Models of Fractal River Basins

Two distinct models for self-similar and self-affine river basins are numerically investigated. They yield fractal aggregation patterns following non-trivial power laws in experimentally relevant distributions. Previous numerical estimates on the critical exponents, when existing, are confirmed and superseded. A physical motivation for both models in the present framework is also discussed.Comment: 16 pages, latex, 9 figures included using uufiles command (for any problem: [email protected]), to be publishes in J. Stat. Phys. (1998

Cellular Models for River Networks

A cellular model introduced for the evolution of the fluvial landscape is revisited using extensive numerical and scaling analyses. The basic network shapes and their recurrence especially in the aggregation structure are then addressed. The roles of boundary and initial conditions are carefully analyzed as well as the key effect of quenched disorder embedded in random pinning of the landscape surface. It is found that the above features strongly affect the scaling behavior of key morphological quantities. In particular, we conclude that randomly pinned regions (whose structural disorder bears much physical meaning mimicking uneven landscape-forming rainfall events, geological diversity or heterogeneity in surficial properties like vegetation, soil cover or type) play a key role for the robust emergence of aggregation patterns bearing much resemblance to real river networks.Comment: 7 pages, revtex style, 14 figure

Electromagnetic Forming of Longitudinal Strengthening Ribs in Roll Formed Automotive Profiles

In the automotive industry, increasing ecological concerns and demands for higher performance have become lightweight construction a key aspect. Due to the gradual introduction of high strength materials on the one side, and greater consideration with regard to continuous manufacturing technologies on the other side, it is possible nowadays to address the demands that structural and complex automotive parts have to face, from the standpoint of lightweight manufacturing. Thickness, shape and impact conditions constitute the main aspects to consider for such parts and shape conditions in particular require from complex, costly and lengthy procedures, especially when discontinuous forming operations such as stamping and hydro forming procedures are selected. However, continuous forming operations like Roll Forming (RF) can prove to be advantageous and suited for scalable parts (e.g in length) and at the same time be economically reasonable. RF lines as well generally incorporate additional installations to perform multiple forming operations destined to imprint strengthening ribs perform punching operations or weld certain parts. It is in this context where the usefulness of the electromagnetic forming technology for completion of auxiliary operations can be proven, given its flexibility and reasonable investment costs. Electromagnetic forming (EMF) is a contact-free technique where large forces can be imparted to a conductive metallic workpiece by a pure electromagnetic interaction. The produced electromagnetic pressure can produce stresses in the workpiece that are several times larger than the material flow stress. Ultimately this can cause the workpiece to deform plastically and to be accelerated achieving high velocities. Once the velocity is imparted to the workpiece, the shape can be developed either by free or die forming. The work described in this paper explores the potential of the EMF process to adequately form shallow longitudinal ribs or stiffeners in components previously formed utilizing an innovative concept called Flexible Roll Forming, developed at The Technical University of Darmstadt in Germany, by means of magnetic pulse forming, maintaining the integrity of the workpiece while trying to meet industry standard tolerances. Profiles exhibiting hat-like cross sections made of AHSS steels were subjected to localized impulses in order to achieve strengthening features in the roll formed part. ZStE340 steel alloy profiles were first roll formed and then inserted in the EM forming installation designed for the occasion. A high strength copper alloy (Cr-Zr-Cu) was used as a conductor for the single turn coil, placed opposite to the sidewall in the moment of the energy delivery. Formed specimens were subsequently measured to account for existing dimensional deviations

Local minimal energy landscapes in river networks

The existence and stability of the universality class associated to local minimal energy landscapes is investigated. Using extensive numerical simulations, we first study the dependence on a parameter $\gamma$ of a partial differential equation which was proposed to describe the evolution of a rugged landscape toward a local minimum of the dissipated energy. We then compare the results with those obtained by an evolution scheme based on a variational principle (the optimal channel networks). It is found that both models yield qualitatively similar river patterns and similar dependence on $\gamma$. The aggregation mechanism is however strongly dependent on the value of $\gamma$. A careful analysis suggests that scaling behaviors may weakly depend both on $\gamma$ and on initial condition, but in all cases it is within observational data predictions. Consequences of our resultsComment: 12 pages, 13 figures, revtex+epsfig style, to appear in Phys. Rev. E (Nov. 2000

Globally and Locally Minimal Weight Spanning Tree Networks

The competition between local and global driving forces is significant in a wide variety of naturally occurring branched networks. We have investigated the impact of a global minimization criterion versus a local one on the structure of spanning trees. To do so, we consider two spanning tree structures - the generalized minimal spanning tree (GMST) defined by Dror et al. [1] and an analogous structure based on the invasion percolation network, which we term the generalized invasive spanning tree or GIST. In general, these two structures represent extremes of global and local optimality, respectively. Structural characteristics are compared between the GMST and GIST for a fixed lattice. In addition, we demonstrate a method for creating a series of structures which enable one to span the range between these two extremes. Two structural characterizations, the occupied edge density (i.e., the fraction of edges in the graph that are included in the tree) and the tortuosity of the arcs in the trees, are shown to correlate well with the degree to which an intermediate structure resembles the GMST or GIST. Both characterizations are straightforward to determine from an image and are potentially useful tools in the analysis of the formation of network structures.Comment: 23 pages, 5 figures, 2 tables, typographical error correcte

Continuum Model for River Networks

The effects of erosion, avalanching and random precipitation are captured in a simple stochastic partial differential equation for modelling the evolution of river networks. Our model leads to a self-organized structured landscape and to abstraction and piracy of the smaller tributaries as the evolution proceeds. An algebraic distribution of the average basin areas and a power law relationship between the drainage basin area and the river length are found.Comment: 9 pages, Revtex 3.0, 7 figures in compressed format using uufiles command, to appear in Phys. Rev. Lett., for an hard copy or problems e-mail to [email protected]

Climate change and the kidney

The worldwide increase in temperature has resulted in a marked increase in heat waves (heat extremes) that carries a markedly increased risk for morbidity and mortality. The kidney has a unique role not only in protecting the host from heat and dehydration but also is an important site of heat-associated disease. Here we review the potential impact of global warming and heat extremes on kidney diseases. High temperatures can result in increased core temperatures, dehydration, and blood hyperosmolality. Heatstroke (both clinical and subclinical whole-body hyperthermia) may have a major role in causing both acute kidney disease, leading to increased risk of acute kidney injury from rhabdomyolysis, or heat-induced inflammatory injury to the kidney. Recurrent heat and dehydration can result in chronic kidney disease (CKD) in animals and theoretically plays a role in epidemics of CKD developing in hot regions of the world where workers are exposed to extreme heat. Heat stress and dehydration also has a role in kidney stone formation, and poor hydration habits may increase the risk for recurrent urinary tract infections. The resultant social and economic consequences include disability and loss of productivity and employment. Given the rise in world temperatures, there is a major need to better understand how heat stress can induce kidney disease, how best to provide adequate hydration, and ways to reduce the negative effects of chronic heat exposure.Published versio

A transition from river networks to scale-free networks

A spatial network is constructed on a two dimensional space where the nodes are geometrical points located at randomly distributed positions which are labeled sequentially in increasing order of one of their co-ordinates. Starting with $N$ such points the network is grown by including them one by one according to the serial number into the growing network. The $t$-th point is attached to the $i$-th node of the network using the probability: $\pi_i(t) \sim k_i(t)\ell_{ti}^{\alpha}$ where $k_i(t)$ is the degree of the $i$-th node and $\ell_{ti}$ is the Euclidean distance between the points $t$ and $i$. Here $\alpha$ is a continuously tunable parameter and while for $\alpha=0$ one gets the simple Barab\'asi-Albert network, the case for $\alpha \to -\infty$ corresponds to the spatially continuous version of the well known Scheidegger's river network problem. The modulating parameter $\alpha$ is tuned to study the transition between the two different critical behaviors at a specific value $\alpha_c$ which we numerically estimate to be -2.Comment: 5 pages, 5 figur

Scale-free Networks from Optimal Design

A large number of complex networks, both natural and artificial, share the presence of highly heterogeneous, scale-free degree distributions. A few mechanisms for the emergence of such patterns have been suggested, optimization not being one of them. In this letter we present the first evidence for the emergence of scaling (and smallworldness) in software architecture graphs from a well-defined local optimization process. Although the rules that define the strategies involved in software engineering should lead to a tree-like structure, the final net is scale-free, perhaps reflecting the presence of conflicting constraints unavoidable in a multidimensional optimization process. The consequences for other complex networks are outlined.Comment: 6 pages, 2 figures. Submitted to Europhysics Letters. Additional material is available at http://complex.upc.es/~sergi/software.ht

Growing dynamics of Internet providers

In this paper we present a model for the growth and evolution of Internet providers. The model reproduces the data observed for the Internet connection as probed by tracing routes from different computers. This problem represents a paramount case of study for growth processes in general, but can also help in the understanding the properties of the Internet. Our main result is that this network can be reproduced by a self-organized interaction between users and providers that can rearrange in time. This model can then be considered as a prototype model for the class of phenomena of aggregation processes in social networks