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[CT045]

Session Date & Time : 3C (Aug.23, 13:20-15:00)
Type : Contributed Talk
Abstract : We study the numerical approximation of the ground state solution in finite temperature density functional theory. We formulate the problem with respect to the density matrix, and justify the convergence of the numerical approximations of the ground state. Finally, we give a quasi-optimal a priori error estimate with some mild assumptions. We also present some numerical experiments to support the theory.
Classification : 35Q55, 65N15, 65N25, 65N30
Author(s) :
- Ge Xu (Beijing Normal University)

Session Date & Time : 3C (Aug.23, 13:20-15:00)
Type : Contributed Talk
Abstract : This talk is concerned with the long-time behavior of solutions to the focusing $L^2$-critical nonlinear Schrodinger equations. Firstly, we briefly review the existence and uniqueness of multi-bubble blow-up solutions and multi-solitons in the context of NLS. Then, we introduce the uniqueness for a large energy class of multi-bubble blow-up solutions, which converge to a sum of $K$ pseudo-conformal blow-up solutions particularly with the low rate $(T-t)^{0+}$. Lastly, we also discuss the uniqueness of multi-solitons which converge to a sum of $K$ solitary waves with convergence rate $(1/t)^{2+}$ in the energy space, and with even lower convergence rate $(1/t)^{1/2+}$ in the pseudo-conformal space. The talk is based on the joint work with Prof. Daomin Cao and Prof. Deng Zhang, which has been published in "Archive for Rational Mechanics and Analysis" in 2023.
Classification : 35Q55, 35B44, 35C08
Author(s) :
- Yiming Su (Zhejiang University of Technology)

Session Date & Time : 3C (Aug.23, 13:20-15:00)
Type : Contributed Talk
Abstract : We focus on fluid modeling for decentralized fleets of autonomous drones with Newtonian models. The corresponding system of hyperbolic conservation laws is obtained through mean field limit and moments closure assumption. The objective is to reduce the complexity for swarm tasks simulations such as zone occupation. Taking advantage of the macroscopic representation of the density, we introduce a new model for this task accounting for the drones inertia, which has been neglected so far.
Classification : 35Q70, 35B40, 35B45
Author(s) :
- Axel Maupoux (ONERA / Institut Mathématique de Toulouse)
- Guillaume Dufour (ONERA)

Session Date & Time : 3C (Aug.23, 13:20-15:00)
Type : Industrial Contributed Talk
Abstract : Given a sensor network set up on an agricultural field, we review methods based on PDE, regression and Principal Component Analysis algorithms to estimate the temperature and moisture of soil. With PCA it is possible to identify those sensors or groups of sensors which are influential at the time of measuring the temperature or moisture at a given point of the field. Validation results are provided based on real data from agricultural fields.
Classification : 35Q79, PDE, regression, PCA
Author(s) :
- Carlos Fresneda-Portillo (Universidad Loyola Andalucía (Spain))
- Carmelina Ierardi (Universidad Loyola Andalucía )
- José Ramón Salvador-Ortiz (Universidad Loyola Andalucía)
- Javier Pérez (Universidad Loyola Andalucía )
- Diego Luis Orihuela (Universidad Loyola Andalucía )

Session Date & Time : 3C (Aug.23, 13:20-15:00)
Type : Contributed Talk
Abstract : Modern Lithium-Ion-Batteries (LIBs) suffer from degradation. This leads to a dependency of the voltage-capacity-curve on the charge-discharge-cycle. However, there are different processes inducing this degradation, each with a different influence on the aforementioned curve. Given such a curve, we recover the ageing dynamic of each effect and identify how much it contributes to the overall degradation using Invertible Neuronal Networks.
Classification : 35Q79, 62F15, 35B27, 65M60
Author(s) :
- Alireza Selahi (Weierstraß Institute for Applied Analysis and Stochastics)