3,515 research outputs found
Simulation and Bisimulation over Multiple Time Scales in a Behavioral Setting
This paper introduces a new behavioral system model with distinct external
and internal signals possibly evolving on different time scales. This allows to
capture abstraction processes or signal aggregation in the context of control
and verification of large scale systems. For this new system model different
notions of simulation and bisimulation are derived, ensuring that they are,
respectively, preorders and equivalence relations for the system class under
consideration. These relations can capture a wide selection of similarity
notions available in the literature. This paper therefore provides a suitable
framework for their comparisonComment: Submitted to 22nd Mediterranean Conference on Control and Automatio
Homogenization of the Poisson-Nernst-Planck Equations for Ion Transport in Charged Porous Media
Effective Poisson-Nernst-Planck (PNP) equations are derived for macroscopic
ion transport in charged porous media under periodic fluid flow by an
asymptotic multi-scale expansion with drift. The microscopic setting is a
two-component periodic composite consisting of a dilute electrolyte continuum
(described by standard PNP equations) and a continuous dielectric matrix, which
is impermeable to the ions and carries a given surface charge. Four new
features arise in the upscaled equations: (i) the effective ionic diffusivities
and mobilities become tensors, related to the microstructure; (ii) the
effective permittivity is also a tensor, depending on the electrolyte/matrix
permittivity ratio and the ratio of the Debye screening length to the
macroscopic length of the porous medium; (iii) the microscopic fluidic
convection is replaced by a diffusion-dispersion correction in the effective
diffusion tensor; and (iv) the surface charge per volume appears as a
continuous "background charge density", as in classical membrane models. The
coefficient tensors in the upscaled PNP equations can be calculated from
periodic reference cell problems. For an insulating solid matrix, all gradients
are corrected by the same tensor, and the Einstein relation holds at the
macroscopic scale, which is not generally the case for a polarizable matrix,
unless the permittivity and electric field are suitably defined. In the limit
of thin double layers, Poisson's equation is replaced by macroscopic
electroneutrality (balancing ionic and surface charges). The general form of
the macroscopic PNP equations may also hold for concentrated solution theories,
based on the local-density and mean-field approximations. These results have
broad applicability to ion transport in porous electrodes, separators,
membranes, ion-exchange resins, soils, porous rocks, and biological tissues
Constructing (Bi)Similar Finite State Abstractions using Asynchronous -Complete Approximations
This paper constructs a finite state abstraction of a possibly
continuous-time and infinite state model in two steps. First, a finite external
signal space is added, generating a so called -dynamical system.
Secondly, the strongest asynchronous -complete approximation of the external
dynamics is constructed. As our main results, we show that (i) the abstraction
simulates the original system, and (ii) bisimilarity between the original
system and its abstraction holds, if and only if the original system is
-complete and its state space satisfies an additional property
Recent advances in the evolution of interfaces: thermodynamics, upscaling, and universality
We consider the evolution of interfaces in binary mixtures permeating
strongly heterogeneous systems such as porous media. To this end, we first
review available thermodynamic formulations for binary mixtures based on
\emph{general reversible-irreversible couplings} and the associated
mathematical attempts to formulate a \emph{non-equilibrium variational
principle} in which these non-equilibrium couplings can be identified as
minimizers.
Based on this, we investigate two microscopic binary mixture formulations
fully resolving heterogeneous/perforated domains: (a) a flux-driven immiscible
fluid formulation without fluid flow; (b) a momentum-driven formulation for
quasi-static and incompressible velocity fields. In both cases we state two
novel, reliably upscaled equations for binary mixtures/multiphase fluids in
strongly heterogeneous systems by systematically taking thermodynamic features
such as free energies into account as well as the system's heterogeneity
defined on the microscale such as geometry and materials (e.g. wetting
properties). In the context of (a), we unravel a \emph{universality} with
respect to the coarsening rate due to its independence of the system's
heterogeneity, i.e. the well-known -behaviour for
homogeneous systems holds also for perforated domains.
Finally, the versatility of phase field equations and their
\emph{thermodynamic foundation} relying on free energies, make the collected
recent developments here highly promising for scientific, engineering and
industrial applications for which we provide an example for lithium batteries
Rate of Convergence of Phase Field Equations in Strongly Heterogeneous Media towards their Homogenized Limit
We study phase field equations based on the diffuse-interface approximation
of general homogeneous free energy densities showing different local minima of
possible equilibrium configurations in perforated/porous domains. The study of
such free energies in homogeneous environments found a broad interest over the
last decades and hence is now widely accepted and applied in both science and
engineering. Here, we focus on strongly heterogeneous materials with
perforations such as porous media. To the best of our knowledge, we present a
general formal derivation of upscaled phase field equations for arbitrary free
energy densities and give a rigorous justification by error estimates for a
broad class of polynomial free energies. The error between the effective
macroscopic solution of the new upscaled formulation and the solution of the
microscopic phase field problem is of order for a material given
characteristic heterogeneity . Our new, effective, and reliable
macroscopic porous media formulation of general phase field equations opens new
modelling directions and computational perspectives for interfacial transport
in strongly heterogeneous environments
Comparing Asynchronous -Complete Approximations and Quotient Based Abstractions
This paper is concerned with a detailed comparison of two different
abstraction techniques for the construction of finite state symbolic models for
controller synthesis of hybrid systems. Namely, we compare quotient based
abstractions (QBA), with different realizations of strongest (asynchronous)
-complete approximations (SAlCA) Even though the idea behind their
construction is very similar, we show that they are generally incomparable both
in terms of behavioral inclusion and similarity relations. We therefore derive
necessary and sufficient conditions for QBA to coincide with particular
realizations of SAlCA. Depending on the original system, either QBA or SAlCA
can be a tighter abstraction
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