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At least 379 records · Page 21Linked to original sources

arXiv2000

Two-color multistep cascading and parametric soliton-induced waveguides

We introduce the concept of two-color multistep cascading for vectorial parametric wave mixing in optical media with quadratic (second-order or chi-2) nonlinear response. We demonstrate that the multistep cascading allows light-guiding-light effects with quadratic spatial solitons. With the help of the so-called `almost exact' analytical solutions, we describe the properties of parametric waveguides created by two-wave quadratic solitons.

patt-sol↗

arXiv1999

Logarithmically Slow Expansion of Hot Bubbles in Gases

We report logarithmically slow expansion of hot bubbles in gases in the process of cooling. A model problem first solved, when the temperature has compact support. Then temperature profile decaying exponentially at large distances is considered. The periphery of the bubble is shown to remain essentially static ("glassy") in the process of cooling until it is taken over by a logarithmically slowly expanding "core". An analytical solution to the problem is obtained by matched asymptotic expansion. This problem gives an example of how logarithmic corrections enter dynamic scaling.

patt-sol↗

arXiv1999

Optical Vortex Solitons in Parametric Wave Mixing

We analyze two-component spatial optical vortex solitons supported by parametric wave mixing processes in a nonlinear bulk medium. We study two distinct cases of such localised waves, namely, parametric vortex solitons due to phase-matched second-harmonic generation in an optical medium with competing quadratic and cubic nonlinear response, and vortex solitons in the presence of third-harmonic generation in a cubic medium. We find, analytically and numerically, the structure of two-component vortex solitons, and also investigate modulational instability of their plane-wave background. In particular, we predict and analyze in detail novel types of vortex solitons, a `halo-vortex', consisting of a two-component vortex core surrounded by a bright ring of its harmonic field, and a `ring-vortex' soliton which is a vortex in a harmonic field that guides a ring-like localized mode of the fundamental-frequency field.

patt-sol↗

arXiv1999

Selfsimilar Domain Growth, Localized Structures and Labyrinthine Patterns in Vectorial Kerr Resonators

We study domain growth in a nonlinear optical system useful to explore different scenarios that might occur in systems which do not relax to thermodynamic equilibrium. Domains correspond to equivalent states of different circular polarization of light. We describe three dynamical regimes: a coarsening regime in which dynamical scaling holds with a growth law dictated by curvature effects, a regime in which localized structures form, and a regime in which polarization domain walls are modulationally unstable and the system freezes in a labyrinthine pattern.

patt-sol↗

arXiv1999

Cross-Newell equations for hexagons and triangles

The Cross-Newell equations for hexagons and triangles are derived for general real gradient systems, and are found to be in flux-divergence form. Specific examples of complex governing equations that give rise to hexagons and triangles and which have Lyapunov functionals are also considered, and explicit forms of the Cross-Newell equations are found in these cases. The general nongradient case is also discussed; in contrast with the gradient case, the equations are not flux-divergent. In all cases, the phase stability boundaries and modes of instability for general distorted hexagons and triangles can be recovered from the Cross-Newell equations.

patt-sol↗

arXiv1999

Origin of Multikinks in Dispersive Nonlinear Systems

We develop {\em the first analytical theory of multikinks} for strongly {\em dispersive nonlinear systems}, considering the examples of the weakly discrete sine-Gordon model and the generalized Frenkel-Kontorova model with a piecewise parabolic potential. We reveal that there are no $2π$-kinks for this model, but there exist {\em discrete sets} of $2πN$-kinks for all N>1. We also show their bifurcation structure in driven damped systems.

patt-sol↗

arXiv1999

Kink motion in the Kramers problem for a chain molecule

We consider the generalization of the Kramers escape over a barrier problem to the case of a long chain molecule. It involves the motion of chain molecule of N segments across a region where the free energy per segment is higher, so that it has to cross a barrier. We use the Rouse model and find that the free energy of activation has a square root dependence on the temperature leading to a non-Arrhenius form for the rate. We also show that there is a special time dependent solution of the model, which corresponds to a kink in the chain, confined to the region of the barrier. The polymer goes from one side to the other by the motion of the kink in the reverse direction. If there is no free energy difference between the two sides of the barrier, then the kink moves by diffusion and the time of crossing t_{cross}~ N^2/T^{3/2}. If there is a free energy difference, then the kink moves with a non-zero velocity from the lower free energy side to the otherleading to t_{cross} ~ N/sqrt{T}.

cond-mat.soft↗

arXiv1999

Approximate solutions and scaling transformations for quadratic solitons

We study quadratic solitons supported by two- and three-wave parametric interactions in chi-2 nonlinear media. Both planar and two-dimensional cases are considered. We obtain very accurate, 'almost exact', explicit analytical solutions, matching the actual bright soliton profiles, with the help of a specially-developed approach, based on analysis of the scaling properties. Additionally, we use these approximations to describe the linear tails of solitary waves which are related to the properties of the soliton bound states.

patt-sol↗

arXiv2000

Wave Number of Maximal Growth in Viscous Magnetic Fluids of Arbitrary Depth

An analytical method within the frame of linear stability theory is presented for the normal field instability in magnetic fluids. It allows to calculate the maximal growth rate and the corresponding wave number for any combination of thickness and viscosity of the fluid. Applying this method to magnetic fluids of finite depth, these results are quantitatively compared to the wave number of the transient pattern observed experimentally after a jump--like increase of the field. The wave number grows linearly with increasing induction where the theoretical and the experimental data agree well. Thereby a long-standing controversy about the behaviour of the wave number above the critical magnetic field is tackled.

patt-sol↗

arXiv1999

Development and geometry of isotropic and directional shrinkage crack patterns

We have studied shrinkage crack patterns which form when a thin layer of an alumina/water slurry dries. Both isotropic and directional drying were studied. The dynamics of the pattern formation process and the geometric properties of the isotropic crack patterns are similar to what is expected from recent models, assuming weak disorder. There is some evidence for a gradual increase in disorder as the drying layer become thinner, but no sudden transition, in contrast to what has been seen in previous experiments. The morphology of the crack patterns is influenced by drying gradients and front propagation effects, with sharp gradients having a strong orienting and ordering effect.

patt-sol↗

arXiv1999

Soliton Interaction with an External Traveling Wave

The dynamics of soliton pulses in the Nonlinear Schrodinger Equation (NLSE) driven by an external Traveling wave is studied analytically and numerically. The Hamiltonian structure of the system is used to show that, in the adiabatic approximation for a single soliton, the problem is integrable despite the large number of degrees of freedom. Fixed points of the system are found, and their linear stability is investigated. The fixed points correspond to a Doppler shifted resonance between the external wave and the soliton. The structure and topological changes of the phase space of the soliton parameters as functions of the strength of coupling are investigated. A physical derivation of the driven NLSE is given in the context of optical pulse propagation in asymmetric, twin-core optical fibers. The results can be applied to soliton stabilization and amplification.

patt-sol↗

arXiv1999

Solitons in anharmonic chains with ultra-long-range interatomic interactions

We study the influence of long-range interatomic interactions on the properties of supersonic pulse solitons in anharmonic chains. We show that in the case of ultra-long-range (e.g., screened Coulomb) interactions three different types of pulse solitons coexist in a certain velocity interval: one type is unstable but the two others are stable. The high-energy stable soliton is broad and can be described in the quasicontinuum approximation. But the low-energy stable soliton consists of two components, short-range and long-range ones, and can be considered as a bound state of these components.

patt-sol↗

arXiv1999

Abnormal Rolls and Regular Arrays of Disclinations in Homeotropic Electroconvection

We present the first quantitative verification of an amplitude description for systems with (nearly) spontaneously broken isotropy, in particular for the recently discovered abnormal-roll states. We also obtain a conclusive picture of the 3d director configuration in a spatial period doubling phenomenon involving disclination loops (CRAZY rolls). The first observation of two Lifshitz frequencies in electroconvection is reported.

patt-sol↗

arXiv1999

Universal Algebraic Relaxation of Velocity and Phase in Pulled Fronts generating Periodic or Chaotic States

We investigate the asymptotic relaxation of so-called pulled fronts propagating into an unstable state. The ``leading edge representation'' of the equation of motion reveals the universal nature of their propagation mechanism and allows us to generalize the universal algebraic velocity relaxation of uniformly translating fronts to fronts, that generate periodic or even chaotic states. Such fronts in addition exhibit a universal algebraic phase relaxation. We numerically verify our analytical predictions for the Swift-Hohenberg and the Complex Ginzburg Landau equation.

patt-sol↗

arXiv1999

Long-Lived Localized Field Configurations in Small Lattices: Application to Oscillons

Long-lived localized field configurations such as breathers, oscillons, or more complex objects naturally arise in the context of a wide range of nonlinear models in different numbers of spatial dimensions. We present a numerical method, which we call the {\it adiabatic damping method}, designed to study such configurations in small lattices. Using 3-dimensional oscillons in $ϕ^4$ models as an example, we show that the method accurately (to a part in 10^5 or better) reproduces results obtained with static or dynamically expanding lattices, dramatically cutting down in integration time. We further present new results for 2-dimensional oscillons, whose lifetimes would be prohibitively long to study with conventional methods.

patt-sol↗

arXiv1999

Multi-Bunch Solutions of Differential-Difference Equation for Traffic Flow

Newell-Whitham type car-following model with hyperbolic tangent optimal velocity function in a one-lane circuit has a finite set of the exact solutions for steady traveling wave, which expressed by elliptic theta function. Each solution of the set describes a density wave with definite number of car-bunches in the circuit. By the numerical simulation, we observe a transition process from a uniform flow to the one-bunch analytic solution, which seems to be an attractor of the system. In the process, the system shows a series of cascade transitions visiting the configurations closely similar to the higher multi-bunch solutions in the set.

patt-sol↗

arXiv2000

Planform selection in two-layer Benard-Marangoni convection

Benard-Marangoni convection in a system of two superimposed liquids is investigated theoretically. Extending previous studies the complete hydrodynamics of both layers is treated and buoyancy is consistently taken into account. The planform selection problem between rolls, squares and hexagons is investigated by explicitly calculating the coefficients of an appropriate amplitude equation from the parameters of the fluids. The results are compared with recent experiments on two-layer systems in which squares at onset have been reported.

patt-sol↗

arXiv1999

Crossover from a square to a hexagonal pattern in Faraday surface waves

We report on surface wave pattern formation in a Faraday experiment operated at a very shallow filling level, where modes with a subharmonic and harmonic time dependence interact. Associated with this distinct temporal behavior are different pattern selection mechanisms, favoring squares or hexagons, respectively. In a series of bifurcations running through a pair of superlattices the surface wave pattern transforms between the two incompatible symmetries. The close analogy to 2D and 3D crystallography is pointed out.

patt-sol↗