Prof. Dr. Peter Karl Friz

Friz@math.tu-berlin.de


Projects as a project leader

  • SE17

    Stochastic methods for the analysis of lithium-ion batteries

    Prof.Dr. Jean-Dominique Deuschel / Prof. Dr. Wolfgang Dreyer / Prof. Dr. Peter Karl Friz / Dr. Clemens Guhlke

    Project heads: Prof.Dr. Jean-Dominique Deuschel / Prof. Dr. Wolfgang Dreyer / Prof. Dr. Peter Karl Friz / Dr. Clemens Guhlke
    Project members: Dr. Pierre-Ètienne Druet / Dr Mario Maurelli
    Duration: -
    Status: running
    Located at: Technische Universität Berlin / Weierstraß-Institut

    Description

    Currently lithium-ion batteries are the most promising storage devices to store and convert chemical energy into electrical energy. An important class of modern lithium batteries contain electrodes that consist of many nano-particles. During the charging process of a battery, lithium is reversibly stored in the ensemble of the nano-particles and the particles undergo a phase transition from a Li-rich to a Li-poor phase. For this type of batteries a successful mathematical model was developed in the previous ECMath project SE8, based on a stochastic mean field interacting particle system. The new project focuses on modeling, analysis and simulations of extreme conditions in battery operation like fast charging, mostly full/empty discharge states, mechanical stresses within the electrode. The aim of the project is to achieve deeper understanding of the behavior of lithium-ion batteries in extreme conditions.

  • SE8

    Stochastic methods for the analysis of lithium-ion batteries

    Prof. Dr. Wolfgang Dreyer / Prof. Dr. Peter Karl Friz

    Project heads: Prof. Dr. Wolfgang Dreyer / Prof. Dr. Peter Karl Friz
    Project members: Paul Gajewski / Dr Mario Maurelli
    Duration: -
    Status: completed
    Located at: Weierstraß-Institut

    Description

    The aim of the project is to better understand and to give simulations for a successful model for the charging and discharging of lithium-ion batteries, which are currently the most promising storage devices to store and convert chemical energy into electrical energy and vice versa. The model exhibits phase transition under different small parameter regimes and gives rise to hysteresis. We study these phenomena using the interpretation of the model as a stochastic particle system, with the goal of providing stability bounds, fast simulations, improvement of the model itself and optimization of the device. More information...

    http://www.wias-berlin.de/projects/ECMath-SE8/
  • CH-AP27

    Application of rough path theory for filtering and numerical integration methods

    Prof. Dr. Peter Karl Friz / Prof. Dr. Wilhelm Stannat

    Project heads: Prof. Dr. Peter Karl Friz / Prof. Dr. Wilhelm Stannat
    Project members: -
    Duration: 01.11.2011 - 31.10.2014
    Status: completed
    Located at: Technische Universität Berlin

    Description

    In 1998 T. Lyons (Oxford) suggested a new approach for the robust pathwise solution of stochastic di fferential equations which is nowadays known as the rough path analysis. Based on this approach a new class of numerical algorithms for the solution of stochastic differential equations have been developed. Recently, the rough path approach has been successfully extended also to stochastic partial di fferential equations. In stochastic filtering, the (unnormalized) conditional distribution of a Markovian signal observed with additive noise is called the optimal fi lter and it can be described as the solution of a stochastic partial diff erential equation which is called the Zakai equation. In the proposed project we want to apply the rough path analysis to a robust pathwise solution of the Zakai equation in order to construct robust versions of the optimal filter. Subsequently, we want to apply known algorithms based on the rough path approach to the numerical approximation of these robust estimators and further investigate their properties.

    http://www.dfg-spp1324.de/abstracts.php?lang=de#8