Cyclic Pursuit: Symmetry, Reduction and Nonlinear Dynamics

In this dissertation, we explore the use of pursuit interactions as a building block for collective behavior, primarily in the context of constant bearing (CB) cyclic pursuit. Pursuit phenomena are observed throughout the natural environment and also play an important role in technological contexts, such as missile-aircraft encounters and interactions between unmanned vehicles. While pursuit is typically regarded as adversarial, we demonstrate that pursuit interactions within a cyclic pursuit framework give rise to seemingly coordinated group maneuvers. We model a system of agents (e.g. birds, vehicles) as particles tracing out curves in the plane, and illustrate reduction to the shape space of relative positions and velocities. Introducing the CB pursuit strategy and associated pursuit law, we consider the case for which agent i pursues agent i+1 (modulo n) with the CB pursuit law. After deriving closed-loop cyclic pursuit dynamics, we demonstrate asymptotic convergence to an invariant submanifold (corresponding to each agent attaining the CB pursuit strategy), and proceed by analysis of the reduced dynamics restricted to the submanifold. For the general setting, we derive existence conditions for relative equilibria (circling and rectilinear) as well as for system trajectories which preserve the shape of the collective (up to similarity), which we refer to as pure shape equilibria. For two illustrative low-dimensional cases, we provide a more comprehensive analysis, deriving explicit trajectory solutions for the two-particle "mutual pursuit" case, and detailing the stability properties of three-particle relative equilibria and pure shape equilibria. For the three-particle case, we show that a particular choice of CB pursuit parameters gives rise to remarkable almost-periodic trajectories in the physical space. We also extend our study to consider CB pursuit in three dimensions, deriving a feedback law for executing the CB pursuit strategy, and providing a detailed analysis of the two-particle mutual pursuit case. We complete the work by considering evasive strategies to counter the motion camouflage (MC) pursuit law. After demonstrating that a stochastically steering evader is unable to thwart the MC pursuit strategy, we propose a (deterministic) feedback law for the evader and demonstrate the existence of circling equilibria for the closed-loop pursuer-evader dynamics.

Asymmetric tunnels in P2MP LSPs as a label space reduction method

The objective of traffic engineering is to optimize network resource utilization. Although several works have been published about minimizing network resource utilization, few works have focused on LSR (label switched router) label space. This paper proposes an algorithm that takes advantage of the MPLS label stack features in order to reduce the number of labels used in LSPs. Some tunnelling methods and their MPLS implementation drawbacks are also discussed. The described algorithm sets up NHLFE (next hop label forwarding entry) tables in each LSR, creating asymmetric tunnels when possible. Experimental results show that the described algorithm achieves a great reduction factor in the label space. The presented works apply for both types of connections: P2MP (point-to-multipoint) and P2P (point-to-point)

A symmetry reduction technique for higher order Painleve systems

The symmetry reduction of higher order Painleve systems is formulated in terms of Dirac procedure. A set of canonical variables that admit Dirac reduction procedure is proposed for Hamiltonian structures governing the A(2M)((1)) and A(2M-1)((1)) Painleve systems for M = 2,3,.... (C) 2012 Elsevier B.V. All rights reserved.

Tin-doped indium oxide nanobelts grown by carbothermal reduction method

This communication discusses the formation of doped nanobelts produced by a simple route. Tin-doped indium oxide (ITO) nanobelts were obtained by a carbothermal reduction method. The nanostructures were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), energy-dispersive X-ray spectroscopy (EDX) and wavelength-dispersive X-ray spectroscopy (WDX). The results show that the nanobelts have a cubic structure, are single crystalline and doped with tin and grow in the [400] direction.

Controlled Synthesis of Layered Sn3O4 Nanobelts by Carbothermal Reduction Method and Their Gas Sensor Properties

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

An adaptive and dynamic dimensionality reduction method for high-dimensional indexing

The notorious "dimensionality curse" is a well-known phenomenon for any multi-dimensional indexes attempting to scale up to high dimensions. One well-known approach to overcome degradation in performance with respect to increasing dimensions is to reduce the dimensionality of the original dataset before constructing the index. However, identifying the correlation among the dimensions and effectively reducing them are challenging tasks. In this paper, we present an adaptive Multi-level Mahalanobis-based Dimensionality Reduction (MMDR) technique for high-dimensional indexing. Our MMDR technique has four notable features compared to existing methods. First, it discovers elliptical clusters for more effective dimensionality reduction by using only the low-dimensional subspaces. Second, data points in the different axis systems are indexed using a single B+-tree. Third, our technique is highly scalable in terms of data size and dimension. Finally, it is also dynamic and adaptive to insertions. An extensive performance study was conducted using both real and synthetic datasets, and the results show that our technique not only achieves higher precision, but also enables queries to be processed efficiently. Copyright Springer-Verlag 2005

Symmetry reduction due to gallium substitution in the garnet Li6.43(2)Ga0.52(3)La2.67(4)Zr2O12

Single-crystal structure refinements on lithium lanthanum zirconate (LLZO; Li7La3Zr2O12) substituted with gallium were successfully carried out in the cubic symmetry space group I [Formula: see text]3d. Gallium was found on two lithium sites as well as on the lanthanum position. Due to the structural distortion of the resulting Li6.43(2)Ga0.52(3)La2.67(4)Zr2O12 (Ga-LLZO) single crystals, a reduction of the LLZO cubic garnet symmetry from Ia[Formula: see text] d to I [Formula: see text]3d was necessary, which could hardly be analysed from X-ray powder diffraction data.

Analyse de groupe d’un modèle de la plasticité idéale planaire et sur les solutions en termes d’invariants de Riemann pour les systèmes quasilinéaires du premier ordre

Les objets d’étude de cette thèse sont les systèmes d’équations quasilinéaires du premier ordre. Dans une première partie, on fait une analyse du point de vue du groupe de Lie classique des symétries ponctuelles d’un modèle de la plasticité idéale. Les écoulements planaires dans les cas stationnaire et non-stationnaire sont étudiés. Deux nouveaux champs de vecteurs ont été obtenus, complétant ainsi l’algèbre de Lie du cas stationnaire dont les sous-algèbres sont classifiées en classes de conjugaison sous l’action du groupe. Dans le cas non-stationnaire, une classification des algèbres de Lie admissibles selon la force choisie est effectuée. Pour chaque type de force, les champs de vecteurs sont présentés. L’algèbre ayant la dimension la plus élevée possible a été obtenues en considérant les forces monogéniques et elle a été classifiée en classes de conjugaison. La méthode de réduction par symétrie est appliquée pour obtenir des solutions explicites et implicites de plusieurs types parmi lesquelles certaines s’expriment en termes d’une ou deux fonctions arbitraires d’une variable et d’autres en termes de fonctions elliptiques de Jacobi. Plusieurs solutions sont interprétées physiquement pour en déduire la forme de filières d’extrusion réalisables. Dans la seconde partie, on s’intéresse aux solutions s’exprimant en fonction d’invariants de Riemann pour les systèmes quasilinéaires du premier ordre. La méthode des caractéristiques généralisées ainsi qu’une méthode basée sur les symétries conditionnelles pour les invariants de Riemann sont étendues pour être applicables à des systèmes dans leurs régions elliptiques. Leur applicabilité est démontrée par des exemples de la plasticité idéale non-stationnaire pour un flot irrotationnel ainsi que les équations de la mécanique des fluides. Une nouvelle approche basée sur l’introduction de matrices de rotation satisfaisant certaines conditions algébriques est développée. Elle est applicable directement à des systèmes non-homogènes et non-autonomes sans avoir besoin de transformations préalables. Son efficacité est illustrée par des exemples comprenant un système qui régit l’interaction non-linéaire d’ondes et de particules. La solution générale est construite de façon explicite.

Reduction and adsorption of Pb2+ in aqueous solution by nano zero-valent iron : a SEM, TEM and XPS study

This study reports the synthesis, characterization and application of nano zero-valent iron (nZVI). The nZVI was produced by a reduction method and compared with commercial available ZVI powder for Pb2+ removal from aqueous phase. Comparing with commercial ZVI, the laboratory made nZVI powder has a much higher specific surface area. XRD patterns have revealed zero valent iron phases in two ZVI materials. Different morphologies have been observed using SEM and TEM techniques. EDX spectrums revealed even distribution of Pb on surface after reaction. The XPS analysis has confirmed that immobilized lead was present in its zero-valent and bivalent forms. ‘Core-shell’ structure of prepared ZVI was revealed based on combination of XRD and XPS characterizations. In addition, comparing with Fluka ZVI, this lab made nZVI has much higher reactivity towards Pb2+ and within just 15 mins 99.9% removal can be reached. This synthesized nano ZVI material has shown great potential for heavy metal immobilization from waste water.

New Insights into Selective Heterogeneous Nucleation of Metal Nanoparticles on Oxides by Microwave-Assisted Reduction: Rapid Synthesis of High-Activity Supported Catalysts

Microwave-based methods are widely employed to synthesize metal nanoparticles on various substrates. However, the detailed mechanism of formation of such hybrids has not been addressed. In this paper, we describe the thermodynamic and kinetic aspects of reduction of metal salts by ethylene glycol under microwave heating conditions. On the basis of this analysis, we identify the temperatures above which the reduction of the metal salt is thermodynamically favorable and temperatures above which the rates of homogeneous nucleation of the metal and the heterogeneous nucleation of the metal on supports are favored. We delineate different conditions which favor the heterogeneous nucleation of the metal on the supports over homogeneous nucleation in the solvent medium based on the dielectric loss parameters of the solvent and the support and the metal/solvent and metal/support interfacial energies. Contrary to current understanding, we show that metal particles can be selectively formed on the substrate even under situations where the temperature of the substrate Is lower than that of the surrounding medium. The catalytic activity of the Pt/CeO(2) and Pt/TiO(2) hybrids synthesized by this method for H(2) combustion reaction shows that complete conversion is achieved at temperatures as low as 100 degrees C with Pt-CeO(2) catalyst and at 50 degrees C with Pt-TiO(2) catalyst. Our method thus opens up possibilities for rational synthesis of high-activity supported catalysts using a fast microwave-based reduction method.

Detecting symmetry in scalar fields using augmented extremum graphs

Visualizing symmetric patterns in the data often helps the domain scientists make important observations and gain insights about the underlying experiment. Detecting symmetry in scalar fields is a nascent area of research and existing methods that detect symmetry are either not robust in the presence of noise or computationally costly. We propose a data structure called the augmented extremum graph and use it to design a novel symmetry detection method based on robust estimation of distances. The augmented extremum graph captures both topological and geometric information of the scalar field and enables robust and computationally efficient detection of symmetry. We apply the proposed method to detect symmetries in cryo-electron microscopy datasets and the experiments demonstrate that the algorithm is capable of detecting symmetry even in the presence of significant noise. We describe novel applications that use the detected symmetry to enhance visualization of scalar field data and facilitate their exploration.