An experimental route to spatiotemporal chaos in an extended 1D oscillators array

We report experimental evidence of the route to spatiotemporal chaos in a large 1D-array of hotspots in a thermoconvective system. Increasing the driving force, a stationary cellular pattern becomes unstable towards a mixed pattern of irregular clusters which consist of time-dependent localized patterns of variable spatiotemporal coherence. These irregular clusters coexist with the basic cellular pattern. The Fourier spectra corresponding to this synchronization transition reveals the weak coupling of a resonant triad. This pattern saturates with the formation of a unique domain of great spatiotemporal coherence. As we further increase the driving force, a supercritical bifurcation to a spatiotemporal beating regime takes place. The new pattern is characterized by the presence of two stationary clusters with a characteristic zig-zag geometry. The Fourier analysis reveals a stronger coupling and enables to find out that this beating phenomena is produced by the splitting of the fundamental spatiotemporal frequencies in a narrow band. Both secondary instabilities are phase-like synchronization transitions with global and absolute character. Far beyond this threshold, a new instability takes place when the system is not able to sustain the spatial frequency splitting, although the temporal beating remains inside these domains. These experimental results may support the understanding of other systems in nature undergoing similar clustering processes.Comment: 12 pages, 13 figure

Fönster som energifaktor : isolerande fönsterluckor - termisk funktion /

cited By 3International audienceno abstrac

Multipole expansion of Bessel and Gaussian beams for Mie scattering calculations

Multipole expansions of Bessel and Gaussian beams, suitable for use in Mie scattering calculations, are derived. These results allow Mie scattering calculations to be carried out considerably faster than existing methods, something that is of particular interest for time evolution simulations where large numbers of scattering calculations must be performed. An analytic result is derived for the Bessel beam that improves on a previously published expression requiring the evaluation of an integral. An analogous expression containing a single integral, similar to existing results quoted, but not derived, in literature, is derived for a Gaussian beam,valid from the paraxial limit all the way to arbitrarily high numerical apertures

Privat hyresrätt i storstad : att skaffa lägenhet i Stockholms innerstad /

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Subcritical instabilities in a convective fluid layer under a quasi-1D heating

The study and characterization of the diversity of spatiotemporal patterns generated when a rectangular layer of fluid is locally heated beneath its free surface is presented. We focus on the instability of a stationary cellular pattern of wave number $k_s$ which undergoes a globally subcritical transition to traveling waves by parity-breaking symmetry. The experimental results show how the emerging traveling mode ($2/3k_{s}$) switches on a resonant triad ($k_s$, $k_s/2$, $2k_{s}/3$) within the cellular pattern yielding a ``mixed'' pattern. The nature of this transition is described quantitatively in terms of the evolution of the fundamental modes by complex demodulation techniques. The B\' enard-Marangoni convection accounts for the different dynamics depending on the depth of the fluid layer and on the vertical temperature difference. The existence of a hysteresis cycle has been evaluated quantitatively. When the bifurcation to traveling waves is measured in the vicinity of the codimension-2 bifurcation point, we measure a decrease of the subcritical interval in which the traveling mode becomes unstable. From the traveling wave state the system under goes a {\it new} global secondary bifurcation to an alternating pattern which doubles the wavelength ($k_{s}/2$) of the primary cellular pattern, this result compares well with theoretical predictions [P. Coullet and G. Ioss, {\em Phys. Rev. Lett.} {\bf 64}, 8 66 (1990)]. In this cascade of bifurcations towards a defect dynamics, bistability due to the subcritical behavior of our system is the reason for the coexistence of two different modulated patterns connected by a front. These fronts are stationary for a finite interval of the control parameters.Comment: 13 pages, 12 figure

Analytical results for a Bessel function times Legendre polynomials class integrals

When treating problems of vector diffraction in electromagnetic theory, the evaluation of the integral involving Bessel and associated Legendre functions is necessary. Here we present the analytical result for this integral that will make unnecessary numerical quadrature techniques or localized approximations. The solution is presented using the properties of the Bessel and associated Legendre functions.Comment: 4 page