Search results for "Pattern formation"
showing 10 items of 408 documents
The damped harmonic oscillator in deformation quantization
2005
We propose a new approach to the quantization of the damped harmonic oscillator in the framework of deformation quantization. The quantization is performed in the Schr\"{o}dinger picture by a star-product induced by a modified "Poisson bracket". We determine the eigenstates in the damped regime and compute the transition probability between states of the undamped harmonic oscillator after the system was submitted to dissipation.
Small and hollow magnetic monopoles
2018
We deal with the presence of magnetic monopoles in a non Abelian model that generalizes the standard 't~Hooft-Polyakov model in three spatial dimensions. We investigate the energy density of the static and spherically symmetric solutions to find first order differential equations that solve the equations of motion. The system is further studied and two distinct classes of solutions are obtained, one that can also be described by analytical solutions which is called small monopole, since it is significantly smaller than the standard 't~Hooft-Polyakov monopole. The other type of structure is the hollow monopole, since the energy density is endowed with a hole at its core. The hollow monopole …
Modified post-bifurcation dynamics and routes to chaos from double-Hopf bifurcations in a hyperchaotic system
2012
In order to understand the onset of hyperchaotic behavior recently observed in many systems, we study bifurcations in the modified Chen system leading from simple dynamics into chaotic regimes. In particular, we demonstrate that the existence of only one fixed point of the system in all regions of parameter space implies that this simple point attractor may only be destabilized via a Hopf or double Hopf bifurcation as system parameters are varied. Saddle-node, transcritical and pitchfork bifurcations are precluded. The normal form immediately following double Hopf bifurcations is constructed analytically by the method of multiple scales. Analysis of this generalized double Hopf normal form …
Cavity solitons in nondegenerate optical parametric oscillation
2000
Abstract We find analytically cavity solitons in nondegenerate optical parametric oscillators. These solitons are exact localised solutions of a pair of coupled parametrically driven Ginzburg–Landau equations describing the system for large pump detuning. We predict the existence of a Hopf bifurcation of the soliton resulting in a periodically pulsing localised structure. We give numerical evidence of the analytical results and address the problem of cavity soliton interaction.
Turing Instability and Pattern Formation for the Lengyel–Epstein System with Nonlinear Diffusion
2014
In this work we study the effect of density dependent nonlinear diffusion on pattern formation in the Lengyel---Epstein system. Via the linear stability analysis we determine both the Turing and the Hopf instability boundaries and we show how nonlinear diffusion intensifies the tendency to pattern formation; in particular, unlike the case of classical linear diffusion, the Turing instability can occur even when diffusion of the inhibitor is significantly slower than activator's one. In the Turing pattern region we perform the WNL multiple scales analysis to derive the equations for the amplitude of the stationary pattern, both in the supercritical and in the subcritical case. Moreover, we c…
Testing the Outflow Process over a Triangular Labyrinth Weir
2017
In this paper, the dimensionless stage-discharge relation for a sharp-crested triangular labyrinth weir, determined in a previous study, is initially tested by some experimental runs carried out in a laboratory flume. According to this relationship, the flow magnification is affected by the length-magnification ratio and the head to one cycle width ratio. The measurements allowed to test the applicability of this dimensionless relation for different values of both the angle of the sidewall to the main flow direction and the weir height. Finally, the proposed dimensionless equation was also tested by using experimental measurements carried out for broad-crested triangular labyrinth weir.
Optical Soliton Molecules in Fiber Lasers
2006
Recent experiments demonstrate that fiber laser cavities are able to support various multisoliton complexes, analogous to soliton molecules, which could have impact on optical information transmission or storage. These advances are guided by the concept of dissipative soliton.
Pattern Formation Kinetics for Charged Molecules on Surfaces: Microscopic Correlation Function Analysis
2011
The kinetics of pattern formation and phase separation in a system of two types of oppositely charged molecules with competing short- and long-range interactions on surfaces/interfaces is studied combining three methods: a microscopic formalism of the joint correlation functions, reverse Monte Carlo, and nonequilibrium charge-screening factors. The molecular ordering occurs on the background of the Ostwald ripening and thus is strongly nonequilibrium. We have demonstrated how initial random distribution of molecules is changed for loose similar-molecule aggregates, with further reorganization into dense macroscopic domains of oppositely charged molecules. Pattern formation process is charac…
Effective interactions of colloids on nematic films.
2008
The elastic and capillary interactions between a pair of colloidal particles trapped on top of a nematic film are studied theoretically for large separations $d$. The elastic interaction is repulsive and of quadrupolar type, varying as $d^{-5}$. For macroscopically thick films, the capillary interaction is likewise repulsive and proportional to $d^{-5}$ as a consequence of mechanical isolation of the system comprised of the colloids and the interface. A finite film thickness introduces a nonvanishing force on the system (exerted by the substrate supporting the film) leading to logarithmically varying capillary attractions. However, their strength turns out to be too small to be of importanc…
Optical propagation loss measurements in electro optical host-guest waveguides
2013
Thin organic waveguiding layers are applied more and more frequently as optical components in novel optoelectronic devices. For development of such devices it is important to know the optical properties of the used waveguides. One of the most important parameters is optical propagation loss in the waveguide. In this paper we present optical propagation loss measurements in planar electro optical waveguides using travelling fiber method. Using this method attenuation coefficient α at 633 nm as a function of chromophore concentration for the first two guiding modes in the slab waveguide was determined.