相关论文: Variational Analysis of Landscape Elevation and Dr…

The hierarchy of channel networks in landscapes displays features that are characteristic of non-equilibrium complex systems. Here we show that a sequence of increasingly complex ridge and valley networks is produced by a system of partial…

Complex topographies exhibit universal properties when fluvial erosion dominates landscape evolution over other geomorphological processes. Similarly, we show that the solutions of a minimalist landscape evolution model display invariant…

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…

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…

In this paper, we consider a system of partial differential equations modeling the evolution of a landscape. A ground surface is eroded by the flow of water over it, either by sedimentation or dilution. The system is composed by three…

Erosion shapes our landscape and occurs when a sufficient shear stress is exerted by a fluid on a sedimented layer. What controls erosion at a microscopic level remains debated, especially near the threshold forcing where it stops. Here we…

Landscape is one of the key notions in literature on biological processes and physics of complex systems with both deterministic and stochastic dynamics. The large deviation theory (LDT) provides a possible mathematical basis for the…

We analyze the Optimal Channel Network model for river networks using both analytical and numerical approaches. This is a lattice model in which a functional describing the dissipated energy is introduced and minimized in order to find the…

Numerous complex systems, both natural and artificial, are characterized by the presence of intertwined supply and/or drainage networks. Here we present a minimalist model of such co-evolving networks in a spatially continuous domain, where…

We study the dynamics of flow-networks in porous media using a pore-network model. First, we consider a class of erosion dynamics assuming a constitutive law depending on flow rate, local velocities, or shear stress at the walls. We show…

This article reviews and evaluates models of network evolution based on the notion of structural diversity. We show that diversity is an underlying theme of three principles of network evolution: the preferential attachment model,…

We investigate the dependence of river network scaling on the relative dominance of slope vs. noise in initial conditions, using an erosion model. Increasing slope causes network patterns to transition from dendritic to parallel and results…

In this paper we derive analytically the evolution equation of the interface for a model of surface growth with relaxation to the minimum (SRM) in complex networks. We were inspired by the disagreement between the scaling results of the…

In this paper, we propose a variational formulation to study the singular evolution equations that govern the dynamics of surface modulations on crystals below the roughening temperature. The basic idea of the formulation is to expand the…

Do ecosystems primarily reflect evolutionary history or current environment? Predicting land-atmosphere exchange hinges on this unresolved question. Plant traits adapt to particular environments over evolutionary timescales, yet their…

For a parabolic surface partial differential equation coupled to surface evolution, convergence of the spatial semidiscretization is studied in this paper. The velocity of the evolving surface is not given explicitly, but depends on the…

Erosion by flowing water is one of the major forces shaping the surface of Earth. Studies in the last decade have shown, in particular, that the drainage region of rivers, where water is collected, exhibits scale invariant features…

Landscapes that are rhythmically dissected by natural drainage channels exist in various geologic and climatic settings. Such landscapes are characterized by a length-scale for the lateral spacing between channels. We observe a small-scale…

Similar evolutionary variational inequalities appear as convenient formulations for continuous quasistationary models for sandpile growth, formation of a network of lakes and rivers, magnetization of type-II superconductors, and…

Vegetation in semi-arid environments self-organizes into striking spatial patterns -- bands, spots, labyrinths, and gaps -- with characteristic wavelengths on the order of tens to hundreds of meters. Existing reaction-diffusion models…