Networks and Heterogeneous Media (NHM)

General purpose

NHM aims to attract original contributions of highest quality in Networks, Heterogeneous Media and related fields. The research in this area are scattered across a wide range of statistical physics, applied mathematics, engineering, socio-economical and bio-medical journals. Networks and Heterogeneous Media brings together all of these different research lines by emphasizing the common underlying mathematics.

Expected papers' scientific contents

While the classical modelling and analysis approach is efficient for systems evolving on Euclidean spaces or manifolds, many recent applications require the development of mathematical tools for state spaces with a more complicated structure, such as a fractal, a stratified set, or a topological graph, or, in the case of many interacting evolutions, for a collection of different state spaces. These special structures arise naturally in a number of applied problems ranging from mechanical ones, as for the static and dynamics of granular media, to biological ones, as vessels pattern formation in angiogenesis. Such problems can be studied by developing an analysis directly on the complicated media or via limiting procedures on the microstructure to obtain auxiliary systems on classical spaces, with the appearance of new terms in classical equations and/or enlarged state spaces. This situation is typical of discrete networks, which can be used to approximate hard problems on continua, or can be studied by continuum limits. Also, an example of limiting procedure is given by homogenization limits for various materials with several constituents. Other important examples include continuum networks, i.e. one dimensional complexes, which are the natural space for car traffic or telecommunication data flow. The determination of the natural dynamics or the typical stochastic behavior at vertices requires an investigation of flows in networks. The presence of different time or space scales may give rise to similar phenomena requiring singular perturbation methods, mean fields analysis, and other limiting procedures.

Papers' characteristics

The emphasis of the journal Networks and Heterogeneous Media is on modelling, analysis, control, numerics, and applications. Occasionally, invited state of the art reviews will be published when they provide a solid background for future research.

Reviewing procedure

Each paper will be assigned by the EiC to an Associate Editor. The AE will (usually) indicate two or more potential referees, which will be contacted directly from NHM with the request of a report within the usual time of two months (unless differently specified). After collecting the reports, the AE will provide the EiC with a final assessment of the paper quality and a recommendation (accept, minor revision, major revision, reject). NHM will then communicate the final decision to authors. In case of required major revision, papers will undergo a second round with similar procedure.

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