Networks and Heterogeneous Media ISSN 1556-1801 (Print)
Networks and Heterogeneous Media ISSN 1556-181X (Online)
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Editor in Chief : Benedetto Piccoli (IAC, Rome)
Henri Berestycki (Ehess, Paris) Claude Le Bris (ENPC, Paris)
Leonid Berlyand (PennState) Pierre-Louis Lions (Paris Dauphine)
Alberto Bressan (PennState) Dag Lukkassen (Narvik)
Suncica Canic (Houston) David MacDonald (Ottawa)
Jennifer Chayes (Microsoft) Masayasu Mimura (Meiji)
Zhangxin Chen (Dallas) Roberto Natalini (IAC, Rome)
Camillo De Lellis (Zurich) Charles Newman (Courant)
Antonio DeSimone (SISSA, Trieste) George Papanicolaou (Stanford)
Emmanuele Di Benedetto (Vanderbilt) Luigi Preziosi (Torino)
Dirk Helbing (Dresden) Alfio Quarteroni (Lausanne)
Thomas Hillen (Alberta) Eitan Tadmor (Maryland)
Shi Jin (Madison) Cedric Villani (ENS, Lyon)
Kenneth Karlsen (Oslo) Hans Van Duijn (Eindhoven)
Axel Klar (Kaiserlautern) Jean Luis Vazquez (Madrid)
Jean-Patrick Lebacque (INRETS) Shih-Hsien Yu (Hong Kong)
Extensive searches (in Zentralblatt and MathSciNet) on published papers about Networks and Heterogeneous Media 2000-present, showed something like 450 papers/yr about networks, 50/yr about multiscale problems, 100/yr about porous media and 25/yr about heterogeneous media. This is a motivation to launch a new journal focused on Networks and Heterogeneous Media.
There are three main features of this journal:
1. Interdisciplinary Character;
2. Specific Focus;
3. Mathematical Core (Deep Mathematical Content).
Clearly there are a number of existing journals sharing some of these features. However, the new journal will offer a unique strong combination of i)--iii). For example, SIAM MMS, Comm. In Math. Sci. and Arch. Rat. Mech. and An., which are somehow close in spirit to our journal, definitely have strong presence of aspects i) and iii), but they are not as specifically focused. On the other hand, journals such as Transp. Porus Media and Mass Transf. Stat. Phys. are interdisciplinary focused on specific applications, but do not address a wide range of fundamental mathematical issues.
This journal also aims at creating a link between the discrete and the continuous communities, which distinguishes it from other journals with strong PDE orientation.
It is expected that research on Networks and Heterogeneous Media, motivated by wide range of applications (such as traffic flows, internet network, bio-medical problems, filtration, granular flow etc...), will be one of the most challenging direction in future mathematical research and will result in the development of new fundamental mathematics.
Aims & Scope
The proposed journal aims at attracting original contributions to solve problems on networks and heterogeneous media , and more generally in complicated framework. This journal would be a breeding ground for research in an area which is presently dispersed across a range of statistical physics, applied mathematics, engineering, biology and medical journals.
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.
NHM is thus devoted to the presentation of original basic and applied research work on the mathematical, physical, engineering, biological and bio-medical aspects of problems on complicated media such as: macroscopic evolutions in complex and random media, multiphase flows in porous media, chemical reactions, biological flows, mechanical and biological properties of tissues, homogenization limits in elastic materials, currents in micronic and submicronic electronic devices, as well as phenomena which occur in networks, such as vehicle traffic or data traffic in the internet. Mass transfer and its interaction with hydrodynamic descriptions of flows is also of considerable interest.
The main focus is on macroscopic models and dynamics, but it will be also of interest to take into account ideas arising from the micro- and mesoscopic levels of description and to steady state solutions and equilibria.
The emphasis of the journal Networks and Heterogeneous Media is on modelling, analysis, control, numerics and simulations, and applications. Occasionally, invited state of the art reviews are included when they provide a solid background for future research.
Main topics: Macroscopic transport phenomena, Mass transfer, Nonlinear transport in porous media: sedimentation, filtration, Random media, Flows on networks (such as communication channels or car traffic flow), Discrete networks and continuum limits, Biological flows and pattern formation, Macroscopic properties of tissues, Kinetic description of hydrodynamic flows, Multiscale phenomena, Homogenization.