Karlstad Applied Analysis Seminar (KAAS)

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Future seminars:

Talk-152

When: 22 Oct 2025, 10:30-11:15
What: Data-Driven Optimal Trading of Renewables on Intraday Energy Markets
Who: Michael Samet, RWTH Aachen, Germany
Where: https://kau-se.zoom.us/j/61616693592

The growing penetration of weather-dependent renewable generation in European power markets increases intraday price volatility and exposes market participants to imbalance penalty risks imposed by transmission system operators, creating a need for robust quantitative trading tools. We develop a data-driven, continuous-time stochastic optimal control (SOC) framework for intraday electricity trading on continuous exchanges. Wind production and energy prices are modeled by forecast-driven Itô–Lévy stochastic differential equations, which incorporate market asymmetries in jumps. The associated Hamilton–Jacobi–Bellman (HJB) partial integro-differential equation (PIDE) is solved via a a proposed semi-implicit finite difference scheme, yielding optimal trading policies that balance expected revenues, liquidity costs, and imbalance penalties. Numerical experiments on German intraday data demonstrate the economic value of forecast-driven and jump-aware strategies, highlighting robustness to volatility and tail risks.

Talk-153

When: 29 Oct 2025, 10:30-11:15
What: Asymptotic and numerical analysis of non-Newtonian flows in networks of blood vessels
Who: Grigory Panasenko (Institute of Applied Mathematics, Vilnius University, Lithuania and Institute Camille Jordan UMR CNRS 5208, University Jean Monnet, Saint-Etienne, France)
Where: 21E202, and online:  https://kau-se.zoom.us/j/61616693592

Partial differential equations in thin domains combining thin plates and thin rods or pipes (so-called multi-structures) are extensively studied in mathematical solid and fluid mechanics (see e.g. [1-3]). In particular, in [3-6] the so called thin tube structures were introduced as geometrical models for networks of thin blood vessels, tubes in catalytic converters, pipelines etc. The asymptotic analysis of the viscous Newtonian flows in these structures allowed to introduce the hybrid dimension models. They combine one-dimensional and multidimensional description of the flow with asymptotically exact coupling conditions between 3D and 1D parts of the model (see [4,5] and a recent monograph [6]). Another approach for junction of models of different dimensions for blood flow in arteries was proposed in [7, 8]. Thus, hybrid dimension models provide the one-dimensional description in the main part of the domain and make small full-dimensional zooms. These zooms give detailed description of the flow in the zones of interest such as the bifurcations of vessels, zones of blood clot formation, stents and so on. The hybrid dimension models allow substantially accelerate computations without loss of accuracy. In [3-6] the so called Newtonian rheology was considered : the Navier-Stokes equations with constant viscosity. However, it is well-known that the blood as well as melted polymers exhibit non-Newtonian rheology, when the viscosity depends on the gradient of velocity (shear rate). In particular, the numerical simulations for the blood show the difference about 10-15% between the results obtained via Newtonian and non-Newtonian models of flows. The talk will present recent results on asymptotic analysis and partial asymptotic reduction for the equations of non-Newtonian flows in thin tube structures, as well as some numerical experiments for real-life networks of vessels. These results are obtained in collaboration with K.Pileckas (see [9]). They are justified via asymptotic analysis of the full-dimensional problem in the whole domain of the flow and the proof of estimates for the difference between the exact solution of the full-dimensional problem and the solution to the hybrid dimension model.

References:

1. P.G. Ciarlet, Plates and Junctions in Elastic Multi-structures. An Asymptotic Analysis, Masson, Paris, 1990.
2. V. Kozlov, V. Maz'ya, A. Movchan, Asymptotic Analysis of Fields in Multi-Structures}, Oxford Mathematical Monographs., Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1999.
3. G. Panasenko, Multi-scale Modeling for Structures and Composites, Springer, Dordrecht, 2005.
4. G. Panasenko, Asymptotic expansion of the solution of Navier-Stokes equation in a tube structure, C.R. Acad. Sci. Paris, 326, IIb, 1998, 867—872.
5. G. Panasenko, Partial asymptotic decomposition of domain: Navier-Stokes equation in tube structure, C.R. Acad. Sci. Paris, 326, IIb, 1998, 893—898.
6. G. Panasenko, K. Pileckas, Multiscale Analysis of Viscoous Flows in Thin Tube Structures, Birkhauser, Springer Nature Switzerland AG, 2024.
7. L. Formaggia, A. Veneziani, Reduced and Multiscale Models for the Human Cardiovascular System. Lecture Notes, VKI, Brussels, 2003.
8. L. Formaggia, A. Moura, F. Nobile, On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations, M2AN, 2007, 743-769.
9. G. Panasenko, K. Pileckas, Partial asymptotic dimension reduction for steady state non-Newtonian flow with strain rate dependent viscosity in thin tube structure, J.Math. Fluid. Mech., 25:11, 2023.