A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented, with emphasis on comparisons between theory and quantitative experiments. Examples include patterns in hydrodynamic systems such as thermal convection in pure fluids and binary mixtures, Taylor-Couette flow, parametric-wave instabilities, as well as patterns in solidification fronts, nonlinear optics, oscillatory chemical reactions and excitable biological media. The theoretical starting point is usually a set of deterministic equations of motion, typically in the form of nonlinear partial differential equations. These are sometimes supplemented by stochastic terms representing thermal or instrumental noise, but for macroscopic systems and carefully designed experiments the stochastic forces are often negligible. An aim of theory is to describe solutions of the deterministic equations that are likely to be reached starting from typical initial conditions and to persist at long times. A unified description is developed, based on the linear instabilities of a homogeneous state, which leads naturally to a classification of patterns in terms of the characteristic wave vector q0 and frequency ω0 of the instability. Type Is systems (ω0=0, q0≠0) are stationary in time and periodic in space; type IIIo systems (ω0≠0, q0=0) are periodic in time and uniform in space; and type Io systems (ω0≠0, q0≠0) are periodic in both space and time. Near a continuous (or supercritical) instability, the dynamics may be accurately described via "amplitude equations," whose form is universal for each type of instability. The specifics of each system enter only through the nonuniversal coefficients. Far from the instability threshold a different universal description known as the "phase equation" may be derived, but it is restricted to slow distortions of an ideal pattern. For many systems appropriate starting equations are either not known or too complicated to analyze conveniently. It is thus useful to introduce phenomenological order-parameter models, which lead to the correct amplitude equations near threshold, and which may be solved analytically or numerically in the nonlinear regime away from the instability. The above theoretical methods are useful in analyzing "real pattern effects" such as the influence of external boundaries, or the formation and dynamics of defects in ideal structures. An important element in nonequilibrium systems is the appearance of deterministic chaos. A greal deal is known about systems with a small number of degrees of freedom displaying "temporal chaos," where the structure of the phase space can be analyzed in detail. For spatially extended systems with many degrees of freedom, on the other hand, one is dealing with spatiotemporal chaos and appropriate methods of analysis need to be developed. In addition to the general features of nonequilibrium pattern formation discussed above, detailed reviews of theoretical and experimental work on many specific systems are presented. These include Rayleigh-Benard convection in a pure fluid, convection in binary-fluid mixtures, electrohydrodynamic convection in nematic liquid crystals, Taylor-Couette flow between rotating cylinders, parametric surface waves, patterns in certain open flow systems, oscillatory chemical reactions, static and dynamic patterns in biological media, crystallization fronts, and patterns in nonlinear optics. A concluding section summarizes what has and has not been accomplished, and attempts to assess the prospects for the future.

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Pattern formation outside of equilibrium

Swarm robotics is an approach to collective robotics that takes inspiration from the self-organized behaviors of social animals. Through simple rules and local interactions, swarm robotics aims at designing robust, scalable, and flexible collective behaviors for the coordination of large numbers of robots. In this paper, we analyze the literature from the point of view of swarm engineering: we focus mainly on ideas and concepts that contribute to the advancement of swarm robotics as an engineering field and that could be relevant to tackle real-world applications. Swarm engineering is an emerging discipline that aims at defining systematic and well founded procedures for modeling, designing, realizing, verifying, validating, operating, and maintaining a swarm robotics system. We propose two taxonomies: in the first taxonomy, we classify works that deal with design and analysis methods; in the second taxonomy, we classify works according to the collective behavior studied. We conclude with a discussion of the current limits of swarm robotics as an engineering discipline and with suggestions for future research directions.

/pdf/swarm-robotics-a-review-from-the-swarm-engineering-46mfc058e6.pdf

Swarm robotics: a review from the swarm engineering perspective

The progress in our understanding of several aspects of turbulent Rayleigh-Benard convection is reviewed. The focus is on the question of how the Nusselt number and the Reynolds number depend on the Rayleigh number Ra and the Prandtl number Pr, and on how the thicknesses of the thermal and the kinetic boundary layers scale with Ra and Pr. Non-Oberbeck-Boussinesq effects and the dynamics of the large scale convection roll are addressed as well. The review ends with a list of challenges for future research on the turbulent Rayleigh-Benard system.

/pdf/heat-transfer-and-large-scale-dynamics-in-turbulent-rayleigh-39oz2czpiy.pdf

Heat transfer and large scale dynamics in turbulent Rayleigh-Bénard convection

The formation of sunspots from the solar toroidal field. the earth's magnetism and magneto hydrodynamics

Physical approach to complex systems

Part 1 Basic concepts Part 2 Investigation tools: experiment theoretical approaches Part 3 Main types of convective-flow structures: two-dimensional rolls and three-dimensional cells patterns of quasi-two-dimensional rolls convection textures roll-pattern defects Part 4 Convection-regime sequences, selection of the wavenumbers of convection rolls: wavenumbers in experiments with random initial disturbances searches for universal selection criteria stability of two-dimensional roll flows Lyapunov function and selection selection mechanisms Part 5 Peculiarities of stratification and vertical structure of convection

Rayleigh‐Bénard Convection: Structures and Dynamics

The evolution of three-dimensional, cellular convective flows in a plane horizontal layer of a Boussinesq fluid heated from below is studied numerically. Slow motion in the form of a spatially periodic pattern of hexagonal cells is introduced initially. In a further development, the flow can undergo a sequence of transitions between various cell types. The features of the flow evolution agree with the idea of the flow seeking an optimal scale. In particular, two-vortex polygonal cells may form at some evolution stages, with an annular planform of the upflow region and downflows localized in both central and peripheral regions of the cells. If short-wave hexagons are stable, they exhibit a specific, stellate fine structure.

/pdf/cellular-flow-patterns-and-their-evolutionary-scenarios-in-27jdmdepys.pdf

Cellular flow patterns and their evolutionary scenarios in three-dimensional Rayleigh-Bénard convection.

The simple procedure of time averaging, when applied to the photospheric brightness eld, reveals quasi-regular structures of the photospheric and subphotospheric flows. We use an 8-h sub-set of the series of photospheric images obtained on 5 June 1993 with the Swedish Vacuum Solar Telescope, La Palma. First, the averaged images are far from completely smeared and contain a multitude of bright, granular-sized blotches even if the averaging period is as long as 8 h. This suggests that granules prefer to originate at certain sites, where they emerge repeatedly, and the granular eld demonstrates a sort of persistence for many hours. Second, the resulting patterns display relatively regular structures, which can be revealed only if the averaging period is suciently long (the optimum seems to lie between 2 and 3 h). The averaged brightness relief is \trenched": it comprises systems of concentric rings and arcs as well as straight or slightly wavy lines and systems of parallel strips. The trenching patterns resemble the so-called target patterns observed in experiments on Rayleigh{B enard convection. In addition, the brightness values at a local averaged-eld maximum and at a nearby minimum exhibit a distinct tendency to vary in antiphase. Thus, a previously unknown type of self-organization is manifest in the solar atmosphere, and our ndings support the suggestion that granules are associated with overheated blobs carried by the convective circulation.

/pdf/regular-structures-of-the-solar-photosphere-persistence-of-1yifcsognj.pdf

Regular structures of the solar photosphere - (Persistence of the granular field and trenching in the brightness relief)

Doubts about the crucial role of the rising-tube mechanism in the formation of sunspot groups

Two series of solar-granulation images – the La Palma series of 5 June 1993 and the SOHO MDI series of 17 – 18 January 1997 – are analysed both qualitatively and quantitatively. New evidence is presented for the existence of long-lived, quasi-regular structures (first reported by Getling and Brandt, Astron. Astrophys. 382, L5 (paper I), 2002), which no longer appear unusual in images averaged over 1 – 2-hour time intervals. Such structures appear as families of light and dark concentric rings or families of light and dark parallel strips (“ridges” and “trenches” in the brightness distributions). In some cases, rings are combined with radial “spokes” and can thus form “web” patterns. The characteristic width of a ridge or trench is somewhat larger than the typical size of granules. Running-average movies constructed from the series of images are used to seek such structures. An algorithm is developed to obtain, for automatically selected centres, the radial distributions of the azimuthally averaged intensity, which highlight the concentric-ring patterns. We also present a time-averaged granulation image processed with a software package intended for the detection of geological structures in aerospace images. A technique of running-average-based correlations between the brightness variations at various points of the granular field is developed and indications are found for a dynamical link between the emergence and sinking of hot and cool parcels of the solar plasma. In particular, such a correlation analysis confirms our suggestion that granules – overheated blobs – may repeatedly emerge on the solar surface. Based on our study, the critical remarks by Rast (Astron. Astrophys. 392, L13, 2002) on the original paper by Getling and Brandt (paper I) can be dismissed.

/pdf/do-quasi-regular-structures-really-exist-in-the-solar-54dy3cuvbp.pdf

A. V. Getling

Papers

Rayleigh‐Bénard Convection: Structures and Dynamics

Cellular flow patterns and their evolutionary scenarios in three-dimensional Rayleigh-Bénard convection.

Regular structures of the solar photosphere - (Persistence of the granular field and trenching in the brightness relief)

Doubts about the crucial role of the rising-tube mechanism in the formation of sunspot groups

Do quasi-regular structures really exist in the solar photosphere? I. Observational evidence