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April 2018

John Harlim, Penn State University, Data-driven methods for estimating operator and parameters of dynamical systems

April 18, 2018 | 3:00 pm - 4:00 pm EDT

I will discuss a nonparametric modeling approach for forecasting stochastic dynamical systems on smooth manifolds embedded in Euclidean space. This approach allows one to evolve the probability distribution of non-trivial dynamical systems with an equation-free modeling. In the second part of this…

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Daphne Klotsa, University of North Carolina at Chapel Hill, A touch of non-linearity at intermediate Reynolds numbers: where spheres “think” collectively and swim together

April 25, 2018 | 3:00 pm - 4:00 pm EDT

From crawling cells to orca whales, swimming in nature occurs at different scales. The study of swimming across length scales can shed light onto the biological functions of natural swimmers or inspire the design of artificial swimmers with applications ranging from…

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September 2018

Roman Shvydkoy, University of Illinois at Chicago, Topological models of singular Cucker-Smale dynamics

September 19, 2018 | 3:00 pm - 4:00 pm EDT

In this talk we will discuss new classes of models that seek to describe evolution of a congregation of agents based on laws of self-organization. These models appear in a broad range of applications -- from biological sciences to social behavior. We…

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February 2019

Rossana Capuani, NC State, Mean field games with state constraints

February 27, 2019 | 3:00 pm - 4:00 pm EST

This talk will address deterministic mean field games for which agents are restricted in a closed domain of R^n with smooth boundary. In this case, the existence and uniqueness of Nash equilibria cannot be deduced as for unrestricted state space…

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March 2019

Pedro Aceves Sanchez, NC State, Fractional diffusion limit of a linear kinetic transport equation in a bounded domain

March 6, 2019 | 3:00 pm - 4:00 pm EST

In recent years, the study of evolution equations featuring a fractional Laplacian has received much attention due to the fact that they have been successfully applied into the modelling of a wide variety of phenomena, ranging from biology, physics to…

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Charis Tsikkou, West Virginia University, Radial solutions to the Cauchy problem for the wave equation and compressible Euler system

March 20, 2019 | 3:00 pm - 4:00 pm EDT

In the first part of this work, we consider the strategy of realizing the solution of the three-dimensional linear wave equation with radial Cauchy data as a limit of radial exterior solutions satisfying vanishing Neumann and Dirichlet conditions, on the exterior of vanishing balls centered at the origin. We insist…

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H.T. Banks, North Carolina State University, Population Models-The Prohorov Metric Framework and Aggregate Data Inverse Problems

March 27, 2019 | 3:00 pm - 4:00 pm EDT

We consider nonparametric estimation of probability measures for parameters in problems where only aggregate (population level) data are available. We summarize an existing computational method for the estimation problem which has been developed over the past several decades. Theoretical results…

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April 2019

Alexander Kiselev, Duke University, Small scale formation in ideal fluids

April 3, 2019 | 3:00 pm - 4:00 pm EDT

The incompressible Euler equation of fluid mechanics describes motion of ideal fluid, and was derived in 1755. In two dimensions, global regularity of solutions is known, and double exponential in time upper bound on growth of the derivatives of solution…

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Wen Shen, Penn State University, Scalar Conservation Laws with Discontinuous and Regulated Flux

April 10, 2019 | 3:00 pm - 4:00 pm EDT

Conservation laws with discontinuous flux functions arise in various models. In this talk we consider solutions to a class of conservation laws with discontinuous flux, where the flux function is discontinuous in both time and space, but regulated in the…

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Peter Wolenski, Louisiana State University, Fully convex Bolza problems with state constraints and impulses

April 17, 2019 | 3:00 pm - 4:00 pm EDT

In this talk, we shall review the Hamilton-Jacobi theory for A Fully Convex Bolza (FCB) problems when the data has no implicit state constraints and is coercive, in which case the minimizing class of arcs are Absolutely Continuous (AC).  

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Boris Mordukhovich, Wayne State University, Criticality of Lagrange Multipliers in Conic Programming with Applications to Superlinear Convergence of SQP

April 18, 2019 | 3:00 pm - 4:00 pm EDT

His talk concerns the study of criticality of Lagrange multipliers in variational systems that have been recognized in both theoretical and numerical aspects of optimization and variational analysis. In contrast to the previous developments dealing with polyhedral KKT systems and…

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Oleksandr Misiats, Virginia Commonwealth University, Patterns around us: a calculus of variations prospective

April 24, 2019 | 3:00 pm - 4:00 pm EDT

Crumples in a sheet of paper, wrinkles on curtains, cracks in metallic alloys, and defects in superconductors are examples of patterns in materials. A thorough understanding of the underlying phenomenon behind the pattern formation provides a different prospective on the properties…

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August 2019

Angot Philippe, Aix-Marseille Université, Mathematical modeling and analysis towards the open problem of flow at a fluid-porous interface

August 21, 2019 | 3:00 pm - 4:00 pm EDT

We discuss mathematical modeling and analysis of the incompressible viscous flow at the interface of permeable media. Very recently, a simplified theory with asymptotic modeling and related approximations was extensively developed by to provide physically relevant jump interface conditions for…

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Michele Palladino, GSSI, Italy, Modeling the root growth: an optimal control approach

August 28, 2019 | 3:00 pm - 4:00 pm EDT

In this talk we will propose a new framework to model control systems in which a dynamic friction occurs. In particular, such a framework is motivated by the study of the movement of a robotic root tip in the soil.…

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September 2019

Kazufumi Ito, NC State, Optimal control of sate constrained PDEs system with Spars controls

September 11, 2019 | 3:00 pm - 4:00 pm EDT

In this talk we discuss a point-wise state constraint problem for a general class of PDEs optimal control problems and sparsity optimization. We use the penalty formulation and derive the necessary optimality condition based on the Lagrange multiplier theory.The existence of…

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Yulong Lu, Duke University, Understanding and accelerating statistical sampling algorithms: a PDE perspective

September 18, 2019 | 3:00 pm - 4:00 pm EDT

A fundamental problem in Bayesian inference and statistical machine learning is to efficiently sample from probability distributions. Standard Markov chain Monte Carlo methods could be prohibitively expensive due to various complexities of the target distribution, such as multimodality, high dimensionality, large datesets, etc.…

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October 2019

Mikhail Klibanov, UNC Charlotte, Carleman Estimates for Globally Convergent Numerical Methods for Coefficient Inverse Problems

October 16, 2019 | 3:00 pm - 4:00 pm EDT

The ill-posedness and nonlinearity are two factors causing the phenomenon of multiple local minima and ravines of conventional least squares cost functionals for Coefficient Inverse Problems. Since any minimization method can stop at any point of a local minimum, then…

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Piermarco Cannarsa, University of Rome “Tor Vergata”, Bilinear control for evolution equations of parabolic type

October 23, 2019 | 3:00 pm - 4:00 pm EDT

Recently, in a series of joint papers with F. Alabau-Boussouira and C. Urbani, I have studied the response of an evolution equation  on a Hilbert space to the action of a bilinear control. As is well-known, a bilinear control is…

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Cass Miller, UNC, Toward a New Generation of Models to Simulate Two-Fluid Flow in Porous Media

October 30, 2019 | 3:00 pm - 4:00 pm EDT

Two fluid flow in porous medium systems is an important application in many different areas of science and engineering.  Overwhelmingly, it is necessary to mathematically model the behavior of applications of concern at an averaged scale where the juxtaposed position…

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November 2019

Shan Gao, Beijing Institute of Technology, Discrete Geometrically-Exact Beams

November 20, 2019 | 3:00 pm - 4:00 pm EST

A geometrically-exact beam is a nonlinear field-theoretic model for elongated elastic objects. It utilizes moving frames to reduce the number of system’s independent spatial variables, which is a further development of Euler’s approach to the rotational dynamics of rigid bodies.…

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