AIMS

Networks and Heterogeneous Media (NHM)

ISSN 1556-1801(print) ISSN 1556-181X(online)	Current volume Go	Journal archive Go	Advanced Search
	NHM is a quarterly publication in March, June, September and December. It is now online only. To submit, send a pdf directly to the Editor in Chief, Benedetto Piccoli, at nhmaims@camden.rutgers.edu. NHM offers a strong combination of three features: Interdisciplinary character, specific focus, and deep mathematical content. Also, the journal aims to create a link between the discrete and the continuous communities, which distinguishes it from other journals with strong PDE orientation. NHM publishes original contributions of high quality in networks, heterogeneous media and related fields. NHM is thus devoted to research work on complex media arising in mathematical, physical, engineering, socio-economical and bio-medical problems. NHM is covered in Science Citation Index Expanded, CompuMath Citation Index, Current Contents/Engineering, Computing, and Technology ISI Alerting Services.

TOP 10 Most Read Articles in NHM, May 2012

1	A distributed model of traffic flows on extended regions Volume 5, Number 3, Pages: 525 - 544, 2010 Fabio Della Rossa, Carlo D’Angelo and Alfio Quarteroni Abstract Full Text Related Articles This work deals with the modelling of traffic flows in complex networks, spanning two-dimensional regions whose size ( macroscale ) is much greater than the characteristic size of the network arcs ( microscale). A typical example is the modelling of traffic flow in large urbanized areas with diameter of hundreds of kilometers, where standard models of traffic flows on networks resolving all the streets are computationally too expensive. Starting from a stochastic lattice gas model with simple constitutive laws, we derive a distributed two-dimensional model of traffic flow, in the form of a non-linear diffusion-advection equation for the particle density. The equation is formally equivalent to a (non-linear) Darcy's filtration law. In particular, it contains two parameters that can be seen as the porosity and the permeability tensor of the network. We provide suitable algorithms to extract these parameters starting from the geometry of the network and a given microscale model of traffic flow (for instance based on cellular automata). Finally, we compare the fully microscopic simulation with the finite element solution of our upscaled model in realistic cases, showing that our model is able to capture the large-scale feature of the flow.
2	Self-organized network flows Volume 2, Number 2, Pages: 193 - 210, 2007 Dirk Helbing, Jan Siegmeier and Stefan Lämmer Abstract Full Text Related Articles A model for traffic flow in street networks or material flows in supply networks is presented, that takes into account the conservation of cars or materials and other significant features of traffic flows such as jam formation, spillovers, and load-dependent transportation times. Furthermore, conflicts or coordination problems of intersecting or merging flows are considered as well. Making assumptions regarding the permeability of the intersection as a function of the conflicting flows and the queue lengths, we find self-organized oscillations in the flows similar to the operation of traffic lights.
3	Conservation laws with discontinuous flux Volume 2, Number 1, Pages: 159 - 179, 2006 Mauro Garavello, Roberto Natalini, Benedetto Piccoli and Andrea Terracina Abstract Full Text Related Articles We consider a hyperbolic conservation law with discontinuous flux. Such a partial differential equation arises in different applications, in particular we are motivated by a model of traffic flow. We provide a new formulation in terms of Riemann Solvers. Moreover, we determine the class of Riemann Solvers which provide existence and uniqueness of the corresponding weak entropic solutions.
4	Nonlinear transmission problems for quasilinear diffusion systems Volume 2, Number 2, Pages: 359 - 381, 2007 F. R. Guarguaglini and R. Natalini Abstract Full Text Related Articles We study degenerate quasilinear parabolic systems in two different domains, which are connected by a nonlinear transmission condition at their interface. For a large class of models, including those modeling pollution aggression on stones and chemotactic movements of bacteria, we prove global existence, uniqueness and stability of the solutions.
5	A review of conservation laws on networks Volume 5, Number 3, Pages: 565 - 581, 2010 Mauro Garavello Abstract Full Text Related Articles This paper deals with various applications of conservation laws on networks. In particular we consider the car traffic, described by the Lighthill-Whitham-Richards model and by the Aw-Rascle-Zhang model, the telecommunication case, by using the model introduced by D'Apice-Manzo-Piccoli and, finally, the case of a gas pipeline, modeled by the classical $p$-system. For each of these models we present a review of some results about Riemann and Cauchy problems in the case of a network, formed by a single vertex with $n$ incoming and $m$ outgoing arcs.
6	Globally stable quasistatic evolution in plasticity with softening Volume 3, Number 3, Pages: 567 - 614, 2008 G. Dal Maso, Antonio DeSimone, M. G. Mora and M. Morini Abstract Full Text Related Articles We study a relaxed formulation of the quasistatic evolution problem in the context of small strain associative elastoplasticity with softening. The relaxation takes place in spaces of generalized Young measures. The notion of solution is characterized by the following properties: global stability at each time and energy balance on each time interval. An example developed in detail compares the solutions obtained by this method with the ones provided by a vanishing viscosity approximation, and shows that only the latter capture a decreasing branch in the stress-strain response.
7	Discrete-to-continuum limits for strain-alignment-coupled systems: Magnetostrictive solids, ferroelectric crystals and nematic elastomers Volume 4, Number 4, Pages: 667 - 708, 2009 Marco Cicalese, Antonio DeSimone and Caterina Ida Zeppieri Abstract Full Text Related Articles In the framework of linear elasticity, we study the limit of a class of discrete free energies modeling strain-alignment-coupled systems by a rigorous coarse-graining procedure, as the number of molecules diverges. We focus on three paradigmatic examples: magnetostrictive solids, ferroelectric crystals and nematic elastomers, obtaining in the limit three continuum models consistent with those commonly employed in the current literature. We also derive the correspondent macroscopic energies in the presence of displacement boundary conditions and of various kinds of applied external fields.
8	Random homogenization of fractional obstacle problems Volume 3, Number 3, Pages: 523 - 554, 2008 Luis Caffarelli and Antoine Mellet Abstract Full Text Related Articles We use a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation to study its obstacle problem in perforated domains.
9	Homogenization approach to filtration through a fibrous medium Volume 2, Number 3, Pages: 529 - 550, 2007 Mohamed Belhadj, Eric Cancès, Jean-Frédéric Gerbeau and Andro Mikelić Abstract Full Text Related Articles We study the flow through fibrous media using homogenization techniques. The fibre network under study is the one already used by M. Briane in the context of heat conduction of biological tissues. We derive and justify the effective Darcy equation and the permeability tensor for such fibrous media. The theoretical results on the permeability are illustrated by some numerical simulations. Finally, the low solid fraction limit is considered. Applying results by G. Allaire to our setting, we justify rigorously the leading order term in the empirical formulas for the effective permeability used in engineering. The results are also confirmed by a direct numerical calculation of the permeability, in which the small diameter of the fibres requires high accuracy approximations.
10	Systemic risk in a network fragility model analyzed with probability density evolution of persistent random walks Volume 3, Number 2, Pages: 185 - 200, 2008 Jan Lorenz and Stefano Battiston Abstract Full Text Related Articles We study the mean field approximation of a recent model of cascades on networks relevant to the investigation of systemic risk control in financial networks. In the model, the hypothesis of a trend reinforcement in the stochastic process describing the fragility of the nodes, induces a trade-off in the systemic risk with respect to the density of the network. Increasing the average link density, the network is first less exposed to systemic risk, while above an intermediate value the systemic risk increases. This result offers a simple explanation for the emergence of instabilities in financial systems that get increasingly interwoven. In this paper, we study the dynamics of the probability density function of the average fragility. This converges to a unique stationary distribution which can be computed numerically and can be used to estimate the systemic risk as a function of the parameters of the model.

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