52 research outputs found
Coupled Systems of Differential-Algebraic and Kinetic Equations with Application to the Mathematical Modelling of Muscle Tissue
We consider a coupled system composed of a linear differential-algebraic
equation (DAE) and a linear large-scale system of ordinary differential
equations where the latter stands for the dynamics of numerous identical
particles. Replacing the discrete particles by a kinetic equation for a
particle density, we obtain in the mean-field limit the new class of partially
kinetic systems. We investigate the influence of constraints on the kinetic
theory of those systems and present necessary adjustments.
We adapt the mean-field limit to the DAE model and show that index reduction
and the mean-field limit commute. As a main result, we prove Dobrushin's
stability estimate for linear systems. The estimate implies convergence of the
mean-field limit and provides a rigorous link between the particle dynamics and
their kinetic description.
Our research is inspired by mathematical models for muscle tissue where the
macroscopic behaviour is governed by the equations of continuum mechanics,
often discretised by the finite element method, and the microscopic muscle
contraction process is described by Huxley's sliding filament theory. The
latter represents a kinetic equation that characterises the state of the
actin-myosin bindings in the muscle filaments. Linear partially kinetic systems
are a simplified version of such models, with focus on the constraints.Comment: 32 pages, 18 figure
I Going Away. I Going Home. : Austin Clarke\u27s Leaving this Island Place
Austin Clarkeâs âLeaving This Island Placeâ is one of scores of Caribbean autobiographical works that focus on a bright, young, lower-class islander leaving his/her small island place and setting out on âEldorado voyages.â The narrative of that journey away from home to Europe or Canada or the United States and the later efforts to return may be said to be the Caribbean story, as suggested in the subtitle of Wilfred Carteyâs study of Caribbean literature, Whispers from the Caribbean: I Going Away, I Going Home, which argues that while in Caribbean literature there is much movement away, there is also a body of literature in which âthe notion of âawayâ and images of movement out are replaced by images of returnâ (xvi). Traditionally, however, the first autobiographical works, such as George Lammingâs In the Castle of My Skin, V. S. Naipaulâs A House for Mr. Biswas, Merle Hodgeâs Crick Crack, Monkey, Jamaica Kincaidâs Annie John, Michelle Cliffâs No Telephone to Heaven, Edwidge Danticatâs Breath, Eyes, Memory, and Elizabeth Nunezâs Beyond the Limbo Silence, have focused on the childhood in the Caribbean and the journey awayâor at least the preparation for that journey. Such is the case with Clarkeâs âLeaving This Island Place.
Systems of Differential Algebraic Equations in Computational Electromagnetics
Starting from space-discretisation of Maxwell's equations, various classical
formulations are proposed for the simulation of electromagnetic fields. They
differ in the phenomena considered as well as in the variables chosen for
discretisation. This contribution presents a literature survey of the most
common approximations and formulations with a focus on their structural
properties. The differential-algebraic character is discussed and quantified by
the differential index concept
Multi-domain modelling and simulation
One starting point for the analysis and design of a control system is the block diagram representation of a plant. Since it is nontrivial to convert a physical model of a plant into a block diagram, this can be performed manually only for small plant models. Based on research from the last 35 years, more and more mature tools are available to achieve this transformation fully automatically. As a result, multi-domain plants, for example, systems with electrical, mechanical, thermal, and fluid parts, can be modeled in a unified way and can be used directly as inputâoutput blocks for control system design. An overview of the basic principles of this approach is given. This provides also the possibility to use nonlinear, multi-domain plant models directly in a controller. Finally, the low-level âFunctional Mockup Interfaceâ standard is sketched to exchange multi-domain models between many different modeling and simulation environments
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