Wolfgang Pauli Institute (WPI) Vienna 


Home  Practical Information for Visitors  Events  People  WPI Projects  
Login  Thematic Programs  Pauli Fellows  Talks  Research Groups 
Texier, Benjamin (Univ. de Paris VII)  WPI, Seminar Room 08.135  Fri, 2. Oct 15, 10:30 
Spacetime resonances and highfrequency instabilities in twofluid EulerMaxwell systems  
We show that spacetime resonances induce highfrequency instabilities in the twofluid EulerMaxwell system. This implies in particular that the Zakharov approximation to EulerMaxwell is stable if and only if the group velocity vanishes. The instability proof relies on a shorttime representation formula for the flows of pseudodifferential operators of order zero. This is joint work with Eric Dumas (Grenoble) and Lu Yong (Prague).  

Watanabe, Tatsuya (Kyoto Sangyo University)  WPI, Seminar Room 08.135  Fri, 2. Oct 15, 9:15 
Uniqueness and asymptotic behavior of ground states for quasilinear Schrodinger equations arising in plasma physics  
In this talk, we consider a quasiinear Schrodinger equation which appears in the study of plasma physics. We are interested in the uniqueness of ground states without assuming any restriction on a physical parameter. We also study asymptotic behavior of ground states as the parameter goes to zero.  

Stimming, HansPeter (Univ. Wien)  WPI, Seminar Room 08.135  Thu, 1. Oct 15, 11:15 
Nonlocal NLS of derivative type for modeling highly nonlocal optical nonlinearities  
A new NLS type equation is employed for modeling longrange interactions in nonlinear optics, in a collaboration with experimental physicists. It is of quasilinear type and models fluctuations around a 'continuouswave polariton' which are chosen according to Bogoliubov theory. We present a numerical discretization method and simulation results. Mathematical theory for this equation is work in progress.  

Pomponio, Alessio (Politecnico di Bari)  WPI, Seminar Room 08.135  Thu, 1. Oct 15, 10:30 
BornInfeld equations in the electrostatic case  
The equation in (BI) appears for instance in the BornInfeld nonlinear electromagnetic theory: in the electrostatic case it corresponds to the Gauss law in the classical Maxwell theory and so is the electric potential and is an assigned extended charge density. We discuss existence, uniqueness and regularity of the solution of (BI). The results have been obtained in a joint work with Denis Bonheure and Pietro d’Avenia.  

Ohta, Masahito (Science University of Tokyo)  WPI, Seminar Room 08.135  Thu, 1. Oct 15, 9:15 
Stability of standing waves for a system of nonlinear Schrodinger equations with cubic nonlinearity  
We consider a system of nonlinear Schrodinger equations with cubic nonlinearity, called a coherently coupled NLS system (CCNLS) in nonlinear optics, in one space dimension. We study orbital stability and instability of standing wave solutions of (CCNLS), and prove similar results to Colin and Ohta (2012) which studies a system of NLS equations with quadratic nonlinearity. This is a joint work with Shotaro Kawahara (Tokyo University of Science).  

Melinand, Benjamin (Univ. de Bordeaux)  WPI, Seminar Room 08.135  Wed, 30. Sep 15, 11:15 
The Proudman resonance  
In this talk, I will explain the Proudman resonance. It is a resonant respond in shallow waters of a water body on a traveling atmospheric disturbance when the speed of the disturbance is close to the typical water wave velocity. In order to explain this phenomenon, I will prove a local wellposedness of the water waves equations with a non constant pressure at the surface, taking into account the dependence of small physical parameters. Then, I will justify mathematically the historical work of Proudman. Finally, I will study the linear water waves equations and I will give dispersion estimates in order to extend The Proudman resonance to deeper waters. To complete these asymptotic models, I will show some numerical simulations.  

Le Coz, Stefan (Univ. De Toulouse)  WPI, Seminar Room 08.135  Wed, 30. Sep 15, 10:30 
On a singularly perturbed GrossPitaevskii equation  
We consider the 1D GrossPitaevskii equation perturbed by a Dirac potential. Using a fine analysis of the properties of the linear propagator, we study the wellposedness of the Cauchy Problem in the energy space of functions with modulus 1 at infinity. Then we study existence and stability of the black solitons with a combination of variational and perturbation arguments. This is a joint work with Isabella Ianni and Julien Royer.  

Klein, Christian (Univ. de Bourgogne)  WPI, Seminar Room 08.135  Wed, 30. Sep 15, 9:15 
Numerical study of fractional nonlinear Schrödinger equations  
Using a Fourier spectral method, we provide a detailed numerical investigation of dispersive Schrödingertype equations involving a fractional Laplacian in an onedimensional case. By an appropriate choice of the dispersive exponent, both mass and energy sub and supercritical regimes can be identified. This allows us to study the possibility of finite time blowup versus global existence, the nature of the blowup, the stability and instability of nonlinear ground states and the longtime dynamics of solutions. The latter is also studied in a semiclassical setting. Moreover, we numerically construct ground state solutions of the fractional nonlinear Schrödinger equation.  

Hirayama; Hiroyuki (Nagoya Univ.)  WPI, Seminar Room 08.135  Tue, 29. Sep 15, 14:15 
Wellposedness for a system of quadratic derivative nonlinear Schrödinger equations with periodic initial data.  
We consider the Cauchy problem of a system of quadratic derivative nonlinear Schrödinger equations which was introduced by M. Colin and T. Colin as a model of laserplasma interaction. In this talk, we prove the wellposedness of this system for the periodic initial data. In particular, if the coefficients of Laplacian satisfy some conditions, then the wellposedness is proved at the scaling critical regularity by using U^2 and V^2 spaces.  

Hayashi, Nakao (Osaka Univ.)  WPI, Seminar Room 08.135  Tue, 29. Sep 15, 11:15 
Asymptotics of solutions to fourthorder nonlinear Schrödinger equations  
We consider the Cauchy problem for the fourthorder nonlinear Schrödinger equation with a critical nonlinearity and prove the asymptotic stability of solutions in the neighborhood of the self similar solutions under the non zero mass condition and the smallness on the data.  

González de Alaiza Martínez, Pedro (CEA)  WPI, Seminar Room 08.135  Tue, 29. Sep 15, 10:30 
Mathematical models for terahertz emissions by lasergas interaction  
Terahertz (THz) emissions have nowadays important applications such as security screening and imaging. Lasergas interaction reveals itself to be a promising technique to generate broadband and intense THz sources suitable for these applications. In this talk, I will explain recent mathematical models and their underlying physics explaining the THz radiation generated when ultrafast laser pulses ionize a gas at high intensities. Solutions to the model equations will be compared with direct numerical simulations.  

Dumas, Eric (Univ. de Grenoble)  WPI, Seminar Room 08.135  Tue, 29. Sep 15, 9:15 
Some variants of the focusing NLS equations Derivation, justification and open problems  
The usual model of nonlinear optics given by the cubic NLS equation is too crude to describe large intensity phenomenas such as filamentation, which modifies the focusing of laser beams. I shall explain how to derive some more appropriate variants of the NLS model from Maxwell's equations, using improved approximations of the original dispersion relation or taking ionization effects into account. I shall provide rigorous error estimates for the models considered, and also discuss some open problems related to these modified NLS equations. This is joint work with David Lannes and Jeremie Szeftel.  

Saut, JeanClaude (Univ. Paris d'Orsay)  WPI, Seminar Room 08.135  Mon, 28. Sep 15, 15:30 
Full dispersion water waves models  
We will survey recent results and open problems on various nonlocal "full dispersion" models of surface water waves.  

Colin, Mathieu (Univ. de Bordeaux)  WPI, Seminar Room 08.135  Mon, 28. Sep 15, 14:30 
Solitons in quadratic media  
In this talk, we investigate the properties of solitonic structures arising in quadratic media. More precisely, we look for stationary states in the context of normal or anomalous dispersion regimes, that lead us to either elliptic or nonelliptic systems and we address the problem of orbital stability. Finally, we present some numerical experiments in order to compute localized states for several regimes.  

Esther Daus  WPI, Seminar Room 08.135  Wed, 16. Sep 15, 10:45 
Crossdiffusion systems: "Population dynamics model (Joint work with A. Jüngel), Diffusion through obstacles (Joint work with M. Bruna, A. Jüngel)"  
In this talk we will discuss two different crossdiffusion models. The first model is used in population dynamics in biology and can be derived from a lattice in the case when we are not taking into account any volumefilling effects. We will present recent results concerning the existence of global weak solutions under the assumption that the system possesses a formal gradientflow structure using ideas of [A. Jüngel: Boundednessbyentropy method. Nonlinearity 28 (2015)]. The second model describes diffusion through obstacles. The underlying crossdiffusion system can be derived from a two species mixture of Brownian hard spheres. We will discuss open questions concerning this model.  

Ulisse Stefanelli  WPI, Seminar Room 08.135  Wed, 16. Sep 15, 10:00 
"The WED principle in metric spaces"  
I will present the WED variational approach to gradientflow evolution in metric spaces. A reference application is to densities and empirical measures. In the linearspace case, the WED strategy entails in an ellipticintime regularization of the problem. The picture in the metric case is confined to the variational level and the discussion relies on a Pontyagintype principle. This is joint work with Riccarda Rossi (Brescia), Giuseppe Savar' (Pavia), and Antonio Segatti (Pavia).  

Ruediger Müller  WPI, Seminar Room 08.135  Tue, 15. Sep 15, 14:45 
"Modeling of Ion Transport in Nanopores"  
Until recently, the (Poisson)NernstPlanck equations have been the standard model for the description of ion transport in diluted electrolyte solutions, although it was known that they fail to reasonably limit the ion concentration in diffuse double layers. This weakness can be remedied by a thermodynamic consistent coupling to the momentum balance and introducing an appropriate elastic law, rather than by a mere modification of the entropy of mixing. In many electrochemical applications, the Debye length that controls the width of the diffuse layers is typically very small compared to the macroscopic dimensions of the system. In these situations a spacial resolution of the layers is often not necessary. By the method of formal asymptotic analysis we derive a reduced model that is locally electric neutral and does not resolve the layers but incorporates all relevant features of the layers into a new set of interface equations. Nanopores typically have a strongly anisotropic geometry where the diameter is close to the Debye length but the length in axial direction is larger by at least one order of magnitude. We discuss the scaling to dimensionless quantities and present a reduced 1dmodel for arbitrary geometries with rotational symmetry. Multidimensional solutions that resolve boundary layers can be recovered from the lowerdimensional solution.  

Ulrich Dobramysl  WPI, Seminar Room 08.135  Tue, 15. Sep 15, 14:00 
"Exploring unknown environments  from robot experiments to numerical modelling"  
I will present examples of modelling collective movement via robot experiments. In the first part I will focus on an investigation on how two communicating individuals can most efficiently navigate a corridor without external sensory input. The second part of my talk will be about robot swarms and their strategies for target finding in an unknown environment. These studies where performed via a combination of robot experiments and numerical simulations.  

Hartmut Loewen  WPI, Seminar Room 08.135  Tue, 15. Sep 15, 11:15 
"Phase separation and turbulence in active Systems"  
Ordinary materials are "passive" in the sense that their constituents are typically made by inert particles which are subjected to thermal fluctuations, internal interactions and external fields but do not move on their own. Living systems, like schools of fish, swarms of birds, pedestrians and swimming microbes are called "active matter" since they are composed of selfpropelled constituents. Active matter is intrinsically in nonequilibrium and exhibits a plethora of novel phenomena as revealed by a recent combined effort of statistical theory, hydrodynamics and realspace experiments. The talk provides an introduction into the modelling of active matter focussing on biological and artificial microswimmers as key examples of active systems. A number of singleparticle and collective phenomena in active matter will be addressed ranging from the most disordered state of matter (turbulence) to the purely kinetic phase separation in active systems.  

Jay Newby  WPI, Seminar Room 08.135  Tue, 15. Sep 15, 10:00 
Metastable dynamics in gene circuits driven by intrinsic noise  
Metastable transitions are rare events, such as bistable switching, that occur under weak noise conditions, causing dramatic shifts in the expression of a gene. Within a gene circuit, one or more genes randomly switch between regulatory states, each having a different mRNA transcription rate. The circuit is self regulating when the proteins it produces affect the rate of switching between gene regulatory states. Under weak noise conditions, the deterministic forces are much stronger than fluctuations from gene switching and protein synthesis. A general tool used to describe metastability is the quasi stationary analysis (QSA). A large deviation principle is der ived so that the QSA can explicitly account for random gene switching without using an adiabatic limit or diffusion approximation, which are unreliable and inaccurate for metastable events.This allows the existing asymptotic and numerical methods that have been developed for continuous Markov processes to be used to analyze the full model.  

Jon Chapman  WPI, Seminar Room 08.135  Mon, 14. Sep 15, 16:15 
"Excluded volume effects in drift Diffusion"  
When diffusing agents interact with each other their motions are correlated, and the configuration space is of very high dimension. Often an equation for the marginal distribution function of one particle (the “concentration”) is sought by “integrating out” the positions of all the others. This leads to the classic problem of closure, since the equation for the concentration so derived depends on the twopoint correlation function. A common closure is to assume independence at this stage, leading to some form of nonlinear (drift) diffusion equation. Such an approach works well for long range interactions (such as electric fields), but fails for short range interactions (such as steric effects). Here we consider an alternative approach using matched asymptotic expansions, in which the approximation is entirely systematic. We show how information about correlations can be recovered from the concentration. Finally we consider some of the difficulties when both long and short range forces are present.  

Ansgar Juengel  WPI, Seminar Room 08.135  Mon, 14. Sep 15, 15:30 
"Modeling and analysis of multispecies systems in biology"  
The nature is dominated by systems composed of many individuals with a collective behavior. Examples include wildlife populations, biological cell dynamics, and tumor growth. There is a fast growing interest in multispecies systems both in theoretical biology and applied mathematics, but because of their enormous complexity, the scientific understanding is still very poor. Instead of calculating the trajectories of all individuals, it is computationally much simpler to describe the dynamics of the individuals on a macroscopic level by averaged quantities such as population densities. This leads to systems of highly nonlinear partial differential equations with cross diffusion, which may reveal surprising effects such as uphill diffusion and diffusioninduced instabilities, seemingly contradicting our intuition on diffusion. Major difficulties of the mathematical analysis of the crossdiffusion equations are their highly nonlinear structure and the lack of positive definiteness of the diffusion matrix. In this talk, a method inspired from nonequilibrium thermodynamics is proposed, which allows for a mathematical theory of some classes of such systems. It is based on a transformation of entropy variables which make the diffusion matrix positive definite. This property is a purely algebraic condition and may be shown by computer algebra systems. We explain the technique for systems modeling populations and transport through ion channels.  

MarieTherese Wolfram  WPI, Seminar Room 08.135  Mon, 14. Sep 15, 14:30 
"Interaction with fluids"  

JanFrederick Pietschmann  WPI, Seminar Room 08.135  Mon, 14. Sep 15, 14:00 
"CrossDiffusion from onlattice and inverse problems"  

Maria Bruna  WPI, Seminar Room 08.135  Mon, 14. Sep 15, 13:30 
"Crossdiffusion models for offlattice and gradient flow"  

© WPI 20012008. Email : wpi@mat.univie.ac.at  webmaster [Printable version] 