MATHEMATICAL MODELLING OF NERVE PULSE TRANSMISSION

In this expository paper some key problems of nerve pulse dynamics are briefly analysed. Instead of the traditional parabolic models, the evolution equation modelling the propagation of a single nerve pulse is used. Such an approach together with the formalism of inner variables permits to bridge the various branches of wave dynamics, especially to distinguish between dissipative and solitonic structures

COUPLED THERMAL AND MOISTURE FIELDS WITH APPLICATION TO COMPOSITES

The mathematical models of heat and moisture transfer have been presented and analysed. The coupling of fields is described by including the Dufour and Soret effects. For high-rate processes, a modification of models is proposed with relaxation effects taken into account. The possible applications in mechanics of composites are discussed

Coupling of Generalized Heat and Moisture Transfer

The paper deals with the interdisciplinary problem of coupled diffusion and convention of crosscoupled heat and moisture. After a summary on the well-known and often used cases, the general governing equations are given with examples

On mathematical modeling of the propagation of a wave ensemble within an individual axon

The long history of studying the propagation of an action potential has revealed that an electrical signal is accompanied by mechanical and thermal effects. All these effects together generate an ensemble of waves. The consistent models of such a complex phenomenon can be derived by using properly the fundamental physical principles. In this paper, attention is paid to the analysis of concepts of continuum physics that constitute a basis for deriving the mathematical models which describe the emergence and propagation of a wave ensemble in an axon. Such studies are interdisciplinary and based on biology, physics, mathematics, and chemistry. The governing equations for the action potential together with mechanical and thermal effects are derived starting from basics: Maxwell equations, conservation of momentum, Fourier's law, etc., but modified following experimental studies in electrophysiology. Several ideas from continuum physics like external forces and internal variables can also be used in deriving the corresponding models. Some mathematical concepts used in modeling are also briefly described. A brief overview of several mathematical models is presented that allows us to analyze the present ideas of modeling. Most mathematical models deal with the propagation of signals in a healthy axon. Further analysis is needed for better modeling the pathological situations and the explanation of the influence of the structural details like the myelin sheath or the cytoskeleton in the axoplasm. The future possible trends in improving the models are envisaged