Patterns in Nature

Growing Order out of Randomness

In my Ph.D. thesis, I study a class of statistical patterns in Nature arising from local stochastic activity and leading to large-scale patterns and order. I study the formation of extremely periodic patterns which are usually observed in sedimentary structures. In this case, Nature separates previously mixed granular materials of different sizes by a selective sieve during transport by wind and avalanching during sedimentation. I address the longstanding question of how the process forms the periodic patterns. I also consider the patterns observed in surfaces and interfaces generated in various non-equilibrium systems. A very general feature of these surfaces is that they typically present scale-invariant power-law correlations ---statistical patterns that apply across the whole object--- both in space and in time, so that their study shares many features with that of critical phenomena.

  • STRATIFICATION IN SAND AND ROCKS

    I present a new type of size segregation in granular matter. I show that when a mixture of small and large grains is poured between two transparent slabs, a size segregation of the mixture in successive layers of small and large grains occurs. I propose a theoretical explanation for the formation of the layers, which is related to the different angles of repose entering in the theory. The formation of periodic layers of small and large grains is reminiscent of the stratified patterns observed in aeolian rocks.

    • SAND EXPERIMENTS AND MODELS

    • LAMINATION IN ROCKS
      MODEL
    • LAMINATION IN AEOLIAN ROCK FROM PETRA
    • LAMINATION IN AEOLIAN ROCK FROM UK
  • NON-EQUILIBRIUM KINETIC ROUGHENING

    I study a subset of non-equilibrium phenomena and disordered systems. I explore the scaling properties of driven surfaces and interfaces in disordered media, and the dynamical properties of surface erosion via ion-sputtering. In particular, I formulate a discrete stochastic model which includes the essential features of large classes of sputter etching processes. The model reproduces dynamical instabilities encountered in several experiments on sputtered surfaces, whereas it displays scaling behavior at later stages of the dynamical evolution.

    • EROSION MODEL: FROM PATTERN FORMATION TO ROUGH MORPHOLOGY

    • INTERFACES BELONGING TO THE KPZ AND QEW UNIVERSALITY CLASSES

  • CHARACTERIZING SPATIAL PATTERNS IN POROUS MEDIA

    I consider porous media, such as sedimentary rocks, which have complex correlated patterns that influence the flow of fluids and hydrocarbons. I quantify these patterns using long-range correlated percolation models.

    • CORRELATED AND UNCORRELATED PERCOLATION MODELS OF ROCKS

  • PATTERN FORMATION IN URBAN GROWTH

    I consider the fractal patterns formed by human agglomerations.

    • GROWTH OF BERLIN <----------->PERCOLATION MODEL
    • PERCOLATION MODEL OF URBAN GROWTH

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