Space-time modeling of soil moisture: Stochastic rainfall forcing with heterogeneous vegetation

The present paper complements that of Isham et al. (2005), who introduced a space-time soil moisture model driven by stochastic space-time rainfall forcing with homogeneous vegetation and in the absence of topographical landscape effects. However, the spatial variability of vegetation may significantly modify the soil moisture dynamics with important implications for hydrological modeling. In the present paper, vegetation heterogeneity is incorporated through a two dimensional Poisson process representing the coexistence of two functionally different types of plants (e.g., trees and grasses). The space-time statistical structure of relative soil moisture is characterized through its covariance function which depends on soil, vegetation, and rainfall patterns. The statistical properties of the soil moisture process averaged in space and time are also investigated. These properties are especially important for any modeling that aggregates soil moisture characteristics over a range of spatial and temporal scales. It is found that particularly at small scales, vegetation heterogeneity has a significant impact on the averaged process as compared with the uniform vegetation case. Also, averaging in space considerably smoothes the soil moisture process, but in contrast, averaging in time up to 1 week leads to little change in the variance of the averaged process

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

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

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

Tailoring the frictional properties of granular media

A method of modifying the roughness of soda-lime glass spheres is presented, with the purpose of tuning inter-particle friction. The effect of chemical etching on the surface topography and the bulk frictional properties of grains is systematically investigated. The surface roughness of the grains is measured using white light interferometry and characterised by the lateral and vertical roughness length scales. The underwater angle of repose is measured to characterise the bulk frictional behaviour. We observe that the co-efficient of friction depends on the vertical roughness length scale. We also demonstrate a bulk surface roughness measurement using a carbonated soft drink.Comment: 10 pages, 17 figures, submitted to Phys. Rev.

Soil nutrient cycles as a nonlinear dynamical system

International audienceAn analytical model for the soil carbon and nitrogen cycles is studied from the dynamical system point of view. Its main nonlinearities and feedbacks are analyzed by considering the steady state solution under deterministic hydro-climatic conditions. It is shown that, changing hydro-climatic conditions, the system undergoes dynamical bifurcations, shifting from a stable focus to a stable node and back to a stable focus when going from dry, to well-watered, and then to saturated conditions, respectively. An alternative degenerate solution is also found in cases when the system can not sustain decomposition under steady external conditions. Different basins of attraction for "normal" and "degenerate" solutions are investigated as a function of the system initial conditions. Although preliminary and limited to the specific form of the model, the present analysis points out the importance of nonlinear dynamics in the soil nutrient cycles and their possible complex response to hydro-climatic forcing

Structure, Scaling and Phase Transition in the Optimal Transport Network

We minimize the dissipation rate of an electrical network under a global constraint on the sum of powers of the conductances. We construct the explicit scaling relation between currents and conductances, and show equivalence to a a previous model [J. R. Banavar {\it et al} Phys. Rev. Lett. {\bf 84}, 004745 (2000)] optimizing a power-law cost function in an abstract network. We show the currents derive from a potential, and the scaling of the conductances depends only locally on the currents. A numerical study reveals that the transition in the topology of the optimal network corresponds to a discontinuity in the slope of the power dissipation.Comment: 4 pages, 3 figure

Two dimensional modulational instability in photorefractive media

We study theoretically and experimentally the modulational instability of broad optical beams in photorefractive nonlinear media. We demonstrate the impact of the anisotropy of the nonlinearity on the growth rate of periodic perturbations. Our findings are confirmed by experimental measurements in a strontium barium niobate photorefractive crystal.Comment: 8 figure

Spatial effects on species persistence and implications for biodiversity

Natural ecosystems are characterized by striking diversity of form and functions and yet exhibit deep symmetries emerging across scales of space, time and organizational complexity. Species-area relationships and species-abundance distributions are examples of emerging patterns irrespective of the details of the underlying ecosystem functions. Here we present empirical and theoretical evidence for a new macroecological pattern related to the distributions of local species persistence times, defined as the timespans between local colonizations and extinctions in a given geographic region. Empirical distributions pertaining to two different taxa, breeding birds and herbaceous plants, analyzed in a new framework that accounts for the finiteness of the observational period, exhibit power-law scaling limited by a cut-off determined by the rate of emergence of new species. In spite of the differences between taxa and spatial scales of analysis, the scaling exponents are statistically indistinguishable from each other and significantly different from those predicted by existing models. We theoretically investigate how the scaling features depend on the structure of the spatial interaction network and show that the empirical scaling exponents are reproduced once a two-dimensional isotropic texture is used, regardless of the details of the ecological interactions. The framework developed here also allows to link the cut-off timescale with the spatial scale of analysis, and the persistence-time distribution to the species-area relationship. We conclude that the inherent coherence obtained between spatial and temporal macroecological patterns points at a seemingly general feature of the dynamical evolution of ecosystems.Comment: 5 pages, 5 figures. Supplementary materials avaliable on http://www.pnas.org/content/108/11/434