Search results for "Nonlinear system"
showing 10 items of 1446 documents
Stochastic Models of Higher Order Dielectric Responses
2018
The nonlinear response for systems exhibiting Markovian stochastic dynamics is calculated using time-dependent perturbation theory for the Green’s function, the conditional probability to find the system in a given configuration at a certain time given it was in another configuration at an earlier time. In general, the Green’s function obeys a so-called master-equation for the balance of the gain and loss of probability in the various configurations of the system. Using various models for the reorientational motion of molecules it is found that the scaled modulus of the third-order response, \(X_3\), shows a hump-like behavior for random rotational motion in some cases and it exhibits “triv…
Nonlinear active micro-rheology in a glass-forming soft-sphere mixture.
2013
We present extensive molecular dynamics computer simulations of a glass-forming Yukawa mixture, investigating the nonlinear response of a single particle that is pulled through the system by a constant force. Structural changes around the pulled particle are analyzed by pair correlation functions, measured in the deeply supercooled state of the system. A regime of intermediate force strengths is found where the structural changes around the pulled particle are small, although its steady-state velocity shows a strong nonlinear response. This nonlinear response regime is characterized by a force-temperature superposition principle of a Peclet number and anisotropic diffusive behavior. In the …
A theoretical study on threshold conditions of modulation instability in oppositely directed couplers
2016
We theoretically investigate threshold conditions to observe modulation instability (MI) in a two-core nonlinear oppositely directed coupler (ODC) with a negative-index material (NIM) channel. Using linear stability analysis, we obtain an expression for the instability gain. The analysis shows, with two discrete instability regions, that the band at lower values of f (ratio of the backward to forward-propagating waves amplitude) is a result of the nonlinear positive index material (PIM) channel while the broader range band is a consequence of the nonlinear NIM channel. Both bands are highly sensitive to system parameters. We demonstrate that MI has a threshold-like condition in the normal d…
Modeling of the photorefractive nonlinear response in Sn_2P_2S_6 crystals
2007
We develop a theory of the photorefractive nonlinear response for Sn2P2S6 crystals. The theory incorporates two types of charge carrier (optically active and passive), provides explicit expressions for the characteristic buildup-relaxation rates and gain factors, explains naturally a big variety of accumulated experimental data, and facilitates characterization-optimization of this important nonlinear material.
Linear inverse filtering improves spatial separation of nonlinear brain dynamics: a simulation study.
2000
We examined topographic variations in nonlinear measures based on scalp voltages, which were generated by two simulated current dipoles each placed in a different hemisphere of a spherical volume conductor (three-shell model). Dipole dynamics were that of a three-torus and the x-component of the Lorenz-system and scalp voltage were calculated for a configuration of 29 electrode positions. Although estimates for correlation dimension D2 and Lyapunov exponent L1 were close to the theoretical values for the original time series, the simulated scalp voltage data showed almost no topographic resolution of dipole positions. In order to enhance topographic differentiation, we constructed linear in…
On the sources of the late integrated Sachs-Wolfe effect
2000
In some scenarios, the peculiar gravitational potential of linear and mildly nonlinear structures depends on time and, as a result of this dependence, a late integrated Sachs-Wolfe effect appears. Here, an appropriate formalism is used which allows us to improve on the analysis of the spatial scales and locations of the main cosmological inhomogeneities producing this effect. The study is performed in the framework of the currently preferred flat model with cosmological constant, and it is also developed in an open model for comparisons. Results from this analysis are used to discuss the contribution of Great Attractor-like objects, voids, and other structures to the CMB anisotropy.
Exponents of non-linear clustering in scale-free one-dimensional cosmological simulations
2012
One dimensional versions of cosmological N-body simulations have been shown to share many qualitative behaviours of the three dimensional problem. They can resolve a large range of time and length scales, and admit exact numerical integration. We use such models to study how non-linear clustering depends on initial conditions and cosmology. More specifically, we consider a family of models which, like the 3D EdS model, lead for power-law initial conditions to self-similar clustering characterized in the strongly non-linear regime by power-law behaviour of the two point correlation function. We study how the corresponding exponent \gamma depends on the initial conditions, characterized by th…
Forward dihadron correlations in deuteron-gold collisions with a Gaussian approximation of JIMWLK
2012
We compute dihadron correlations in forward deuteron-gold or proton-gold collisions. The running coupling BK equation is used to calculate the energy dependence of the dipole cross sections and extended to higher point Wilson line correlators using a factorized Gaussian approximation. Unlike some earlier works we include both the "inelastic" and "elastic" contributions to the dihadron cross section. We show that the double parton scattering contribution is included in our calculation and obtain both an away side peak that roughly agrees with experimental observations and an estimate for the azimuthal angle-independent pedestal. We find that nonlinear effects for momenta close to the saturat…
Thermalization of the dispersive three-wave interaction
2007
We investigate the role of dispersion effects on the long-term evolution of the nonlinear three-wave interaction. We show that the three waves exhibit, as a general rule, an irreversible evolution towards a thermodynamic equilibrium state in which they propagate with identical velocities. As a result of this thermalization process, the three-wave system is driven away from spatio-temporal resonance, so that the equilibrium state does not satisfy the (phase-matching) resonant conditions of energy and momentum conservation for the averaged frequencies. Moreover, we show that the interplay between temporal dispersion and spatial diffraction leads to the emergence of a peculiar equilibrium stat…
Multipole solitary wave solutions of the higher-order nonlinear Schrödinger equation with quintic non-Kerr terms
2013
We consider a high-order nonlinear Schrodinger (HNLS) equation with third- and fourth-order dispersions, quintic non-Kerr terms, self steepening, and self-frequency-shift effects. The model applies to the description of ultrashort optical pulse propagation in highly nonlinear media. We propose a complex envelope function ansatz composed of single bright, single dark and the product of bright and dark solitary waves that allows us to obtain analytically different shapes of solitary wave solutions. Parametric conditions for the existence and uniqueness of such solitary waves are presented. The solutions comprise fundamental solitons, kink and anti-kink solitons, W-shaped, dipole, tripole, and…