Search results for "nonlinear"
showing 10 items of 3684 documents
Path integral solution by fractional calculus
2008
In this paper, the Path Integral solution is developed in terms of complex moments. The method is applied to nonlinear systems excited by normal white noise. Crucial point of the proposed procedure is the representation of the probability density of a random variable in terms of complex moments, recently proposed by the first two authors. Advantage of this procedure is that complex moments do not exhibit hierarchy. Extension of the proposed method to the study of multi degree of freedom systems is also discussed.
On damping characteristics of frictional hysteresis in pre-sliding range
2016
Frictional hysteresis at relative motion in the pre-sliding range is considered. This effect is characterized by an elasto-plastic interaction, and that on the micro-scale, between two rubbing surfaces in contact that gives rise to nonlinear friction force. The pre-sliding friction force yields hysteresis in displacement. In this study, the damping characteristics of frictional hysteresis are analyzed. It is worth noting that we exclude the viscous damping mechanisms and focus on the pure hysteresis damping to be accounted in the friction modeling. The general properties of pre-sliding friction hysteresis are demonstrated and then compared with the limit case of discontinuous Coulomb fricti…
Gluon correlations in the glasma
2010
The physics of the initial conditions of heavy ion collisions is dominated by the nonlinear gluonic interactions of QCD. These lead to the concepts of parton saturation and the Color Glass Condensate (CGC). We discuss recent progress in calculating multi-gluon correlations in this framework, prompted by the observation that these correlations are in fact easier to compute in a dense system (nucleus-nucleus) than a dilute one (proton-proton).
Holographic recording in amorphous As2S3 films at 633nm
2006
Abstract Holographic grating recording with focused (light intensity I = 14–124 W/cm 2 ) and unfocused ( I = 0.50–0.78 W/cm 2 ) 633 nm He–Ne laser sub-bandgap light in non-annealed and annealed a-As 2 S 3 films has been experimentally studied. The focused light recording is found to be much more efficient (diffraction efficiency up to 14.9%, specific recording energy down to 216 J/(cm 2 %)) than the unfocused light recording (0.11%, 72 400 J/(cm 2 %)). Some other properties are also different. The hologram lifetime of more than two years and positive refractive index changes take place in the case of focused recording versus two days and negative refractive index changes for unfocused r…
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 …
Post-Double Hopf Bifurcation Dynamics and Adaptive Synchronization of a Hyperchaotic System
2012
In this paper a four-dimensional hyperchaotic system with only one equilibrium is considered and its double Hopf bifurcations are investigated. The general post-bifurcation and stability analysis are carried out using the normal form of the system obtained via the method of multiple scales. The dynamics of the orbits predicted through the normal form comprises possible regimes of periodic solutions, two-period tori, and three-period tori in parameter space. Moreover, we show how the hyperchaotic synchronization of this system can be realized via an adaptive control scheme. Numerical simulations are included to show the effectiveness of the designed control.
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.
Two-photon laser dynamics.
1995
Degenerate as well as nondegenerate three-level two-photon laser (TPL) models are derived. In the limit of equal cavity losses for both fields, it is shown that the nondegenerate model reduces to the degenerate one. We also demonstrate the isomorphism existing between our degenerate TPL model and that of a dressed-state TPL. All these models contain ac-Stark and population-induced shifts at difference from effective Hamiltonian models. The influence of the parameters that control these shifts on the nonlinear dynamics of a TPL is investigated. In particular, the stability of the periodic orbits that arise at the Hopf bifurcation of the system and the extension of the self-pulsing domains of…
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…
Erratum: “The Role of Humidity in Associations of High Temperature with Mortality: A Multicountry, Multicity Study”
2019
There is strong experimental evidence that physiologic stress from high temperatures is greater if humidity is higher. However, heat indices developed to allow for this have not consistently predicted mortality better than dry-bulb temperature.We aimed to clarify the potential contribution of humidity an addition to temperature in predicting daily mortality in summer by using a large multicountry dataset.In 445 cities in 24 countries, we fit a time-series regression model for summer mortality with a distributed lag nonlinear model (DLNM) for temperature (up to lag 3) and supplemented this with a range of terms for relative humidity (RH) and its interaction with temperature. City-specific as…