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Discrete spectral incoherent solitons in nonlinear media with noninstantaneous response

2011

International audience; We show theoretically that nonlinear optical media characterized by a finite response time may support the existence of discrete spectral incoherent solitons. The structure of the soliton consists of three incoherent spectral bands that propagate in frequency space toward the low-frequency components in a discrete fashion and with a constant velocity. Discrete spectral incoherent solitons do not exhibit a confinement in the space-time domain, but exclusively in the frequency domain. The kinetic theory describes in detail all the essential properties of discrete spectral incoherent solitons: A quantitative agreement has been obtained between simulations of the kinetic…

ORBITALLY NONEXPANSIVE MAPPINGS

2015

We define a class of nonlinear mappings which is properly larger than the class of nonexpansive mappings. We also give a fixed point theorem for this new class of mappings.

Global Existence for Nonlinear Parabolic Problems With Measure Data– Applications to Non-uniqueness for Parabolic Problems With Critical Gradient ter…

2011

Abstract In the present article we study global existence for a nonlinear parabolic equation having a reaction term and a Radon measure datum: where 1 < p < N, Ω is a bounded open subset of ℝN (N ≥ 2), Δpu = div(|∇u|p−2∇u) is the so called p-Laplacian operator, sign s ., ϕ(ν0) ∈ L1(Ω), μ is a finite Radon measure and f ∈ L∞(Ω×(0, T)) for every T > 0. Then we apply this existence result to show wild nonuniqueness for a connected nonlinear parabolic problem having a gradient term with natural growth.

On Whitham and Related Equations

2017

The aim of this paper is to study, via theoretical analysis and numerical simulations, the dynamics of Whitham and related equations. In particular, we establish rigorous bounds between solutions of the Whitham and Korteweg–de Vries equations and provide some insights into the dynamics of the Whitham equation in different regimes, some of them being outside the range of validity of the Whitham equation as a water waves model.

Abstracts from the CECAM workshop on computer simulations of cellular automata

1989

Constant sign and nodal solutions for nonlinear robin equations with locally defined source term

2020

We consider a parametric Robin problem driven by a nonlinear, nonhomogeneous differential operator which includes as special cases the p-Laplacian and the (p,q)-Laplacian. The source term is parametric and only locally defined (that is, in a neighborhood of zero). Using suitable cut-off techniques together with variational tools and comparison principles, we show that for all big values of the parameter, the problem has at least three nontrivial smooth solutions, all with sign information (positive, negative and nodal).

Random Tensor Theory: Extending Random Matrix Theory to Mixtures of Random Product States

2012

We consider a problem in random matrix theory that is inspired by quantum information theory: determining the largest eigenvalue of a sum of p random product states in $${(\mathbb {C}^d)^{\otimes k}}$$ , where k and p/d k are fixed while d → ∞. When k = 1, the Marcenko-Pastur law determines (up to small corrections) not only the largest eigenvalue ( $${(1+\sqrt{p/d^k})^2}$$ ) but the smallest eigenvalue $${(\min(0,1-\sqrt{p/d^k})^2)}$$ and the spectral density in between. We use the method of moments to show that for k > 1 the largest eigenvalue is still approximately $${(1+\sqrt{p/d^k})^2}$$ and the spectral density approaches that of the Marcenko-Pastur law, generalizing the random matrix…

ABSOLUTE THERMOELECTRIC POWER OF Pb–Sn ALLOYS

2011

International audience; In this work, absolute thermoelectric power (ATP) of Pb, Sn, Pb-20 wt.% Sn, Pb-40 wt.% Sn, Pb-60 wt.% Sn, Pb-80 wt.% Sn are measured. Measurements are performed in a temperature gradient furnace from 20 degrees C to 500 degrees C, for both solid and liquid states. Temperatures are measured with T-type copper-constantan thermocouples, while voltage signal between copper electrodes of those thermocouples is recorded in order to calculate ATP of the sample metal.

Isothermal relaxation of discommensurations in K2ZnCl4

1994

At the incommensurate-ferroelectric transition temperature T c of K 2 ZnCl 4 , the dielectric susceptibility contains an anomalous contribution both above and below T c . Previous quasi-static dielectric measurements and hysteresis loops demonstrated that this anomalous part arises from the peculiar dynamics of discommensurations. We have used isothermal dielectric measurements to get some insight into the long time dynamics of these discommensurations. We have found that the characteristic relaxation times τ are of the order of 10 4 s in the incommensurate and in the ferroelectric phase. Even more unusual is a non-monotonous relaxation which is observed in a restricted temperature range ab…

Analysis of nonlinear time-dependent properties of carbon fiber reinforced plastic under off-axis loading

2021

Abstract Polymeric composites are rheonomic materials and their deformation can be described using the hereditary elasticity relations which allow for describing the mechanical behavior under time-variable loading with consideration of the influence of temperature and other operational factors. A system of hereditary-type constitutive relations is proposed for off-axis specimens of a unidirectional carbon fiber-reinforced plastic subjected to loading at different strain rates. Using the algebra of resolvent operators and inverted transformation, the constitutive equations allowing of description of anisotropy of rheological properties and, in particular, sensitivity to strain rates are deri…