Noise-covered drift bifurcation of dissipative solitons in a planar gas-discharge system

Abstract

The trajectories of propagating self-organized, well-localized solitary patterns (dissipative solitons) in the form of electrical current filaments are experimentally investigated in a planar quasi-two-dimensional dc gas-discharge system with high Ohmic semiconductor barrier. Earlier phenomenological models qualitatively describing the experimental observations in terms of a particle model predict a transition from stationary filaments to filaments traveling with constant finite speed due to an appropriate change of the system parameters. This prediction motivates a search for a drift bifurcation in the experimental system, but a direct comparison of experimentally recorded trajectories with theoretical predictions is impossible due to the strong influence of noise. To solve this problem, the filament dynamics is modeled using an appropriate Langevin equation, allowing for the application of a stochastic data analysis technique to separate deterministic and stochastic parts of the dynamics. Simulations carried out with the particle model demonstrate the efficiency of the method. Applying the technique to the experimentally recorded trajectories yields good agreement with the predictions of the model equations. Finally, the predicted drift bifurcation is found using the semiconductor resistivity as control parameter. In the resulting bifurcation diagram, the square of the equilibrium velocity scales linearly with the control parameter.

Non-equilibrium thermodynamical description of rhythmic motion patterns of active systems: A canonical-dissipative approach

“…For gas discharge systems the friction function has been determined from experimental data and in line with the above considerations a velocity-dependent friction function was found that exhibits a velocity domain of negative friction (Bödeker et al, 2003). The SET model has been used to study the dynamics of single active Brownian agents moving in ratchet potentials Fiasconaro et al, 2008;Burada and Lindner, 2012) and performing foraging movements in two-dimensional planes (Ebeling et al, 1999Erdmann et al, 2000).…”

Self-propelled running droplets on solid substrates driven by chemical reactions

“…This type of bifurcation is well known from reaction-diffusion (see, for instance, [54,55,56,57,58] and references therein) and hydrodynamic systems (see, for instance, [59,60,61,62] and references therein), where it mediates the transition between steady and travelling structures. In our system it breaks the reflectional symmetry of the sitting droplets leading to moving asymmetric droplets and acompanying travelling asymmetric adsorbate profiles.…”

On the characterization of nanoporous materials by means of empirical and intrinsic transport coefficients

“…Illustration of the model: free diffusion within the channel and channel walls in y-and z-directions (reflective boundaries). Table 1 Applications of intrinsic transport coefficients Turbulence [3] Human tremor [7] Engineering [4] Surface sciences [8] Economics [5] Traffic [9] Time-delayed systems [6] Porous materials [2] Reaction-diffusion systems [10] that the definition of diffusion tensors by means of BD theory is not affected by the presence or absence of external or internal forces. More precisely, the evolution of the MSD components will of course depend for large times on the detailed forces acting on and between the fluid particles in a nanoporous material.…”