Mathematical Models of Cancer Evolution

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

21.05.2019 14:00, Seminarraum 05.002, Spiegelgasse 5, Departement Mathematik und Informatik

Tags: TAG Events DMI, TAG Events Studium Informatik]]>

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Thresholds for Measuring Degree in fractional Sobolev Spaces

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

The degree of a map between two spheres of same dimension can be estimated by Sobolev norm of said map (of the right class). In this talk I will discuss to what extend this is possible for the Hopf degree as well – and why the estimate we have is “analytically optimal” but probably not “topologically optimal”. Joint work with J. Van Schaftingen.

]]>Quantitative seismic imaging using reciprocity waveform inversion with arbitrary probing sources

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

We investigate the deployment of new devices developed in the acoustic setting: the dual-sensors, which are able to capture both the pressure field and the vertical velocity of the waves. For solving the inverse problem, we define a new cost function, adapted to these two types of data and based upon the reciprocity. We first note that the stability of the problem can be shown to be Lipschitz, assuming piecewise linear parameters. In addition, reciprocity waveform inversion allows a separation between the observational and numerical acquisitions. In fact, the numerical sources do not have to coincide with the observational ones, offering new possibilities to create adapted computational acquisitions, consequently reducing the numerical cost. We illustrate our approach with three-dimensional medium reconstructions, where we start with minimal information on the target models. We also extend the methodology for elasticity.

Eventually, if time allows, we shall explore the model representation in numerical seismic inversion, where the adaptive eigenspace method appears as a promising approach to have a compromise between number of unknowns and resolution.

References

[1] G. Alessandrini, M. V. de Hoop, F. Faucher, R. Gaburro and E. Sincich, Inverse problem for the Helmholtz equation with Cauchy data: reconstruction with conditional well-posedness driven iterative regularization, ESAIM: M2AN (2019).

[2] E. Beretta, M. V. De Hoop, F. Faucher, and O. Scherzer, Inverse boundary value problem for the Helmholtz equation: quantitative conditional Lipschitz stability estimates. SIAM Journal on Mathematical Analysis, 48(6), pp.3962-3983 (2016).

[3] M. J. Grote, M. Kray, and U. Nahum, Adaptive eigenspace method for inverse scattering problems in the frequency domain. Inverse Problems, 33(2), 025006 (2017).

[4] H. Barucq, F. Faucher, and O. Scherzer, Eigenvector Model Descriptors for Solving an Inverse Problem of Helmholtz Equation. arXiv preprint arXiv:1903.08991 (2019).

For further information about the seminar, please visit this webpage.

Recent results on singular limits for Vlasov-Poisson

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

The Vlasov-Poisson system is a kinetic equation that models collisionless plasma. A plasma has a characteristic scale called the Debye length, which is typically much shorter than the scale of observation. In this case the plasma is called ‘quasineutral’. This motivates studying the limit in which the ratio between the Debye length and the observation scale tends to zero. Under this scaling, the formal limit of the Vlasov-Poisson system is the Kinetic Isothermal Euler system.

The Vlasov-Poisson system itself can formally be derived as the limit of a system of ODEs describing the dynamics of a system of N interacting particles, as the number of particles approaches infinity. The rigorous justification of this mean field limit remains a fundamental open problem.

In this talk we present how the mean field and quasineutral limits can be combined to derive the Kinetic Isothermal Euler system from a regularised particle model.

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

02.09.2019 08:00 - 12.09.2019 17:00, Alte Universität, Rheinsprung 9

One week of mini-courses and a week-long conference held from September 2 till 13, 2019

Tags: TAG Events DMI, TAG Events Forschung Mathematik, TAG Events Zahlentheorie]]>

Website: numbertheory.dmi.unibas.ch/trip2019

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