161 resultados para 230112 Topology and Manifolds
Resumo:
In this work we explore the application of wireless sensor technologies for the benefit of small and marginal farmers in semi-arid regions. The focus in this paper is to discuss the merits and demerits of data gathering & relay paradigms that collect localized data over a wide area. The data gathered includes soil moisture, temperature, pressure, rain data and humidity. The challenge to technology intervention comes mainly due to two reasons: (a) Farmers in general are interested in crop yield specific to their piece of land. This is because soil texture can vary rapidly over small regions. (b) Due to a high run-off, the soil moisture retention can vary from region to region depending on the topology of the farm. Both these reasons alter the needs drastically. Additionally, small and marginal farms can be sandwiched between rich farm lands. The village has very little access to grid power. Power cuts can extend up to 12 hours in a day and upto 3 or 4 days during some months in the year. In this paper, we discuss 3 technology paradigms for data relaying. These include Wi-Fi (Wireless Fidelity), GPRS (General Packet Radio Service) and DTN (Delay and Disruption Tolerant Network) technologies. We detail the merits and demerits of each of these solutions and provide our final recommendations. The project site is a village called Chennakesavapura in the state of Karnataka, India.
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By reacting cadmium salts with H2SO4 in the presence of organic amines or directly with amine sulfates under hydrothermal conditions, it has been possible to prepare three linear cadmium sulfates of linarite topology, with the compositions [H3N(CH2)(2)NH3](2)[CdCl2(SO4)][SO4].H2O, I, [HN(CH2)(6)NH][CdBr2(SO4)], II, [HN(CH2)(6)NH][CdCl2-(SO4)], III. A layered cadmium sulfate of composition [H3N(CH2)(3)NH3][Cd-2(H2O)(2)(SO4)(3)], IV, has also been obtained. These sulfates are the first examples of a family of organically templated metal sulfates with interesting structural features. In the linarite chains, the CdX4O2 (X = Cl, Br) octahedron shares two trans-edges to form an [Mphi(4)] (phi = anionic ligand) chain decorated by the SO4 tetrahedron that adopts a staggered arrangement on either side of the chain. IV is constructed by the fusion of four-membered ring ladders involving edge sharing between the sulfate tetrahedron and metal octahedron. IV appears to be the first member of a family of organically templated metal sulfates containing an octahedral-tetrahedral 2D net wherein the sulfate tetrahedron is connected at all four corners.
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Consider a sequence of closed, orientable surfaces of fixed genus g in a Riemannian manifold M with uniform upper bounds on the norm of mean curvature and area. We show that on passing to a subsequence, we can choose parametrisations of the surfaces by inclusion maps from a fixed surface of the same genus so that the distance functions corresponding to the pullback metrics converge to a pseudo-metric and the inclusion maps converge to a Lipschitz map. We show further that the limiting pseudo-metric has fractal dimension two. As a corollary, we obtain a purely geometric result. Namely, we show that bounds on the mean curvature, area and genus of a surface F subset of M, together with bounds on the geometry of M, give an upper bound on the diameter of F. Our proof is modelled on Gromov's compactness theorem for J-holomorphic curves.
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We present the concept, prototypes, and an optimal design method for a compliant mechanism kit as a parallel to the kits available for rigid-body mechanisms. The kit consists of flexible beams and connectors that can be easily hand-assembled using snap fits. It enables users, using their creativity and mechanics intuition, to quickly realize a compliant mechanism. The mechanisms assembled in this manner accurately capture the essential behavior of the topology, shape, size and material aspects and thereby can lead the way for a real compliant mechanism for practical use. Also described in this paper are the design of the connector to which flexible beams can be added in eight different directions; and prototyping of the spring steel connectors as well as beams using wire-cut electro discharge machining. It is noted in this paper that the concept of the kit also resolves a discrepancy in the finite element (FE) modeling of beam-based compliant mechanisms. The discrepancy arises when two or more beams are joining at one point and thus leading to increased stiffness. After resolving this discrepancy, this work extends the topology optimization to automatically generate designs that can be assembled with the kit. Thus, the kit and the accompanying analysis and optimal synthesis procedures comprise a self-contained educational as well as a research and pragmatic toolset for compliant mechanisms. The paper also illustrates how human creativity finds new ways of using the kit beyond the original intended use and how it is useful even for a novice to design compliant mechanisms.
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We describe a System-C based framework we are developing, to explore the impact of various architectural and microarchitectural level parameters of the on-chip interconnection network elements on its power and performance. The framework enables one to choose from a variety of architectural options like topology, routing policy, etc., as well as allows experimentation with various microarchitectural options for the individual links like length, wire width, pitch, pipelining, supply voltage and frequency. The framework also supports a flexible traffic generation and communication model. We provide preliminary results of using this framework to study the power, latency and throughput of a 4x4 multi-core processing array using mesh, torus and folded torus, for two different communication patterns of dense and sparse linear algebra. The traffic consists of both Request-Response messages (mimicing cache accesses)and One-Way messages. We find that the average latency can be reduced by increasing the pipeline depth, as it enables higher link frequencies. We also find that there exists an optimum degree of pipelining which minimizes energy-delay product.
Resumo:
The focus of this paper is on designing useful compliant micro-mechanisms of high-aspect-ratio which can be microfabricated by the cost-effective wet etching of (110) orientation silicon (Si) wafers. Wet etching of (110) Si imposes constraints on the geometry of the realized mechanisms because it allows only etch-through in the form of slots parallel to the wafer's flat with a certain minimum length. In this paper, we incorporate this constraint in the topology optimization and obtain compliant designs that meet the specifications on the desired motion for given input forces. Using this design technique and wet etching, we show that we can realize high-aspect-ratio compliant micro-mechanisms. For a (110) Si wafer of 250 µm thickness, the minimum length of the etch opening to get a slot is found to be 866 µm. The minimum achievable width of the slot is limited by the resolution of the lithography process and this can be a very small value. This is studied by conducting trials with different mask layouts on a (110) Si wafer. These constraints are taken care of by using a suitable design parameterization rather than by imposing the constraints explicitly. Topology optimization, as is well known, gives designs using only the essential design specifications. In this work, we show that our technique also gives manufacturable mechanism designs along with lithography mask layouts. Some designs obtained are transferred to lithography masks and mechanisms are fabricated on (110) Si wafers.
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The topology optimization problem for the synthesis of compliant mechanisms has been formulated in many different ways in the last 15 years, but there is not yet a definitive formulation that is universally accepted. Furthermore, there are two unresolved issues in this problem. In this paper, we present a comparative study of five distinctly different formulations that are reported in the literature. Three benchmark examples are solved with these formulations using the same input and output specifications and the same numerical optimization algorithm. A total of 35 different synthesis examples are implemented. The examples are limited to desired instantaneous output direction for prescribed input force direction. Hence, this study is limited to linear elastic modeling with small deformations. Two design parameterizations, namely, the frame element based ground structure and the density approach using continuum elements, are used. The obtained designs are evaluated with all other objective functions and are compared with each other. The checkerboard patterns, point flexures, the ability to converge from an unbiased uniform initial guess, and the computation time are analyzed. Some observations are noted based on the extensive implementation done in this study. Complete details of the benchmark problems and the results are included. The computer codes related to this study are made available on the internet for ready access.
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Study of symmetric or repeating patterns in scalar fields is important in scientific data analysis because it gives deep insights into the properties of the underlying phenomenon. Though geometric symmetry has been well studied within areas like shape processing, identifying symmetry in scalar fields has remained largely unexplored due to the high computational cost of the associated algorithms. We propose a computationally efficient algorithm for detecting symmetric patterns in a scalar field distribution by analysing the topology of level sets of the scalar field. Our algorithm computes the contour tree of a given scalar field and identifies subtrees that are similar. We define a robust similarity measure for comparing subtrees of the contour tree and use it to group similar subtrees together. Regions of the domain corresponding to subtrees that belong to a common group are extracted and reported to be symmetric. Identifying symmetry in scalar fields finds applications in visualization, data exploration, and feature detection. We describe two applications in detail: symmetry-aware transfer function design and symmetry-aware isosurface extraction.
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Topology optimization methods have been shown to have extensive application in the design of microsystems. However, their utility in practical situations is restricted to predominantly planar configurations due to the limitations of most microfabrication techniques in realizing structures with arbitrary topologies in the direction perpendicular to the substrate. This study addresses the problem of synthesizing optimal topologies in the out-of-plane direction while obeying the constraints imposed by surface micromachining. A new formulation that achieves this by defining a design space that implicitly obeys the manufacturing constraints with a continuous design parameterization is presented in this paper. This is in contrast to including manufacturing cost in the objective function or constraints. The resulting solutions of the new formulation obtained with gradient-based optimization directly provide the photolithographic mask layouts. Two examples that illustrate the approach for the case of stiff structures are included.
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In this paper, we present a novel formulation for performing topology optimization of electrostatically actuated constrained elastic structures. We propose a new electrostatic-elastic formulation that uses the leaky capacitor model and material interpolation to define the material state at every point of a given design domain continuously between conductor and void states. The new formulation accurately captures the physical behavior when the material in between a conductor and a void is present during the iterative process of topology optimization. The method then uses the optimality criteria method to solve the optimization problem by iteratively pushing the state of the domain towards that of a conductor or a void in the appropriate regions. We present examples to illustrate the ability of the method in creating the stiffest structure under electrostatic force for different boundary conditions.
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Ad hoc networks are being used in applications ranging from disaster recovery to distributed collaborative entertainment applications. Ad hoc networks have become one of the most attractive solution for rapid deployment of interconnecting large number of mobile personal devices. The user community of mobile personal devices are demanding a variety of value added multimedia entertainment services. The popularity of peer group is increasing and one or some members of the peer group need to send data to some or all members of the peer group. The increasing demand for group oriented value added services is driving for efficient multicast service over ad hoc networks. Access control mechanisms need to be deployed to provide guarantee that the unauthorized users cannot access the multicast content. In this paper, we present a topology aware key management and distribution scheme for secure overlay multicast over MANET to address node mobility related issues for multicast key management. We use overlay approach for key distribution and our objective is to keep communication overhead low for key management and distribution. We also incorporate reliability using explicit acknowledgments with the key distribution scheme. Through simulations we show that the proposed key management scheme has low communication overhead for rekeying and improves the reliability of key distribution.