Localized states beyond the asymptotic parametrically driven amplitude equation

Stability and Spin Waves of Skyrmion Tubes in Curved FeGe Nanowires

In this work, we investigate the influence of curvature on the dynamic susceptibility in FeGe nanowires, both curved and straight, hosting a skyrmionic tube texture under the action of an external bias field, using micromagnetic simulations. Our results demonstrate that both the resonance frequencies and the number of resonant peaks are highly dependent on the curvature of the system. To further understand the nature of the spin wave modes, we analyze the spatial distributions of the resonant mode amplitudes and phases, describing the differences among resonance modes observed. The ability to control the dynamic properties and frequencies of these nanostructures underscores their potential application in frequency-selective magnetic devices.

Stability of bubble-like fluxons in disk-shaped Josephson junctions in the presence of a coaxial dipole current

We investigate analytically and numerically the stability of bubble-like fluxons in disk-shaped heterogeneous Josephson junctions. Using ring solitons as a model of bubble fluxons in the two-dimensional sine-Gordon equation, we show that the insertion of coaxial dipole currents prevents their collapse. We characterize the onset of instability by introducing a single parameter that couples the radius of the bubble fluxon with the properties of the injected current. For different combinations of parameters, we report the formation of stable oscillating bubbles, the emergence of internal modes, and bubble breakup due to internal mode instability. We show that the critical germ depends on the ratio between its radius and the steepness of the wall separating the different phases in the system. If the steepness of the wall is increased (decreased), the critical radius decreases (increases). Our theoretical findings are in good agreement with numerical simulations.

Two-dimensional localized chaotic patterns in parametrically driven systems

We study two-dimensional localized patterns in weakly dissipative systems that are driven parametrically. As a generic model for many different physical situations we use a generalized nonlinear Schrödinger equation that contains parametric forcing, damping, and spatial coupling. The latter allows for the existence of localized pattern states, where a finite-amplitude uniform state coexists with an inhomogeneous one. In particular, we study numerically two-dimensional patterns. Increasing the driving forces, first the localized pattern dynamics is regular, becomes chaotic for stronger driving, and finally extends in area to cover almost the whole system. In parallel, the spatial structure of the localized states becomes more and more irregular, ending up as a full spatiotemporal chaotic structure.

Stochastic dissipative solitons

By the effect of aggregating currents, some systems display an effective diffusion coefficient that becomes negative in a range of the order parameter, giving rise to bistability among homogeneous states (HSs). By applying a proper multiplicative noise, localized (pinning) states are shown to become stable at the expense of one of the HSs. They are, however, not static, but their location fluctuates with a variance that increases with the noise intensity. The numerical results are supported by an analytical estimate in the spirit of the so-called solvability condition.

Traveling pulse on a periodic background in parametrically driven systems

Macroscopic systems with dissipation and time-modulated injection of energy, parametrically driven systems, can self-organize into localized states and/or patterns. We investigate a pulse that travels over a one-dimensional pattern in parametrically driven systems. Based on a minimal prototype model, we show that the pulses emerge through a subcritical Andronov-Hopf bifurcation of the underlying pattern. We describe a simple physical system, a magnetic wire forced with a transverse oscillatory magnetic field, which displays these traveling pulses.

From the granular Leidenfrost state to buoyancy-driven convection

Grains inside a vertically vibrated box undergo a transition from a density-inverted and horizontally homogeneous state, referred to as the granular Leidenfrost state, to a buoyancy-driven convective state. We perform a simulational study of the precursors of such a transition and quantify their dynamics as the bed of grains is progressively fluidized. The transition is preceded by transient convective states, which increase their correlation time as the transition point is approached. Increasingly correlated convective flows lead to density fluctuations, as quantified by the structure factor, that also shows critical behavior near the transition point. The amplitude of the modulations in the vertical velocity field are seen to be best described by a quintic supercritical amplitude equation with an additive noise term. The validity of such an amplitude equation, and previously observed collective semiperiodic oscillations of the bed of grains, suggests a new interpretation of the transition analogous to a coupled chain of vertically vibrated damped oscillators. Increasing the size of the container shows metastability of convective states, as well as an overall invariant critical behavior close to the transition.

The Kibble-Zurek mechanism in a subcritical bifurcation

We present a study of the freezing dynamics of topological defects in a subcritical system by testing the Kibble-Zurek (KZ) mechanism while crossing a tri-stable region in a one-dimensional quintic complex Ginzburg-Landau equation. The critical exponents of the KZ mechanism and the horizon (KZ-scaling regime) are predicted from the quasistatic study, and are in full accordance with the quenched study. The correlation length, in the KZ freezing regime, is corroborated from the number of topological defects and from the spatial correlation function of the order parameter. Furthermore, we characterize the dynamics to differentiate three out-of-equilibrium regimes: the adiabatic, the impulse and the free relaxation. We show that the impulse regime shares a common temporal domain with a fast exponential increase of the order parameter.

Phase shielding soliton in parametrically driven systems

Parametrically driven extended systems exhibit dissipative localized states. Analytical solutions of these states are characterized by a uniform phase and a bell-shaped modulus. Recently, a type of dissipative localized state with a nonuniform phase structure has been reported: the phase shielding solitons. Using the parametrically driven and damped nonlinear Schrödinger equation, we investigate the main properties of this kind of solution in one and two dimensions and develop an analytical description for its structure and dynamics. Numerical simulations are consistent with our analytical results, showing good agreement. A numerical exploration conducted in an anisotropic ferromagnetic system in one and two dimensions indicates the presence of phase shielding solitons. The structure of these dissipative solitons is well described also by our analytical results. The presence of corrective higher-order terms is relevant in the description of the observed phase dynamical behavior.

Bifurcations of emerging patterns in the presence of additive noise

A universal description of the effects of additive noise on super- and subcritical spatial bifurcations in one-dimensional systems is theoretically, numerically, and experimentally studied. The probability density of the critical spatial mode amplitude is derived. From this generalized Rayleigh distribution we predict the shape of noisy bifurcations by means of the most probable value of the critical mode amplitude. Comparisons with numerical simulations are in quite good agreement for cubic or quintic amplitude equations accounting for stochastic supercritical bifurcation and for cubic-quintic amplitude equation accounting for stochastic subcritical bifurcation. Experimental results obtained in a one-dimensional Kerr-like slice subjected to optical feedback confirm the analytical expression prediction for the supercritical bifurcation shape.

Symmetry-induced pinning-depinning transition of a subharmonic wave pattern

The stationary to drifting transition of a subharmonic wave pattern is studied in the presence of inhomogeneities and drift forces as the pattern wavelength is comparable with the system size. We consider a pinning-depinning transition of stationary subharmonic waves in a tilted quasi-one-dimensional fluidized shallow granular bed driven by a periodic air flow in a small cell. The transition is mediated by the competition of the inherent periodicity of the subharmonic pattern, the asymmetry of the system, and the finite size of the cell. Measurements of the mean phase velocity of the subharmonic pattern are in good agreement with those inferred from an amplitude equation, which takes into account asymmetry and finite-size effects of the system, emphasizing the main ingredients and mechanism of the transition.

Coalescence cascade of dissipative solitons in parametrically driven systems

Parametrically driven spatially extended systems exhibit uniform oscillations which are modulationally unstable. The resulting periodic state evolves to the creation of a gas of dissipative solitons. Driven by the interaction of dissipative solitons, the multisoliton state undergoes a cascade of coalescence processes, where the average soliton separation distance obeys a temporal self-similar law. Starting from the soliton pair interaction law, we have derived analytically and characterized the law of this multisoliton coarsening process. A comparison of numerical results obtained with different models such as the parametrically driven damped nonlinear Schrödinger equation, a vertically driven chain of pendula, and a parametrically forced magnetic wire, shows remarkable agreement. Both phenomena, the pair interaction law and the coarsening process, are also observed experimentally in a quasi-one-dimensional layer of Newtonian fluid which is oscillated vertically.

Chaotic dynamics of a magnetic nanoparticle

We study the deterministic spin dynamics of an anisotropic magnetic particle in the presence of a magnetic field with a constant longitudinal and a time-dependent transverse component using the Landau-Lifshitz-Gilbert equation. We characterize the dynamical behavior of the system through calculation of the Lyapunov exponents, Poincaré sections, bifurcation diagrams, and Fourier power spectra. In particular we explore the positivity of the largest Lyapunov exponent as a function of the magnitude and frequency of the applied magnetic field and its direction with respect to the main anisotropy axis of the magnetic particle. We find that the system presents multiple transitions between regular and chaotic behaviors. We show that the dynamical phases display a very complicated structure of intricately intermingled chaotic and regular phases.

Time-periodic solitons in a damped-driven nonlinear Schrödinger equation

Time-periodic solitons of the parametrically driven damped nonlinear Schrödinger equation are obtained as solutions of the boundary-value problem on a two-dimensional spatiotemporal domain. We follow the transformation of the periodic solitons as the strength of the driver is varied. The resulting bifurcation diagrams provide a natural explanation for the overall form and details of the attractor chart compiled previously via direct numerical simulations. In particular, the diagrams confirm the occurrence of the period-doubling transition to temporal chaos for small values of dissipation and the absence of such transitions for larger dampings. This difference in the soliton's response to the increasing driving strength can be traced to the difference in the radiation frequencies in the two cases. Finally, we relate the soliton's temporal chaos to the homoclinic bifurcation.

Soliton pair interaction law in parametrically driven Newtonian fluid

An experimental and theoretical study of the motion and interaction of the localized excitations in a vertically driven small rectangular water container is reported. Close to the Faraday instability, the parametrically driven damped nonlinear Schrödinger equation models this system. This model allows one to characterize the pair interaction law between localized excitations. Experimentally we have a good agreement with the pair interaction law.