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Dienstag, 22.06.2021, 15:15 Uhr (Online Event)
Oberseminar Nonlinear Dynamics
Bhumika Thakur, Jacobs University, Bremen:
Data driven identification of nonlinear dynamics using sparse regression with applications in plasma physics
mehr ... Veranstaltungsort
Online Event

Abstrakt
Data driven techniques are increasingly finding applications in physical sciences and plasma physics is no exception. Many plasma processes are highly complex and nonlinear and often the exact form of the equations governing their dynamics is not known. If we can construct these equations from the experimental data, then we can further our understanding of these processes and use techniques such as model reduction to isolate dominant physical mechanisms. A large number of regression techniques are available for identification of system dynamics from data, with varying degrees of generality and complexity. Sparse identification of nonlinear dynamics (SINDy) algorithm is one such technique that can be used to find parsimonious models. I will talk about this algorithm and discuss some examples where it is being applied in plasma physics with a focus on our ongoing attempt at finding the model equations for anode glow oscillations observed in a glow discharge plasma device.

Veranstalter
Freie Universität Berlin
WIAS Berlin
Mittwoch, 23.06.2021, 11:30 Uhr (Online Event)
Seminar Interacting Random Systems
Tejas Iyer, WIAS Berlin:
Degree and Edge Distributions in Inhomogeneous Random Recursive Trees (online talk)
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Online Event

Abstrakt
.We introduce general models of inhomogeneous random recursive trees, where either one or several nodes arrive at a time, and are equipped with i.i.d random weights. At each time-step, an existing vertex is chosen with probability proportional to its fitness function, and the newly arriving node(s) connect to it. This may be a function of its weight, and possibly the weights of its neighbours. We study two main quantities: the empirical measures associated with the number of vertices with a given degree and weight and the empirical measure corresponding proportion of edges in the structure with endpoint having a given weight. We show that, under certain technical conditions, the limit of both quantities exists when normalised by the size of the network, as the number of nodes tends to infinity. However, when the trees take certain forms, we show that interesting, non-trivial behaviour can emerge when these conditions fail: in particular, the trees may exhibit emphcondensation where a positive proportion of edges accumulate around vertices with weight that maximises the reinforcement of their fitness, or, more drastically, may have a emphdegenerate limiting degree distribution where the entire proportion of edges accumulate around these vertices. This non-trivial behaviour may be of interest when considering the trees as toy models for the evolution of complex networks.

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Seminar Interacting Random Systems (Online Event)

Veranstalter
WIAS Berlin
Mittwoch, 23.06.2021, 15:15 Uhr (Online Event)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Martin Brokate, Technische Universität München:
A variational inequality for the derivative of the play operator (online talk)
mehr ... Veranstaltungsort
Online Event

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Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
Donnerstag, 24.06.2021, 13:00 Uhr (Online Event)
Seminar Numerische Mathematik
Felipe Galarce Marín, WIAS Berlin:
Inverse problems in haemodynamics. Fast estimation of blood flows on non-parametric domains from medical data
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Online Event

Abstrakt
This seminar presents a work at the interface between applied mathematics and biomedical engineering. The work's main subject is the estimation of blood flows and quantities of medical interest in diagnosing certain diseases concerning the cardiovascular system. We propose a complete pipeline, providing the theoretical foundations for state estimation from medical data using reduced-order models, and addressing inter-patient variability. Extensive numerical tests are shown in realistic 3D scenarios that verify the potential impact of the work in the medical comunnity.

Weitere Informationen
For zoom login details please contact Alexander Linke linke@wias-berlin.de

Veranstalter
WIAS Berlin
Dienstag, 29.06.2021, 10:15 Uhr (Online Event)
Seminar Nichtlineare Optimierung und Inverse Probleme
Dr. Ingo Bremer, WIAS Berlin:
Parameterbestimmung zur Anpassung des SEIR-Models an Covid-19 Zeitreihen
mehr ... Veranstaltungsort
Online Event

Weitere Informationen
You can follow this talk by zoom: https://zoom.us/j/98493865627.

Veranstalter
WIAS Berlin
Mittwoch, 30.06.2021, 15:15 Uhr (Online Event)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Stefanie Schindler, WIAS Berlin:
Self-similar diffusive equilibration for a coupled reaction-diffusion system with mass-action kinetics (online talk)
mehr ... Veranstaltungsort
Online Event

Abstrakt
We study a coupled system of two nonlinear reaction-diffusion equations on the unbounded domain ℝ, where we consider reaction kinetics of the reaction nX1 ⇌ mX2 according to the mass-action law. We show the global existence and uniqueness of classical solutions and prove the existence of invariant rectangles, that is, bounded regions ∑ ⊂ ℝ2 in which the solutions stay for all times, provided that the initial data lies entirely in ∑. Further, by assuming that the reaction is equilibrated and that the asymptotic boundary conditions at infinity are given by constant steady-state solutions, the diffusive mixing is studied. Here the theory of self-similar solutions in the sense of Barenblatt is applicable. Combined with the theory of monotone operators, this enables us to prove that there exists for each choice of asymptotic boundary conditions a similarity profile. This research is joint work with Alexander Mielke.

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Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
Dienstag, 06.07.2021, 10:15 Uhr (Online Event)
Seminar Nichtlineare Optimierung und Inverse Probleme
Luisa Plato, WIAS Berlin:
Biological pest control -- Analysis and numerics for a spatio-temporal predator-prey system
mehr ... Veranstaltungsort
Online Event

Weitere Informationen
You can follow this talk by zoom: https://zoom.us/j/98493865627.

Veranstalter
WIAS Berlin
Mittwoch, 07.07.2021, 11:30 Uhr (Online Event)
Seminar Interacting Random Systems
Daoyi Wang, TU Berlin:
The Parabolic Anderson Model on a Galton-Watson tree with unbounded degrees (online talk)
mehr ... Veranstaltungsort
Online Event

Abstrakt
A detailed analysis was given by den Hollander, König and dos Santos (2020), of the large-time asymptotics of the total mass of the solution to the parabolic Anderson model on a supercritical Galton-Watson random tree, with an i.i.d. random potential whose marginal distribution is double-exponential. Under the assumption that the degree distribution has bounded support, two terms in the asymptotic expansion were identified under the quenched law, i.e., conditional on the realisation of the random tree and the random potential. We extend the analysis to degree distributions with unbounded support. We identify the weakest condition on the tail of the degree distribution under which the arguments can be pushed through. This is joint work with my supervisor Frank den Hollander.

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Seminar Interacting Random Systems (Online Event)

Veranstalter
WIAS Berlin
8. Juli 2021 (Online Event)
Workshop/Konferenz: Minisymposium ”Perspectives of Gradient-Robustness”
mehr ... Veranstaltungsort
Online Event

Veranstalter
WIAS Berlin