Search results for "PD"

Viscous-Inviscid Interactions in a Boundary-Layer Flow Induced by a Vortex Array

2014

In this paper we investigate the asymptotic validity of boundary layer theory. For a flow induced by a periodic row of point-vortices, we compare Prandtl's solution to Navier-Stokes solutions at different $Re$ numbers. We show how Prandtl's solution develops a finite time separation singularity. On the other hand Navier-Stokes solution is characterized by the presence of two kinds of viscous-inviscid interactions between the boundary layer and the outer flow. These interactions can be detected by the analysis of the enstrophy and of the pressure gradient on the wall. Moreover we apply the complex singularity tracking method to Prandtl and Navier-Stokes solutions and analyze the previous int…

Singularity formation for Prandtl’s equations

2009

Abstract We consider Prandtl’s equations for an impulsively started disk and follow the process of the formation of the singularity in the complex plane using the singularity tracking method. We classify Van Dommelen and Shen’s singularity as a cubic root singularity. We introduce a class of initial data, uniformly bounded in H 1 , which have a dipole singularity in the complex plane. These data lead to a solution blow-up whose time can be made arbitrarily short within the class. This is numerical evidence of the ill-posedness of the Prandtl equations in H 1 . The presence of a small viscosity in the streamwise direction changes the behavior of the singularities. They stabilize at a distanc…

Determining a Random Schrödinger Operator : Both Potential and Source are Random

2020

We study an inverse scattering problem associated with a Schr\"odinger system where both the potential and source terms are random and unknown. The well-posedness of the forward scattering problem is first established in a proper sense. We then derive two unique recovery results in determining the rough strengths of the random source and the random potential, by using the corresponding far-field data. The first recovery result shows that a single realization of the passive scattering measurements uniquely recovers the rough strength of the random source. The second one shows that, by a single realization of the backscattering data, the rough strength of the random potential can be recovered…

Local regularity for time-dependent tug-of-war games with varying probabilities

2016

We study local regularity properties of value functions of time-dependent tug-of-war games. For games with constant probabilities we get local Lipschitz continuity. For more general games with probabilities depending on space and time we obtain H\"older and Harnack estimates. The games have a connection to the normalized $p(x,t)$-parabolic equation $(n+p(x,t))u_t=\Delta u+(p(x,t)-2) \Delta_{\infty}^N u$.

Resonances over a potential well in an island

2020

In this paper we study the distribution of scattering resonances for a multidimensional semi-classical Schr\"odinger operator, associated to a potential well in an island at energies close to the maximal one that limits the separation of the well and the surrounding sea.

A population genetic study of the endangered plant speciesLimonium dufourii(Plumbaginaceae) based on amplified fragment length polymorphism (AFLP)

1999

Limonium dufourii (Plumbaginaceae) is a triploid species with obligate apomictic reproduction and is endemic to the East Mediterranean coast of Spain, where it is present in only six populations, most of which have a very low number of individuals. Genetic variation and population structure in this species was studied using amplified fragment length polymorphisms (AFLPs) as markers, using the same individuals as in a previous study with random amplified polymorphic DNA (RAPD). Three different primers provided 252 bands of which 51 were polymorphic among the 152 individuals analysed. Those polymorphic bands were able to define 65 different phenotypes, of which all but two were present in onl…

Exact controllability to trajectories for entropy solutions to scalar conservation laws in several space dimensions

2019

We describe a new method which allows us to obtain a result of exact controllability to trajectories of multidimensional conservation laws in the context of entropy solutions and under a mere non-degeneracy assumption on the flux and a natural geometric condition.

Ceļš: Latvijas Universitātes Teoloģijas fakultātes teoloģisks, reliģijpētniecisks un kultūrvēsturisks izdevums, Nr. 65

2015

Symmetry breaking in a constrained cheeger type isoperimetric inequality

2015

We study the optimal constant in a Sobolev inequality for BV functions with zero mean value and vanishing outside a bounded open set. We are interested in finding the best possible embedding constant in terms of the measure of the domain alone. We set up an optimal shape problem and we completely characterize the behavior of optimal domains.

Sensitivities of Amazonian clouds to aerosols and updraft speed

2017

Abstract. The effects of aerosol particles and updraft speed on warm-phase cloud microphysical properties are studied in the Amazon region as part of the ACRIDICON-CHUVA experiment. Here we expand the sensitivity analysis usually found in the literature by concomitantly considering cloud evolution, putting the sensitivity quantifications into perspective in relation to in-cloud processing, and by considering the effects on droplet size distribution (DSD) shape. Our in situ aircraft measurements over the Amazon Basin cover a wide range of particle concentration and thermodynamic conditions, from the pristine regions over coastal and forested areas to the southern Amazon, which is highly poll…