Search results for "Linear system"

Stationary semiconductor equations

1996

The behaviour of a semiconductor device is usually modelled by three coupled nonlinear partial differential equations of elliptic type. Such a system for the transport of mobile charge carriers was first introduced by Van Roosbroeck [Van Roosbroeck] in 1950. Nowadays there are many models which differ in their choice of unknowns, scales, various types of nonlinearities etc. (see, e.g., [Brezzi], [Groger], [Markowich], [Markowich, Ringhofer, Schmeiser], [Mock, 1972], [Polak, den Heijer, Schilders, Markowich], [Pospisek], [Pospisek, Segeth, Silhan], [Selberherr], [Sze], [Zlamal, 1986]).

Relaxation of polar order in suspensions with Quincke effect

2014

The Quincke effect---spontaneous rotation of dielectric particles in a liquid with low conductivity under the action of an electric field---is considered. The distribution functions for the orientation of particle rotation planes are introduced and a set of nonlinear kinetic equations is derived in the mean field approximation considering the dynamics of their orientation in the flow induced by rotating particles. As a result the nonequilibrium phase transition to the polar order, if the concentration of the particles is sufficiently high, is predicted and the condition of the synchronization of particle rotations is established. Two cases are considered: the layer of the Quincke suspension…

NEW NON LINEAR EXCITATIONS IN (CD3)4NMnCl3 (TMMC)

1989

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…