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"pattern formation"
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Multiscale structural complexity of natural patterns
Complexity of patterns is key information for human brain to differ objects of about the same size and shape. Like other innate human senses, the complexity perception cannot be easily quantified. We propose a transparent and universal machine method for estimating structural (effective) complexity of two-dimensional and three-dimensional patterns that can be straightforwardly generalized onto other classes of objects. It is based on multistep renormalization of the pattern of interest and computing the overlap between neighboring renormalized layers. This way, we can define a single number characterizing the structural complexity of an object. We apply this definition to quantify complexity of various magnetic patterns and demonstrate that not only does it reflect the intuitive feeling of what is “complex” and what is “simple” but also, can be used to accurately detect different phase transitions and gain information about dynamics of nonequilibrium systems. When employed for that, the proposed scheme is much simpler and numerically cheaper than the standard methods based on computing correlation functions or using machine learning techniques.
Journal Article
Hydrodynamics control shear-induced pattern formation in attractive suspensions
Dilute suspensions of repulsive particles exhibit a Newtonian response to flow that can be accurately predicted by the particle volume fraction and the viscosity of the suspending fluid. However, such a description fails when the particles are weakly attractive. In a simple shear flow, suspensions of attractive particles exhibit complex, anisotropic microstructures and flow instabilities that are poorly understood and plague industrial processes. One such phenomenon, the formation of log-rolling flocs, which is ubiquitously observed in suspensions of attractive particles that are sheared while confined between parallel plates, is an exemplar of this phenomenology. Combining experiments and discrete element simulations, we demonstrate that this shear-induced structuring is driven by hydrodynamic coupling between the flocs and the confining boundaries. Clusters of particles trigger the formation of viscous eddies that are spaced periodically and whose centers act as stable regions where particles aggregate to form flocs spanning the vorticity direction. Simulation results for the wavelength of the periodic pattern of stripes formed by the logs and for the log diameter are in quantitative agreement with experimental observations on both colloidal and noncolloidal suspensions. Numerical and experimental results are successfully combined by means of rescaling in terms of a Mason number that describes the strength of the shear flow relative to the rupture force between contacting particles in the flocs. The introduction of this dimensionless group leads to a universal stability diagram for the log-rolling structures and allows for application of shear-induced structuring as a tool for assembling and patterning suspensions of attractive particles.
Journal Article
Pattern formation in multiplex networks
The advances in understanding complex networks have generated increasing interest in dynamical processes occurring on them. Pattern formation in activator-inhibitor systems has been studied in networks, revealing differences from the classical continuous media. Here we study pattern formation in a new framework, namely multiplex networks. These are systems where activator and inhibitor species occupy separate nodes in different layers. Species react across layers but diffuse only within their own layer of distinct network topology. This multiplicity generates heterogeneous patterns with significant differences from those observed in single-layer networks. Remarkably, diffusion-induced instability can occur even if the two species have the same mobility rates; condition which can never destabilize single-layer networks. The instability condition is revealed using perturbation theory and expressed by a combination of degrees in the different layers. Our theory demonstrates that the existence of such topology-driven instabilities is generic in multiplex networks, providing a new mechanism of pattern formation.
Journal Article
Design in Nature : how the constructal law governs evolution in biology, physics, technology, and social organization
Reveals how recurring patterns in nature are accounted for by a single governing principle of physics, explaining how all designs in the world from biological life to inanimate systems evolve in a sequence of ever-improving designs that facilitate flow.
Book
From a vortex gas to a vortex crystal in instability-driven two-dimensional turbulence
We study structure formation in two-dimensional turbulence driven by an external force, interpolating between linear instability forcing and random stirring, subject to nonlinear damping. Using extensive direct numerical simulations, we uncover a rich parameter space featuring four distinct branches of stationary solutions: large-scale vortices, hybrid states with embedded shielded vortices (SVs) of either sign, and two states composed of many similar SVs. Of the latter, the first is a dense vortex gas where all SVs have the same sign and diffuse across the domain. The second is a hexagonal vortex crystal forming from this gas when the linear instability is sufficiently weak. These solutions coexist stably over a wide parameter range. The late-time evolution of the system from small-amplitude initial conditions is nearly self-similar, involving three phases: initial inverse cascade, random nucleation of SVs from turbulence and, once a critical number of vortices is reached, a phase of explosive nucleation of SVs, leading to a statistically stationary state. The vortex gas is continued in the forcing parameter, revealing a sharp transition towards the crystal state as the forcing strength decreases. This transition is analysed in terms of the diffusivity of individual vortices using ideas from statistical physics. The crystal can also decay via an inverse cascade resulting from the breakdown of shielding or insufficient nonlinear damping acting on SVs. Our study highlights the importance of the forcing details in two-dimensional turbulence and reveals the presence of non-trivial SV states in this system, specifically the emergence and melting of a vortex crystal.
Journal Article
The beauty of physics : patterns, principles, and perspectives
\"The beauty of physics lies in its coherence in terms of a few fundamental concepts and principles. Even physicists have occasion to marvel at the overarching reach of basic principles and their ability to account for features stretching from the microscopic sub-atomic world to the cosmological expanses of the Universe. While mathematics is its natural language, physics is mostly about patterns, connections, and relations between objects and phenomena, and it is this aspect that is emphasized in this book. Since science tries to connect phenomena that at first sight appear widely different, while boiling them down to a small set of essential principles and laws, metaphor and analogy pervade our subject. Consider the pendulum, its swing from one extreme to the other often invoked in social or economic contexts. In molecular vibrations, such as in the CO2 molecule, the quantum motions of electrons and nuclei are metaphorically the pendulums. In electromagnetic radiation, including the visible light we observe, there are not even any concrete material particles, only electric and magnetic fields executing simple harmonic motion. But, to a physicist, they are all \"just a pendulum\". The selection of topics reflects the author's own four-decade career in research physics and his resultant perspective on the subject. While aimed primarily at physicists, including junior students, this book also addresses other readers who are willing to think with symbols and simple algebra in understanding the physical world around us. Each chapter, on themes such as dimensions, transformations, symmetries, or maps, begins with simple examples accessible to all while connecting them later to more sophisticated realizations in more advanced topics of physics.\" -- Publisher's description.
Book
Vegetation patterning can both impede and trigger critical transitions from savanna to grassland
Tree-grass coexistence is a defining feature of savanna ecosystems, which play an important role in supporting biodiversity and human populations worldwide. While recent advances have clarified many of the underlying processes, how these mechanisms interact to shape ecosystem dynamics under environmental stress is not yet understood. Here, we present and analyse a minimalistic spatially extended model of tree-grass dynamics in dry savannas. We incorporate tree facilitation of grasses through shading and grass competing with trees for water, both varying with tree life stage. Our model shows that these mechanisms lead to grass-tree coexistence and bistability between savanna and grassland states. Moreover, the model predicts vegetation patterns consisting of trees and grasses, particularly under harsh environmental conditions, which can persist in situations where a non-spatial version of the model predicts ecosystem collapse from savanna to grassland instead (a phenomenon called ‘Turing-evades-tipping’). Additionally, we identify a novel ‘Turing-triggers-tipping’ mechanism, where unstable pattern formation drives tipping events that are overlooked when spatial dynamics are not included. These transient patterns act as early warning signals for ecosystem transitions, offering a critical window for intervention. Further theoretical and empirical research is needed to determine when spatial patterns prevent tipping or drive collapse.
Journal Article