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Lauesen Banke posted an update a month ago
The generation of a variety of harmonics within the oscillations of the condensate’s width and center-of-mass coordinate is a consequence of the modulation. Multiple and combinational harmonics, discernible as sharp peaks, are present in the system’s spectra. By systematically simulating the underlying Gross-Pitaevskii equation, the approximate analytical results derived via the variational approach are validated. This article is part of the thematic publication ‘New trends in pattern formation and nonlinear dynamics of extended systems’.
The liquid film, positioned on a heated substrate with minimal thermal conductivity, is studied dynamically. The stationary, long-wave Marangoni instability is numerically simulated directly, utilizing a system of coupled partial differential equations. These equations, derived previously using the lubrication approximation, chart the evolution of film thickness and fluid temperature. A comparison of our results is made with the initial results presented from the weakly nonlinear analysis. Values of the Marangoni number near the convective threshold exhibit a strong qualitative agreement. Our results for amplitudes are dependent on the square root of the supercriticality factor, under conditions of supercritical excitation. Subcritical excitation instances are marked by the reported hysteresis. Highly supercritical conditions lead to the evolution of convective regimes, culminating in film rupture through the development of secondary swells. Three-dimensional patterns exhibit either a roll-like shape or a square pattern, contingent on the specific problem parameters. Our results lend support to the prediction of asymptotic outcomes associated with nonlinear feedback control strategies for pattern selection. Within the thematic collection ‘New trends in pattern formation and nonlinear dynamics of extended systems,’ this article resides.
An auxiliary complex field couples a one-dimensional array of phase oscillators. Although the pioneering chimera studies of Kumamoto and Battogtokh focused solely on field diffusion, our analysis incorporates advection, thereby introducing a left-right asymmetry in the coupling. A weakly turbulent pattern of movement is observed as the chimera commences its motion. The system displays a sizable synchronous region, where phase consistency is high, juxtaposed with a less organized area, marked by a diminished local driving force. Within a densely packed system of oscillators, powerful local correlations emerge within the disordered area, presenting, in many locations, as a smooth phase transition. In addition, there exist precise, regular, traveling wave solutions that exhibit chimera-like behavior, varying in complexity, but only some of these solutions manifest stability. This article is included in the special issue dedicated to ‘New trends in pattern formation and nonlinear dynamics of extended systems’.
Considering a non-reciprocally coupled two-field Cahn-Hilliard system, we analyze its oscillatory nature and its ability to restrict coarsening. Having introduced the model, the initial analysis scrutinizes the linear stability of constant, uniform states. The result reveals that the instability thresholds are indistinguishable from those within the equivalent two-species reaction-diffusion system. We now examine a particular interaction of linear modes, specifically a ‘Hopf-Turing’ resonance, and determine the corresponding amplitude equations employing a weakly nonlinear method. We delve into the weakly nonlinear findings and ultimately contrast them with fully nonlinear simulations for a particular conserved amended FitzHugh-Nagumo system. Finally, we delve into the limitations of the implemented weakly nonlinear technique. This article forms a part of the themed collection exploring ‘New trends in pattern formation and nonlinear dynamics of extended systems’.
Viewing liquid bridges’ particle accumulation structures (PAS) as model systems for analyzing particle self-assembly in laminar, cyclical flows, this effort seeks to disentangle the complex network of connections between the numerous aggregation locations (streamtubes, vying as attractors within the physical space) and the resulting particle structures. Whereas the prior relies on purely topological (fluid-dynamic) principles, the compelling factors influencing the consequences of fluid-particle interaction exhibit a much more intricate structure, resulting in diverse particle configurations from one instance to the next. Through numerical analysis of the governing Eulerian and Lagrangian equations for liquid and mass transfer, we show that, with a constant aspect ratio of the liquid bridge, particles can be gradually moved from one streamtube to another in response to changes in the Stokes and/or Marangoni numbers. Furthermore, regions exist where these attractors contend, leading to overlapping or interwoven particle structures, some of which, exhibiting a pronounced degree of asymmetry, have never been documented previously. This theme issue, ‘New trends in pattern formation and nonlinear dynamics of extended systems,’ features this article.
Within this article, the outcomes of a theoretical and experimental investigation into buoyancy-driven instabilities provoked by a neutralization reaction within an immiscible two-layer system are presented, focusing on a vertical Hele-Shaw cell. Flow patterns are forecast by a reaction-induced buoyancy number , calculated as the ratio of the reaction zone density to the density of the lower layer. From our experimental investigations, we detected the development of cellular convection (), the finger-like pattern with fingers arranged along a denser reactive area (), and the customary Rayleigh-Taylor convection process for . In the mathematical model, reaction-diffusion-convection equations are defined under the heuristic of the Hele-Shaw approximation. A key innovation in the model is its treatment of the water formed during the reaction, an often neglected element. The persistent, regular fingering during the reaction zone’s disintegration is attributed to the dynamic water release, which offsets the heavy fluid’s downward movement and stabilizes the pattern. We conclude with a stability map plotted against the initial concentrations of the solutions. The experimental results show a positive correlation with the theoretical predictions, exhibiting a high degree of agreement. This article is featured in a special issue dedicated to ‘New trends in pattern formation and nonlinear dynamics of extended systems’.
Through experimental and computational methods, spanning two stages, we scrutinized convective behavior in a liquid bridge () developing in the presence of a parallel gas stream. Increasing the applied temperature difference and the temperature of the gas moving at velocity is the strategy used in this study to monitor the evolution of hydrothermal waves. Our investigation into oscillatory states, as control parameters increased, uncovered a consistent pattern. Nonlinear dynamics, at levels above the instability threshold, encounters three oscillatory patterns, that are remarkably similar at greater values of the controlling parameters. Periodic, or more precisely quasi-periodic, with a range of two to three frequencies, they transition into a multi-frequency state when the Fourier spectrum’s clusters include duplex, triplex, or more complex frequency patterns. Experimental flow patterns, examined through three-dimensional numerical simulation and a deep spectral analysis, illustrate their evolution. The developed method identified conditions crucial for a multi-frequency regime: a discernible low-frequency mode influencing strong high-frequency modes; the existence of robust azimuthal modes with varying wave numbers; the mode; and an organized pattern of peaks in the Fourier spectrum. In the themed issue ‘New trends in pattern formation and nonlinear dynamics of extended systems’, this article finds its place.
Pattern formation, a widespread characteristic, is observed across physical, chemical, and biological systems. Over the past decades, the realm of experimental and theoretical instruments has evolved to offer superior tools for the investigation of that observed phenomenon. Furthermore, the system of patterns was broadened in its scope. The present issue reveals a sweeping overview of pattern formation, accompanied by other nonlinear dynamical phenomena, throughout diverse natural and engineered contexts. Fluid dynamics’ non-linear elements receive special attention. alvespimycin inhibitor The analysis also delves into non-equilibrium phenomena observed in both chemical and quantum systems. The current article falls under the umbrella theme ‘New trends in pattern formation and nonlinear dynamics of extended systems’.
The formation of bimolecular fronts within solutions often results in their dynamical behavior being impacted by chemically-driven convective processes, like buoyancy- and Marangoni-driven flows. One-dimensional reaction-diffusion concentration profiles successfully predict front dynamics associated with buoyancy-driven convection, yet this predictive accuracy is absent when examining the effects of Marangoni-driven convection. A two-dimensional reaction-diffusion-Marangoni convection model is employed to investigate the convective impacts on front property time-scales, and how the reversibility of the reaction and the ratio of initial reactant concentrations affect the dynamics of the front. By assuming the reactive system to be in a zero-gravity state and/or the solution density to be spatially uniform, the effect of buoyancy forces is disregarded here. This article is one of many that contribute to the ‘New trends in pattern formation and nonlinear dynamics of extended systems’ issue.
Two resonance-derived interfacial instabilities are scrutinized, with particular attention given to the effects of side walls on the discretization of interfacial modes in recent research.