135 research outputs found

    On the transition to turbulence of wall-bounded flows in general, and plane Couette flow in particular

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    The main part of this contribution to the special issue of EJM-B/Fluids dedicated to Patrick Huerre outlines the problem of the subcritical transition to turbulence in wall-bounded flows in its historical perspective with emphasis on plane Couette flow, the flow generated between counter-translating parallel planes. Subcritical here means discontinuous and direct, with strong hysteresis. This is due to the existence of nontrivial flow regimes between the global stability threshold Re_g, the upper bound for unconditional return to the base flow, and the linear instability threshold Re_c characterized by unconditional departure from the base flow. The transitional range around Re_g is first discussed from an empirical viewpoint ({\S}1). The recent determination of Re_g for pipe flow by Avila et al. (2011) is recalled. Plane Couette flow is next examined. In laboratory conditions, its transitional range displays an oblique pattern made of alternately laminar and turbulent bands, up to a third threshold Re_t beyond which turbulence is uniform. Our current theoretical understanding of the problem is next reviewed ({\S}2): linear theory and non-normal amplification of perturbations; nonlinear approaches and dynamical systems, basin boundaries and chaotic transients in minimal flow units; spatiotemporal chaos in extended systems and the use of concepts from statistical physics, spatiotemporal intermittency and directed percolation, large deviations and extreme values. Two appendices present some recent personal results obtained in plane Couette flow about patterning from numerical simulations and modeling attempts.Comment: 35 pages, 7 figures, to appear in Eur. J. Mech B/Fluid

    Fourth SIAM Conference on Applications of Dynamical Systems

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    MULTISCALE PHENOMENA IN MATERIALS

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    A Comprehensible Review: Magnonic Magnetoelectric Coupling in Ferroelectric/ Ferromagnetic Composites

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    Composite materials consisting of coupled magnetic and ferroelectric layers hold the promise for new emergent properties such as controlling magnetism with electric fields. Obviously, the interfacial coupling mechanism plays a crucial role and its understanding is the key for exploiting this material class for technological applications. This short review is focused on the magnonic-based magnetoelectric coupling that forms at the interface of a metallic ferromagnet with a ferroelectric insulator. After analyzing the physics behind this coupling, the implication for the magnetic, transport, and optical properties of these composite materials is discussed. Furthermore, examples for the functionality of such interfaces are illustrated by the electric field controlled transport through ferroelectric/ferromagnetic tunnel junctions, the electrically and magnetically controlled optical properties, and the generation of electromagnon solitons for the use as reliable information carriers.Comment: Physica Status Solidi B 1, 1900750 (2020

    Fractal Analysis

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    Fractal analysis is becoming more and more common in all walks of life. This includes biomedical engineering, steganography and art. Writing one book on all these topics is a very difficult task. For this reason, this book covers only selected topics. Interested readers will find in this book the topics of image compression, groundwater quality, establishing the downscaling and spatio-temporal scale conversion models of NDVI, modelling and optimization of 3T fractional nonlinear generalized magneto-thermoelastic multi-material, algebraic fractals in steganography, strain induced microstructures in metals and much more. The book will definitely be of interest to scientists dealing with fractal analysis, as well as biomedical engineers or IT engineers. I encourage you to view individual chapters

    Spiral defect chaos and the skew-varicose instability in generalizations of the Swift-Hohenberg equation

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    Mean flows are known to play an important role in the dynamics of the Spiral Defect Chaos state and in the existence of the skew-varicose instability in Rayleigh-Bernard Convection. SDC only happens in large domains, so computations involving the full three-dimensional PDEs for convection are very time-consuming. We therefore explore the phenomena of Spiral Defect Chaos and the skew-varicose instability in Generalized Swift-Hohenberg (GSH) models that include the effects of long-range mean flows. Our analysis is aimed at linking the two phenomena. We apply analytical and numerical methods to study the linear stability of stripe patterns in two generalizations of the two-dimensional Swift-Hohenberg equation that include coupling to a mean flow. A projection operator is included in our models to allow exact stripe solutions. In the generalized models, stripes become unstable to the skew-varicose, oscillatory skew-varicose and cross-roll instabilities, in addition to the usual Eckhaus and zigzag instabilities. We analytically derive stability boundaries for the skew varicose instability in various cases, including several asymptotic limits. Close to the onset of pattern formation, the skew varicose instability has the same dependence on wave number as the Eckhaus instability provided the coupling to the mean flow is greater than a critical value. We use numerical techniques to determine eigenvalues and hence stability boundaries of other instabilities. We extend our analysis to both stress-free and no-slip boundary conditions and we note a cross-over from the behaviour characteristic of no-slip to that of stress-free boundaries as the coupling to the mean flow increases or as the Prandtl number decreases. The region of stable stripes is completely eliminated by the cross-roll instability for large coupling to the mean flow or small Prandtl number. We characterize the nonlinear evolution of the modes that are responsible for the skew varicose instability in order to understand whether the bifurcation from stable stripes at the skew-varicose instability is supercritical or subcritical. The systems of ODEs, which are derived from the PDEs by selecting 3 relevant modes and truncating, show that the skew-varicose instability is supercritical whereas for an extension with 5 relevant modes shows the skew-varicose instability is subcritical. We solve the PDEs of one GSH model in spatially-extended domains for very long times, much longer than previous efforts in the literature. We are able to investigate the influence of domain size and other parameters much more systematically, and to develop a criterion for when the spiral defect chaos state could be expected to persist in the long time limit. The importance of the mean flow can be adjusted via the Prandtl number or parameter that accounts for the fluid boundary conditions on the horizontal surfaces in a convecting layer and hence we establish a relation between these parameters that preserves the same pattern. We further analyze the onset of chaotic state, and its dependence on the Prandtl number and the domain size. An outstanding issue in the understanding of SDC is that it exists at parameter values where simple straight roll convection is also stable, and the region of co-existence increases as the domain size increases. The results of our numerical simulations are coupled with the analysis of the skew-varicose instability of the straight-roll pattern in the Generalized Swift-Hohenberg equation, allowing us to identify the role that skew-varicose events in local patches of stripes play in maintaining Spiral Defect Chaos.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

    Control of pattern formation in excitable systems

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    Pattern formation embodies the beauty and complexity of nature. Some patterns like traveling and rotating waves are dynamic, while others such as dots and stripes are static. Both dynamic and static patterns have been observed in a variety of physiological and biological processes such as rotating action potential waves in the brain during sleep, traveling calcium waves in the cardiac muscle, static patterns on the skins of animals, and self-regulated patterns in the animal embryo. Excitable systems represent a class of ultrasensitive systems that are capable of generating different kinds of patterns depending on the interplay between activator and inhibitor dynamics. Through manipulation of different excitable parameters, a diverse array of traveling wave and standing wave patterns can be obtained. In this thesis, I use pattern formation theory to control the excitable systems involved in cell migration and neuroscience to alter the observed phenotype, in an attempt to affect the underlying biological process. Cell migration is critical in many processes such as cancer metastasis and wound healing. Cells move by extending periodic protrusions of their cortex, and recent years have shown that the cellular cortex is an excitable medium where waves of biochemical species organize the cellular protrusion. Altering the protrusive phenotype can drastically alter cell migration — that can potentially affect critical physiological processes. In the first part of this thesis, I use excitable wave theory to model and predict wave pattern changes in amoeboid cells. Using theories of pattern formation, key nodes of the underlying excitable network governing cell migration are altered — to drastically change the cellular migratory phenotype, moving from amoeboid cells to oscillatory cells and from cells that extend long finger-like protrusions to cells that sustain stable rings on the cortex, potentially uncovering a novel method of pattern formation. Excitable systems originated in neuroscience, where different patterns of activity reflect different brain states. Sleep is associated with slow waves, while repeated high-frequency waves are associated with epileptic seizures. These patterns arise from the interplay between the cerebral cortex and the thalamus, which form a closed-loop architecture. In the second part of this thesis, I use a three-layer two-dimensional thalamocortical model, to explore the different parameters that may influence different spatio-temporal dynamics on the cortex. This study reveals that inter- and intra-cortical connectivity, excitation-inhibition balance and synaptic strengths can influence the wave activity patterns, to recreate different dynamic patterns observed in different brain states

    Instabilities in crystal growth by atomic or molecular beams

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    The planar front of a growing a crystal is often destroyed by instabilities. In the case of growth from a condensed phase, the most frequent ones are diffusion instabilities, which will be but briefly discussed in simple terms in chapter II. The present review is mainly devoted to instabilities which arise in ballistic growth, especially Molecular Beam Epitaxy (MBE). The reasons of the instabilities can be geometric (shadowing effect), but they are mostly kinetic or thermodynamic. The kinetic instabilities which will be studied in detail in chapters IV and V result from the fact that adatoms diffusing on a surface do not easily cross steps (Ehrlich-Schwoebel or ES effect). When the growth front is a high symmetry surface, the ES effect produces mounds which often coarsen in time according to power laws. When the growth front is a stepped surface, the ES effect initially produces a meandering of the steps, which eventually may also give rise to mounds. Kinetic instabilities can usually be avoided by raising the temperature, but this favours thermodynamic instabilities. Concerning these ones, the attention will be focussed on the instabilities resulting from slightly different lattice constants of the substrate and the adsorbate. They can take the following forms. i) Formation of misfit dislocations (chapter VIII). ii) Formation of isolated epitaxial clusters which, at least in their earliest form, are `coherent' with the substrate, i.e. dislocation-free (chapter X). iii) Wavy deformation of the surface, which is presumably the incipient stage of (ii) (chapter IX). The theories and the experiments are critically reviewed and their comparison is qualitatively satisfactory although some important questions have not yet received a complete answer.Comment: 90 pages in revtex, 45 figures mainly in gif format. Review paper to be published in Physics Reports. Postscript versions for all the figures can be found at http://www.theo-phys.uni-essen.de/tp/u/politi
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