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 Clarke’s “Leaving This Island Place” 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 “Eldorado voyages.” 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 Cartey’s 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 “the notion of ‘away’ and images of movement out are replaced by images of return” (xvi). Traditionally, however, the first autobiographical works, such as George Lamming’s In the Castle of My Skin, V. S. Naipaul’s A House for Mr. Biswas, Merle Hodge’s Crick Crack, Monkey, Jamaica Kincaid’s Annie John, Michelle Cliff’s No Telephone to Heaven, Edwidge Danticat’s Breath, Eyes, Memory, and Elizabeth Nunez’s Beyond the Limbo Silence, have focused on the childhood in the Caribbean and the journey away—or at least the preparation for that journey. Such is the case with Clarke’s “Leaving 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 input–output 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 “Functional Mockup Interface” standard is sketched to exchange multi-domain models between many different modeling and simulation environments