The Redner - Ben-Avraham - Kahng coagulation system with constant coefficients: the finite dimensional case

We study the behaviour as $t\to\infty$ of solutions $(c_j(t))$ to the Redner--Ben-Avraham--Kahng coagulation system with positive and compactly supported initial data, rigorously proving and slightly extending results originally established in [4] by means of formal arguments.Comment: 13 pages, 1 figur

The Redner - Ben-Avraham - Kahng cluster system

We consider a coagulation model first introduced by Redner, Ben-Avraham and Krapivsky in [Redner, Ben-Avraham, Kahng: Kinetics of 'cluster eating', J. Phys. A: Math. Gen., 20 (1987), 1231-1238], the main feature of which is that the reaction between a j-cluster and a k-cluster results in the creation of a |j-k|-cluster, and not, as in Smoluchowski's model, of a (j+k)-cluster. In this paper we prove existence and uniqueness of solutions under reasonably general conditions on the coagulation coefficients, and we also establish differenciability properties and continuous dependence of solutions. Some interesting invariance properties are also proved. Finally, we study the long-time behaviour of solutions, and also present a preliminary analysis of their scaling behaviour.Comment: 24 pages. 2 figures. Dedicated to Carlos Rocha and Luis Magalhaes on the occasion of their sixtieth birthday

Point island dynamics under fixed rate deposition

We consider the dynamics of point islands during submonolayer deposition, in which the fragmentation of subcritical size islands is allowed. To understand asymptotics of solutions, we use methods of centre manifold theory, and for globalisation, we employ results from the theories of compartmental systems and of asymptotically autonomous dynamical systems. We also compare our results with those obtained by making the quasi-steady state assumption

Modelling silicosis: dynamics of a model with piecewise constant rate coefficients

We study the dynamics about equilibria of an infinite dimensional system of ordinary differential equations of coagulation–fragmentation–death type that was introduced recently by da Costa et al. (Eur J Appl Math 31(6):950–967, 2020) as a model for the silicosis disease mechanism. For a class of piecewise constant rate coefficients an appropriate change of variables allows for the appearance of a closed finite dimensional subsystem of the infinite-dimensional system and the analysis of the eigenvalues of the linearizations of this finite dimensional subsystem about the equilibria is then used to obtain the results on the stability of the equilibria in the original infinite dimensional model.Research partially supported by Fundação para a Ciência e a Tecnologia (Portugal) through project CAMGSD UID/04459/2020.info:eu-repo/semantics/publishedVersio

Perforin and granzyme B as markers for acute rejection in heart transplantation

Histological analysis of endomyocardial biopsies (EMB) is regarded as the most satisfactory technique for monitoring crisis of rejection in heart transplanted patients. In this study, 42 biopsies from 14 patients who underwent heart transplantation were examined. Three patients did not present any rejection crisis at the date of the biopsy analysis, six were examined during an early rejection crisis (day 7-70 post-graft), and five were examined during a late rejection crisis (day 74-960 post-graft). Since granzyme B and perforin are proteins associated with cell lysis histological grading and cell phenotype analysis, in situ hybridization using granzyme B and perforin [35S]RNA probes was performed on 30 EMB to characterize the cytolytic activation of heart infiltrating cells. Our data suggest that granzyme B and perforin could be used as predictive markers for acute rejection in patients with early rejection crisis. Their detection might be an indication to administrate corticoids to resolve an acute rejection crisis. In contrast, their absence in patients with late rejection crisis appears as a good prognostic factor for the outcome of rejection and raises the question of the necessity to treat such patients with additional corticoid treatment