61,233 research outputs found
A Model Reduction Framework for Efficient Simulation of Li-Ion Batteries
In order to achieve a better understanding of degradation processes in
lithium-ion batteries, the modelling of cell dynamics at the mircometer scale
is an important focus of current mathematical research. These models lead to
large-dimensional, highly nonlinear finite volume discretizations which, due to
their complexity, cannot be solved at cell scale on current hardware. Model
order reduction strategies are therefore necessary to reduce the computational
complexity while retaining the features of the model. The application of such
strategies to specialized high performance solvers asks for new software
designs allowing flexible control of the solvers by the reduction algorithms.
In this contribution we discuss the reduction of microscale battery models with
the reduced basis method and report on our new software approach on integrating
the model order reduction software pyMOR with third-party solvers. Finally, we
present numerical results for the reduction of a 3D microscale battery model
with porous electrode geometry.Comment: 7 pages, 2 figures, 2 table
Dynamics on geometrically finite hyperbolic manifolds with applications to Apollonian circle packings and beyond
We present recent results on counting and distribution of circles in a given
circle packing invariant under a geometrically finite Kleinian group and
discuss how the dynamics of flows on geometrically finite hyperbolic
manifolds are related. Our results apply to Apollonian circle packings,
Sierpinski curves, Schottky dances, etc.Comment: To appear in the Proceedings of ICM, 201
Lattice Delone simplices with super-exponential volume
In this short note we give a construction of an infinite series of Delone
simplices whose relative volume grows super-exponentially with their dimension.
This dramatically improves the previous best lower bound, which was linear.Comment: 7 pages; v2: revised version improves our exponential lower bound to
a super-exponential on
Towards the Formalization of Fractional Calculus in Higher-Order Logic
Fractional calculus is a generalization of classical theories of integration
and differentiation to arbitrary order (i.e., real or complex numbers). In the
last two decades, this new mathematical modeling approach has been widely used
to analyze a wide class of physical systems in various fields of science and
engineering. In this paper, we describe an ongoing project which aims at
formalizing the basic theories of fractional calculus in the HOL Light theorem
prover. Mainly, we present the motivation and application of such formalization
efforts, a roadmap to achieve our goals, current status of the project and
future milestones.Comment: 9 page
Apollonian circle packings: Dynamics and Number theory
We give an overview of various counting problems for Apollonian circle
packings, which turn out to be related to problems in dynamics and number
theory for thin groups. This survey article is an expanded version of my
lecture notes prepared for the 13th Takagi lectures given at RIMS, Kyoto in the
fall of 2013.Comment: To appear in Japanese Journal of Mat
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