like the radial distribution functions and the distributions of contacts.

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Theory of slow-light solitons.

In the framework of the nonlinear lambda model we investigate propagation of solitons in atomic vapors and Bose-Einstein condensates. We show how the complicated nonlinear interplay between fast solitons and slow-light solitons in the lambda-type media points to the possibility to create optical gates and, thus, to control the optical transparency of the lambda-type media. We provide an exact analytic description of decelerating, stopping and reaccelerating of slow-light solitons in atomic media in the nonadiabatic regime. Dynamical control over slow-light solitons is realized via a controlling field generated by an auxiliary laser. For a rather general time dependence of the field; we find the dynamics of the slow-light soliton inside the medium. We provide an analytical description for the nonlinear dependence of the velocity of the signal on the controlling field. If the background field is turned off at some moment of time, the signal stops. We find the location and shape of the spatially localized memory bit imprinted into the medium. We discuss physically interesting features of our solution, which are in a good agreement with recent experiments.

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Spectral density of polychromatic electromagnetic waves.

We investigate theoretically how the vectorial nature of polychromatic electromagnetic fields results in polarization components with different spectral characteristics, thus leading to redshifts, blueshifts, and spectral distributions with multiple peaks. We discuss how these effects can be used to design spatially localized spectra with tailored spectral densities.

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Dynamics of ternary mixtures with photosensitive chemical reactions: creating three-dimensionally ordered blends.

Using computer simulations, we establish an approach for creating defect-free, periodically ordered polymeric materials. The system involves ABC ternary mixtures where the A and B components undergo a reversible photochemical reaction. In addition, all three components are mutually immiscible and undergo phase separation. Through the simulations, we model the effects of illuminating a three-dimensional (3D) sample with spatially and temporally dependent light irradiation. Experimentally, this situation can be achieved by utilizing both a uniform background light and a spatially localized, higher intensity light, and then rastering a higher-intensity light over the 3D sample. We first focus on the case where the higher-intensity light is held stationary and focused in a distinct region within the system. The C component is seen to displace the A and B within this region and replicate the pattern formed by the higher-intensity light. In effect, one can write a pattern of C onto the AB binary system by focusing the higher-intensity light in the desired arrangement. We isolate the conditions that are necessary for producing clearly written patterns of C (i.e., for obtaining sharp interfaces between the C and A/B domains). We next consider the effect of rastering a higher-intensity light over this sample and find that this light "combs out" defects in the AB blend as it moves through the system. The resulting material displays a defect-free structure that encompasses both a periodic ordering of the A and B domains and a well-defined motif of C. In this manner, one can create hierarchically patterned materials that exhibit periodicity over two distinct length scales. The approach is fully reversible, noninvasive, and points to a novel means of patterning with homopolymers, which normally do not self-assemble into periodic structures.

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Characterization of the domain chaos convection state by the largest Lyapunov exponent.

Using numerical integrations of the Boussinesq equations in rotating cylindrical domains with realistic boundary conditions, we have computed the value of the largest Lyapunov exponent lambda1 for a variety of aspect ratios and driving strengths. We study in particular the domain chaos state, which bifurcates supercritically from the conducting fluid state and involves extended propagating fronts as well as point defects. We compare our results with those from Egolf, [Nature 404, 733 (2000)], who suggested that the value of lambda1 for the spiral defect chaos state of a convecting fluid was determined primarily by bursts of instability arising from short-lived, spatially localized dislocation nucleation events. We also show that the quantity lambda1 is not intensive for aspect ratios Gamma over the range 20<Gamma<40 and that the scaling exponent of lambda1 near onset is consistent with the value predicted by the amplitude equation formalism.

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Nonlinear emission of semiconductor microcavities in the strong coupling regime

We report on the nonlinear laserlike emission from semiconductor microcavities in the strong coupling regime. Under resonant continuous wave excitation we observe a highly emissive state. The energy, dispersion, and spatial extent of this state is measured and is found to be dispersionless and spatially localized. This state coexists with luminescence that follows the usual cavity-polariton dispersion. It is attributed to the amplification of luminescence by a parametric gain due to cavity-polariton scattering. Despite the resonant excitation at 1.6 K, we observe no sign of Bose-Einstein condensation nor Boser action.

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Spin wave wells in nonellipsoidal micrometer size magnetic elements.

We show experimentally and by model calculations that in finite, nonellipsoidal, micrometer size magnetic thin film elements the dynamic magnetic eigenexcitations (spin waves) may exhibit strong spatial localization. This localization is due to the formation of a potential well for spin waves in the highly inhomogeneous internal magnetic field within the element.

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