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Archive : Inverse Problems and Analysis

 

 

Prof. Hugo Woerdeman, Drexel University Prof. Hugo Woerdeman, Drexel University EWG 205<div>Title: Multivariable moment problems </div> <br> <div>Abstract: The moment problem asks when a list of complex numbers may be represented as the moments of a positive measure. Its applications are numerous and include linear prediction and digital filtering. Methods used to solve them range from completions of positive semidefinite matrices, orthogonal polynomials, study of structured matrices, Schur/reflection parameter techniques, to commutant lifting theorems, reproducing kernel Hilbert spaces, and an algebraic scheme called the band method. </div> <br> <div>This lecture concerns the active area of multivariable moment problems, with a special focus on the challenges that one encounters when going from one variable results to the multivariable case. </div>5/19/2017 5:00:00 PM5/19/2017 6:00:00 PMFalse
Irene De Teresa Trueba, Department of Mathematical Sciences, UD Irene De Teresa Trueba, Department of Mathematical Sciences, UDEWG205<div dir="LTR">Title; A method to detect planar flaws using electromagnetic waves </div> <br> <div dir="LTR">Abstract; In this talk I will present a method to solve the inverse problem of detecting planar openings between two materials using far-field measurements of electromagnetic waves. Applications include, for example, the detection of flaws in integrated circuits. In the first part I will briefly explain the derivation of a reduced model for electromagnetic scattering in the presence of thin domains. This model will later be used to provide a solution to the inverse problem. After briefly presenting some well-posedness results for specific cases of this model, the second part of the talk will concern the inverse problem solution. I will show how a well-known method in inverse scattering, the linear sampling method, can be adapted to develop a reconstruction algorithm to identify the location of the flaw, assuming that the undamaged configuration of the object is well known. </div>5/12/2017 5:00:00 PM5/12/2017 6:00:00 PMFalse
Prof. Gonzalo Arce, Department of Electrical and Computer Engineering, UDProf. Gonzalo Arce, Department of Electrical and Computer Engineering, UDEWG 205<div dir="LTR">Title: Blue Noise Graph Sampling </div> <br> <div dir="LTR">Abstract: Interesting phenomena can be often be captured by graphs since objects and data are invariable interrelated in some sense. Algorithms to compute the shortest path, centrality, spectra and other parameters of a complete graph become impractical when the graphs under study are large. Graph sampling thus becomes essential. This talk will describe new approaches for graph sampling, based on the notion of stochastic sampling in irregular sampling grids. In the context of graph signal processing on graphs, the notion of stochastic sampling is compelling as graphs do not have a concept of equal spacing in time or space. We develop adaptive sampling algorithms based on the fundamental concept of Blue Noise, which is an extended concept from the applications of stochastic sampling in digital signal processing. </div>5/5/2017 5:00:00 PM5/5/2017 6:00:00 PMFalse
Prof. Gregory Panasenko, University Jean Monnet, Laboratory of Mathematics of the University of Saint Etienne, FranceProf. Gregory Panasenko, University Jean Monnet, Laboratory of Mathematics of the University of Saint Etienne, FranceEWG 205<div dir="LTR">Title: Towards models of uncertainties in thin tube structures</div> <div dir="LTR">Abstract: Thin structures are some finite unions of thin rectangles (in 2D settings) or cylinders (in 3D settings) depending on small parameter epsilon << 1 that is, the ratio of the thickness of the rectangle (cylinder) to its length. We consider a steady and then a non-steady Navier-Stokes equations in thin structures with the no-slip boundary condition at the lateral boundary and with the inflow and outflow conditions with the given velocity of order one. The steady state Navier-Stokes equations in thin structures were considered in [1-3]. The asymptotic expansion of the solution is constructed. For the steady state case it consists of the Poiseuille flows within the tubes and the exponentially decaying boundary layer (in-space) correctors. The gradient drops in each tube are defined by a steady elliptic problem on a graph of the structure. The error estimates for high order asymptotic approximations are proved. Asymptotic analysis is applied for an asymptotically exact condition of junction of 1D and 2D (or 3D) models. These results are generalized (in co-authorship with K.Pileckas) to the case of a non-steady Navier-Stokes equations in tube structures: [4-8]. The structure of the asymptotic expansion is more complex: the Poiseuille type flow now depends on time and the boundary layer-in-space is now completed by two fast boundary layers: in-time only and in-time-and-in space. The fast-in-time pressure drops are now described by a new non-local in time problem on the graph (see [6]). </div> <div dir="LTR"> Earlier, equations in thin structures with random thickness of its elements was studied in [9]. We will discuss the possibility of analogous setting for a viscous flow in a tube structure with random sections of the cylinders. </div> <br> <div dir="LTR">References: </div> <div dir="LTR">1. Panasenko G.P. Asymptotic expansion of the solution of Navier-Stokes equation in a tube structure , C.R.Acad.Sci.Paris, t. 326, Série IIb, 1998, pp. 867-872 </div> <div dir="LTR">2. Panasenko G.P. Partial asymptotic decomposition of domain: Navier-Stokes equation in tube structure , C.R.Acad.Sci.Paris, t. 326, Série IIb, 1998, pp. 893-898 </div> <div dir="LTR">3. Panasenko G.P. Multi-Scale Modelling for Structures and Composites, Springer, Dordrecht, 2005, 398 pp. </div> <div dir="LTR">4. Panasenko G.,Pileckas K., Asymptotic analysis of the nonsteady viscous flow with a given flow rate in a thin pipe, Applicable Analysis, 2012, 91, 3, 559-574 </div> <div dir="LTR">5. Panasenko G., Pileckas K., Divergence equation in thin-tube structure, Applicable Analysis, 94,7, pp. 1450-1459, 2015, doi 10.1080/00036811.2014.933476. </div> <div dir="LTR">6. Panasenko G., Pileckas K., Flows in a tube structure: equation on the graph, Journal of Mathematical Physics, 55, 081505 (2014); doi: 10.1063/1.4891249. </div> <div dir="LTR">7. Panasenko G., Pileckas K., Asymptotic analysis of the non-steady Navier-Stokes equations in a tube structure.I. The case without boundary layer-in-time. Nonlinear Analysis, Series A, Theory, Methods and Applications, 122, 2015, 125-168, http://dx.doi.org/10.1016/j.na.2015.03.008 </div> <div dir="LTR">8. Panasenko G., Pileckas K., Asymptotic analysis of the non-steady Navier-Stokes equations in a tube structure. II. General case. Nonlinear Analysis, Series A, Theory, Methods and Applications, 125, 2015, 582-607, http://dx.doi.org/10.1016/j.na.2015.05.018 </div> <div dir="LTR">9. Panasenko G.P. "Averaging processes in frame constructions with random properties." USSR Computational Mathematics and Mathematical Physics (Zh.Vych.Mat.Mat.Fiz.), 1983, 23, No 5,1098-1109 (in Russian). English transl. in USSR Comput. Maths. Math. Phys., 1983, 23, No 5, 48-55. </div>4/28/2017 5:00:00 PM4/28/2017 6:00:00 PMFalse

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