Telegraph systems on networks and port-Hamiltonians. I. Boundary conditions and well-posedness

The paper is concerned with a system of linear hyperbolic differential equations on a network coupled through general transmission conditions of Kirchhoff's type at the nodes. We discuss the reduction of such a problem to a system of 1-dimensional hyperbolic problems for the associated Riemann invariants and provide a semigroup theoretic proof of its well-posedness. A number of examples showing the relation of our results with recent research is also provided.Comment: 35 page

Telegraph systems on networks and port-Hamiltonians. Ⅲ. Explicit representation and long-term behaviour

The research was completed while A. B. was a doctoral candidate in the Interdisciplinary Doctoral School at Łodź University of Technology, Poland.In this paper we present an explicit formula for the semigroup governing the solution to hyperbolic systems on a metric graph, satisfying general linear Kirchhoff's type boundary conditions. Further, we use this representation to establish the long term behaviour of the solutions. The crucial role is played by the spectral decomposition of the boundary matrix.Partial support from the National Science Centre of Poland and the National Research Foundation of South Africa.https://www.aimsciences.org/journal/A0000-0000hj2023Mathematics and Applied Mathematic

Coagulation and fragmentation processes with evolving size and shape profiles : a semigroup approach

We investigate a class of bivariate coagulation-fragmentation equations. These equations describe the evolution of a system of particles that are characterised not only by a discrete size variable but also by a shape variable which can be either discrete or continuous. Existence and uniqueness of strong solutions to the associated abstract Cauchy problems are established by using the theory of substochastic semigroups of operators

Insights on coccolith chemistry from a new ion probe method for analysis of individually picked coccoliths

Author Posting. © American Geophysical Union, 2007. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Geochemistry Geophysics Geosystems 8 (2007): Q06020, doi:10.1029/2006GC001546.The elemental chemistry of calcareous nannofossils may provide valuable information on past ocean conditions and coccolithophorid physiology, but artifacts from noncoccolith particles and from changing nannofossil assemblages may bias geochemical records from coccolith size fractions. We describe the first method for picking individual coccoliths using a tungsten needle in micromanipulator. Epoxy-mounted individuals and populations of coccoliths can be analyzed by secondary ion mass spectrometry (SIMS). For Paleocene sediments the technique distinguishes the high Sr/Ca ratios of coccoliths (0.3 to 2.8 mmol/mol) from low ratios in abiogenic calcite blades (0.1 mmol/mol). The large heterogeneity of Sr/Ca ratios among different genera suggests that primary geochemical differences have not been homogenized by diagenetic overgrowth and the thick massive coccoliths of the late Paleocene are a primary feature of biomineralization. Sr/Ca ratios for modern genera are on average higher than those of Paleogene genera but exhibit a comparable level of variability.Research supported by NSF OCE-0424474 to H. Stoll and a fellowship to H. Stoll from the Spanish Ministry of Education cofunded by the European Social Fund