Events

Oct 1 - Oct 7, 2023

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  Several derivations of the degenerate Cahn-Hilliard equation via singular limits

  Dr. Jakub Skrzeczkowski,Mathematical Institute, University of Oxford

  Oct 4, 16:00 - 17:00

  B1 L4 R4214

  The degenerate Cahn-Hilliard equation, initially introduced in material science, is nowadays used in several different fields, including biology (tumor growth, cell-cell adhesion) and fluid dynamics (high-friction limit in the Euler-Korteweg equation).

Sep 10 - Sep 16, 2023

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  Stability and Asymptotics in Electrohydrodynamics

  Nuno J. Alves, Ph.D. Student, Applied Mathematics and Computational Sciences

  Sep 12, 15:00 - 17:00

  B1 L4 R4214

  Relative Energy Analysis relative energy method

  This dissertation focuses on the relative energy analysis of two-species fluids composed of charged particles. In particular, it explores several applications of the relative energy method to Euler-Poisson systems, enabling a comprehensive stability analysis of these systems.

Jul 2 - Jul 8, 2023

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  Axisymmetric flows with swirl for Euler and Navier-Stokes equations

  Ioanna Mousikou, Ph.D. Student, Applied Mathematics and Computational Sciences

  Jul 6, 15:00 - 16:00

  B1 L4 R4214

  We consider the incompressible axisymmetric Navier-Stokes equations as an idealized model of tornado-like flows. Assuming that an infinite vortex line that interacts with a boundary surface resembles the tornado core, we look for stationary self-similar solutions of the axisymmetric Euler and the axisymmetric Navier-Stokes equations emphasizing the connection among them as the viscosity ν → 0.

Mar 12 - Mar 18, 2023

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  Gravitational Collapse of Self-similar stars

  Dr. Matthew Schrecker, Departments of Mathematics, University College London

  Mar 16, 16:00 - 17:00

  B1 L4 R4102

  Nonlinear Partial Differential Equation Gravitational collapse UCL

  The Euler-Poisson equations give the classical model of a self-gravitating star under Newtonian gravity. It is widely expected that, in certain regimes, initially smooth initial data may give rise to blow-up solutions, corresponding to the collapse of a star under its own gravity. In this talk, I will present recent work with Yan Guo, Mahir Hadzic and Juhi Jang that demonstrates the existence of smooth, radially symmetric, self-similar blow-up solutions for this problem. I will also comment on the stability of the obtained solution. At the heart of the analysis is the presence of a sonic point, a singularity in the self-similar model that poses serious analytical challenges in the search for a smooth solution.

Jan 8 - Jan 14, 2023

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  Nonlocal Aggregation-Diffusion Equations: entropies, gradient flows, phase transitions and applications

  Prof. Jose Carrillo, Department of Mathematics, University of Oxford, UK

  Jan 10, 15:30 - 17:00

  B2 L5 R5209

  Fokker-Planck equations Cucker-Smale orientation dynamics McKean-Vlasov equations Keller-Segel-type models

  This talk will be devoted to an overview of recent results in understanding the bifurcation analysis of nonlinear Fokker-Planck equations arising in a myriad of applications such as consensus formation, optimization, granular media, swarming behavior, opinion dynamics, and financial mathematics to name a few. We will present several results related to localized Cucker-Smale orientation dynamics, McKean-Vlasov equations, and nonlinear diffusion Keller-Segel-type models in several settings. We will show the existence of continuous or discontinuous phase transitions on the torus under suitable assumptions on the Fourier modes of the interaction potential.

Dec 11 - Dec 17, 2022

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  Liquid crystals from a mathematical perspective

  Prof. Sir John Ball, Department of Mathematics, Heriot-Watt University, Edinburgh, UK

  Dec 12, 12:00 - 13:00

  B1 L4 R4102

  Liquid crystals are materials whose properties are intermediate between normal fluids and solid crystals, and have widespread use as the working substance for computers, TV, and watch displays. The lecture will introduce these materials and what mathematics can say about them, and in particular, discuss how different theories of liquid crystals describe orientational defects in different ways.

Dec 4 - Dec 10, 2022

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  On the role of pair correlations in the evolution of Bose-Einstein condensates

  Prof. Manoussos Grillakis, Department of Mathematics, University of Maryland in College Park.

  Dec 7, 15:30 - 17:00

  B1 L3 R3119

  nonlinear Schr¨odinger equation

  A Bose gas at zero temperature is described by a mean field which satisfies the cubic nonlinear Schr¨odinger equation (NLS) otherwise known as the Gross- Pitaevski equation. The mean field describes the evolution of the condensate in an average sense. I will describe a technique that introduces pair correlations in the evolution of the condensate. The resulting approximation tracks the evolu- tion of the condensate in norm provided that the pair wave-function satisfies an interesting system of coupled NLS equations. I will discuss the nonlinear struc- ture of the NLS system as well as a novel approach to the question of global existence of solutions of the system.

Nov 27 - Dec 3, 2022

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  On the collapse mechanism of Wave Maps

  Prof. Manoussos Grillakis, Departments of Mathematics, University of Maryland

  Nov 27, 13:00 - 15:00

  B1 L4 R4214

  Partial Differential Equations

  The Wave Map system describes the evolution of waves constrained on a (Riemannian) manifold. For the 2 + 1 dimensional problem, when the target manifold is a sphere, the solution collapses in finite time. The Analysis is due to the pioneering work of Merle, Paphael and Rodnianski. Motivated by their work I will present a somewhat novel approach of the collapsing mechanism which is based on a view of the equations as a nonlinear gauge system. This is joint work with Dan Geba.

May 22 - May 28, 2022

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  Mathematical Problems in Deep Learning

  Prof. Hailiang Liu, Department of Mathematics, Iowa State University, USA

  May 25, 15:00 - 16:00

  B1 L4 R4102

  I shall present some mathematical problems encountered in deep learning models. The results include optimal control of selection dynamics for deep neural networks, and gradient methods adaptive with energy. Some of the computational questions that will be addressed have a more general interest in engineering and sciences.

Nov 8 - Nov 14, 2020

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  The equations of polyconvex thermoelasticity

  Myrto Galanopoulou, Ph.D. Student, Applied Mathematics and Computational Sciences

  Nov 9, 17:00 - 19:00

  KAUST

  In my thesis, I consider the system of thermoelasticity endowed with polyconvex energy. After presenting the equations in their mathematical and physical context, I embed the equations of polyconvex thermoviscoelasticity into an augmented, symmetrizable, hyperbolic system which possesses a convex entropy. This allows to prove many important stability results, such as convergence from thermoviscoelasticity (with Newtonian viscosity and Fourier heat conduction) to smooth solutions of the system of adiabatic thermoelasticity, and convergence from thermoviscoelasticity to smooth solutions of thermoelasticity in the zero-viscosity limit. In addition, I establish a weak-strong uniqueness result in the class of entropy weak solutions and in a suitable class of measure-valued solutions, defined by means of generalized Young measures that describe both oscillatory and concentration effects. Also, I construct a variational scheme for isentropic processes of adiabatic polyconvex thermoelasticity: I establish existence of minimizers which converge to a measure-valued solution that dissipates the total energy, while the scheme converges when the limiting solution is smooth.

Feb 23 - Feb 29, 2020

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  Deterministic particle approximation for nonlinear transport equations

  Marco Di Francesco, Associate Professor, Department of Information Engineering, Computer Science and Mathematics, University of L'Aquila (Italy)

  Feb 25, 14:00 - 15:00

  Building L3 R3119

  PDE numerical methods nonlinear models

  Approximating the solution to an evolutionary partial differential equation by a set of "moving particles" has several advantages. It validates the use of a continuity equation in an "individuals-based" modeling setting, it provides a link between Lagrangian and Eulerian description, and it defines a "natural" numerical approach to those equations. I will describe recent rigorous results in that context. The main one deals with one-dimensional scalar conservation laws with nonnegative initial data, for which we prove that the a suitably designed "follow-the-leader" particle scheme approximates entropy solutions in the sense of Kruzkov in the many particle limit. Said result represents a new way to solve scalar conservation laws with bounded and integrable initial data. The same method applies to second order traffic flow models, to nonlocal transport equations, and to the Hughes model for pedestrian movements.

Feb 9 - Feb 15, 2020

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  Weak solutions of the 2D Euler equations

  Stefano Spirito, Assistant Professor, Department of Mathematics, University of L’Aquila, Italy

  Feb 11, 15:00 - 16:00

  B1 L3 R3119

  Cauchy problem Euler equations

  In this talk we consider the Cauchy problem for the 2D Euler equations for incompressible inviscid fluids. It is well-known that given a smooth initial datum, the Cauchy problem is well-posed and in particular the energy is conserved and the vorticity is transported by the flow of the velocity. When we consider weak solutions this might not be the case anymore. We will review some recent results obtained in collaboration with Gianluca Crippa and Gennaro Ciampa where we extend those properties to the case of irregular vorticities. In particular, under low integrability assumptions on the vorticity we show that certain approximations important from a physical and a numerical point of view converge to solutions satisfying those properties.

Feb 2 - Feb 8, 2020

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  A regularized shallow-water waves system with slip-wall boundary conditions: Theory and numerical analysis

  Dimitrios Mitsotakis, Senior Lecturer, School of Mathematics and Statistic Victoria University of Wellington, New Zealand

  Feb 5, 16:00 - 17:00

  B1 L4 R4214

  In this talk we present the derivation of a new Boussinesq-type system to describe the propagation of long waves of small amplitude in a basin with mildly varying bottom topography. We prove the existence and uniqueness of weak solutions for maximal times that do not depend on the amplitude of the waves. We then present the numerical solution of the new system using Galerkin finite element methods and prove the convergence of the semidiscrete solution to the exact solution. The system appears to describe well water waves even in benchmark experiments that involve also general bathymetries.

Sep 15 - Sep 21, 2019

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  High friction limits for Euler flows

  Athanasios Tzavaras, Professor, Applied Mathematics and Computational Sciences

  Sep 19, 12:00 - 13:00

  B9 L2 H1 R2322

  High friction limits Euler flows

  Abstract Brief Biography Athanasios (Thanos) Tzavaras is a Professor in the Applied Mathematics and Computational Science program (AMCS) and Principal Investigator of the Applied Partial Differential Equations (AppliedPDE) research group at the King Abdullah University of Science and Technology, Saudi Arabia. Professor Tzavaras' research focus lies on Nonlinear Analysis, Continuum Physics, and Kinetic Theory. Tzavaras obtained a Diploma in Naval Architecture and Marine Engineering from the National Technical University of Athens, Greece, and subsequently moved to the USA, where he obtained M

Apr 7 - Apr 13, 2019

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  Mini Course Part 3-3 - Modelling and numerical methods for diffuse interface models in compressible multi-phase flows

  Prof. Jan Giesselmann, Technical University of Darmstadt, Germany

  Apr 9, 16:00 - 17:00

  B1 L3 R3119

  Multi-face flows numerical methods

  In this course we consider multi-phase flows, i.e., flows of one substance which is present as liquid as well as vapor. We focus on models that resolve individual bubbles/droplets and that treat both phases as compressible. We will also discuss incompressible/low Mach limits, since in most applications the liquid is nearly incompressible. Understanding and simulating such small-scale models is important in order to obtain information which can be used in larger scale models for e.g. sprays which play important roles in processes of practical interest as diverse as combustion, chemical engineering, and cloud formation
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  Mini Course Part 2-3 - Modelling and numerical methods for diffuse interface models in compressible multi-phase flows

  Prof. Jan Giesselmann, Technical University of Darmstadt, Germany

  Apr 7, 16:00 - 17:00

  B1 L3 R3119

  Multi-face flows numerical methods

  In this course we consider multi-phase flows, i.e., flows of one substance which is present as liquid as well as vapor. We focus on models that resolve individual bubbles/droplets and that treat both phases as compressible. We will also discuss incompressible/low Mach limits, since in most applications the liquid is nearly incompressible. Understanding and simulating such small-scale models is important in order to obtain information which can be used in larger scale models for e.g. sprays which play important roles in processes of practical interest as diverse as combustion, chemical engineering, and cloud formation

Mar 31 - Apr 6, 2019

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  Mini Course Part 1-3 - Modelling and numerical methods for diffuse interface models in compressible multi-phase flows

  Prof. Jan Giesselmann, Technical University of Darmstadt, Germany

  Apr 2, 16:00 - 17:00

  B1 L3 R3119

  Multi-face flows numerical methods

  In this course we consider multi-phase flows, i.e., flows of one substance which is present as liquid as well as vapor. We focus on models that resolve individual bubbles/droplets and that treat both phases as compressible. We will also discuss incompressible/low Mach limits, since in most applications the liquid is nearly incompressible. Understanding and simulating such small-scale models is important in order to obtain information which can be used in larger scale models for e.g. sprays which play important roles in processes of practical interest as diverse as combustion, chemical engineering, and cloud formation

Mar 17 - Mar 23, 2019

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  On Nonlocal Keller-Segel Type Equations

  Dr. Suleyman Ulusoy, American University of Ras Al Khaimah, UAE

  Mar 20, 16:00 - 17:00

  B1 L3 R3119

  Applied Partial Differential Equations Mathematical Biology

  In the first part of the talk we investigate a Keller-Segel model with quorum sensing and a fractional diffusion operator. This model describes the collective cell movement due to chemical sensing with flux limitation for high cell densities and with anomalous media represented by a nonlinear, degenerate fractional diffusion operator. The purpose here is to introduce and prove the existence of a properly defined entropy solution. In the second part of the talk we will analyze an equation that is gradient flow of a functional related to Hardy-Littlewood-Sobolev inequality in whole Euclidean space of higher dimensions.

Feb 10 - Feb 16, 2019

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  AMCS Mini Course: Mathematical and numerical modelling of water waves

  Dimitrios Mitsotakis, Victoria Univ. Wellington New Zealand

  Feb 10, 16:00 - Feb 17, 17:30

  B1 L3 R3119

  Water wave propagation mathematical modelling

  Abstract : The mathematical modelling of water waves continues to attract great interest both from a mathematical point of view, due to the difficulty of solving the systems of nonlinear partial differential equations that describe the relevant physical phenomena, and also from that of fluid mechanics, due to complexity of the physical phenomena that occur during the propagation of water waves and their importance in oceanography and coastal dynamics. The basic mathematical model is the system of the Euler equation for the motion of the free surface and the evolution of the velocity field of