Search results for "Nonlinear system"
showing 10 items of 1446 documents
Nonlocality and fluctuations near the optical analog of a sonic horizon
2013
We consider the behavior of fluctuations near the sonic horizon and the role of the nonlocality of interaction (nonlinearity) on their regularization. The nonlocality dominates if its characteristic length scale is larger than the regularization length. The influence of nonlocality may be important in the current experiments on the transonic flow in Kerr nonlinear media. Experimental conditions, under which the observation of straddled fluctuations can be observed, are discussed.
Large data scattering for NLKG on waveguide ℝd × 𝕋
2020
We consider the pure-power defocusing nonlinear Klein–Gordon equation, in the [Formula: see text]-subcritical case, posed on the product space [Formula: see text], where [Formula: see text] is the one-dimensional flat torus. In this framework, we prove that scattering holds for any initial data belonging to the energy space [Formula: see text] for [Formula: see text]. The strategy consists in proving a suitable profile decomposition theorem on the whole manifold to pursue a concentration-compactness and rigidity method along with the proofs of (global in time) Strichartz estimates.
KPZ equation with realistic short-range-correlated noise
2003
We study a realistic simulation model for the propagation of slow-combustion fronts in paper. In the simulations the deterministic part of the dynamics is that of the KPZ equation. The stochastic part, including in particular the short-range noise correlations, is taken from images of the structure of real paper samples. The parameters of the simulations are determined by using an inverse method applied to the experimental front data and by comparing the simulated and the experimental effective-noise distributions. Our model predicts well the shape of the spatial and temporal correlation functions, including the location of the crossovers from short-range (SR) to long-range (LR) behavior. T…
X-shaped space-time coherence in optical parametric generation
2007
We study the spatiotemporal coherence properties of superfluorescence radiation generated in optical parametric amplification of quantum noise. We show that the angular dispersion properties of the spatiotemporal spectra, measured in different phase-matching conditions, lead to a clear X-shaped structure of the mutual correlation function of the radiation. Within a statistical picture, we interpret the generated superfluorescence as a stochastic “gas” of quasistationary modes characterized by a skewed correlation in the spatiotemporal domain, with characteristics similar to linear and nonlinear X waves not describable within a separable approach in space and time.
Determination of the stochastic evolution equation from noisy experimental data
2003
We have determined the coefficients of the Kardar-Parisi-Zhang equation as functions of coarse graining, which best describe the time evolution and spatial behavior observed for slow-combustion fronts in sheets of paper and magnetic flux fronts in a thin-film high-Tc superconductor. Reconstruction of the relevant equation of motion and its coefficients was mainly based on the inverse method proposed by Lam and Sander [Phys. Rev. Lett. 71, 561 (1993)]. The coefficient of the nonlinear term was also determined from the local slope-dependence of the front velocity.
Polar Sets in a Nonlinear Potential Theory
1988
In this lecture we discuss nonlinear potential theory based on “A-super-harmonic functions”; the theory can be viewed as a (nonlinear) extension of the classical study of superharmonic functions in ℝn.
Experimental Investigation of Random Vibration Control Through Dry Friction
1997
The purpose of this experimental investigation is to measure the response statistics in the presence of base friction and other friction sources. The experimental model emulates a one-floor building supported on four leaf springs, subjected to band limited random excitation. Two different types of model base are considered, a friction base and a frictionless base. In both cases friction can also be applied at two sides of the model’s main mass against the direction of its motion. Excitation and response transducer signals are processed to estimate excitation and response statistics in the presence and in the absence of top mass friction. Measured statistics include mean squares, autocorrela…
Transverse patterns in degenerate optical parametric oscillation and degenerate four-wave mixing.
1996
Transverse pattern formation in both degenerate optical parametric oscillation and degenerate four-wave mixing is considered both theoretically and numerically. In the limit of small signal detuning both systems are shown to be described by the real Swift-Hohenberg equation. Contrarily, for small signal and large pump detunings the Swift-Hohenberg equation is modified differently in both systems, by the appearance of additional nonlinear terms, which signal the existence of nonlinear resonances that are theoretically studied through the derivation of the amplitude equation for the roll pattern in both systems. Numerical analysis supports the theoretical predictions. \textcopyright{} 1996 Th…
Solitary excitations in one-dimensional magnets
1991
Abstract The present status of theoretical and experimental investigations of solitary excitations in one-dimensional magnetic systems is reviewed. A survey of exact solutions to the nonlinear equations of motion for pertinent classical chain systems (sine-Gordon chain and ferromagnetic Heisenberg chains with various anisotropies) is given. Particular emphasis is devoted to the role of solitons in the thermodynamics of such systems. Models corresponding to real quasi-one-dimensional magnets are broadly discussed to demonstrate the properties of their solitary excitations. The experimental significance of such nonlinear excitations in the static and dynamic quantities of such systems is disc…
GAP solitons in 1D asymmetric physical systems
2008
We present a general approach for studying the nonlinear transmittance and gap solitons characteristics of asymmetric and one dimensional (1 D) systems in the low amplitude or Nonlinear Schrodinger limit. Included in this approach are some novel results on naturally asymmetric systems and systems where the symmetry is broken by an external constant force.