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Shatah, Jalal (Courant Inst. NY)  WPI, Seminar Room 08.135  Tue, 12. Jul 16, 11:00 
Large Box Limit of Nonlinear Schrödinger equations  
The long time dynamics of the nonlinear Schrödinger equation, on a bounded domain, is very rich. Even for small amplitude initial data there can be quasiperiodic solutions, or solutions whose energy cascades between characteristically different length scales. Our aim in this talk is to explain how the longtime dynamics of the equation begin{equation*} left{ begin{array}{l}  i partial_t u + frac{1}{2pi} Delta u = epsilon^{2p} u^{2p} u qquad mbox{set on $(t,x) in mathbb{R} times mathbb{T}^n_L$} u(t=0) =epsilon u_0 end{array} right. end{equation*} can be described when $epsilon$ is small and $L$ is large. We will show how to derive an equation that describe the dynamics beyond the nonlinear time scale which is of order $mathcal{O}(frac1{epsilon^2})$.  

Schilling, Christian (U. Oxford)  WPI, OMP1, Seminar Room 08.135  Thu, 11. Aug 16, 13:30 
“Quantum marginal problem and generalized Pauli constraints”  
The question whether given reduced density operators (marginals) for subsystems of a multipartite quantum system are compatible to a common total state is called quantum marginal problem (QMP). We present the solution found by A. Klyachko just a few years ago as well as the main steps for its derivation. Applying those concepts to fermionic systems reveals further constraints on fermionic occupation numbers beyond Pauli's famous exclusion principle. We introduce and discuss these socalled generalized Pauli constraints in great detail and comment on their potential physical relevance.  

BenavidesRiveros, Carlos (U. HalleWittenberg)  WPI, OMP1, Seminar Room 08.135  Thu, 11. Aug 16, 14:30 
“Pinning and quasipinning in quantum chemistry”  
It is now known that fermionic natural occupation numbers (NONs) do not only obey Pauli’s exclusion principle but are even stronger restricted by the socalled generalized Pauli constraints (GPC). Whenever given NONs lie on or close to the boundary of the allowed region the corresponding Nfermion quantum state has a significantly simpler structure. We explore this phenomenon in the context of quantum chemistry.  

Gottlieb, Alexander (WPI)  WPI, OMP1, Seminar Room 08.135  Thu, 11. Aug 16, 16:00 
“Geometry of the BorlandDennis setting: the Wtype class”  
We call the Hilbert space for three fermions in six orbitals the BorlandDennis setting. It is isomorphic to the alternating tensor product of three copies of the standard 6dimensional Hilbert space C^6. Slater determinant states in the BorlandDennis setting correspond to "decomposable" trivectors, i.e., simple wedge products of three vectors from C^6. Generic wave functions in the BorlandDennis setting can be written as a sum of just two decomposable trivectors. The wave functions that cannot be written as a sum of fewer than three decomposables constitute the "Wtype entanglement class." I will discuss the geometry of the Wtype class within the ambient BorlandDennis space.  

Gottlieb, Alexander (WPI)  WPI, OMP1, Seminar Room 08.135  Fri, 12. Aug 16, 10:00 
“Quasiseparated electron pairs in small molecules”  
Some of the electrons in a molecule are tightly bound to the nuclei. The closely bound "core electrons" can be relatively uncorrelated with the rest of the electrons in the molecule, and may even form what we call a "quasiseparated" pair. [Let F be the electronic wave function of a molecule with N+2 electrons. We say that F features a "quasiseparated pair" if it is approximately equal to the wedge product G ^ H of a geminal G that describes the state of the separated pair and an Nelectron wave function H that is strongly orthogonal to G.] We have computational evidence of such quasiseparated electron pairs in the ground states of very small molecules (like LiH or the Be atom) whose correlated electronic structure can be very accurately approximated with full CI calculations.  

Brezinova, Iva (TU. Wien)  WPI, OMP1, Seminar Room 08.135  Fri, 12. Aug 16, 11:00 
“Solving timedependent manybody quantum problems using the twoparticle reduced density matrix”  
In this talk we will give an overview over our recent progress in solving timedependent manybody problems using the twoparticle reduced density matrix (2RDM) as the fundamental variable. The wavefunction is completely avoided and with this all problems arising from the exponentially increasing complexity with particle number. Key is the reconstruction of the 3RDM which couples to the dynamics of the 2RDM. At this point the approximation to the full solution of the Schrödinger equation enters: while twoparticle correlations are fully incorporated, threeparticle correlations are only approximated. We will discuss the reconstruction of the 3RDM, how we overcome the Nrepresentability problem, and demonstrate the accuracy of our theory on twoexamples: multielectron atoms in strong fields, and ultracold atoms in optical lattices.  

Schilling, Christian (U. Oxford)  WPI, OMP1, Seminar Room 08.135  Fri, 12. Aug 16, 14:00 
“Fermionic exchange symmetry: quantifying its influence beyond Pauli's Exclusion Principle"  
The Pauli exclusion principle has a strong impact on the properties and the behavior of most fermionic quantum systems. Remarkably, even stronger restrictions on fermionic natural occupation numbers follow from the fermionic exchange symmetry. We develop an operationally meaningful measure which allows one to quantify the potential physical relevance of those generalized Pauli constraints beyond the wellestablished relevance of Pauli's exclusion principle. It is based on a geometric hierarchy induced by Pauli exclusion principle constraints. The significance of that measure is illustrated for a fewfermion model which also confirms such nontrivial relevance of the generalized Pauli constraints.  

BenavidesRiveros, Carlos (U. HalleWittenberg)  WPI, OMP1, Seminar Room 08.135  Fri, 12. Aug 16, 15:15 
“Natural extension of HartreeFock through extremal 1fermion Information”  
By employing the simpler structure arising from pinning and quasipinnig a variational optimization method for few fermion ground states is elaborated. We quantitatively confirm its high accuracy for systems whose vector of NON is close to the boundary of the polytope. In particular, we derive an upper bound on the error of the correlation energy given by the ratio of the distance to the boundary of the polytope and the distance of the vector of NON to the HartreeFock point. These geometric insights shed some light on the concept of active spaces, correlation energy, frozen electrons and virtual orbitals.  

Philippe Gravejat (U. CergyPontoise)  WPI, OMP 1, Seminar Room 08.135  Tue, 20. Sep 16, 9:30 
"Stability of solitons for the LandauLifshitz equation with an easyplane anisotropy"  
We describe recent results concerning the orbital and asymptotic stability of dark solitons and multi solitons for the LandauLifshitz equation with an easyplane anisotropy. This is joint work with André de Laire (University of Lille Nord de France), and by Yakine Bahri (Nice Sophia Antipolis University).  

Nicola Visciglia (U. Pisa)  WPI, OMP 1, Seminar Room 08.135  Tue, 20. Sep 16, 10:30 
"Existence and Stability of Standing Waves for NLS in a partial confinement"  
I will discuss a joint work with Bellazzini, Boussaid, Jeanjean about the existence and orbital stability of standing waves for NLS with a partial confinement in a supercritical regime. The main point is to show the existence of local minimizers of the constraint energy.  

Laurent Thomann (U. Lorraine)  WPI, OMP 1, Seminar Room 08.135  Tue, 20. Sep 16, 11:30 
"Invariant measures for NLS in dimension two"  
We consider the defocusing nonlinear Schrödinger equations on a twodimensional compact Riemannian manifold without boundary or a bounded domain in dimension two. In particular, we discuss the Wick renormalization in terms of the Hermite polynomials and the Laguerre polynomials and construct the Gibbs measures corresponding to the Wick ordered Hamiltonian. Then, we construct globalintime solutions with initial data distributed according to the Gibbs measure and show that the law of the random solutions, at any time, is again given by the Gibbs measure.  

Thomas Kappeler (U. Zürich)  WPI, OMP 1, Seminar Room 08.135  Tue, 20. Sep 16, 14:30 
"Analytic extensions of frequencies of integrable PDEs and applications"  
In form of a case study for the mKdV and the KdV2 equation we discuss a novel approach of representing frequencies of integrable PDEs which allows to extend them analytically to spaces of low regularity and to study their asymptotics. Applications include wellposedness results in spaces of low regularity as well as properties of the actions to frequencies map. This is joint work with Jan Molnar.  

Christian Klein (U.Bourgogne)  WPI, OMP 1, Seminar Room 08.135  Tue, 20. Sep 16, 15:30 
"Numerical study of breakup in KadomtsevPetviashvili equations"  
The onset of a dispersive shock in solutions to the KadomtsevPetviashvili (KP) equations is studied numerically. First we study the shock formation in the dispersionless KP equation by using a map inspired by the characteristic coordinates for the onedimensional Hopf equation. This allows to numerically identify the shock and to unfold the singularity. A conjecture for the KP solution near this critical point in the small dispersion limit is presented. It is shown that dispersive shocks for KPI solutions can have a second breaking where modulated lump solutions appear.  

Vincent Duchêne (U. Rennes I)  WPI, OMP 1, Seminar Room 08.135  Wed, 21. Sep 16, 9:30 
"On the wellposedness of the GreenNaghdi System"  
The GreenNaghdi system is an asymptotic model for the waterwaves system, describing the propagation of surface waves above a layer of ideal, homogeneous, incompressible and irrotational fluid, when the depth of the layer is assumed to be small with respect to wavelength of the flow. It can be seen as a perturbation of the standard quasilinear (dispersionless) SaintVenant system, with additional nonlinear higherorder terms. Because of the latter, the wellposedness theory concerning the GN system is not satisfactory, in particular outside of the onedimensional framework. We will discuss novel results, obtained with Samer Israwi, that emphasize the role of the irrotationality assumption.  

Hajer Bahouri (UPEC)  WPI, OMP 1, Seminar Room 08.135  Wed, 21. Sep 16, 10:30 
"Qualitative study of 2D Schrodinger equation with exponential nonlinearity"  
In this lecture, we investigate the behavior of the solutions to the nonlinear Schrodinger equation: (1) ( i@tu + u = f(u); ujt=0 = u0 2 H1 rad(R2); where the nonlinearity f : C ! C is dened by (2) f(u) = p( p 4 juj) u with p > 1 and p(s) = es2 pX1 k=0 s2k k! Recall that the solutions of the Cauchy problem (1)(2) formally satisfy the conservation laws: (3) M(u; t) = Z R2 ju(t; x)j2dx = M(u0) and (4) H(u; t) = Z R2 jru(t; x)j2 + Fp(u(t; x)) dx = H(u0) ; where Fp(u) = 1 4 p+1 p 4 juj It is known (see [4], [6] and [2]) that global wellposedness for the Cauchy problem (1)(2) holds in both subcritical and critical regimes in the functional space C(R;H1(R2)) L4(R;W1;4(R2)). Here the notion of criticity is related to the size of the initial Hamiltonian H(u0) with respect to 1. More precisely, the concerned Cauchy problem is said to be subcritical if H(u0) < 1, critical if H(u0) = 1 and supercritical if H(u0) > 1. Structures theorems originates in the elliptic framework in the studies by H. Brezis and J. M. Coron in [3] and M. Struwe in [8]. The approach that we shall adopt in this article consists in comparing the evolution of oscillations and concentration eects displayed by sequences of solutions of the nonlinear Schrodinger equation (1)(2) and solutions of the linear Schrodinger equation associated to the same sequence of Cauchy data. Our source of inspiration here is the pioneering works [1] and [7] whose aims were to describe the structure of bounded sequences of solutions to semilinear defocusing wave and Schrodinger equations, up to small remainder terms in Strichartz norms. The analysis we conducted in this work emphasizes that the nonlinear eect in this framework only stems from the 1oscillating component of the sequence of the Cauchy data, using the terminology introduced in [5]. This phenomenon is strikingly dierent from those obtained for critical semi linear dispersive equations, such as for instance in [1, 7] where all the oscillating components induce the same nonlinear eect, up to a change of scale. To carry out our analysis, we have been led to develop a prole decomposition of bounded sequences of solutions to the linear Schrodinger equation both in the framework of Strichartz and Orlicz norms. The linear structure theorem we have obtained in this work highlights the distinguished role of the 1oscillating component of the sequence of the Cauchy data. It turns out that there is a form of orthogonality between the Orlicz and the Strichartz norms for the evolution under the ow of the free Schrodinger equation of the unrelated component to the scale 1 of the Cauchy data (according to the vocabulary of [5]), while this is not the case for the 1oscillating component.  

Thomas Alazard (ENS)  WPI, OMP 1, Seminar Room 08.135  Wed, 21. Sep 16, 11:30 
"Control and stabilization of the incompressible Euler equation with free surface"  
The incompressible Euler equation with free surface dictates the dynamics of the interface separating the air from a perfect incompressible fluid. This talk is about the controllability and the stabilization of this equation. The goal is to understand the generation and the absorption of water waves in a wave tank. These two problems are studied by two different methods: microlocal analysis for the controllability (this is a joint work with Pietro Baldi and Daniel HanKwan), and study of global quantities for the stabilization (multiplier method, Pohozaev identity, hamiltonian formulation, Luke’s variational principle, conservation laws…).  

Eric Wahlen (NTNU)  WPI, OMP 1, Seminar Room 08.135  Wed, 21. Sep 16, 14:30 
"On the highest wave for Whitham’s wave equation"  
In the 1960’s G. B. Whitham suggested a nonlocal version of the KdV equation as a model for water waves. Unlike the KdV equation it is not integrable, but it has certain other advantages. In particular, it has the same dispersion relation as the full water wave problem and it allows for wave breaking. The equation has a family of periodic, travelling wave solutions for any given wavelength. Whitham conjectured that this family contains a highest wave which has a cusp at the crest. I will outline a proof of this conjecture using global bifurcation theory and precise information about an integral operator which appears in the equation. Joint work with M. Ehrnström.  

Mats Ehrnström (NTNU)  WPI, OMP 1, Seminar Room 08.135  Wed, 21. Sep 16, 15:30 
"Existence of a Highest Wave in a FullDispersion Shallow Water Model"  
We consider the existence of periodic traveling waves in a bidirectional Whitham equation, combining the full twoway dispersion relation from the incompressible Euler equations with a canonical quadratic shallow water nonlinearity. Of particular interest is the existence of a highest, cusped, traveling wave solution, which we obtain as a limiting case at the end of the main bifurcation branch of $2pi$periodic traveling wave solutions. Unlike the unidirectional Whitham equation, containing only one branch of the full Euler dispersion relation, where such a highest wave behaves like $x^{1/2}$ near its peak, the cusped waves obtained here behave like $xlogx$ at their peak and are smooth away from their highest points. This is joint work with Mathew A. Johnson and Kyle M. Claassen at University of Kansas.  

Thomas Duyckaerts (U. Paris XIII)  WPI, OMP 1, Seminar Room 08.135  Thu, 22. Sep 16, 9:30 
"Dynamics of the energycritical wave equation"  
It is conjectured that bounded solutions of the focusing energycritical wave equation decouple asymptotically as a sum of a radiation term and a finite number of solitons . In this talk, I will review recent works on the subject, including the proof of a weak form of this conjecture (joint work with Hao Jia, Carlos Kenig and Frank Merle)  

Oana Ivanovici (U. Nizza)  WPI, OMP 1, Seminar Room 08.135  Thu, 22. Sep 16, 10:30 
"Dispersion for the wave and the Schrödinger Equations outside strictly convex Domains and counterexamples"  
We consider the linear wave equation and the linear Schr dingier equation outside a compact, strictly convex obstacle in R^d with smooth boundary. In dimension d = 3 we show that for both equations, the linear flow satises the (corresponding) dispersive estimates as in R^3. For d>3, if the obstacle is a ball, we show that there exists at least one point (the Poisson spot) where the dispersive estimates fail. This is joint work with Gilles Lebeau.  

Evelyne Miot (U. Grenoble Alpes)  WPI, OMP 1, Seminar Room 08.135  Thu, 22. Sep 16, 11:30 
"Collision of vortex Filaments"  
In this talk we will present some results on the dynamics of vortex filaments according to a model introduced by Klein, Majda and Damodaran, focusing on the issue of collisions. This is a joint work with Valeria Banica and Erwan Faou.  

Mathieu Colin (U. Bordeaux I)  WPI, OMP 1, Seminar Room 08.135  Thu, 22. Sep 16, 14:30 
"Stability properties for a MaxwellSchrödinger System"  
The aim of this talk is to present some qualitative properties of a coupled MaxwellSchrödinger system. First, I will describe conditions for the existence of minimizers with prescribed charge in terms of a coupling constant e. Secondly, I will study the existence of ground states for the stationary problem, the uniqueness of ground states for small e and finish with the orbital stability for the quadratic nonlinearity. This is a joint work with Tatsuya Watanabe.  

Francois Golse (U.Ecole Polytechnique)  WPI, OMP 1, Seminar Room 08.135  Thu, 22. Sep 16, 15:30 
"The MeanField Limit for the Quantum NBody Problem: Uniform in Convergence Rate"  
The Hartree equation can be derived from the Nbody Heisenberg equation by the meanfield limit assuming that the particle number N tends to infinity. The first rigorous result in this direction is due to Spohn (1980) (see also [BardosGolseMauser, Meth. Applic. Anal. 7:275294, (2000)] for more details), and is based on analyzing the Dyson series representing the solution of the BBGKY hierarchy in the case of bounded interaction potentials.This talk will (1) provide an explicit convergence rate for the Spohn method, and (2) interpolate the resulting convergence rate with the vanishing h bound obtained in [GolseMouhotPaul, Commun. Math. Phys. 343:165205 (2016)] by a quantum variant of optimal transportation modulo O(h) terms. The final result is a bound for a MongeKantorovichtype distance between the Husimi transforms of the Hartree solution and of the first marginal of the Nbody Heisenberg solution which is independent of h and vanishes as N tends to infinity. (Work in collaboration with T. Paul and M. Pulvirenti).  

Felipe Linares (IMPA)  WPI, OMP 1, Seminar Room 08.135  Fri, 23. Sep 16, 9:30 
"On special regularity properties of solutions to the kgeneralized Kortewegde Vries equation"  
We will discuss special regularity properties of solutions to the IVP associated to the kgeneralized KdV equations. We show that for data u0 2 H3=4+(R) whose restriction belongs to Hk((b;1)) for some k 2 Z+ and b 2 R, the restriction of the corresponding solution u(; t) belongs to Hk((;1)) for any 2 R and any t 2 (0; T). Thus, this type of regularity propagates with innite speed to its left as time evolves. This kind of regularity can be extended to a general class of nonlinear dispersive equations. Recently, we proved that the solution ow of the kgeneralized KdV equation does not preserve other kind of regularities exhibited by the initial data u0.  

Hung Luong (U. Wien)  WPI, OMP 1, Seminar Room 08.135  Fri, 23. Sep 16, 10:30 
"ZakharovRubenchik/BenneyRoskes system on the background of a line soliton"  
In order to study the transverse (in) stability of a line soliton, we consider the 2d ZakharovRubenchik/BenneyRoskes system with initial data localized by a line soliton. The new terms in perturbed system lead to some diculties, for example, the lack of mass conservation. In this talk, I will present our recent work on this problem. This is a joint work with Norbert Mauser and JeanClaude Saut. 1  

Lode Axel (U. of Basel)  ATI; Stadionallee 2, 1020 Wien  Thu, 9. Feb 17, 11:00 
The multiconfigurational timedependent Hartree method for indistinguishable particles  overview and application to composite fragmentation of ultracold multicomponent bosons  
In this talk, I will review recent research and progress using the multiconfigurational timedependent Hartree for indistinguishable particles method to obtain highly accurate solutions of the timedependent manybody Schr"odinger equation for interacting, indistinguishable particles. As an example, I will focus on ultracold bosonic particles with internal degrees of freedom described by the multiconfigurational timedependent Hartree for bosons method. For the groundstate of N=100 parabolically confined bosons with two internal states, fragmentation emerges as a function of the separation between the statedependent minima of the two parabolic potentials: for small separations, the bosons occupy only one singleparticle state while for larger separations, two singleparticle states contribute macroscopically. The coherence of the system is maintained within each internal state of the atoms. Between the different internal states, however, correlations are built up and the coherence is lost for larger separations. This is a hallmark of a new kind of fragmentation  "composite fragmentation"  which is absent in bosons without internal structure.  

Casas Fernando (U. Jaume I Castellón)  WPI, OMP 1, Seminar Room 08.135  Tue, 7. Mar 17, 16:15 
Time dependent perturbation theory in matrix mechanics and time averaging  
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Blanes Sergio (U. Politècnica de València)  WPI, OMP 1, Seminar Room 08.135  Tue, 7. Mar 17, 17:15 
Time average on the numerical integration of nonautonomous differential equations  
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Zhang Yong (WPI c/o Courant & NJIT)  WPI, OMP 1, Seminar Room 08.135  Wed, 8. Mar 17, 13:45 
Analysisbased fast algorithms for convolutiontype nonlocal potential in Nonlinear Schrödinger equation  
Convolutiontype potential are common and important in many science and engineering fields. Efficient and accurate evaluation of such nonlocal potentials are essential in practical simulations.In this talk, I will focus on those arising from quantum physics/chemistry and lightningshield protection, including Coulomb, dipolar and Yukawa potentials that are generated by isotropic and anisotropic smooth and fastdecaying density. The convolution kernel is usually singular or discontinuous at the origin and/or at the far field, and density might be anisotropic, which together present great challenges for numerics in both accuracy and efficiency. The stateofart fast algorithms include Wavelet based Method(WavM), kernel truncation method(KTM), NonUniformFFT based method(NUFFT) and GaussianSumbased method(GSM). Gaussiansum/exponentialsum approximation and kernel truncation technique, combined with finite Fourier series and Taylor expansion, finally lead to a O(NlogN) fast algorithm achieving spectral accuracy. Applications to NLSE are reviewed.  

Boualem Khouider  WPI, OMP 1, Seminar Room 08.135  Wed, 14. Jun 17, 17:00 
A zonally symmetric model for the monsoonHadley circulation with stochastic convective forcing  
Idealized models of reduced complexity are important tools to understand key processes underlying a complex system. In climate science in particular, they are important for helping the community improve our ability to predict the eect of climate change on the earth system. Climate models are large computer codes based on the discretization of the uid dynamics equations on grids of horizontal resolution in the order of 100 km, whereas unresolved processes are handled by subgrid models. For instance, simple models are routinely used to help understand the interactions between smallscale processes due to atmospheric moist convection and largescale circulation patterns. Here, a zonally symmetric model for the monsoon circulation is presented and solved numerically. The model is based on the Galerkin projection of the primitive equations of atmospheric synoptic dynamics onto the rst modes of vertical structure to represent free tropospheric circulation and is coupled to a bulk atmospheric boundary layer (ABL) model. The model carries bulk equations for water vapor in both the free troposphere and the ABL, while the processes of convection and precipitation are represented through a stochastic model for clouds. The model equations are coupled through advective nonlinearities, and the resulting system is not conservative and not necessarily hyperbolic. This makes the design of a numerical method for the solution of this system particularly dicult. We develop a numerical scheme based on the operator timesplitting strategy, which decomposes the system into three pieces: a conservative part and two purely advective parts, each of which is solved iteratively using an appropriate method. The conservative system is solved via a central scheme, which does not require hyperbolicity since it avoids the Riemann problem by design. One of the advective parts is a hyperbolic diagonal matrix, which is easily handled by classical methods for hyperbolic equations, while the other advective part is a nilpotent matrix, which is solved via the method of lines. Validation tests using a synthetic exact solution are presented, and formal secondorder convergence under grid renement is demonstrated. Moreover, the model is tested under realistic monsoon conditions, and the ability of the model to simulate key features of the monsoon circulation is illustrated in two distinct parameter regimes. This is joint work with Michale De La Chevrotiare.  

Tom Dörffel  WPI, OMP 1, Seminar Room 08.135  Thu, 15. Jun 17, 9:00 
Intensification of atmospheric vortices through asymmetric diabatic heating (with Ariane Papke, Rupert Klein)  
The dynamics of atmospheric vortices such as tropical storms, hurricanes and midlatitude cyclones is driven by a variety of interacting scales. [1] developed an asymptotic theory for the dynamics of strongly tilted atmospheric vortices in the gradientwind regime, embedded into a synopticscale geostrophic background eld. One central outcome of the theory is the evolution equation for the nearly axisymmetric primary circulation. It predicts that Fouriermode 1 of asymmetric diabatic heating/ cooling patterns can spin up or spin down a vortex depending on the relative arrangement of the heating dipole relative to the vortex tilt. Based on this methodology further investigations led to the conclusion that this theory is generalizable to Rossby numbers of order 1 and higher, i.e. cyclostrophic balance. Accompaning the asymptotics numerical experiments are conducted to test the theory within an anelastic model [2]. In this talk we present the latest results showing consistency of numerical simulations and theoretical predictions. [1] E. Paschke, P. Marschalik, A. Z. Owinoh and R. Klein, Motion and structure of at mospheric mesoscale baroclinic vortices: dry air and weak environmental shear, J. Fluid Mech. 701: 137{170, (2012) [2] J. M. Prusa, P. K. Smolarkiewicz and A. A. Wyszogrodzki, EULAG, a computational model for multiscale ows, Comput. Fluids 37: 1193{1207 (2008)  

Rupert Klein  WPI, OMP 1, Seminar Room 08.135  Thu, 15. Jun 17, 10:00 
The role of multiscale convection in hurricane intensication  
Paeschke et al (2012) showed analytically how nonaxisymmetric external diabatic forcing of a tilted vortex in dry air can amplify or attenuated the ow depending on the relative orientation of vortex tilt and the "heating dipole". Here we include a bulk moist microphysics closure and describe how boundary layer processes and multiscale deep moist convection can interact to produce this eect selfconsistently.  

Piotr Smolarkiewicz  WPI, OMP 1, Seminar Room 08.135  Thu, 15. Jun 17, 11:00 
Finitevolume integrators for cloudresolving simulations of global atmospheric flows  
This work extends to moistprecipitating dynamics a recently documented highperformance nitevolume integrators for simulating global allscale atmospheric ows (doi:10.1016/j.jcp. 2016.03.015). A key objective of the current development is a seamless coupling of the conservation laws for moist variables engendered by cloud physics with the semiimplicit, nonoscillatory forwardintime integrators already proven for dry dynamics. The representation of the water substance and the associated processes in weather and climate models can vary widely in formulation details and complexity levels. The adopted representation assumes a canonical warmrain" bulk microphysics parametrisation, recognised for its minimal physical intricacy while accounting for the essential mathematical complexity of cloudresolving models. A key feature of the presented numerical approach is global conservation of the water substance to machine precision  implied by the local conservativeness and positivity preservation of the numerics  for all water species including water vapour, cloud water, and precipitation. The moist formulation assumes the compressible Euler equations as default, but includes reduced anelastic equations as an option. The theoretical considerations are illustrated with a benchmark simulation of a tornadic thunderstorm on a reduced size planet, supported with a series of numerical experiments addressing the accuracy of the associated water budget.  

Wojciech W. Grabowski  WPI, OMP 1, Seminar Room 08.135  Thu, 15. Jun 17, 14:00 
Modeling condensation in cloudscale models  
Condensation of water vapor to form and grow cloud droplets is the most fundamental process of cloud and precipitation formation. It drives cloud dynamics through the release of latent heat and determines the strength of convective updrafts. Cloudscale models simulate condensation by applying two drastically dierent methods. The rst one is the bulk condensation where condensation/evaporation is assumed to always maintain saturated conditions. The second approach involves prediction of the incloud super or subsaturation and can be used in models that predict not only condensate mass but also relevant features of the droplet size distribution (e.g., models with the 2moment microphysics or with the bin microphysics). This presentation will address the question whether the dierence between the two approaches has a noticeable impact on convective dynamics. Model simulations with the bin microphysics for shallow nonprecipitating convection and with the doublemoment bulk microphysics for deep convection will be discussed to document the dierences in cloud eld simulations applying the two methodologies. For the shallow convection, the dierences in cloud eld simulated with bulk and bin schemes come not from small dierences in the condensation, but from more signicant dierences in the evaporation of cloud water near cloud edges as a result of entrainment and mixing. For the deep convection, results show a signicant dynamical impact of nite supersaturations and a strong microphysical eect associated with uppertropospheric anvils. Implications of these results for modeling convective dynamics will be discussed and a possible intermediate modeling methodology will be suggested.  

Annette Muller  WPI, OMP 1, Seminar Room 08.135  Thu, 15. Jun 17, 15:30 
The DSI as an indicator for diabatic processes across the scales  
In atmospheric ows, the Dynamic State Index (DSI) indicates local deviations from a steady wind solution. This steady wind solution is based on the primitive equations under adiabatic and inviscid conditions. Hence, from theoretical point of view, atmospheric dynamics is regarded relative to a solution derived from uid mechanic's rst principles. Thus, this parameter provides a tool to capture diabatic processes. The DSI can be designed for dierent uid mechanical models on distinguished scales, we will introduce a DSIQG for the quasigeostrophic ow, a DSIRo for the Rossby model and DSImois that is based on the equations of motions including moisture processes.  

Matthias Hieber  WPI, OMP 1, Seminar Room 08.135  Fri, 16. Jun 17, 9:00 
Thermodynamical Consistent Modeling and Analysis of HeatConducting Fluids  
In this talk, we derive and discuss thermodynamically consistent models for heatconduction fluids. Our approach is based on the entropy principle.  

Manuel Baumgartner  WPI, OMP 1, Seminar Room 08.135  Fri, 16. Jun 17, 10:00 
Diffusional Growth in Clouds (with Peter Spichtinger)  
Diusional growth is the most important growth mechanism for newly formed cloud droplets and ice crystals. Nonlinear diusion equations control the transport of water vapor towards the cloud particles. Although the solution of these diusion equations is circumvented in numerical cloud models, it remains computationally expensive to include the details of diusional growth due to severe timestep restrictions. Moreover, as soon as ice crystals are present in a cloud consisting mostly of cloud droplets, the Wegener BergeronFindeisen process becomes active and the ice crystals grow at the expense of the cloud droplets. In the rst part of the talk, we discuss the aspect of locality of the WegenerBergeron Findeisen process, i.e. an ice crystal does only aect its immediate vicinity. Its presence decouples the diusional growth behavior of nearby droplets from environmental conditions. We show some simulation results and a possible way to include locality in the context of bulkmicrophysics. The second part considers the case of a liquid cloud. In the context of numerical models, the microphysical details of the diusional growth and the timestep restrictions are eectively avoided through the technique of saturation adjustment. We will show some of these techniques and analyze an air parcel model containing activation of new droplets using asymptotics.  

Jinkai Li  WPI, OMP 1, Seminar Room 08.135  Fri, 16. Jun 17, 11:00 
Some mathematical analyses on two dynamical models for atmosphere with moisture (with Sabine Hittmeir, Rupert Klein, Edriss S. Titi)  
In this talk, we will present some recent mathematical results, mainly the global wellposedness and convergence of the relaxation limit, on two kinds of dynamical models for the atmosphere with moisture. In the rst part of this talk, which is a joint work with Edriss S. Titi [1], we will consider a tropical atmosphere model introduced by Frierson, Majda, and Pauluis (Commum. Math. Sci. 2004); for this model, we will present the global wellposedness of strong solutions and the strong convergence of the relaxation limit, as the relaxation time " tends to zero. It will be shown that, for both the nitetime and instantaneousrelaxation systems, the H1 regularities on the initial data are sucient for both the global existence and uniqueness of strong solutions, but slightly more regularities than H1 are required for both the continuous dependence and strong convergence of the relaxation limit. In the second part of this talk, which is a joint work with Sabine Hittmeir, Rupert Klein, and Edriss S. Titi [2], we will consider a moisture model for warm clouds used by Klein and Majda (Theor. Comput. Fluid Dyn. 2006), where the phase changes are allowed, and we will present the global wellposedness of this system. [1] Jinkai Li; Edriss S. Titi: A tropical atmosphere model with moisture: global well posedness and relaxation limit, Nonlinearity, 29 (2016), 2674{2714. [2] Sabine Hittmeir; Rupert Klein; Jinkai Li; Edriss S. Titi: Global wellposedness for passively transported nonlinear moisture dynamics with phase changes, arXiv:1610.00060  

Olof Runborg (Mathematik Institution, Stockholm)  WPI, OMP 1, Seminar Room 08.135  Tue, 20. Jun 17, 10:00 
Uncertainty Quantification for High Frequency Wave Propagation  
We consider the wave equation with highly oscillatory initial data, where there is uncertainty in the wave speed, initial phase and/or initial amplitude. To estimate quantities of interest (QoI) related to the solution $u^\varepsilon$ and their statistics, we combine a highfrequency method based on Gaussian beams with sparse stochastic collocation. In the talk we will discuss how the rate of convergence for the stochastic collocation and the complexity of evaluating the QoI depend on the short wavelength $\varepsilon$. We find in particular that QoIs based on local averages of $\vert u^\varepsilon\vert ^2$ can give fast convergence rates, despite the fact that $u^\varepsilon$ is highly oscillatory in both physical and stochastic space.  

Mohammed Lemou  WPI, OMP 1, Seminar Room 08.135  Tue, 20. Jun 17, 15:30 
"Averaging techniques and application to numerical methods for highly oscillatory Vlasov and KleinGordon models"  
A brief description of averaging theory for highlyoscillatory problems will be first presented with an emphasis on the socalled classical and stroboscopic averaging methods. Then I will present two general strategies to construct efficient numerical schemes for a class of highly oscillatory PDEs: the soobtained numerical schemes have a uniform accuracy with respect to the frequency. Two applications will be considered: the Vlasov kinetic equation with strong magnetic field and the KleinGordon equation in the nonrelativistic regime.  

Shi Jin (University of WisconsinMadison and Shanghai Jiao Tong University)  WPI, OMP 1, Seminar Room 08.135  Wed, 21. Jun 17, 10:00 
Semiclassical computational methods for oscillatory and uncertain quantum dynamics with bandcrossings  
Bandcrossing is a quantum dynamical behavior that contributes to important physics and chemistry phenomena such as quantum tunneling, Berry connection, charge transfer, chemical reaction etc. In this talk, we will discuss some recent works in developing semiclassical methods for bandcrossing in surface hopping. For such systems we will also introduce an nonlinear geometric optics method based "asymptoticpreserving" method that is accurate uniformly for all wave numbers, including the problem with random uncertain band gaps.  

Olivier Pinaud (Colorado State University)  WPI, OMP 1, Seminar Room 08.135  Wed, 21. Jun 17, 14:00 
Waves in random media and applications  
We will review some results concerning uncertainties in the derivation of kinetic equations from wave propagation in random media, that is modeled by a wave or a Schroedinger equation. Kinetic equations usually describe quadratic quantities in the wavefield such as the energy or wavewave correlations, and can be used to solve some imaging problems in complex media.  

François Golse  WPI, OMP 1, Seminar Room 08.135  Thu, 22. Jun 17, 10:00 
A convergence rate estimate for the semiclassical limit with Lipschitz continuous force field  
We propose an explicit bound for the convergence rate in the semiclassical limit for the Schrödinger equation which holds for potentials with Lipschitz continuous gradient. This bound is based on an analogue of the Wasserstein metric used in optimal transportation, adapted to measuring the distance between a quantum and a classical density.  

Yong Zhang  WPI, OMP 1, Seminar Room 08.135  Thu, 22. Jun 17, 14:00 
“Numerical methods/analysis for Schrödinger equations and micromagnetism”  
We present some mathematical methods occurring in the modeling and simulation of Nonlinear Schrödinger equations and nonlocal potentials. We focus on GrossPitaevskii equations describing Bose Einstein Condensates and stray field calculations in micromagnetism.  

Blakie Blair  WPI, OMP 1, Seminar Room 08.135  Fri, 23. Jun 17, 11:00 
Selfbound droplets of a dipolar BoseEinstein condensate  
Recent experiments with BoseEinstein condensates of dysprosium [1] and erbium [2] atoms have observed the formation of droplets that can preserve their form, even in the absence of any external confinement [3]. These droplets occur when the longranged dipoledipole interaction between the atoms dominates over the shortranged contact interaction. In this regime meanfield theory predicts that the condensate is unstable to collapse, however the LeeHuangYang corrections to the meanfield energy [3] can stabilize the system as one or many finite sized droplets. I will discuss our current understanding of these droplets, and introduce a new type of nonlinear Schrodinger equation used to describe their equilibrium and dynamical properties.  
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