Dissipative parametric modulation instability and pattern formation in nonlinear optical systems

We present the essential features of the dissipative parametric instability, in the universal complex Ginzburg- Landau equation. Dissipative parametric instability is excited through a parametric modulation of frequency dependent losses in a zig-zag fashion in the spectral domain. Such damping is introduced respectively for spectral components in the +ΔF and in the -ΔF region in alternating fashion, where F can represent wavenumber or temporal frequency depending on the applications. Such a spectral modulation can destabilize the homogeneous stationary solution of the system leading to growth of spectral sidebands and to the consequent pattern formation: both stable and unstable patterns in one- and in two-dimensional systems can be excited. The dissipative parametric instability provides an useful and interesting tool for the control of pattern formation in nonlinear optical systems with potentially interesting applications in technological applications, like the design of mode- locked lasers emitting pulse trains with tunable repetition rate; but it could also find realizations in nanophotonics circuits or in dissipative polaritonic Bose-Einstein condensates.

Multimode Atomic Pattern Formation via Enhanced Light-atom Interactions

The nonlinear interaction between light and atoms is an extensive field of study with a broad range of applications in quantum information science and condensed matter physics. Nonlinear optical phenomena occurring in cold atoms are particularly interesting because such slowly moving atoms can spatially organize into density gratings, which allows for studies involving optical interactions with structured materials. In this thesis, I describe a novel nonlinear optical effect that arises when cold atoms spatially bunch in an optical lattice. I show that employing this spatial atomic bunching provides access to a unique physical regime with reduced thresholds for nonlinear optical processes and enhanced material properties. Using this method, I observe the nonlinear optical phenomenon of transverse optical pattern formation at record-low powers. These transverse optical patterns are generated by a wave- mixing process that is mediated by the cold atomic vapor. The optical patterns are highly multimode and induce rich non-equilibrium atomic dynamics. In particular, I find that there exists a synergistic interplay between the generated optical pat- terns and the atoms, wherein the scattered fields help the atoms to self-organize into new, multimode structures that are not externally imposed on the atomic sample. These self-organized structures in turn enhance the power in the optical patterns. I provide the first detailed investigation of the motional dynamics of atoms that have self-organized in a multimode geometry. I also show that the transverse optical patterns induce Sisyphus cooling in all three spatial dimensions, which is the first observation of spontaneous three-dimensional cooling. My experiment represents a unique means by which to study nonlinear optics and non-equilibrium dynamics at ultra-low required powers.

Pattern formation with a conservation law

Pattern formation in systems with a conserved quantity is considered by studying the appropriate amplitude equations. The conservation law leads to a large-scale neutral mode that must be included in the asymptotic analysis for pattern formation near onset. Near a stationary bifurcation, the usual Ginzburg--Landau equation for the amplitude of the pattern is then coupled to an equation for the large-scale mode. These amplitude equations show that for certain parameters all roll-type solutions are unstable. This new instability differs from the Eckhaus instability in that it is amplitude-driven and is supercritical. Beyond the stability boundary, there exist stable stationary solutions in the form of strongly modulated patterns. The envelope of these modulations is calculated in terms of Jacobi elliptic functions and, away from the onset of modulation, is closely approximated by a sech profile. Numerical simulations indicate that as the modulation becomes more pronounced, the envelope broadens. A number of applications are considered, including convection with fixed-flux boundaries and convection in a magnetic field, resulting in new instabilities for these systems.

Controlling Pattern Formation in Nanoparticle Assemblies via Directed Solvent Dewetting

We have achieved highly localised control of pattern formation in two dimensional nanoparticle assemblies by direct modification of solvent dewetting dynamics. A striking dependence of nanoparticle organisation on the size of atomic force microscope-generated surface heterogeneities is observed and reproduced in numerical simulations. Nanoscale features induce rupture of the solvent-nanoparticle film, causing the local flow of solvent to carry nanoparticles into confinement. Microscale heterogeneities instead slow the evaporation of the solvent, producing a remarkably abrupt interface between different nanoparticle patterns.

Dinâmica complexa no sistema bromato/hipofosfito/acetona/manganês e ferroína

New chemical systems have been recently designed for the study of complex phenomena such as oscillatory dynamics in the temporal domain and spatiotemporal pattern formation. Systems derived from oscillators based on the chemistry of bromate are the most extensively studied, with the celebrated Belousov-Zhabotinsky (BZ) reaction being the most popular example. Problems such as the formation of bubbles (CO2) and solid precipitate in the course of the reaction and the occurrence of simply short-lived oscillations under batch conditions are very common and, in some cases, compromise the use of some of these systems. It is investigated in this paper the dynamic behavior of the bromate/hypophosphite/acetone/dual catalyst system, which has been sugested as an interesting alternative to circumvent those inconvenients. In this work, manganese and ferroin are employed as catalysts and the complete system (BrO3-/H2PO2-/acetone/Mn(II)-ferroin) is studied under batch conditions. Temporal symmetry breaking was studied in a reactor under agitation by means of simultaneous records of the potential changes of platinum and Ag/AgBr electrodes, both measured versus a reversible hydrogen electrode. Additionally, spatio-temporal formation of target patterns and spiral waves were obtained when the oscillating mixture was placed in a quasi two-dimensional reactor.

APARATO ELETROQUÍMICO PARA SISTEMA DE AQUISIÇÃO DE DADOS MULTICANAL COM RESOLUÇÃO ESPAÇO-TEMPORAL

Spatiotemporal pattern formation in reaction-transport systems takes place spontaneously when the system is kept far from thermodynamic equilibrium. Targets, reaction fronts, waves, spirals, spots and stripes are some typical examples of selforganized structuring. In electrochemical systems, monitoring spatiotemporal patterns of potential in the solid/liquid interface can be done by the use of equally distributed microprobes located close to the working electrode. However, the physical size of each probe can limit the spatial resolution and alter mass transport properties. In contrast, the direct measurement of discrete electrodes does not suffer from this limitation and allows the accurate manipulation of the spatial coupling through changes in resistors connected to the electric circuit. In this paper, the development of an electrochemical setup for multichannel data acquisition with spatiotemporal resolution is described, especially to monitor low levels of currents usually observed in the electro-oxidation of small organic molecules.

Structure et dynamique des communautés multi-espèces : le rôle de l’espace

Cette thèse porte sur le rôle de l’espace dans l’organisation et dans la dynamique des communautés écologiques multi-espèces. Deux carences peuvent être identifiées dans les études théoriques actuelles portant sur la dimension spatiale des communautés écologiques : l’insuffisance de modèles multi-espèces représentant la dimension spatiale explicitement, et le manque d’attention portée aux interactions positives, tel le mutualisme, en dépit de la reconnaissance de leur ubiquité dans les systèmes écologiques. Cette thèse explore cette problématique propre à l’écologie des communautés, en utilisant une approche théorique s’inspirant de la théorie des systèmes complexes et de la mécanique statistique. Selon cette approche, les communautés d’espèces sont considérées comme des systèmes complexes dont les propriétés globales émergent des interactions locales entre les organismes qui les composent, et des interactions locales entre ces organismes et leur environnement. Le premier objectif de cette thèse est de développer un modèle de métacommunauté multi-espèces, explicitement spatial, orienté à l’échelle des individus et basé sur un réseau d’interactions interspécifiques générales comprenant à la fois des interactions d’exploitation, de compétition et de mutualisme. Dans ce modèle, les communautés locales sont formées par un processus d’assemblage des espèces à partir d’un réservoir régional. La croissance des populations est restreinte par une capacité limite et leur dynamique évolue suivant des mécanismes simples de reproduction et de dispersion des individus. Ces mécanismes sont dépendants des conditions biotiques et abiotiques des communautés locales et leur effet varie en fonction des espèces, du temps et de l’espace. Dans un deuxième temps, cette thèse a pour objectif de déterminer l’impact d’une connectivité spatiale croissante sur la dynamique spatiotemporelle et sur les propriétés structurelles et fonctionnelles de cette métacommunauté. Plus précisément, nous évaluons différentes propriétés des communautés en fonction du niveau de dispersion des espèces : i) la similarité dans la composition des communautés locales et ses patrons de corrélations spatiales; ii) la biodiversité locale et régionale, et la distribution locale de l’abondance des espèces; iii) la biomasse, la productivité et la stabilité dynamique aux échelles locale et régionale; et iv) la structure locale des interactions entre les espèces. Ces propriétés sont examinées selon deux schémas spatiaux. D’abord nous employons un environnement homogène et ensuite nous employons un environnement hétérogène où la capacité limite des communautés locales évoluent suivant un gradient. De façon générale, nos résultats révèlent que les communautés écologiques spatialement distribuées sont extrêmement sensibles aux modes et aux niveaux de dispersion des organismes. Leur dynamique spatiotemporelle et leurs propriétés structurelles et fonctionnelles peuvent subir des changements profonds sous forme de transitions significatives suivant une faible variation du niveau de dispersion. Ces changements apparaissent aussi par l’émergence de patrons spatiotemporels dans la distribution spatiale des populations qui sont typiques des transitions de phases observées généralement dans les systèmes physiques. La dynamique de la métacommunauté présente deux régimes. Dans le premier régime, correspondant aux niveaux faibles de dispersion des espèces, la dynamique d’assemblage favorise l’émergence de communautés stables, peu diverses et formées d’espèces abondantes et fortement mutualistes. La métacommunauté possède une forte diversité régionale puisque les communautés locales sont faiblement connectées et que leur composition demeure ainsi distincte. Par ailleurs dans le second régime, correspondant aux niveaux élevés de dispersion, la diversité régionale diminue au profit d’une augmentation de la diversité locale. Les communautés locales sont plus productives mais leur stabilité dynamique est réduite suite à la migration importante d’individus. Ce régime est aussi caractérisé par des assemblages incluant une plus grande diversité d’interactions interspécifiques. Ces résultats suggèrent qu’une augmentation du niveau de dispersion des organismes permet de coupler les communautés locales entre elles ce qui accroît la coexistence locale et favorise la formation de communautés écologiques plus riches et plus complexes. Finalement, notre étude suggère que le mutualisme est fondamentale à l’organisation et au maintient des communautés écologiques. Les espèces mutualistes dominent dans les habitats caractérisés par une capacité limite restreinte et servent d’ingénieurs écologiques en facilitant l’établissement de compétiteurs, prédateurs et opportunistes qui bénéficient de leur présence.

Modeling the skin pattern of fishes

Complicated patterns showing various spatial scales have been obtained in the past by coupling Turing systems in such a way that the scales of the independent systems resonate. This produces superimposed patterns with different length scales. Here we propose a model consisting of two identical reaction-diffusion systems coupled together in such a way that one of them produces a simple Turing pattern of spots or stripes, and the other traveling wave fronts that eventually become stationary. The basic idea is to assume that one of the systems becomes fixed after some time and serves as a source of morphogens for the other system. This mechanism produces patterns very similar to the pigmentation patterns observed in different species of stingrays and other fishes. The biological mechanisms that support the realization of this model are discussed.

Dynamic formation of SEBS copolymer submicrometric structures

Highly ordered A-B-A block copolymer arrangements in the submicrometric scale, resulting from dewetting and solvent evaporation of thin films, have inspired a variety of new applications in the nanometric world. Despite the progress observed in the control of such structures, the intricate scientific phenomena related to regular patterns formation are still not completely elucidated. SEBS is a standard example of a triblock copolymer that forms spontaneously impressive pattern arrangements. From macroscopic thin liquid films of SEBS solution, several physical effects and phenomena act synergistically to achieve well-arranged patterns of stripes and/or droplets. That is, concomitant with dewetting, solvent evaporation, and Marangoni effect, Rayleigh instability and phase separation also play important role in the pattern formation. These two last effects are difficult to be followed experimentally in the nanoscale, which render difficulties to the comprehension of the whole phenomenon. In this paper, we use computational methods for image analysis, which provide quantitative morphometric data of the patterns, specifically comprising stripes fragmentation into droplets. With the help of these computational techniques, we developed an explanation for the final part of the pattern formation, i.e. structural dynamics related to the stripes fragmentation. (C) 2010 Elsevier Ltd. All rights reserved.

A zebrafish homologue of deleted in colorectal cancer (zdcc) is expressed in the first neuronal clusters of the developing brain

DCC (deleted in colon cancer), Neogenin and UNC-5 are all members of the immunoglobulin superfamily of transmembrane receptors which are believed to play a role in axon guidance by binding to their ligands, the Netrin/UNC-40 family of secreted molecules (Cell. Mol. Life Sci. 56 (1999) 62; Curr. Opin. Genet. Dev. 7 (1997) 87). Although zebrafish homologues of the Netrin family of secreted molecules have been reported, to date there has been no published description of zebrafish DCC homologues (Mol. Cell. Neurosci. 9 (1997) 293., Mol. Cell. Neurosci. I I ( 1998) 194; Mech. Dev. 62 (1997) 147). We report here the expression pattern of a zebrafish dcc (zdcc) homologue during the initial period of neurogenesis and axon tract formation within the developing central nervous system. Between 12 and 33 h post-fertilisation zdcc is expressed in a dynamic spatiotemporal pattern in all major subdivisions of the central nervous system. Double-labelling for zdcc and the post-mitotic neuronal marker HNK-1 revealed that subpopulations of neurons within the first nuclei of the zebrafish brain express zdcc. These results support our previous observation that patterning of neuronal clusters in the zebrafish brain occurs early in development (Dev. Bioi, 229 (2001) 271). (C) 2001 Elsevier Science Ireland Ltd. All rights reserved.

The spatiotemporal trajectory of a dengue epidemic in a medium-sized city

Understanding the transmission dynamics of infectious diseases is important to allow for improvements of control measures. To investigate the spatiotemporal pattern of an epidemic dengue occurred at a medium-sized city in the Northeast Region of Brazil in 2009, we conducted an ecological study of the notified dengue cases georeferenced according to epidemiological week (EW) and home address. Kernel density estimation and space-time interaction were analysed using the Knox method. The evolution of the epidemic was analysed using an animated projection technique. The dengue incidence was 6.918.7/100,000 inhabitants; the peak of the epidemic occurred from 8 February-1 March, EWs 6-9 (828.7/100,000 inhabitants). There were cases throughout the city and was identified space-time interaction. Three epicenters were responsible for spreading the disease in an expansion and relocation diffusion pattern. If the health services could detect in real time the epicenters and apply nimbly control measures, may possibly reduce the magnitude of dengue epidemics.

Generation of the primary hair follicle pattern.

Hair follicles are spaced apart from one another at regular intervals through the skin. Although follicles are predominantly epidermal structures, classical tissue recombination experiments indicated that the underlying dermis defines their location during development. Although many molecules involved in hair follicle formation have been identified, the molecular interactions that determine the emergent property of pattern formation have remained elusive. We have used embryonic skin cultures to dissect signaling responses and patterning outcomes as the skin spatially organizes itself. We find that ectodysplasin receptor (Edar)-bone morphogenetic protein (BMP) signaling and transcriptional interactions are central to generation of the primary hair follicle pattern, with restriction of responsiveness, rather than localization of an inducing ligand, being the key driver in this process. The crux of this patterning mechanism is rapid Edar-positive feedback in the epidermis coupled with induction of dermal BMP4/7. The BMPs in turn repress epidermal Edar and hence follicle fate. Edar activation also induces connective tissue growth factor, an inhibitor of BMP signaling, allowing BMP action only at a distance from their site of synthesis. Consistent with this model, transgenic hyperactivation of Edar signaling leads to widespread overproduction of hair follicles. This Edar-BMP activation-inhibition mechanism appears to operate alongside a labile prepattern, suggesting that Edar-mediated stabilization of beta-catenin active foci is a key event in determining definitive follicle locations.

Pattern selection in a lattice of pulse-coupled oscillators

We study spatio-temporal pattern formation in a ring of N oscillators with inhibitory unidirectional pulselike interactions. The attractors of the dynamics are limit cycles where each oscillator fires once and only once. Since some of these limit cycles lead to the same pattern, we introduce the concept of pattern degeneracy to take it into account. Moreover, we give a qualitative estimation of the volume of the basin of attraction of each pattern by means of some probabilistic arguments and pattern degeneracy, and show how they are modified as we change the value of the coupling strength. In the limit of small coupling, our estimative formula gives a pefect agreement with numerical simulations.

Self-organization mechanisms for the formation on nearshore crescentic and transverse sand bars

The formation and development of transverse and crescentic sand bars in the coastal marine environment has been investigated by means of a nonlinear numerical model based on the shallow-water equations and on a simpli ed sediment transport parameterization. By assuming normally approaching waves and a saturated surf zone, rhythmic patterns develop from a planar slope where random perturbations of small amplitude have been superimposed. Two types of bedforms appear: one is a crescentic bar pattern centred around the breakpoint and the other, herein modelled for the rst time, is a transverse bar pattern. The feedback mechanism related to the formation and development of the patterns can be explained by coupling the water and sediment conservation equations. Basically, the waves stir up the sediment and keep it in suspension with a certain cross-shore distribution of depth-averaged concentration. Then, a current flowing with (against) the gradient of sediment concentration produces erosion (deposition). It is shown that inside the surf zone, these currents may occur due to the wave refraction and to the redistribution of wave breaking produced by the growing bedforms. Numerical simulations have been performed in order to understand the sensitivity of the pattern formation to the parameterization and to relate the hydro-morphodynamic input conditions to which of the patterns develops. It is suggested that crescentic bar growth would be favoured by high-energy conditions and ne sediment while transverse bars would grow for milder waves and coarser sediment. In intermediate conditions mixed patterns may occur.

Towards a unifying framework for pattern transformation in swarm systems

This paper identifies the major challenges in the area of pattern formation. The work is also motivated by the need for development of a single framework to surmount these challenges. A framework based on the control of macroscopic parameters is proposed. The issue of transformation of patterns is specifically considered. A definition for transformation and four special cases, namely elementary and geometrical transformations by repositioning all or some robots in the pattern are provided. Two feasible tools for pattern transformation namely, a macroscopic parameter method and a mathematical tool - Moebius transformation also known as the linear fractional transformation are introduced. The realization of the unifying framework considering planning and communication is reported.