5,032 research outputs found
Efficient electrochemical model for lithium-ion cells
Lithium-ion batteries are used to store energy in electric vehicles. Physical
models based on electro-chemistry accurately predict the cell dynamics, in
particular the state of charge. However, these models are nonlinear partial
differential equations coupled to algebraic equations, and they are
computationally intensive. Furthermore, a variable solid-state diffusivity
model is recommended for cells with a lithium ion phosphate positive electrode
to provide more accuracy. This variable structure adds more complexities to the
model. However, a low-order model is required to represent the lithium-ion
cells' dynamics for real-time applications. In this paper, a simplification of
the electrochemical equations with variable solid-state diffusivity that
preserves the key cells' dynamics is derived. The simplified model is
transformed into a numerically efficient fully dynamical form. It is proved
that the simplified model is well-posed and can be approximated by a low-order
finite-dimensional model. Simulations are very quick and show good agreement
with experimental data
Convergence Rates for Inverse Problems with Impulsive Noise
We study inverse problems F(f) = g with perturbed right hand side g^{obs}
corrupted by so-called impulsive noise, i.e. noise which is concentrated on a
small subset of the domain of definition of g. It is well known that
Tikhonov-type regularization with an L^1 data fidelity term yields
significantly more accurate results than Tikhonov regularization with classical
L^2 data fidelity terms for this type of noise. The purpose of this paper is to
provide a convergence analysis explaining this remarkable difference in
accuracy. Our error estimates significantly improve previous error estimates
for Tikhonov regularization with L^1-fidelity term in the case of impulsive
noise. We present numerical results which are in good agreement with the
predictions of our analysis
Almost periodic evolution systems with impulse action at state-dependent moments
We study the existence of almost periodic solutions for semi-linear abstract
parabolic evolution equations with impulse action at state-dependent moments.
In particular, we present conditions excluding the beating phenomenon in these
systems. The main result is illustrated with an example of impulsive diffusive
logistic equation.Comment: 16 pages, minor changes from the previous versio
Global algebras of nonlinear generalized functions with applications in general relativity
We give an overview of the development of algebras of generalized functions
in the sense of Colombeau and recent advances concerning diffeomorphism
invariant global algebras of generalized functions and tensor fields. We
furthermore provide a survey on possible applications in general relativity in
light of the limitations of distribution theory
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