Search results for "Statistical and Nonlinear Physics"

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.

Abstracts from the CECAM workshop on computer simulations of cellular automata

1989

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…

Magneto-optical properties of two-layer film systems based on Fe and Cr

2020

The results of the investigation of two-layer Fe/Cr systems using the magneto-optical Kerr effect (MOKE) are presented in this paper. The samples were obtained by thermal evaporation in a vacuum with a thickness of individual layers from 2 nm to 50 nm. It was found that the presence of the Cr layer significantly affects the values of the coercivity and the Kerr angle. At a substrate temperature of 450 K, the value of the coercivity is almost half that of the same sample obtained at room temperature of the substrate. In addition, the influence of the order of deposition of layers, as well as the effect of a thin gold protective layer on the parameters measured by the Kerr method, is shown. …

Non-Linearity Extremum in Niobium Doped Potassium Tantalate

1997

We report non-linear dielectric measurements in the KTaO 3 :Nb system (x Nb ≤ 0.05). The non-linear susceptibility diverges at low temperatures and reaches maximum values in the intermediate range (0.0075 ≤ x Nb ≤ 0.02). To account for this extremum non linearity, we propose a model of temperature dependent clusters which fits with a number of experimental reports. We also suggest that this model may be applied to the related compounds SrTiO 3 :Ca and KTaO 3 :Na.

Effective characterization of the phase and intensity profiles of asymmetrically distorted light pulses in optical fiber systems

2009

International audience; We address the problem of characterization of light pulses that propagate in long-haul high-bit-rate optical communication systems under strongly perturbed conditions. We show that the conventional technique for characterization of the phase and intensity profile of such pulses becomes qualitatively inconsistent when the pulse's profile is asymmetrically distorted with respect to its center of mass. We resolve these inconsistencies by partially reformulating the conventional technique by means of appropriate pulse parameters, which we call upgraded parameters, that allow a fair characterization of the intensity and phase of all types of light pulses, including those …

The role of noise on the steady state distributions of phytoplankton populations

2016

The spatio-temporal behaviour of total chlorophyll concentration is investigated in the middle of the Tyrrhenian Sea by using a stochastic approach. The study is based on a reaction-diffusion-taxis model, which is used to analyse the dynamics of five phytoplankton groups, responsible for about 80% of the total chlorophyll a inside the euphotic zone of the water column. The analysis is performed by considering: (i) the intraspecific competition of the phytoplanktonic groups for limiting factors, i.e. light intensity and nutrient concentration, (ii) the seasonal changes of environmental variables, and (iii) the random fluctuations of the components of the velocity field and temperature. Speci…

Intermittent targeted therapies and stochastic evolution in patients affected by chronic myeloid leukemia

2016

Front line therapy for the treatment of patients affected by chronic myeloid leukemia (CML) is based on the administration of tyrosine kinase inhibitors, namely imatinib or, more recently, axitinib. Although imatinib is highly effective and represents an example of a successful molecular targeted therapy, the appearance of resistance is observed in a proportion of patients, especially those in advanced stages. In this work, we investigate the appearance of resistance in patients affected by CML, by modeling the evolutionary dynamics of cancerous cell populations in a simulated patient treated by an intermittent targeted therapy. We simulate, with the Monte Carlo method, the stochastic evolu…