A mathematical study of the plasticity effects in muscle contraction

Hill's three-element model of contracting muscle is expanded by replacing the series and the parallel elastic elements with elastoplastic elements. The contractile element is structurally described making use of the sliding filament theory. The resulting mathematical model is formulated in terms of an evolution variational inequality for a nonlinear and nonlocal transport-type operator. The existence and uniqueness of the solution are described along with a numerical approach.This work was supported by M.P.I. (fondi per la ricerca scientifica) and by I.A.N. of C.N.R. Pavia.     

A theoretical and numerical approach to some free boundary problems

Summary In this paper some free boundary problems related to the flow of fluids in porous media are studied. Using a method due to Baiocchi, for these problems we not only establish theoretical results (existence and uniqueness theorems for the solution) but at the same time develop an algorithm for the numerical approach of the solution. Such an algorithm is rigorous from a mathematical point of view and it competes very well with the ones already known both in simplicity of programming and in speed of execution. Entrata in Redazione il 18 luglio 1973. ? Laboratorio di Analisi Numerica del C.N.R. di Pavia ? and ? Università di Pavia ?. This work was supported by C.N.R. in the frame of L.A.N. at Pavia.     

Reactivity of monoenic and conjugated diene systems present in unsaturated olefin terpolymers—II. Reactions with methyl radicals

The experimental rate constants for the reactions of methyl radicals with model compounds simulating ethylidene-norbornene (ENB), methylene-norbornene (MNB) and isopropylidene-dicyclopentadiene (IPDCP) units in EPDM and EPTM elastomers are reported. These constants, as well as others reported in a previous paper or derived from the literature, have been used to perform a kinetic analysis of the grafting of styrene onto EPM, EP-ENB or EP-IPDCP in inert solvent. The systems of kinetic differential equations have been solved by numerical integration without steady state approximation. Valuable information has been obtained on the role of the nature of radical initiators and the sensitivity of the results to change with constants in the various steps.     

Un risultato relativo a disequazioni variazionali d’evoluzione per operatori del primo ordine int con termini di ritardo

Résumé On donne en utilisant la méthode de pénalisation un théorème d’existence et d’unicité de la solution des inequations variationelles d’évolution pour les opérateurs du 1. er ordre en t à argument retardé.

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Lavoro eseguito in parte mentre l’autore fruiva di una Borsa del C.N.R. presso l’Università di Parigi e in parte presso il Laboratorio di Analisi Numerica del C.N.R. in Pavia.

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Entrata in Redazione il 12 novembre 1970.     

A mathematical study of a continuum-state cross-bridge model of muscle contraction

In the framework of the sliding-filament theory of muscle contraction, we develop a model which describes physioiogical cross-bridge activity with a continuum of states, from those which are detached and refractory to those which are attached. The latter are kinetically more important. An analytical study of the non-linear partial differential equations of the mathematical model shows existence and uniqueness of the solution.     

Free boundary problems in the theory of fluid flow through porous media: Existence and uniqueness theorems

Summary Elliptic free boundary problems in the theory of fluid flow through porous media are studied by a new method, which reduces the problems to variational inequalities: existence and uniqueness theorems are proved. Entrata in Redazione il 3 agosto 1972. Research supported by C.N.R. in the frame of the collaboration between L.A.N. of Pavia and E.R.A. 215 of C.N.R.S. and of Paris University. ? Laboratorio di Analisi Numerica del C.N.R. di Pavia ? and ? Università di Pavia ?. ? Università di Pavia ? and ? G.N.A.F.A. del C.N.R. ?.     

Model simulation studies of complex free radical reactions: The graft copolymerization of styrene and acrylonitrile onto ethylene-propylene-isopropylidendicyclopentadiene terpolymer

A kinetic analysis without steady approximation of the graft copolymerization of styrene-acrylonitrile onto ethylene- propylene-isopropylidendicyclopentadiene terpolymer (EP-IPDCP) is described. Some of the kinetic constants were experimentally determined. The grafting process is interpreted mainly in terms of the attack on EP-IPDCP by benzoyloxy radicals; phenyl radicals play a minor negative role by enhancing the rate of homopolymerization. A major contribution to the grafting yield is made by the propagation steps in graft polymerization and by crossed termination between grafted and ungrafted chains; of minor importance are the cross terminations between ungrafted growing chains and rubber radicals. The ole played by the solvent (benzene) and by saturated and unsaturated units in the EP-IPDCP chains is analyzed. Diffusion effects caused by the poor solvent compatibility of grafted and ungrafted chains were taken into account by allowing the termination and propagation rate constants to change in a controlled way during the reaction. The trapping of EP-IPDCP units caused by the aggregation of polymer particles seems to be indispensable to explain the decreasing trend of the grafting efficiency curve. Other information of interest pertains to the distribution of initiating radicals among the various competing reactions in the process and to the data of concentrations versus reaction time for reactants, products, and free radical intermediates. The results of a sensitivity analysis and the rate constants used in the calculations are given.     

On some oblique derivative problems arising in the fluid flow in porous media. A theoretical and numerical approach

In this paper we consider some free boundary problems related to the fluid flow in a porous medium. By applying a method due to Baiocchi [1] these problems are reduced to nonlinear problems on a fixed domain. The main difficulty here lies in the fact that such problems are not variational because of jump discontinuities in the direction of the oblique derivative in the boundary condition. We give a uniqueness result and by a constructive method we establish at the same time an existence result and a new algorithm for the numerical solution of the original free boundary problem. Some numerical results are given.