Sample records for reactant inlet manifold

  1. Role of inlet reactant mixedness on the thermodynamic performance of a rotating detonation engine

    Nordeen, C. A.; Schwer, D.; Schauer, F.; Hoke, J.; Barber, T.; Cetegen, B. M.


    Rotating detonation engines have the potential to achieve the high propulsive efficiencies of detonation cycles in a simple and effective annular geometry. A two-dimensional Euler simulation is modified to include mixing factors to simulate the imperfect mixing of injected reactant streams. Contrary to expectations, mixing is shown to have a minimal impact on performance. Oblique detonation waves are shown to increase local stream thermal efficiency, which compensates for other losses in the flow stream. The degree of reactant mixing is, however, a factor in controlling the stability and existence of rotating detonations.

  2. Aluminum Alloy Inlet Manifold of Micro-car in Metal Mold Casting%铝合金进气歧管铸件的金属型铸造



    A new casting technology for inlet manifold in tilt casting machine for gravity die casting was described. In order to producte qualified inlet manifold casting, top gating system with lip riser and shell core made of precoated sand is used. The gas hole, shrinkage cavity and crack were eliminated through up-grading technology.%介绍了在可倾式金属型浇注机上制造进气歧管的铸造新工艺。为了获得合格的进气歧管铸件,采用压边顶铸浇注系统和覆膜砂壳芯制作工艺。并且改进工艺,以消除气孔、收缩和裂纹。

  3. Flow and Pressure Distribution in Fuel Cell Manifolds

    Lebæk, Jesper; Bang, Mads; Kær, Søren Knudsen


    The manifold is an essential part of the fuel cell stack. Evidently, evenly distributed reactants are a prerequisite for an efficient fuel cell stack. In this study, the cathode manifold ability to distribute air to the cells of a 70 cell stack is investigated experimentally. By means of 20...... differential pressure gauges, the flow distribution is mapped for several geometrical and operating conditions. Special attention is given to the inlet conditions of the manifold. Here, a diffuser design was constructed in order to replace the conventional circular inlet design. The diffuser design showed...... significant improvements to the flow distribution in comparison to the circular design. Moreover, the best flow distribution was found using a U-shaped configuration....

  4. Modeling of the inlet and exhaust manifolds by using the wave action and her influence on the accuracy of the results obtained from the internal combustion engines simulator program; Modelagem dos coletores de admissao e descarga pelo metodo da acao das ondas e sua influencia sobre a precisao dos resultados do programa simulador de motores de combustao interna

    Vianna, Joao Nildo de S.; Oliveira, Guilherme L. de; Oliveira, Lucio H.H. de [Brasilia Univ., DF (Brazil). Dept. de Engenharia Mecanica


    This work presents a comparative study of the performance of a simulation computer program where the inlet and exhaust manifolds are modeled by the control volume method and the by the wave action method. Results obtained by both methods are compared with experimental data. To validate the method of wave action an exhaust manifold wa specifically built. The results show that the wave action method improves considerably the performance of the simulation software, although it increases the processing time. (author)

  5. Nash manifolds

    Shiota, Masahiro


    A Nash manifold denotes a real manifold furnished with algebraic structure, following a theorem of Nash that a compact differentiable manifold can be imbedded in a Euclidean space so that the image is precisely such a manifold. This book, in which almost all results are very recent or unpublished, is an account of the theory of Nash manifolds, whose properties are clearer and more regular than those of differentiable or PL manifolds. Basic to the theory is an algebraic analogue of Whitney's Approximation Theorem. This theorem induces a "finiteness" of Nash manifold structures and differences between Nash and differentiable manifolds. The point of view of the author is topological. However the proofs also require results and techniques from other domains so elementary knowledge of commutative algebra, several complex variables, differential topology, PL topology and real singularities is required of the reader. The book is addressed to graduate students and researchers in differential topology and real algebra...

  6. Reactant-Product Quantum Coherence in Electron Transfer Reactions

    Kominis, I K


    We investigate the physical meaning of quantum superposition states between reactants and products in electron transfer reactions. We show that such superpositions are strongly suppressed and to leading orders of perturbation theory do not pertain in electron transfer reactions. This is because of the intermediate manifold of states separating the reactants from the products. We provide an intuitive description of these considerations with Feynman diagrams. We also discuss the relation of such quantum coherences to understanding the fundamental quantum dynamics of spin-selective radical-ion-pair reactions.

  7. Backfire prediction in a manifold injection hydrogen internal combustion engine

    Liu, Xing-hua; Liu, Fu-shui; Zhou, Lei; Sun, Bai-gang [School of Mechanical and Vehicular Engineering, Beijing Institute of Technology, Beijing 100081 (China); Schock, Harold J. [Engine Research Laboratory, Michigan State University, East Lansing, MI (United States)


    Hydrogen internal combustion engine (H2ICE) easily occur inlet manifold backfire and other abnormal combustion phenomena because of the low ignition energy, wide flammability range and rapid combustion speed of hydrogen. In this paper, the effect of injection timing on mixture formation in a manifold injection H2ICE was studied in various engine speed and equivalence ratio by CFD simulation. It was concluded that H2ICE of manifold injection have an limited injection end timing in order to prevent backfire in the inlet manifold. Finally, the limit of injection end timing of the H2ICE was proposed and validated by engine experiment. (author)

  8. Topological Manifolds

    Pąk Karol


    Full Text Available Let us recall that a topological space M is a topological manifold if M is second-countable Hausdorff and locally Euclidean, i.e. each point has a neighborhood that is homeomorphic to an open ball of E n for some n. However, if we would like to consider a topological manifold with a boundary, we have to extend this definition. Therefore, we introduce here the concept of a locally Euclidean space that covers both cases (with and without a boundary, i.e. where each point has a neighborhood that is homeomorphic to a closed ball of En for some n.

  9. Differential manifolds

    Kosinski, Antoni A


    The concepts of differential topology form the center of many mathematical disciplines such as differential geometry and Lie group theory. Differential Manifolds presents to advanced undergraduates and graduate students the systematic study of the topological structure of smooth manifolds. Author Antoni A. Kosinski, Professor Emeritus of Mathematics at Rutgers University, offers an accessible approach to both the h-cobordism theorem and the classification of differential structures on spheres.""How useful it is,"" noted the Bulletin of the American Mathematical Society, ""to have a single, sho

  10. Equalization equations in reactant resolution

    Jacek Korchowiec


    The chemical system can be analyzed in different resolutions. The assumed resolution imposes a given partitioning of the system in physical or functional space. The most frequently explored are global, reactant, atoms-in-molecule, orbital, and local resolutions. In this paper we have considered reactant resolution, i.e., the mutually polarized reactants before the charge-transfer among them. We have demonstrated that a certain type of generalized sensitivity, the system responses to the population variables, is equalized throughout the space up to the infinite order in the perturbation expansion.

  11. Particle Image Velocimetry and Computational Fluid Dynamics Analysis of Fuel Cell Manifold

    Lebæk, Jesper; Blazniak Andreasen, Marcin; Andresen, Henrik Assenholm


    The inlet effect on the manifold flow in a fuel cell stack was investigated by means of numerical methods (computational fluid dynamics) and experimental methods (particle image velocimetry). At a simulated high current density situation the flow field was mapped on a 70 cell simulated cathode...... manifold. Three different inlet configurations were tested: plug flow, circular inlet, and a diffuser inlet. A very distinct jet was formed in the manifold, when using the circular inlet configuration, which was confirmed both experimentally and numerically. This jet was found to be an asymmetric confined...

  12. Modeling the Uniformity of Manifold with Various Configurations

    Jafar M. Hassan


    Full Text Available The flow distribution in manifolds is highly dependent on inlet pressure, configuration, and total inlet flow to the manifold. The flow from a manifold has many applications and in various fields of engineering such as civil, mechanical, and chemical engineering. In this study, physical and numerical models were employed to study the uniformity of the flow distribution from manifold with various configurations. The physical model consists of main manifold with uniform longitudinal section having diameter of 10.16 cm (4 in, five laterals with diameter of 5.08 cm (2 in, and spacing of 22 cm. Different inlet flows were tested and the values of these flows are 500, 750, and 1000 L/min. A manifold with tapered longitudinal section having inlet diameters of 10.16 cm (4 in and dead end diameter of 5.08 cm (2 in with the same above later specifications and flow rates was tested for its uniformity too. The percentage of absolute mean deviation for manifold with uniform diameter was found to be 34% while its value for the manifold with nonuniform diameter was found to be 14%. This result confirms the efficiency of the nonuniform distribution of fluids.

  13. Complex nonlinear behaviour of a fixed bed reactor with reactant recycle

    Recke, Bodil; Jørgensen, Sten Bay


    The fixed bed reactor with reactant recycle investigated in this paper can exhibit periodic solutions. These solutions bifurcate from the steady state in a Hopf bifurcation. The Hopf bifurcation encountered at the lowest value of the inlet concentration turns the steady state unstable and marks......,that the dynamic behaviour of a fixed bed reactor with reactant recycle is much more complex than previously reported....

  14. Coastal Inlet Model Facility

    Federal Laboratory Consortium — The Coastal Inlet Model Facility, as part of the Coastal Inlets Research Program (CIRP), is an idealized inlet dedicated to the study of coastal inlets and equipped...

  15. Manifolds, Tensors, and Forms

    Renteln, Paul


    Preface; 1. Linear algebra; 2. Multilinear algebra; 3. Differentiation on manifolds; 4. Homotopy and de Rham cohomology; 5. Elementary homology theory; 6. Integration on manifolds; 7. Vector bundles; 8. Geometric manifolds; 9. The degree of a smooth map; Appendixes; References; Index.

  16. TQFT and Whitehead's manifold

    Funar, L


    The aim of this note is to derive some invariants at infinity for open 3-manifolds in the framework of Topological Quantum Field Theories. These invariants may be used to test if an open manifold is simply connected at infinity as we done for Whitehead's manifold in case of the sl_{2}({\\bf C})-TQFT in level 4.

  17. Two-Manifold Problems

    Boots, Byron


    Recently, there has been much interest in spectral approaches to learning manifolds---so-called kernel eigenmap methods. These methods have had some successes, but their applicability is limited because they are not robust to noise. To address this limitation, we look at two-manifold problems, in which we simultaneously reconstruct two related manifolds, each representing a different view of the same data. By solving these interconnected learning problems together and allowing information to flow between them, two-manifold algorithms are able to succeed where a non-integrated approach would fail: each view allows us to suppress noise in the other, reducing bias in the same way that an instrumental variable allows us to remove bias in a {linear} dimensionality reduction problem. We propose a class of algorithms for two-manifold problems, based on spectral decomposition of cross-covariance operators in Hilbert space. Finally, we discuss situations where two-manifold problems are useful, and demonstrate that sol...

  18. Causes for "ghost" manifolds

    Borok, S.; Goldfarb, I.; Gol'dshtein, V.


    The paper concerns intrinsic low-dimensional manifold (ILDM) method suggested in [Maas U, Pope SB. Simplifying chemical kinetics: intrinsic low-dimensional manifolds in composition space, combustion and flame 1992;88:239-64] for dimension reduction of models describing kinetic processes. It has been shown in a number of publications [Goldfarb I, Gol'dshtein V, Maas U. Comparative analysis of two asymptotic approaches based on integral manifolds. IMA J Appl Math 2004;69:353-74; Kaper HG, Kaper TJ, Asymptotic analysis of two reduction methods for systems of chemical reactions. Phys D 2002;165(1-2):66-93; Rhodes C, Morari M, Wiggins S. Identification of the low order manifolds: validating the algorithm of Maas and Pope. Chaos 1999;9(1):108-23] that the ILDM-method works successfully and the intrinsic low-dimensional manifolds belong to a small vicinity of invariant slow manifolds. The ILDM-method has a number of disadvantages. One of them is appearance of so-called "ghost"-manifolds, which do not have connection to the system dynamics [Borok S, Goldfarb I, Gol'dshtein V. "Ghost" ILDM - manifolds and their discrimination. In: Twentieth Annual Symposium of the Israel Section of the Combustion Institute, Beer-Sheva, Israel; 2004. p. 55-7; Borok S, Goldfarb I, Gol'dshtein V. About non-coincidence of invariant manifolds and intrinsic low-dimensional manifolds (ILDM). CNSNS 2008;71:1029-38; Borok S, Goldfarb I, Gol'dshtein V, Maas U. In: Gorban AN, Kazantzis N, Kevrekidis YG, Ottinger HC, Theodoropoulos C, editors. "Ghost" ILDM-manifolds and their identification: model reduction and coarse-graining approaches for multiscale phenomena. Berlin-Heidelberg-New York: Springer; 2006. p. 55-80; Borok S, Goldfarb I, Gol'dshtein V. On a modified version of ILDM method and its asymptotic analysis. IJPAM 2008; 44(1): 125-50; Bykov V, Goldfarb I, Gol'dshtein V, Maas U. On a modified version of ILDM approach: asymptotic analysis based on integral manifolds. IMA J Appl Math 2006

  19. Compressed gas manifold

    Hildebrand, Richard J.; Wozniak, John J.


    A compressed gas storage cell interconnecting manifold including a thermally activated pressure relief device, a manual safety shut-off valve, and a port for connecting the compressed gas storage cells to a motor vehicle power source and to a refueling adapter. The manifold is mechanically and pneumatically connected to a compressed gas storage cell by a bolt including a gas passage therein.

  20. Adaptive manifold learning.

    Zhang, Zhenyue; Wang, Jing; Zha, Hongyuan


    Manifold learning algorithms seek to find a low-dimensional parameterization of high-dimensional data. They heavily rely on the notion of what can be considered as local, how accurately the manifold can be approximated locally, and, last but not least, how the local structures can be patched together to produce the global parameterization. In this paper, we develop algorithms that address two key issues in manifold learning: 1) the adaptive selection of the local neighborhood sizes when imposing a connectivity structure on the given set of high-dimensional data points and 2) the adaptive bias reduction in the local low-dimensional embedding by accounting for the variations in the curvature of the manifold as well as its interplay with the sampling density of the data set. We demonstrate the effectiveness of our methods for improving the performance of manifold learning algorithms using both synthetic and real-world data sets.


    R. K. TYAGI


    Full Text Available The Spark Ignition engine has been extensively used in multifaceted sectors, viz. Automobiles, Industry engineering, etc. due to their exceptional driveability, performance and minimal maintenance. However, gasoline engines have their share of complications as they release a variety of air pollutants, viz. CO, NOx, HC and CO2 etc. and other harmful emissions. In this paper a comparison of these gases with the Government policies or norms have been studied and the parameters which are responsible for increasing the more Air pollution have been minimised using innovative engineering solutions. This paper depicts research done on inlet manifolds and their modifications to achieve exemplary fuel-air swirl. During subsequent analysis at idle condition (1300 rpm, it has been concluded that the venturi-based intake manifold has shown remarkable results in decreasing the HC levels from 180 ppm to 60 ppm (66.6 % at Idle Range. The work is also complementary to the various other designs of inlet manifolds, viz. Inlet manifold Modified 1 and Inlet Manifold Modified 2 out of which it is concluded that the Inlet manifold Modified 2 results in better reduction of pollutants.

  2. Ensemble manifold regularization.

    Geng, Bo; Tao, Dacheng; Xu, Chao; Yang, Linjun; Hua, Xian-Sheng


    We propose an automatic approximation of the intrinsic manifold for general semi-supervised learning (SSL) problems. Unfortunately, it is not trivial to define an optimization function to obtain optimal hyperparameters. Usually, cross validation is applied, but it does not necessarily scale up. Other problems derive from the suboptimality incurred by discrete grid search and the overfitting. Therefore, we develop an ensemble manifold regularization (EMR) framework to approximate the intrinsic manifold by combining several initial guesses. Algorithmically, we designed EMR carefully so it 1) learns both the composite manifold and the semi-supervised learner jointly, 2) is fully automatic for learning the intrinsic manifold hyperparameters implicitly, 3) is conditionally optimal for intrinsic manifold approximation under a mild and reasonable assumption, and 4) is scalable for a large number of candidate manifold hyperparameters, from both time and space perspectives. Furthermore, we prove the convergence property of EMR to the deterministic matrix at rate root-n. Extensive experiments over both synthetic and real data sets demonstrate the effectiveness of the proposed framework.

  3. Analysis on manifolds

    Munkres, James R


    A readable introduction to the subject of calculus on arbitrary surfaces or manifolds. Accessible to readers with knowledge of basic calculus and linear algebra. Sections include series of problems to reinforce concepts.

  4. Hierarchical manifold learning.

    Bhatia, Kanwal K; Rao, Anil; Price, Anthony N; Wolz, Robin; Hajnal, Jo; Rueckert, Daniel


    We present a novel method of hierarchical manifold learning which aims to automatically discover regional variations within images. This involves constructing manifolds in a hierarchy of image patches of increasing granularity, while ensuring consistency between hierarchy levels. We demonstrate its utility in two very different settings: (1) to learn the regional correlations in motion within a sequence of time-resolved images of the thoracic cavity; (2) to find discriminative regions of 3D brain images in the classification of neurodegenerative disease,

  5. On manifolds with corners

    Joyce, Dominic


    Manifolds without boundary, and manifolds with boundary, are universally known in Differential Geometry, but manifolds with corners (locally modelled on [0,\\infty)^k x R^{n-k}) have received comparatively little attention. The basic definitions in the subject are not agreed upon, there are several inequivalent definitions in use of manifolds with corners, of boundary, and of smooth map, depending on the applications in mind. We present a theory of manifolds with corners which includes a new notion of smooth map f : X --> Y. Compared to other definitions, our theory has the advantage of giving a category Man^c of manifolds with corners which is particularly well behaved as a category: it has products and direct products, boundaries behave in a functorial way, and there are simple conditions for the existence of fibre products X x_Z Y in Man^c. Our theory is tailored to future applications in Symplectic Geometry, and is part of a project to describe the geometric structure on moduli spaces of J-holomorphic curv...

  6. Compact mixed-reactant fuel cells

    Priestnall, Michael A.; Kotzeva, Vega P.; Fish, Deborah J.; Nilsson, Eva M.

    The compact mixed-reactant (CMR) fuel cell is an important new "platform" approach to the design and operation of all types of fuel cell stacks. Amongst several other advantages, CMR has the potential to reduce polymer electrolyte membrane (PEM) stack component costs by around a third and to raise volumetric power densities by an order of magnitude. Mixed-reactant fuel cells, in which the fuel and oxidant within a cell are allowed to mix, rely upon the selectivity of anode and cathode electrocatalysts to separate the electrochemical oxidation of fuel and reduction of oxidant. A comprehensive review of the 50-year history of mixed-reactant literature has demonstrated that such systems can perform as well as and, in some circumstances, much better than conventional fuel cells. The significant innovation that Generics has introduced to this field is to combine the concept of mixed-reactant fuel cells with that of a fully porous membrane electrode assembly (MEA) structure. Passing a fuel-oxidant mixture through a stack of porous cells allows the conventional bipolar flow-field plates required in many fuel cell designs to be eliminated. In a conventional PEM stack, for example, the bipolar carbon flow-field plates may block up to half of the active cell area and account for up to 90% of the volume of the stack and of the order of one-third of the materials costs. In addition to all the advantages of mixed-reactant systems, the "flow-through" mode, embodied in Generics' CMR approach, significantly enhances mass-transport of reactants to the electrodes and can reduce reactant pressure drops across the stack. Redesigning fuel cells to operate in a CMR mode with selective electrodes offers the attractive prospect of much reduced stack costs and significantly higher stack power densities for all types of fuel cell. Initial modeling and proof of principle experiments using an alkaline system have confirmed the validity of the CMR approach and the potential for substantial

  7. Riemannian manifold learning.

    Lin, Tong; Zha, Hongbin


    Recently, manifold learning has been widely exploited in pattern recognition, data analysis, and machine learning. This paper presents a novel framework, called Riemannian manifold learning (RML), based on the assumption that the input high-dimensional data lie on an intrinsically low-dimensional Riemannian manifold. The main idea is to formulate the dimensionality reduction problem as a classical problem in Riemannian geometry, i.e., how to construct coordinate charts for a given Riemannian manifold? We implement the Riemannian normal coordinate chart, which has been the most widely used in Riemannian geometry, for a set of unorganized data points. First, two input parameters (the neighborhood size k and the intrinsic dimension d) are estimated based on an efficient simplicial reconstruction of the underlying manifold. Then, the normal coordinates are computed to map the input high-dimensional data into a low-dimensional space. Experiments on synthetic data as well as real world images demonstrate that our algorithm can learn intrinsic geometric structures of the data, preserve radial geodesic distances, and yield regular embeddings.

  8. Hybrid manifold embedding.

    Liu, Yang; Liu, Yan; Chan, Keith C C; Hua, Kien A


    In this brief, we present a novel supervised manifold learning framework dubbed hybrid manifold embedding (HyME). Unlike most of the existing supervised manifold learning algorithms that give linear explicit mapping functions, the HyME aims to provide a more general nonlinear explicit mapping function by performing a two-layer learning procedure. In the first layer, a new clustering strategy called geodesic clustering is proposed to divide the original data set into several subsets with minimum nonlinearity. In the second layer, a supervised dimensionality reduction scheme called locally conjugate discriminant projection is performed on each subset for maximizing the discriminant information and minimizing the dimension redundancy simultaneously in the reduced low-dimensional space. By integrating these two layers in a unified mapping function, a supervised manifold embedding framework is established to describe both global and local manifold structure as well as to preserve the discriminative ability in the learned subspace. Experiments on various data sets validate the effectiveness of the proposed method.

  9. Manifolds, sheaves, and cohomology

    Wedhorn, Torsten


    This book explains techniques that are essential in almost all branches of modern geometry such as algebraic geometry, complex geometry, or non-archimedian geometry. It uses the most accessible case, real and complex manifolds, as a model. The author especially emphasizes the difference between local and global questions. Cohomology theory of sheaves is introduced and its usage is illustrated by many examples. Content Topological Preliminaries - Algebraic Topological Preliminaries - Sheaves - Manifolds - Local Theory of Manifolds - Lie Groups - Torsors and Non-abelian Cech Cohomology - Bundles - Soft Sheaves - Cohomology of Complexes of Sheaves - Cohomology of Sheaves of Locally Constant Functions - Appendix: Basic Topology, The Language of Categories, Basic Algebra, Homological Algebra, Local Analysis Readership Graduate Students in Mathematics / Master of Science in Mathematics About the Author Prof. Dr. Torsten Wedhorn, Department of Mathematics, Technische Universität Darmstadt, Germany.

  10. Manifold Learning by Graduated Optimization.

    Gashler, M; Ventura, D; Martinez, T


    We present an algorithm for manifold learning called manifold sculpting , which utilizes graduated optimization to seek an accurate manifold embedding. An empirical analysis across a wide range of manifold problems indicates that manifold sculpting yields more accurate results than a number of existing algorithms, including Isomap, locally linear embedding (LLE), Hessian LLE (HLLE), and landmark maximum variance unfolding (L-MVU), and is significantly more efficient than HLLE and L-MVU. Manifold sculpting also has the ability to benefit from prior knowledge about expected results.

  11. Manifold Regularized Reinforcement Learning.

    Li, Hongliang; Liu, Derong; Wang, Ding


    This paper introduces a novel manifold regularized reinforcement learning scheme for continuous Markov decision processes. Smooth feature representations for value function approximation can be automatically learned using the unsupervised manifold regularization method. The learned features are data-driven, and can be adapted to the geometry of the state space. Furthermore, the scheme provides a direct basis representation extension for novel samples during policy learning and control. The performance of the proposed scheme is evaluated on two benchmark control tasks, i.e., the inverted pendulum and the energy storage problem. Simulation results illustrate the concepts of the proposed scheme and show that it can obtain excellent performance.

  12. Continuous-Flow Inlet Systems for Low Pressure Curie-Point Pyrolysis. Introduction of Pulse-Pyrolysis

    Egsgaard, Helge; Carlsen, Lars


    With emphasis on a constant reactant flow, a series of inlet systems for gas-phase Curie-point pyrolysis—mass spectrometry experiments have been studied. Inlet systems for the handling of gaseous, liquid and oligomeric (solid) samples have been designed and their performances evaluated. The princ....... The principle of pulse-pyrolysis is introduced and its applicability to kinetic studies outlined....



    An inlet stratification device (5) for a circuit circulating a fluid through a tank (1 ) and for providing and maintaining stratification of the fluid in the tank (1 ). The stratification de- vice (5) is arranged vertically in the tank (1) and comprises an inlet pipe (6) being at least partially...... formed of a flexible porous material and having an inlet (19) and outlets formed of the pores of the porous material. The stratification device (5) further comprises at least one outer pipe (7) surrounding the inlet pipe (6) in spaced relationship thereto and being at least partially formed of a porous...

  14. Yamabe flow on Berwald manifolds

    Azami, Shahroud; Razavi, Asadollah


    Studying the geometric flow plays a powerful role in mathematics and physics. We introduce the Yamabe flow on Finsler manifolds and we will prove the existence and uniqueness for solution of Yamabe flow on Berwald manifolds.

  15. Space Manifold dynamics

    Gómez, Gerard; Barrabés Vera, Esther


    The term Space Manifold Dynamics (SMD) has been proposed for encompassing the various applications of Dynamical Systems methods to spacecraft mission analysis and design, ranging from the exploitation of libration orbits around the collinear Lagrangian points to the design of optimal station-keeping and eclipse avoidance manoeuvres or the determination of low energy lunar and interplanetary transfers

  16. Eigenvalue pinching on spinc manifolds

    Roos, Saskia


    We derive various pinching results for small Dirac eigenvalues using the classification of spinc and spin manifolds admitting nontrivial Killing spinors. For this, we introduce a notion of convergence for spinc manifolds which involves a general study on convergence of Riemannian manifolds with a principal S1-bundle. We also analyze the relation between the regularity of the Riemannian metric and the regularity of the curvature of the associated principal S1-bundle on spinc manifolds with Killing spinors.

  17. Manifold Insulation for Solar Collectors


    Results of computer analysis of effects of various manifold insulation detailed in 23-page report show that if fluid is distributed to and gathered from array of solar collectors by external rather than internal manifold, effectiveness of manifold insulation has major influence on efficiency. Report describes required input data and presents equations that govern computer model. Provides graphs comparing collector efficiencies for representative manifold sizes and insulations.

  18. Pulse Distributing Manifold; Pulse Distributing Manifold

    Schutting, Eberhard [Technische Univ. Graz (Austria); Sams, Theodor [AVL List GmbH, Graz (Austria); Glensvig, Michael [Forschungsgesellschaft mbH, Graz (AT). Kompetenzzentrum ' ' Das virtuelle Fahrzeug' ' (VIF)


    The Pulse Distributing Manifold is a new charge exchange method for turbocharged diesel engines with exhaust gas recirculation (EGR). The method is characterized in that the EGR mass flow is not diverted from the exhaust gas mass flow continuously, but over time broken into sub-streams. The temporal interruption is achieved by two phase-shifted outlet valves which are connected via separate manifolds only with the turbocharger or only with the EGR path. The time points of valve opening are chosen such that the turbocharger and the aftertreatment process of exhaust gas is perfused by high-energy exhaust gas of the blowdown phase while cooler and less energy-rich exhaust gas of the exhaust period is used for the exhaust gas recirculation. This increases the enthalpy for the turbocharger and the temperature for the exhaust gas treatment, while the cooling efficiency at the EGR cooler is reduced. The elimination of the continuous EGR valve has a positive effect on pumping losses. The principle functioning and the potential of this system could be demonstrated by means of a concept study using one-dimensional simulations. Without disadvantages in fuel consumption for the considered commercial vehicle engine, a reduction the EGR cooler performance by 15 % and an increase in exhaust temperature of 35 K could be achieved. The presented charge exchange method was developed, evaluated and patented within the scope of the research program 'K2-mobility' of the project partners AVL (Mainz, Federal Republic of Germany) and University of Technology Graz (Austria). The research project 'K2-Mobility' is supported by the competence center 'The virtual vehicle' Forschungsgesellschaft mbH (Graz, Austria).

  19. Hashing on nonlinear manifolds.

    Shen, Fumin; Shen, Chunhua; Shi, Qinfeng; van den Hengel, Anton; Tang, Zhenmin; Shen, Heng Tao


    Learning-based hashing methods have attracted considerable attention due to their ability to greatly increase the scale at which existing algorithms may operate. Most of these methods are designed to generate binary codes preserving the Euclidean similarity in the original space. Manifold learning techniques, in contrast, are better able to model the intrinsic structure embedded in the original high-dimensional data. The complexities of these models, and the problems with out-of-sample data, have previously rendered them unsuitable for application to large-scale embedding, however. In this paper, how to learn compact binary embeddings on their intrinsic manifolds is considered. In order to address the above-mentioned difficulties, an efficient, inductive solution to the out-of-sample data problem, and a process by which nonparametric manifold learning may be used as the basis of a hashing method are proposed. The proposed approach thus allows the development of a range of new hashing techniques exploiting the flexibility of the wide variety of manifold learning approaches available. It is particularly shown that hashing on the basis of t-distributed stochastic neighbor embedding outperforms state-of-the-art hashing methods on large-scale benchmark data sets, and is very effective for image classification with very short code lengths. It is shown that the proposed framework can be further improved, for example, by minimizing the quantization error with learned orthogonal rotations without much computation overhead. In addition, a supervised inductive manifold hashing framework is developed by incorporating the label information, which is shown to greatly advance the semantic retrieval performance.

  20. Inlet stratification device


    ) with an inlet passage way (16). The upper end of the inlet pipe (6) is connected with a top cap (9). The top cap (9) and the bottom cap (10) are mutually connected by means of a wire (8) and the top cap (9) is configured as a floating device providing a buoyancy force larger than the downwardly directed force......An inlet stratification (5) is adapted to be arranged vertically in a tank (1) during operation. The stratification device (5) comprises an inlet pipe (6) formed of a flexible porous material and having a lower and upper end. The lower end of the inlet pipe (6) is connected to a bottom cap (10...

  1. Stein 4-manifolds and corks

    Akbulut, Selman


    It is known that every compact Stein 4-manifolds can be embedded into a simply connected, minimal, closed, symplectic 4-manifold. Using this property, we give simple constructions of various cork structures of 4-manifolds. We also give an example of infinitely many disjoint embeddings of a fixed cork into a non-compact 4-manifold which produce infinitely many exotic smooth structures (recall that [7] gives examples arbitrarily many disjoint imbeddings of different corks in a closed manifold inducing mutually different exotic structures). Furthermore, here we construct arbitrary many simply connected compact codimention zero submanifolds of S^4 which are mutually homeomorphic but not diffeomorphic.

  2. Canonical metrics on complex manifold

    YAU Shing-Tung


    @@ Complex manifolds are topological spaces that are covered by coordinate charts where the Coordinate changes are given by holomorphic transformations. For example, Riemann surfaces are one dimensional complex manifolds. In order to understand complex manifolds, it is useful to introduce metrics that are compatible with the complex structure. In general, we should have a pair (M, ds2M) where ds2M is the metric. The metric is said to be canonical if any biholomorphisms of the complex manifolds are automatically isometries. Such metrics can naturally be used to describe invariants of the complex structures of the manifold.

  3. Canonical metrics on complex manifold

    YAU; Shing-Tung(Yau; S.-T.)


    Complex manifolds are topological spaces that are covered by coordinate charts where the coordinate changes are given by holomorphic transformations.For example,Riemann surfaces are one dimensional complex manifolds.In order to understand complex manifolds,it is useful to introduce metrics that are compatible with the complex structure.In general,we should have a pair(M,ds~2_M)where ds~2_M is the metric.The metric is said to be canonical if any biholomorphisms of the complex manifolds are automatically isometries.Such metrics can naturally be used to describe invariants of the complex structures of the manifold.

  4. Invariant manifolds and global bifurcations.

    Guckenheimer, John; Krauskopf, Bernd; Osinga, Hinke M; Sandstede, Björn


    Invariant manifolds are key objects in describing how trajectories partition the phase spaces of a dynamical system. Examples include stable, unstable, and center manifolds of equilibria and periodic orbits, quasiperiodic invariant tori, and slow manifolds of systems with multiple timescales. Changes in these objects and their intersections with variation of system parameters give rise to global bifurcations. Bifurcation manifolds in the parameter spaces of multi-parameter families of dynamical systems also play a prominent role in dynamical systems theory. Much progress has been made in developing theory and computational methods for invariant manifolds during the past 25 years. This article highlights some of these achievements and remaining open problems.

  5. Parabolic Stein Manifolds

    Aytuna, Aydin


    An open Riemann surface is called parabolic in case every bounded subharmonic function on it reduces to a constant. Several authors introduced seemingly different analogs of this notion for Stein manifolds of arbitrary dimension. In the first part of this note we compile these notions of parabolicity and give some immediate relations among them. In section 3 we relate some of these notions to the linear topological type of the Fr\\'echet space of analytic functions on the given manifold. In sections 4 and 5 we look at some examples and show, for example, that the complement of the zero set of a Weierstrass polynomial possesses a continuous plurisubharmonic exhaustion function that is maximal off a compact subset.

  6. Advanced Scavenge Systems for an Integrated Engine Inlet Particle Separator


    Fully machined centerbody and outer casing. Four strut (. 093 nch constant thickless. were silver - soldered to form the assembly. AIR SPLITTER ASSEMBLY...pieces of ice, nominally 1/2-inch cubes, weee introduced a.s well. In order that some degree of randomness be present, the objects were directed, unde...section (. 125-inch orifice/ •415-in. duct) followed by a high-pressure manifold to which the nozzle is silver brazed. In the secondary duct, an inlet

  7. Learning Smooth Pattern Transformation Manifolds

    Vural, Elif


    Manifold models provide low-dimensional representations that are useful for processing and analyzing data in a transformation-invariant way. In this paper, we study the problem of learning smooth pattern transformation manifolds from image sets that represent observations of geometrically transformed signals. In order to construct a manifold, we build a representative pattern whose transformations accurately fit various input images. We examine two objectives of the manifold building problem, namely, approximation and classification. For the approximation problem, we propose a greedy method that constructs a representative pattern by selecting analytic atoms from a continuous dictionary manifold. We present a DC (Difference-of-Convex) optimization scheme that is applicable to a wide range of transformation and dictionary models, and demonstrate its application to transformation manifolds generated by rotation, translation and anisotropic scaling of a reference pattern. Then, we generalize this approach to a s...

  8. Holonomy groups of Lorentzian manifolds

    Galaev, Anton S


    In this paper, a survey of the recent results about the classification of the connected holonomy groups of the Lorentzian manifolds is given. A simplification of the construction of the Lorentzian metrics with all possible connected holonomy groups is obtained. As the applications, the Einstein equation, Lorentzian manifolds with parallel and recurrent spinor fields, conformally flat Walker metrics and the classification of 2-symmetric Lorentzian manifolds are considered.

  9. Quantum manifolds with classical limit

    Hohmann, Manuel; Wohlfarth, Mattias N R


    We propose a mathematical model of quantum spacetime as an infinite-dimensional manifold locally homeomorphic to an appropriate Schwartz space. This extends and unifies both the standard function space construction of quantum mechanics and the manifold structure of spacetime. In this picture we demonstrate that classical spacetime emerges as a finite-dimensional manifold through the topological identification of all quantum points with identical position expectation value. We speculate on the possible relevance of this geometry to quantum field theory and gravity.

  10. Analysis, manifolds and physics

    Choquet-Bruhat, Y


    Twelve problems have been added to the first edition; four of them are supplements to problems in the first edition. The others deal with issues that have become important, since the first edition of Volume II, in recent developments of various areas of physics. All the problems have their foundations in volume 1 of the 2-Volume set Analysis, Manifolds and Physics. It would have been prohibitively expensive to insert the new problems at their respective places. They are grouped together at the end of this volume, their logical place is indicated by a number of parenthesis following the title.

  11. Decompositions of manifolds

    Daverman, Robert J


    Decomposition theory studies decompositions, or partitions, of manifolds into simple pieces, usually cell-like sets. Since its inception in 1929, the subject has become an important tool in geometric topology. The main goal of the book is to help students interested in geometric topology to bridge the gap between entry-level graduate courses and research at the frontier as well as to demonstrate interrelations of decomposition theory with other parts of geometric topology. With numerous exercises and problems, many of them quite challenging, the book continues to be strongly recommended to eve

  12. Moment-angle manifolds, intersection of quadrics and higher dimensional contact manifolds

    Barreto, Yadira; Verjovsky, Alberto


    We construct new examples of contact manifolds in arbitrarily large dimensions. These manifolds which we call quasi moment-angle manifolds, are closely related to the classical moment-angle manifolds.

  13. Incremental Alignment Manifold Learning

    Zhi Han; De-Yu Meng; Zong-Sen Xu; Nan-Nan Gu


    A new manifold learning method, called incremental alignment method (IAM), is proposed for nonlinear dimensionality reduction of high dimensional data with intrinsic low dimensionality. The main idea is to incrementally align low-dimensional coordinates of input data patch-by-patch to iteratively generate the representation of the entire dataset. The method consists of two major steps, the incremental step and the alignment step. The incremental step incrementally searches neighborhood patch to be aligned in the next step, and the alignment step iteratively aligns the low-dimensional coordinates of the neighborhood patch searched to generate the embeddings of the entire dataset. Compared with the existing manifold learning methods, the proposed method dominates in several aspects: high efficiency, easy out-of-sample extension, well metric-preserving, and averting of the local minima issue. All these properties are supported by a series of experiments performed on the synthetic and real-life datasets. In addition, the computational complexity of the proposed method is analyzed, and its efficiency is theoretically argued and experimentally demonstrated.

  14. Excited state charge transfer reaction in (mixed solvent + electrolyte) systems: Role of reactant-solvent and reactant-ion interactions

    Harun Al Rasid Gazi; Ranjit Biswas


    Fluorescence spectroscopic techniques have been used to study the excited state intramolecular charge transfer reaction of 4-(1-azetidinyl)benzonitrile (P4C) in two sets of mixed solvents, (1-propanol + ethyl acetate) and (propylene carbonate + acetonitrile), in the absence and presence of a strong electrolyte, lithium perchlorate. These two sets of mixed solvent systems represent binary solvent mixtures of low and high polarities, respectively. Density, sound velocity and viscosity measurements indicate that these two mixed solvent systems are structurally different. Stronger ion-reactant interaction is evidenced in the mole fraction independence of emission frequencies in electrolyte solutions of low polar binary solvent mixtures. For both these mixtures, the reaction driving force (- ) decreases with increase in mole fraction of the relatively less polar solvent component of the mixture. Interestingly, - increases significantly on addition of electrolyte in low polar mixtures and exhibits mixture composition dependence but, in contrast, - in high polar mixtures does not sense variation in mixture composition in presence of electrolyte. This insensitivity to mixture composition for high polar mixtures is also observed for the measured reaction time constant. In addition, the reaction time constant does not sense the presence of electrolyte in the high polar solvent mixtures. The reaction time constant in low polar mixtures, which becomes faster on addition of electrolyte, lengthens on increasing the mole fraction of the relatively less polar solvent component of the mixture. These observations have been qualitatively explained in terms of the measured solvent reorganization energy and reaction driving force by using expressions from the classical theory of electron transfer reaction.

  15. Esophageal Inlet Patch

    C. Behrens


    Full Text Available An inlet patch is a congenital anomaly consisting of ectopic gastric mucosa at or just distal to the upper esophageal sphincter. Most inlet patches are largely asymptomatic, but in problematic cases complications related to acid secretion such as esophagitis, ulcer, web and stricture may occur. The diagnosis of inlet patch is strongly suggested on barium swallow where the most common pattern consists of two small indentations on the wall of the esophagus. The diagnosis of inlet patch is confirmed via endoscopy with biopsy. At endoscopy, the lesion appears salmon-coloured and velvety and is easily distinguished from the normal grey-white squamous epithelium of the esophagus. The prominent margins correlate with the radiological findings of indentations and rim-like shadows on barium swallow. Histopathology provides the definitive diagnosis by demonstrating gastric mucosa adjacent to normal esophageal mucosa. No treatment is required for asymptomatic inlet patches. Symptomatic cases are treated with proton pump inhibitors to relieve symptoms related to acid secretion. Strictures and webs are treated with serial dilatation and should be biopsied to rule out malignancy.

  16. Manifold statistics for essential matrices

    Dubbelman, G.; Dorst, L.; Pijls, H.; Fitzgibbon, A.; et al.,


    Riemannian geometry allows for the generalization of statistics designed for Euclidean vector spaces to Riemannian manifolds. It has recently gained popularity within computer vision as many relevant parameter spaces have such a Riemannian manifold structure. Approaches which exploit this have been

  17. Selectivity and mixed reactant fuel cells

    Riess, Ilan


    Mixed reactant fuel cells (MR-FCs), are aimed at using a uniform mixture of fuel and oxygen applied to both the anode and the cathode. This allows redesign of fuel cells with a significantly simpler construction, having potentially a higher power density, better fuel utilization and be less expensive. The challenge in realizing MR-FCs is finding selective electrodes that can enhance oxygen reduction at the cathode, fuel oxidation at the anode while inhibiting the chemical reaction between the fuel and oxygen in the gas mixture. This task is in particular challenging in solid oxide fuel cells (SOFCs), as they operate at elevated temperatures, where many reactions are easily activated and selectivity is difficult to achieve. As a result no true MR-FC of the SOFC type were reported while some were found for low temperature fuel cells (FCs). The so-called single-chamber-SOFC are not true MR-FCs as they do not contain two selective electrodes, as required. We shall discuss potential ways to search for and develop selective anodes and cathodes for SOFC type MR-FCs. We first consider material properties which should contribute to that goal. This refers to electronic properties of the bulk, band banding under adsorbed specie, point defects in the bulk and on the surface. We then proceed to show how cell design, in particular electrode structure, can contribute to selectivity. Finally operation conditions are considered and it is shown that they also can contribute to selectivity. The operation condition considered are gas mixture composition, gas mixture residence time in the hot zone, hence gas flow rate, current density and temperature. The topics discussed hold for all FC types but are crucial for the SOFC type because of the difficulty to achieve selectivity at elevated temperatures. It is suggested that a concerted effort taking advantage of all those options should allow development of a true SOFC type MR-FC.

  18. Cohomotopy sets of 4-manifolds

    Kirby, Robion; Teichner, Peter


    Elementary geometric arguments are used to compute the group of homotopy classes of maps from a 4-manifold X to the 3-sphere, and to enumerate the homotopy classes of maps from X to the 2-sphere. The former completes a project initiated by Steenrod in the 1940's, and the latter provides geometric arguments for and extensions of recent homotopy theoretic results of Larry Taylor. These two results complete the computation of all the cohomotopy sets of closed oriented 4-manifolds and provide a framework for the study of Morse 2-functions on 4-manifolds, a subject that has garnered considerable recent attention.

  19. Haantjes Manifolds and Integrable Systems

    Tempesta, Piergiulio


    A general theory of integrable systems is proposed, based on the theory of Haantjes manifolds. We introduce the notion of symplectic-Haantjes manifold (or $\\omega \\mathcal{H}$ manifold), as the natural setting where the notion of integrability can be formulated. We propose an approach to the separation of variables for classical systems, related to the geometry of Haantjes manifolds. A special class of coordinates, called Darboux-Haantjes coordinates, will be constructed from the Haantjes structure associated with an integrable systems. They enable the additive separation of variables of the Hamilton-Jacobi equation. We also present an application of our approach to the study of some finite-dimensional integrable models, as the H\\'enon-Heiles systems and a stationary reduction of the KdV hierarchy.

  20. An introduction to differential manifolds

    Lafontaine, Jacques


    This book is an introduction to differential manifolds. It gives solid preliminaries for more advanced topics: Riemannian manifolds, differential topology, Lie theory. It presupposes little background: the reader is only expected to master basic differential calculus, and a little point-set topology. The book covers the main topics of differential geometry: manifolds, tangent space, vector fields, differential forms, Lie groups, and a few more sophisticated topics such as de Rham cohomology, degree theory and the Gauss-Bonnet theorem for surfaces. Its ambition is to give solid foundations. In particular, the introduction of “abstract” notions such as manifolds or differential forms is motivated via questions and examples from mathematics or theoretical physics. More than 150 exercises, some of them easy and classical, some others more sophisticated, will help the beginner as well as the more expert reader. Solutions are provided for most of them. The book should be of interest to various readers: undergra...

  1. Vector Fields on Product Manifolds

    Kurz, Stefan


    This short report establishes some basic properties of smooth vector fields on product manifolds. The main results are: (i) On a product manifold there always exists a direct sum decomposition into horizontal and vertical vector fields. (ii) Horizontal and vertical vector fields are naturally isomorphic to smooth families of vector fields defined on the factors. Vector fields are regarded as derivations of the algebra of smooth functions.

  2. Invariant Manifolds and Collective Coordinates

    Papenbrock, T


    We introduce suitable coordinate systems for interacting many-body systems with invariant manifolds. These are Cartesian in coordinate and momentum space and chosen such that several components are identically zero for motion on the invariant manifold. In this sense these coordinates are collective. We make a connection to Zickendraht's collective coordinates and present certain configurations of few-body systems where rotations and vibrations decouple from single-particle motion. These configurations do not depend on details of the interaction.

  3. Coastal Inlets Research Program


    2003 2005 2007 2009 2011 2013 Calendar Year CIRP Website: Tech Transfer What new technology transfer do we have to discuss...etc.), nested grids; integrated with CMS-Flow Verification & Validation Cases (14) Bouss-2D: Phase -resolving shallow- water, nonlinear wave model for...Port Orford, OR Tillamook Inlet, OR  SPN: Half Moon Bay CA Waves at  Navigation  Structures ,  SWG: Matagorda Ship Channel, TX West Galveston

  4. Near Critical Catalyst Reactant Branching Processes with Controlled Immigration

    Budhiraja, Amarjit


    Near critical catalyst-reactant branching processes with controlled immigration are studied. The reactant population evolves according to a branching process whose branching rate is proportional to the total mass of the catalyst. The bulk catalyst evolution is that of a classical continuous time branching process; in addition there is a specific form of immigration. Immigration takes place exactly when the catalyst population falls below a certain threshold, in which case the population is instantaneously replenished to the threshold. Such models are motivated by problems in chemical kinetics where one wants to keep the level of a catalyst above a certain threshold in order to maintain a desired level of reaction activity. A diffusion limit theorem for the scaled processes is presented, in which the catalyst limit is described through a reflected diffusion, while the reactant limit is a diffusion with coefficients that are functions of both the reactant and the catalyst. Stochastic averaging principles under ...

  5. An Explicit Nonlinear Mapping for Manifold Learning

    Qiao, Hong; Zhang, Peng; Wang, Di; Zhang, Bo


    Manifold learning is a hot research topic in the field of computer science and has many applications in the real world. A main drawback of manifold learning methods is, however, that there is no explicit mappings from the input data manifold to the output embedding. This prohibits the application of manifold learning methods in many practical problems such as classification and target detection. Previously, in order to provide explicit mappings for manifold learning methods, many methods have...

  6. Nonlinear manifold representations for functional data

    Chen, Dong; Müller, Hans-Georg


    For functional data lying on an unknown nonlinear low-dimensional space, we study manifold learning and introduce the notions of manifold mean, manifold modes of functional variation and of functional manifold components. These constitute nonlinear representations of functional data that complement classical linear representations such as eigenfunctions and functional principal components. Our manifold learning procedures borrow ideas from existing nonlinear dimension reduction methods, which...

  7. Principal Curves on Riemannian Manifolds.

    Hauberg, Soren


    Euclidean statistics are often generalized to Riemannian manifolds by replacing straight-line interpolations with geodesic ones. While these Riemannian models are familiar-looking, they are restricted by the inflexibility of geodesics, and they rely on constructions which are optimal only in Euclidean domains. We consider extensions of Principal Component Analysis (PCA) to Riemannian manifolds. Classic Riemannian approaches seek a geodesic curve passing through the mean that optimizes a criteria of interest. The requirements that the solution both is geodesic and must pass through the mean tend to imply that the methods only work well when the manifold is mostly flat within the support of the generating distribution. We argue that instead of generalizing linear Euclidean models, it is more fruitful to generalize non-linear Euclidean models. Specifically, we extend the classic Principal Curves from Hastie & Stuetzle to data residing on a complete Riemannian manifold. We show that for elliptical distributions in the tangent of spaces of constant curvature, the standard principal geodesic is a principal curve. The proposed model is simple to compute and avoids many of the pitfalls of traditional geodesic approaches. We empirically demonstrate the effectiveness of the Riemannian principal curves on several manifolds and datasets.

  8. Fivebranes and 3-manifold homology

    Gukov, Sergei; Vafa, Cumrun


    Motivated by physical constructions of homological knot invariants, we study their analogs for closed 3-manifolds. We show that fivebrane compactifications provide a universal description of various old and new homological invariants of 3-manifolds. In terms of 3d/3d correspondence, such invariants are given by the Q-cohomology of the Hilbert space of partially topologically twisted 3d N=2 theory T[M_3] on a Riemann surface with defects. We demonstrate this by concrete and explicit calculations in the case of monopole/Heegaard Floer homology and a 3-manifold analog of Khovanov-Rozansky link homology. The latter gives a categorification of Chern-Simons partition function. Some of the new key elements include the explicit form of the S-transform and a novel connection between categorification and a previously mysterious role of Eichler integrals in Chern-Simons theory.

  9. Principal Curves on Riemannian Manifolds

    Hauberg, Søren


    Euclidean statistics are often generalized to Riemannian manifolds by replacing straight-line interpolations with geodesic ones. While these Riemannian models are familiar-looking, they are restricted by the inflexibility of geodesics, and they rely on constructions which are optimal only...... in Euclidean domains. We consider extensions of Principal Component Analysis (PCA) to Riemannian manifolds. Classic Riemannian approaches seek a geodesic curve passing through the mean that optimize a criteria of interest. The requirements that the solution both is geodesic and must pass through the mean tend...... from Hastie & Stuetzle to data residing on a complete Riemannian manifold. We show that for elliptical distributions in the tangent of spaces of constant curvature, the standard principal geodesic is a principal curve. The proposed model is simple to compute and avoids many of the pitfalls...

  10. Lattice QCD on nonorientable manifolds

    Mages, Simon; Tóth, Bálint C.; Borsányi, Szabolcs; Fodor, Zoltán; Katz, Sándor D.; Szabó, Kálmán K.


    A common problem in lattice QCD simulations on the torus is the extremely long autocorrelation time of the topological charge when one approaches the continuum limit. The reason is the suppressed tunneling between topological sectors. The problem can be circumvented by replacing the torus with a different manifold, so that the connectivity of the configuration space is changed. This can be achieved by using open boundary conditions on the fields, as proposed earlier. It has the side effect of breaking translational invariance strongly. Here we propose to use a nonorientable manifold and show how to define and simulate lattice QCD on it. We demonstrate in quenched simulations that this leads to a drastic reduction of the autocorrelation time. A feature of the new proposal is that translational invariance is preserved up to exponentially small corrections. A Dirac fermion on a nonorientable manifold poses a challenge to numerical simulations: the fermion determinant becomes complex. We propose two approaches to circumvent this problem.

  11. Parallel spinors on flat manifolds

    Sadowski, Michał


    Let p(M) be the dimension of the vector space of parallel spinors on a closed spin manifold M. We prove that every finite group G is the holonomy group of a closed flat spin manifold M(G) such that p(M(G))>0. If the holonomy group Hol(M) of M is cyclic, then we give an explicit formula for p(M) another than that given in [R.J. Miatello, R.A. Podesta, The spectrum of twisted Dirac operators on compact flat manifolds, Trans. Am. Math. Soc., in press]. We answer the question when p(M)>0 if Hol(M) is a cyclic group of prime order or dim⁡M≤4.

  12. Motion Planning via Manifold Samples

    Salzman, Oren; Raveh, Barak; Halperin, Dan


    We present a general and modular algorithmic framework for path planning of robots. Our framework combines geometric methods for exact and complete analysis of low-dimensional configuration spaces, together with practical, considerably simpler sampling-based approaches that are appropriate for higher dimensions. In order to facilitate the transfer of advanced geometric algorithms into practical use, we suggest taking samples that are entire low-dimensional manifolds of the configuration space that capture the connectivity of the configuration space much better than isolated point samples. Geometric algorithms for analysis of low-dimensional manifolds then provide powerful primitive operations. The modular design of the framework enables independent optimization of each modular component. Indeed, we have developed, implemented and optimized a primitive operation for complete and exact combinatorial analysis of a certain set of manifolds, using arrangements of curves of rational functions and concepts of generi...

  13. Fivebranes and 3-manifold homology

    Gukov, Sergei; Putrov, Pavel; Vafa, Cumrun


    Motivated by physical constructions of homological knot invariants, we study their analogs for closed 3-manifolds. We show that fivebrane compactifications provide a universal description of various old and new homological invariants of 3-manifolds. In terms of 3d/3d correspondence, such invariants are given by the Q-cohomology of the Hilbert space of partially topologically twisted 3d N=2 theory T[ M 3] on a Riemann surface with defects. We demonstrate this by concrete and explicit calculations in the case of monopole/Heegaard Floer homology and a 3-manifold analog of Khovanov-Rozansky link homology. The latter gives a categorification of Chern-Simons partition function. Some of the new key elements include the explicit form of the S-transform and a novel connection between categorification and a previously mysterious role of Eichler integrals in Chern-Simons theory.

  14. Inlet Geomorphology Evolution Work Unit


    the expected behavior and benefits of nearshore placement. Nearshore placement studies have been documented in two journal papers, one technical...Coastal Inlets Research Program Inlet Geomorphology Evolution Work Unit The Inlet Geomorphology Evolution work unit of the CIRP develops methods...sensing measurements, and USACE projects to create valuable guidance that address geomorphic questions. The present focus of the work unit is a common

  15. Killing Symmetry on Finsler Manifold

    Ootsuka, Takayoshi; Ishida, Muneyuki


    Killing vector fields $K$ are defined on Finsler manifold. The Killing symmetry is reformulated simply as $\\delta K^\\flat =0$ by using the Killing non-linear 1-form $K^\\flat$ and the spray operator $\\delta$ with the Finsler non-linear connection. $K^\\flat$ is related to the generalization of Killing tensors on Finsler manifold, and the condition $\\delta K^\\flat =0$ gives an analytical method of finding higher derivative conserved quantities, which may be called hidden conserved quantities. We show two examples: the Carter constant on Kerr spacetime and the Runge-Lentz vectors in Newtonian gravity.

  16. Invariant manifolds and collective coordinates

    Papenbrock, T. [Centro Internacional de Ciencias, Cuernavaca, Morelos (Mexico); Institute for Nuclear Theory, University of Washington, Seattle, WA (United States); Seligman, T.H. [Centro Internacional de Ciencias, Cuernavaca, Morelos (Mexico); Centro de Ciencias Fisicas, University of Mexico (UNAM), Cuernavaca (Mexico)


    We introduce suitable coordinate systems for interacting many-body systems with invariant manifolds. These are Cartesian in coordinate and momentum space and chosen such that several components are identically zero for motion on the invariant manifold. In this sense these coordinates are collective. We make a connection to Zickendraht's collective coordinates and present certain configurations of few-body systems where rotations and vibrations decouple from single-particle motion. These configurations do not depend on details of the interaction. (author)

  17. Stein Manifolds and Holomorphic Mappings

    Forstneric, Franc


    The main theme of this book is the homotopy principle for holomorphic mappings from Stein manifolds to the newly introduced class of Oka manifolds. This book contains the first complete account of Oka-Grauert theory and its modern extensions, initiated by Mikhail Gromov and developed in the last decade by the author and his collaborators. Included is the first systematic presentation of the theory of holomorphic automorphisms of complex Euclidean spaces, a survey on Stein neighborhoods, connections between the geometry of Stein surfaces and Seiberg-Witten theory, and a wide variety of applicat

  18. Flow in the Inlet Region in Tangential Inlet Cyclones

    Peng, W.; Boot, P.J.A.J.; Hoffmann, A.C; Dries, H.W.A.; Kater, J.


    In this paper the flow pattern in a tangential inlet cyclone is studied by laser Doppler anemometry, with emphasis on the inlet region. The particular focus is on axial asymmetry in the flow, which was studied by determining radial profiles of the axial and tangential gas velocity components at four

  19. Layered models for closed 3-manifolds

    Johnson, Jesse


    We define a combinatorial structure on 3-manifolds that combines the model manifolds constructed in Minsky's proof of the ending lamination conjecture with the layered triangulations defined by Jaco and Rubinstein.

  20. Holomorphic flexibility properties of complex manifolds


    We obtain results on approximation of holomorphic maps by algebraic maps, jet transversality theorems for holomorphic and algebraic maps, and the homotopy principle for holomorphic submersions of Stein manifolds to certain algebraic manifolds.

  1. Nonlinear manifold representations for functional data

    Chen, Dong; 10.1214/11-AOS936


    For functional data lying on an unknown nonlinear low-dimensional space, we study manifold learning and introduce the notions of manifold mean, manifold modes of functional variation and of functional manifold components. These constitute nonlinear representations of functional data that complement classical linear representations such as eigenfunctions and functional principal components. Our manifold learning procedures borrow ideas from existing nonlinear dimension reduction methods, which we modify to address functional data settings. In simulations and applications, we study examples of functional data which lie on a manifold and validate the superior behavior of manifold mean and functional manifold components over traditional cross-sectional mean and functional principal components. We also include consistency proofs for our estimators under certain assumptions.

  2. PMR polyimide composites for aerospace applications. [Polymerization of Monomer Reactants

    Serafini, T. T.


    A novel class of addition-type polyimides has been developed in response to the need for high temperature polymers with improved processability. The new plastic materials are known as PMR (for in situ polymerization of monomer reactants) polyimides. The highly processable PMR polyimides have made it possible to realize much of the potential of high temperature resistant polymers. Monomer reactant combinations for several PMR polyimides have been identified. The present investigation is concerned with a review of the current status of PMR polyimides. Attention is given to details of PMR polyimide chemistry, the processing of composites and their properties, and aerospace applications of PMR-15 polyimide composites.

  3. Periodic solutions and slow manifolds

    Verhulst, F.


    After reviewing a number of results from geometric singular perturbation theory, we give an example of a theorem for periodic solutions in a slow manifold. This is illustrated by examples involving the van der Pol-equation and a modified logistic equation. Regarding nonhyperbolic transitions we disc

  4. Melnikov Vector and Heteroclinic Manifolds



    Using the exponential dichotomies,the transversality theory and the generalized Melnikov method,we consider the conditions for the persistence and the transversality of the singular orbit,with high degeneracy,situated on the heteroclinic or homoclinic manifold under perturbation.The results obtained extend,include and improve the corresponding ones given in certain papers well known in this area.

  5. Cobordism Independence of Grassmann Manifolds

    Ashish Kumar Das


    This note proves that, for $F=\\mathbb{R},\\mathbb{C}$ or $\\mathbb{H}$, the bordism classes of all non-bounding Grassmannian manifolds $G_k(F^{n+k})$, with < and having real dimension , constitute a linearly independent set in the unoriented bordism group $\\mathfrak{N}_d$ regarded as a $\\mathbb{Z}_2$-vector space.

  6. Fluid delivery manifolds and microfluidic systems

    Renzi, Ronald F.; Sommer, Gregory J.; Singh, Anup K.; Hatch, Anson V.; Claudnic, Mark R.; Wang, Ying-Chih; Van de Vreugde, James L.


    Embodiments of fluid distribution manifolds, cartridges, and microfluidic systems are described herein. Fluid distribution manifolds may include an insert member and a manifold base and may define a substantially closed channel within the manifold when the insert member is press-fit into the base. Cartridges described herein may allow for simultaneous electrical and fluidic interconnection with an electrical multiplex board and may be held in place using magnetic attraction.

  7. Quantization of Presymplectic Manifolds and Circle Actions

    Silva, A C; Tolman, S; Silva, Ana Canas da; Karshon, Yael; Tolman, Susan


    We prove several versions of "quantization commutes with reduction" for circle actions on manifolds that are not symplectic. Instead, these manifolds possess a weaker structure, such as a spin^c structure. Our theorems work whenever the quantization data and the reduction data are compatible; this condition always holds if we start from a presymplectic (in particular, symplectic) manifold.

  8. Natural Connections on Riemannian Product Manifolds

    Gribacheva, Dobrinka


    A Riemannian almost product manifold with integrable almost product structure is called a Riemannian product manifold. In the present paper the natural connections on such manifolds are studied, i.e. the linear connections preserving the almost product structure and the Riemannian metric.

  9. Invariant manifolds for flows in Banach Spaces

    Lu Kening.


    The author considers the existence, smoothness and exponential attractivity of global invariant manifolds for flow in Banach Spaces. He shows that every global invariant manifold can be expressed as a graph of a C{sup k} map, provided that the invariant manifolds are exponentially attractive. Applications go to the Reaction-Diffusion equation, the Kuramoto-Sivashinsky equation, and singular perturbed wave equation.

  10. Local Schrodinger flow into Kahler manifolds

    丁伟岳; 王友德


    In this paper we show that there exists a unique local smooth solution for the Cauchy problem of the Schrodinger flow for maps from a compact Riemannian manifold into a complete Kahler manifold, or from a Euclidean space Rm into a compact Kahler manifold. As a consequence, we prove that Heisenberg spin system is locally well-posed in the appropriate Sobolev spaces.


    Tsoy-Wo Ma


    Based on locally compact perturbations of the identity map similar to the Fredholm structures on real Banach manifolds, complex manifolds with inverse mapping theorem as part of the defintion are proposed. Standard topics including holomorphic maps, morphisms, derivatives, tangent bundles, product manifolds and submanifolds are presented. Although this framework is elementary, it lays the necessary foundation for all subsequent developments.

  12. On the manifold-mapping optimization technique

    Echeverria, D.; Hemker, P.W.


    In this paper, we study in some detail the manifold-mapping optimization technique introduced in an earlier paper. Manifold mapping aims at accelerating optimal design procedures that otherwise require many evaluations of time-expensive cost functions. We give a proof of convergence for the manifold

  13. Conductive polymer layers to limit transfer of fuel reactants to catalysts of fuel cells to reduce reactant crossover

    Stanis, Ronald J.; Lambert, Timothy N.


    An apparatus of an aspect includes a fuel cell catalyst layer. The fuel cell catalyst layer is operable to catalyze a reaction involving a fuel reactant. A fuel cell gas diffusion layer is coupled with the fuel cell catalyst layer. The fuel cell gas diffusion layer includes a porous electrically conductive material. The porous electrically conductive material is operable to allow the fuel reactant to transfer through the fuel cell gas diffusion layer to reach the fuel cell catalyst layer. The porous electrically conductive material is also operable to conduct electrons associated with the reaction through the fuel cell gas diffusion layer. An electrically conductive polymer material is coupled with the fuel cell gas diffusion layer. The electrically conductive polymer material is operable to limit transfer of the fuel reactant to the fuel cell catalyst layer.

  14. Conductive polymer layers to limit transfer of fuel reactants to catalysts of fuel cells to reduce reactant crossover

    Stanis, Ronald J.; Lambert, Timothy N.


    An apparatus of an aspect includes a fuel cell catalyst layer. The fuel cell catalyst layer is operable to catalyze a reaction involving a fuel reactant. A fuel cell gas diffusion layer is coupled with the fuel cell catalyst layer. The fuel cell gas diffusion layer includes a porous electrically conductive material. The porous electrically conductive material is operable to allow the fuel reactant to transfer through the fuel cell gas diffusion layer to reach the fuel cell catalyst layer. The porous electrically conductive material is also operable to conduct electrons associated with the reaction through the fuel cell gas diffusion layer. An electrically conductive polymer material is coupled with the fuel cell gas diffusion layer. The electrically conductive polymer material is operable to limit transfer of the fuel reactant to the fuel cell catalyst layer.

  15. Preliminary Experimental Study on Pressure Loss Coefficients of Exhaust Manifold Junction

    Xiao-lu Lu


    Full Text Available The flow characteristic of exhaust system has an important impact on inlet boundary of the turbine. In this paper, high speed flow in a diesel exhaust manifold junction was tested and simulated. The pressure loss coefficient of the junction flow was analyzed. The steady experimental results indicated that both of static pressure loss coefficients L13 and L23 first increased and then decreased with the increase of mass flow ratio of lateral branch and public manifold. The total pressure loss coefficient K13 always increased with the increase of mass flow ratio of junctions 1 and 3. The total pressure loss coefficient K23 first increased and then decreased with the increase of mass flow ratio of junctions 2 and 3. These pressure loss coefficients of the exhaust pipe junctions can be used in exhaust flow and turbine inlet boundary conditions analysis. In addition, simulating calculation was conducted to analyze the effect of branch angle on total pressure loss coefficient. According to the calculation results, total pressure loss coefficient was almost the same at low mass flow rate of branch manifold 1 but increased with lateral branch angle at high mass flow rate of branch manifold 1.

  16. A Fixed Bed Barrier Reactor with Separate Feed of Reactants

    Neomagus, H.W.J.P.; Saracco, G.; Versteeg, G.F.


    A new type of gas-solid reactor was developed and characterised in the series of reactor configurations with separate feed of reactants studied by our group. The novelty in the proposed design lies in the use of a fixed bed of small catalytic particles instead of a porous catalytic membrane. The maj

  17. A Fixed Bed Barrier Reactor with Separate Feed of Reactants

    Neomagus, H.W.J.P.; Saracco, G.; Versteeg, G.F.


    A new type of gas-solid reactor was developed and characterised in the series of reactor configurations with separate feed of reactants studied by our group. The novelty in the proposed design lies in the use of a fixed bed of small catalytic particles instead of a porous catalytic membrane. The maj

  18. Singular reduction of generalized complex manifolds

    Goldberg, Timothy E


    In this paper, we develop the analogue of Sjamaar and Lerman's singular reduction of Hamiltonian symplectic manifolds in the context of Hamiltonian generalized complex manifolds (in the sense of Lin and Tolman). Specifically, we prove that if a compact Lie group acts on a generalized complex manifold in a Hamiltonian fashion, then the partition of the global quotient by orbit types induces a partition of the Lin-Tolman quotient into generalized complex manifolds. This result holds also for reduction of Hamiltonian generalized Kaehler manifolds.

  19. Environmental continuous air monitor inlet with combined preseparator and virtual impactor

    Rodgers, John C.


    An inlet for an environmental air monitor is described wherein a pre-separator interfaces with ambient environment air and removes debris and insects commonly associated with high wind outdoors and a deflector plate in communication with incoming air from the pre-separator stage, that directs the air radially and downward uniformly into a plurality of accelerator jets located in a manifold of a virtual impactor, the manifold being cylindrical and having a top, a base, and a wall, with the plurality of accelerator jets being located in the top of the manifold and receiving the directed air and accelerating directed air, thereby creating jets of air penetrating into the manifold, where a major flow is deflected to the walls of the manifold and extracted through ports in the walls. A plurality of receiver nozzles are located in the base of the manifold coaxial with the accelerator jets, and a plurality of matching flow restrictor elements are located in the plurality of receiver nozzles for balancing and equalizing the total minor flow among all the plurality of receiver nozzles, through which a lower, fractional flow extracts large particle constituents of the air for collection on a sample filter after passing through the plurality of receiver nozzles and the plurality of matching flow restrictor elements.

  20. Manifold seal structure for fuel cell stack

    Collins, William P.


    The seal between the sides of a fuel cell stack and the gas manifolds is improved by adding a mechanical interlock between the adhesive sealing strip and the abutting surface of the manifolds. The adhesive is a material which can flow to some extent when under compression, and the mechanical interlock is formed providing small openings in the portion of the manifold which abuts the adhesive strip. When the manifolds are pressed against the adhesive strips, the latter will flow into and through the manifold openings to form buttons or ribs which mechanically interlock with the manifolds. These buttons or ribs increase the bond between the manifolds and adhesive, which previously relied solely on the adhesive nature of the adhesive.

  1. Minimal Webs in Riemannian Manifolds

    Markvorsen, Steen


    are of instrumental importance for the applications. We apply these properties to show that minimal webs in ambient Riemannian spaces share several analytic and geometric properties with their smooth (minimal submanifold) counterparts in such spaces. In particular we use appropriate versions of the divergence......)$ into Riemannian manifolds $(N^{n}, h)$. Such immersions we call {\\em{minimal webs}}. They admit a natural 'geometric' extension of the intrinsic combinatorial discrete Laplacian. The geometric Laplacian on minimal webs enjoys standard properties such as the maximum principle and the divergence theorems, which...... theorems together with the comparison techniques for distance functions in Riemannian geometry and obtain bounds for the first Dirichlet eigenvalues, the exit times and the capacities as well as isoperimetric type inequalities for so-called extrinsic $R-$webs of minimal webs in ambient Riemannian manifolds...

  2. Invariance for Single Curved Manifold

    Castro, Pedro Machado Manhaes de


    Recently, it has been shown that, for Lambert illumination model, solely scenes composed by developable objects with a very particular albedo distribution produce an (2D) image with isolines that are (almost) invariant to light direction change. In this work, we provide and investigate a more general framework, and we show that, in general, the requirement for such in variances is quite strong, and is related to the differential geometry of the objects. More precisely, it is proved that single curved manifolds, i.e., manifolds such that at each point there is at most one principal curvature direction, produce invariant is surfaces for a certain relevant family of energy functions. In the three-dimensional case, the associated energy function corresponds to the classical Lambert illumination model with albedo. This result is also extended for finite-dimensional scenes composed by single curved objects. © 2012 IEEE.

  3. Symmetries from the solution manifold

    Aldaya, Víctor; Guerrero, Julio; Lopez-Ruiz, Francisco F.; Cossío, Francisco


    We face a revision of the role of symmetries of a physical system aiming at characterizing the corresponding Solution Manifold (SM) by means of Noether invariants as a preliminary step towards a proper, non-canonical, quantization. To this end, "point symmetries" of the Lagrangian are generally not enough, and we must resort to the more general concept of contact symmetries. They are defined in terms of the Poincaré-Cartan form, which allows us, in turn, to find the symplectic structure on the SM, through some sort of Hamilton-Jacobi (HJ) transformation. These basic symmetries are realized as Hamiltonian vector fields, associated with (coordinate) functions on the SM, lifted back to the Evolution Manifold through the inverse of this HJ mapping, that constitutes an inverse of the Noether Theorem. The specific examples of a particle moving on S3, at the mechanical level, and nonlinear SU(2)-sigma model in field theory are sketched.

  4. Rigid subsets of symplectic manifolds

    Entov, Michael


    We show that there is an hierarchy of intersection rigidity properties of sets in a closed symplectic manifold: some sets cannot be displaced by symplectomorphisms from more sets than the others. We also find new examples of rigidity of intersections involving, in particular, specific fibers of moment maps of Hamiltonian torus actions, monotone Lagrangian submanifolds (following the previous work of P.Albers) as well as certain, possibly singular, sets defined in terms of Poisson-commutative subalgebras of smooth functions. In addition, we get some geometric obstructions to semi-simplicity of the quantum homology of symplectic manifolds. The proofs are based on the Floer-theoretical machinery of partial symplectic quasi-states.

  5. Torsions of 3-dimensional manifolds

    Wurzbacher, T


    From the reviews: "This is an excellent exposition about abelian Reidemeister torsions for three-manifolds." ―Zentralblatt Math "This monograph contains a wealth of information many topologists will find very handy. …Many of the new points of view pioneered by Turaev are gradually becoming mainstream and are spreading beyond the pure topology world. This monograph is a timely and very useful addition to the scientific literature." ―Mathematical Reviews

  6. Koppelman formulas on flag manifolds

    Samuelsson, Håkan


    We construct Koppelman formulas on manifolds of flags in $\\C^N$ for forms with values in any holomorphic line bundle as well as in the tautological vector bundles and their duals. As an application we obtain new explicit proofs of some vanishing theorems of the Bott-Borel-Weil type by solving the corresponding $\\debar$-equation. We also construct reproducing kernels for harmonic $(p,q)$-forms in the case of Grassmannians.

  7. Polynomial Regression on Riemannian Manifolds

    Hinkle, Jacob; Fletcher, P Thomas; Joshi, Sarang


    In this paper we develop the theory of parametric polynomial regression in Riemannian manifolds and Lie groups. We show application of Riemannian polynomial regression to shape analysis in Kendall shape space. Results are presented, showing the power of polynomial regression on the classic rat skull growth data of Bookstein as well as the analysis of the shape changes associated with aging of the corpus callosum from the OASIS Alzheimer's study.

  8. Deformations of extremal toric manifolds

    Rollin, Yann


    Let $X$ be a compact toric extremal K\\"ahler manifold. Using the work of Sz\\'ekelyhidi, we provide a simple criterion on the fan describing $X$ to ensure the existence of complex deformations of $X$ that carry extremal metrics. As an example, we find new CSC metrics on 4-points blow-ups of $\\C\\P^1\\times\\C\\P^1$.

  9. The Operator Manifold Formalism, 1

    Ter-Kazarian, G T


    The suggested operator manifold formalism enables to develop an approach to the unification of the geometry and the field theory. We also elaborate the formalism of operator multimanifold yielding the multiworld geometry involving the spacetime continuum and internal worlds, where the subquarks are defined implying the Confinement and Gauge principles. This formalism in Part II (hep-th/9812182) is used to develop further the microscopic approach to some key problems of particle physics.

  10. Coincidence classes in nonorientable manifolds


    Full Text Available We study Nielsen coincidence theory for maps between manifolds of same dimension regardless of orientation. We use the definition of semi-index of a class, review the definition of defective classes, and study the occurrence of defective root classes. We prove a semi-index product formula for lifting maps and give conditions for the defective coincidence classes to be the only essential classes.

  11. Manifolds of interconvertible pure states

    Sinolecka, Magdalena M.; Zyczkowski, Karol; Kus, Marek


    Local orbits of a pure state of an N x N bi-partite quantum system are analyzed. We compute their dimensions which depends on the degeneracy of the vector of coefficients arising by the Schmidt decomposition. In particular, the generic orbit has 2N^2 -N-1 dimensions, the set of separable states is 4(N-1) dimensional, while the manifold of maximally entangled states has N^2-1 dimensions.

  12. Manifolds of interconvertible pure states

    Sinolecka, M M; Kus, M; Sinolecka, Magdalena M.; Zyczkowski, Karol; Kus, Marek


    Local orbits of a pure state of an N x N bi-partite quantum system are analyzed. We compute their dimensions which depends on the degeneracy of the vector of coefficients arising by the Schmidt decomposition. In particular, the generic orbit has 2N^2 -N-1 dimensions, the set of separable states is 4(N-1) dimensional, while the manifold of maximally entangled states has N^2-1 dimensions.

  13. On Einstein, Hermitian 4-Manifolds

    LeBrun, Claude


    Let (M,h) be a compact 4-dimensional Einstein manifold, and suppose that h is Hermitian with respect to some complex structure J on M. Then either (M,J,h) is Kaehler-Einstein, or else, up to rescaling and isometry, it is one of the following two exceptions: the Page metric on CP2 # (-CP2), or the Einstein metric on CP2 # 2 (-CP2) constructed in Chen-LeBrun-Weber.

  14. Model Reduction by Manifold Boundaries

    Transtrum, Mark K.; Qiu, Peng


    Understanding the collective behavior of complex systems from their basic components is a difficult yet fundamental problem in science. Existing model reduction techniques are either applicable under limited circumstances or produce “black boxes” disconnected from the microscopic physics. We propose a new approach by translating the model reduction problem for an arbitrary statistical model into a geometric problem of constructing a low-dimensional, submanifold approximation to a high-dimensional manifold. When models are overly complex, we use the observation that the model manifold is bounded with a hierarchy of widths and propose using the boundaries as submanifold approximations. We refer to this approach as the manifold boundary approximation method. We apply this method to several models, including a sum of exponentials, a dynamical systems model of protein signaling, and a generalized Ising model. By focusing on parameters rather than physical degrees of freedom, the approach unifies many other model reduction techniques, such as singular limits, equilibrium approximations, and the renormalization group, while expanding the domain of tractable models. The method produces a series of approximations that decrease the complexity of the model and reveal how microscopic parameters are systematically “compressed” into a few macroscopic degrees of freedom, effectively building a bridge between the microscopic and the macroscopic descriptions. PMID:25216014

  15. Combustion flame-plasma hybrid reactor systems, and chemical reactant sources

    Kong, Peter C


    Combustion flame-plasma hybrid reactor systems, chemical reactant sources, and related methods are disclosed. In one embodiment, a combustion flame-plasma hybrid reactor system comprising a reaction chamber, a combustion torch positioned to direct a flame into the reaction chamber, and one or more reactant feed assemblies configured to electrically energize at least one electrically conductive solid reactant structure to form a plasma and feed each electrically conductive solid reactant structure into the plasma to form at least one product is disclosed. In an additional embodiment, a chemical reactant source for a combustion flame-plasma hybrid reactor comprising an elongated electrically conductive reactant structure consisting essentially of at least one chemical reactant is disclosed. In further embodiments, methods of forming a chemical reactant source and methods of chemically converting at least one reactant into at least one product are disclosed.

  16. Smooth Maps of a Foliated Manifold in a Symplectic Manifold

    Mahuya Datta; Md Rabiul Islam


    Let be a smooth manifold with a regular foliation $\\mathcal{F}$ and a 2-form which induces closed forms on the leaves of $\\mathcal{F}$ in the leaf topology. A smooth map $f:(M,\\mathcal{F})\\longrightarrow(N, )$ in a symplectic manifold $(N, )$ is called a foliated symplectic immersion if restricts to an immersion on each leaf of the foliation and further, the restriction of $f^∗$ is the same as the restriction of on each leaf of the foliation. If is a foliated symplectic immersion then the derivative map $Df$ gives rise to a bundle morphism $F:TM\\longrightarrow TN$ which restricts to a monomorphism on $T\\mathcal{F}\\subseteq TM$ and satisfies the condition $F^∗=$ on $T\\mathcal{F}$. A natural question is whether the existence of such a bundle map ensures the existence of a foliated symplectic immersion . As we shall see in this paper, the obstruction to the existence of such an is only topological in nature. The result is proved using the ℎ-principle theory of Gromov.

  17. Differential Calculus on N-Graded Manifolds

    Sardanashvily, G.; W. Wachowski


    The differential calculus, including formalism of linear differential operators and the Chevalley–Eilenberg differential calculus, over N-graded commutative rings and on N-graded manifolds is developed. This is a straightforward generalization of the conventional differential calculus over commutative rings and also is the case of the differential calculus over Grassmann algebras and on Z2-graded manifolds. We follow the notion of an N-graded manifold as a local-ringed space whose body is a s...

  18. Discrete equations and the singular manifold method

    Estévez, P G


    The Painleve expansion for the second Painleve equation (PII) and fourth Painleve equation (PIV) have two branches. The singular manifold method therefore requires two singular manifolds. The double singular manifold method is used to derive Miura transformations from PII and PIV to modified Painleve type equations for which auto-Backlund transformations are obtained. These auto-Backlund transformations can be used to obtain discrete equations.



    The design and management of the objects about the numerical manifold method are studied by abstracting the finite cover system of numerical manifold method as independent data classes and the theoretical basis for the researching and expanding of numerical manifold method is also put forward. The Hammer integration of triangular area coordinates is used in the integration of the element. The calculation result shows that the program is accuracy and effective.

  20. Homology group on manifolds and their foldings

    M. Abu-Saleem


    Full Text Available In this paper, we introduce the definition of the induced unfolding on the homology group. Some types of conditional foldings restricted on the elements of the homology groups are deduced. The effect of retraction on the homology group of a manifold is dicussed. The unfolding of variation curvature of manifolds on their homology group are represented. The relations between homology group of the manifold and its folding are deduced.

  1. Similarity Learning of Manifold Data.

    Chen, Si-Bao; Ding, Chris H Q; Luo, Bin


    Without constructing adjacency graph for neighborhood, we propose a method to learn similarity among sample points of manifold in Laplacian embedding (LE) based on adding constraints of linear reconstruction and least absolute shrinkage and selection operator type minimization. Two algorithms and corresponding analyses are presented to learn similarity for mix-signed and nonnegative data respectively. The similarity learning method is further extended to kernel spaces. The experiments on both synthetic and real world benchmark data sets demonstrate that the proposed LE with new similarity has better visualization and achieves higher accuracy in classification.

  2. Hidden torsion, 3-manifolds, and homology cobordism

    Cha, Jae Choon


    This paper continues our exploration of homology cobordism of 3-manifolds using our recent results on Cheeger-Gromov rho-invariants associated to amenable representations. We introduce a new type of torsion in 3-manifold groups we call hidden torsion, and an algebraic approximation we call local hidden torsion. We construct infinitely many hyperbolic 3-manifolds which have local hidden torsion in the transfinite lower central subgroup. By realizing Cheeger-Gromov invariants over amenable groups, we show that our hyperbolic 3-manifolds are not pairwise homology cobordant, yet remain indistinguishable by any prior known homology cobordism invariants.

  3. Differential Calculus on N-Graded Manifolds

    G. Sardanashvily


    Full Text Available The differential calculus, including formalism of linear differential operators and the Chevalley–Eilenberg differential calculus, over N-graded commutative rings and on N-graded manifolds is developed. This is a straightforward generalization of the conventional differential calculus over commutative rings and also is the case of the differential calculus over Grassmann algebras and on Z2-graded manifolds. We follow the notion of an N-graded manifold as a local-ringed space whose body is a smooth manifold Z. A key point is that the graded derivation module of the structure ring of graded functions on an N-graded manifold is the structure ring of global sections of a certain smooth vector bundle over its body Z. Accordingly, the Chevalley–Eilenberg differential calculus on an N-graded manifold provides it with the de Rham complex of graded differential forms. This fact enables us to extend the differential calculus on N-graded manifolds to formalism of nonlinear differential operators, by analogy with that on smooth manifolds, in terms of graded jet manifolds of N-graded bundles.

  4. Pro jective vector fields on Finsler manifolds

    TIAN Huang-jia


    In this paper, we give the equation that characterizes projective vector fields on a Finsler manifold by the local coordinate. Moreover, we obtain a feature of the projective fields on the compact Finsler manifold with non-positive flag curvature and the non-existence of projective vector fields on the compact Finsler manifold with negative flag curvature. Furthermore, we deduce some expectable, but non-trivial relationships between geometric vector fields such as projective, affine, conformal, homothetic and Killing vector fields on a Finsler manifold.

  5. Stability of Strongly Gauduchon Manifolds under Modifications

    Popovici, Dan


    In our previous works on deformation limits of projective and Moishezon manifolds, we introduced and made crucial use of the notion of strongly Gauduchon metrics as a reinforcement of the earlier notion of Gauduchon metrics. Using direct and inverse images of closed positive currents of type $(1, \\, 1)$ and regularisation, we now show that compact complex manifolds carrying strongly Gauduchon metrics are stable under modifications. This stability property, known to fail for compact K\\"ahler manifolds, mirrors the modification stability of balanced manifolds proved by Alessandrini and Bassanelli.

  6. The Fibered Isomorphism Conjecture for Complex Manifolds



    In this paper we show that the Fibered Isomorphism Conjecture of Farrell and Jones,corresponding to the stable topological pseudoisotopy functor, is true for the fundamental groups of a class of complex manifolds. A consequence of this result is that the Whitehead group, reduced projective class groups and the negative K-groups of the fundamental groups of these manifolds vanish whenever the fundamental group is torsion free. We also prove the same results for a class of real manifolds including a large class of 3-manifolds which has a finite sheeted cover fibering over the circle.

  7. Manifold knowledge extraction and target recognition

    Chao, Cai; Hua, Zhou


    Advanced mammalian target identification derived from the perception of target's manifold and measurement manifolddistance. It does not rely on object's segmented accuracy, not depend on target's variety model, and adapt to a range of changes on targets. In this paper, based on the existed manifold learning algorithm, set up a new bionic automatic target recognition model, discussed the targets manifold knowledge acquisition and the knowledge expression architecture, gave a manifold knowledge-based new method for automatic target recognition. Experiments show that the new method has a strong adaptability to targets various transform, and has a very high correctly identification probability.

  8. Spectral gaps, inertial manifolds and kinematic dynamos

    Nunez, Manuel [Departamento de Analisis Matematico, Universidad de Valladolid, 47005 Valladolid (Spain)]. E-mail:


    Inertial manifolds are desirable objects when ones wishes a dynamical process to behave asymptotically as a finite-dimensional ones. Recently [Physica D 194 (2004) 297] these manifolds are constructed for the kinematic dynamo problem with time-periodic velocity. It turns out, however, that the conditions imposed on the fluid velocity to guarantee the existence of inertial manifolds are too demanding, in the sense that they imply that all the solutions tend exponentially to zero. The inertial manifolds are meaningful because they represent different decay rates, but the classical dynamos where the magnetic field is maintained or grows are not covered by this approach, at least until more refined estimates are found.

  9. Manifold learning in protein interactomes.

    Marras, Elisabetta; Travaglione, Antonella; Capobianco, Enrico


    Many studies and applications in the post-genomic era have been devoted to analyze complex biological systems by computational inference methods. We propose to apply manifold learning methods to protein-protein interaction networks (PPIN). Despite their popularity in data-intensive applications, these methods have received limited attention in the context of biological networks. We show that there is both utility and unexplored potential in adopting manifold learning for network inference purposes. In particular, the following advantages are highlighted: (a) fusion with diagnostic statistical tools designed to assign significance to protein interactions based on pre-selected topological features; (b) dissection into components of the interactome in order to elucidate global and local connectivity organization; (c) relevance of embedding the interactome in reduced dimensions for biological validation purposes. We have compared the performances of three well-known techniques--kernel-PCA, RADICAL ICA, and ISOMAP--relatively to their power of mapping the interactome onto new coordinate dimensions where important associations among proteins can be detected, and then back projected such that the corresponding sub-interactomes are reconstructed. This recovery has been done selectively, by using significant information according to a robust statistical procedure, and then standard biological annotation has been provided to validate the results. We expect that a byproduct of using subspace analysis by the proposed techniques is a possible calibration of interactome modularity studies. Supplementary Material is available online at

  10. Characterizing humans on Riemannian manifolds.

    Tosato, Diego; Spera, Mauro; Cristani, Marco; Murino, Vittorio


    In surveillance applications, head and body orientation of people is of primary importance for assessing many behavioral traits. Unfortunately, in this context people are often encoded by a few, noisy pixels so that their characterization is difficult. We face this issue, proposing a computational framework which is based on an expressive descriptor, the covariance of features. Covariances have been employed for pedestrian detection purposes, actually a binary classification problem on Riemannian manifolds. In this paper, we show how to extend to the multiclassification case, presenting a novel descriptor, named weighted array of covariances, especially suited for dealing with tiny image representations. The extension requires a novel differential geometry approach in which covariances are projected on a unique tangent space where standard machine learning techniques can be applied. In particular, we adopt the Campbell-Baker-Hausdorff expansion as a means to approximate on the tangent space the genuine (geodesic) distances on the manifold in a very efficient way. We test our methodology on multiple benchmark datasets, and also propose new testing sets, getting convincing results in all the cases.

  11. Characteristics of liquid water removal from the gas diffusion layer by reactant flow in a PEM fuel cell

    Jiao, K.; Park, J.; Li, X. [Waterloo Univ., ON (Canada). Dept. of Mechanical and Mechatronics Engineering


    Water in proton exchange membrane (PEM) fuel cells is accumulated in the gas diffusion layer (GDL) and removed by the static pressure gradient caused by the fast reactant flow in the flow channel. Reactants can leak into the neighbouring channels via the porous GDL and inhibit the removal of liquid water. This study examined the characteristics of liquid water removal from the GDL by measuring unsteady pressure drop in a PEM fuel cell in which the GDL was initially wetted with liquid water. GDL thickness was controlled by inserting metal shims between the fuel cell plates. The experiment showed that the amount of pressure drop is inversely proportional to GDL thickness. Thicker GDLs with higher porosity levels increased cross flow. Liquid water removal was also influenced by the change of inlet Reynolds number, which demonstrated that air flow rates must be high enough for efficient water removal. Various GDL porosities and permeabilities were calculated, and their influence on the characteristics of liquid water removal were evaluated. A transparent flow channel design was used to visualize water movement in the GDL. It was concluded that the effects of cross flow and GDL compression levels should be considered in the analysis and design of PEM fuel cells. 23 refs., 8 figs.

  12. Addition-type polyimides from solutions of monomeric reactants

    Delvigs, P.; Serafini, T. T.; Lightsey, G. R.


    The monomeric reactants approach was used to fabricate addition-type polyimide/graphite fiber composites with improved mechanical properties and thermal stability characteristics over those of composites derived from addition-type amide acid prepolymers. A screening study of 24 different monomer combinations was performed. The results of a more extensive investigation of a selected number of monomer combinations showed that the combination providing the best thermomechanical properties was 5-norbornene-2,3-dicarboxylic acid monomethyl ester/4,4'-methylenedianiline/3,3'4,4'-benzophenone tetracarboxylic acid dimethyl ester at a molar ratio of 2/3.09/2.09.

  13. Optimization of manifold design for 1 kW-class flat-tubular solid oxide fuel cell stack operating on reformed natural gas

    Rashid, Kashif; Dong, Sang Keun; Khan, Rashid Ali; Park, Seung Hwan


    This study focuses on optimizing the manifold design for a 1 kW-class flat-tubular solid oxide fuel cell stack by performing extensive three-dimensional numerical simulations on numerous manifold designs. The stack flow uniformity and the standard flow deviation indexes are implemented to characterize the flow distributions in the stack and among the channels of FT-SOFC's, respectively. The results of the CFD calculations demonstrate that the remodeled manifold without diffuser inlets and 6 mm diffuser front is the best among investigated designs with uniformity index of 0.996 and maximum standard flow deviation of 0.423%. To understand the effect of manifold design on the performance of stack, both generic and developed manifold designs are investigated by applying electrochemical and internal reforming reactions modeling. The simulation results of the stack with generic manifold are validated using experimental data and then validated models are adopted to simulate the stack with the developed manifold design. The results reveal that the stack with developed manifold design achieves more uniform distribution of species, temperature, and current density with comparatively lower system pressure drop. In addition, the results also showed ∼8% increase in the maximum output power due to the implementation of uniform fuel velocity distributions in the cells.

  14. Practical experience applied to the design of injection and sample manifolds to perform in-place surveillance tests according to ANSI/ASME N-510

    Banks, E.M.; Wikoff, W.O.; Shaffer, L.L. [NUCON International, Inc., Columbus, OH (United States)


    At the current level of maturity and experience in the nuclear industry, regarding testing of air treatment systems, it is now possible to design and qualify injection and sample manifolds for most applications. While the qualification of sample manifolds is still in its infancy, injection manifolds have reached a mature stage that helps to eliminate the {open_quotes}hit or miss{close_quotes} type of design. During the design phase, manifolds can be adjusted to compensate for poor airflow distribution, laminar flow conditions, and to take advantage of any system attributes. Experience has shown that knowing the system attributes before the design phase begins is an essential element to a successful manifold design. The use of a spreadsheet type program commonly found on most personal computers can afford a greater flexibility and a reduction in time spent in the design phase. The experience gained from several generations of manifold design has culminated in a set of general design guidelines. Use of these guidelines, along with a good understanding of the type of testing (theoretical and practical), can result in a good manifold design requiring little or no field modification. The requirements for manifolds came about because of the use of multiple banks of components and unconventional housing inlet configurations. Multiple banks of adsorbers and pre and post HEPA`s required that each bank be tested to insure that each one does not exceed a specific allowable leakage criterion. 5 refs., 5 figs., 1 tab.

  15. Integrability conditions on Engel-type manifolds

    Calin, Ovidiu; Chang, Der-Chen; Hu, Jishan


    We introduce the concept of Engel manifold, as a manifold that resembles locally the Engel group, and find the integrability conditions of the associated sub-elliptic system , . These are given by , . Then an explicit construction of the solution involving an integral representation is provided, which corresponds to a Poincaré-type lemma for the Engel's distribution.

  16. Target manifold formation using a quadratic SDF

    Hester, Charles F.; Risko, Kelly K. D.


    Synthetic Discriminant Function (SDF) formulation of correlation filters provides constraints for forming target subspaces for a target set. In this paper we extend the SDF formulation to include quadratic constraints and use this solution to form nonlinear manifolds in the target space. The theory for forming these manifolds will be developed and demonstrated with data.

  17. Einstein Constraints on Asymptotically Euclidean Manifolds

    Choquet-Bruhat, Y; York, J W; Choquet-Bruhat, Yvonne; Isenberg, James; York, James W.


    We consider the Einstein constraints on asymptotically euclidean manifolds $M$ of dimension $n \\geq 3$ with sources of both scaled and unscaled types. We extend to asymptotically euclidean manifolds the constructive method of proof of existence. We also treat discontinuous scaled sources. In the last section we obtain new results in the case of non-constant mean curvature.

  18. Rank and genus of 3-manifolds

    Li, Tao


    We construct a counterexample to the Rank versus Genus Conjecture, i.e. a closed orientable hyperbolic 3-manifold with rank of its fundamental group smaller than its Heegaard genus. Moreover, we show that the discrepancy between rank and Heegaard genus can be arbitrarily large for hyperbolic 3-manifolds. We also construct toroidal such examples containing hyperbolic JSJ pieces.

  19. An Explicit Nonlinear Mapping for Manifold Learning.

    Qiao, Hong; Zhang, Peng; Wang, Di; Zhang, Bo


    Manifold learning is a hot research topic in the held of computer science and has many applications in the real world. A main drawback of manifold learning methods is, however, that there are no explicit mappings from the input data manifold to the output embedding. This prohibits the application of manifold learning methods in many practical problems such as classification and target detection. Previously, in order to provide explicit mappings for manifold learning methods, many methods have been proposed to get an approximate explicit representation mapping with the assumption that there exists a linear projection between the high-dimensional data samples and their low-dimensional embedding. However, this linearity assumption may be too restrictive. In this paper, an explicit nonlinear mapping is proposed for manifold learning, based on the assumption that there exists a polynomial mapping between the high-dimensional data samples and their low-dimensional representations. As far as we know, this is the hrst time that an explicit nonlinear mapping for manifold learning is given. In particular, we apply this to the method of locally linear embedding and derive an explicit nonlinear manifold learning algorithm, which is named neighborhood preserving polynomial embedding. Experimental results on both synthetic and real-world data show that the proposed mapping is much more effective in preserving the local neighborhood information and the nonlinear geometry of the high-dimensional data samples than previous work.

  20. Gauged supergravities from Bianchi's group manifolds

    Bergshoeff, E; Gran, U; Linares, R; Nielsen, M; Ortin, T; Roest, D


    We construct maximal D = 8 gauged supergravities by the reduction of D = I I supergravity over three-dimensional group manifolds. Such manifolds are classified into two classes, A and B, and eleven types. This Bianchi classification carries over to the gauged supergravities. The class A theories hav

  1. Simplicial approach to derived differential manifolds

    Borisov, Dennis


    Derived differential manifolds are constructed using the usual homotopy theory of simplicial rings of smooth functions. They are proved to be equivalent to derived differential manifolds of finite type, constructed using homotopy sheaves of homotopy rings (D.Spivak), thus preserving the classical cobordism ring. This reduction to the usual algebraic homotopy can potentially lead to virtual fundamental classes beyond obstruction theory.

  2. Strictly convex functions on complete Finsler manifolds



    The purpose of the present paper is to investigate the influence of strictly convex functions on the metric structures of complete Finsler manifolds. More precisely we discuss the properties of the group of isometries and the exponential maps on a complete Finsler manifold admitting strictly convex functions.

  3. Persistence of noncompact normally hyperbolic invariant manifolds in bounded geometry

    Eldering, Jaap


    We prove a persistence result for noncompact normally hyperbolic invariant manifolds in Riemannian manifolds of bounded geometry. The bounded geometry of the ambient manifold is a crucial assumption in order to control the uniformity of all estimates throughout the proof.

  4. Warped product submanifolds of Lorentzian paracosymplectic manifolds

    Perkta\\cs, Selcen Yüksel; Kele\\cs, Sad\\ik


    In this paper we study the warped product submanifolds of a Lorentzian paracosymplectic manifold and obtain some nonexistence results. We show that a warped product semi-invariant submanifold in the form {$M=M_{T}\\times_{f}M_{\\bot}$} of Lorentzian paracosymplectic manifold such that the characteristic vector field is normal to $M$ is an usual Riemannian product manifold where totally geodesic and totally umbilical submanifolds of warped product are invariant and anti-invariant, respectively. We prove that the distributions involved in the definition of a warped product semi-invariant submanifold are always integrable. A necessary and sufficient condition for a semi-invariant submanifold of a Lorentzian paracosymplectic manifold to be warped product semi-invariant submanifold is obtained. We also investigate the existence and nonexistence of warped product semi-slant and warped product anti-slant submanifolds in a Lorentzian paracosymplectic manifold.

  5. Manifold-based learning and synthesis.

    Huang, Dong; Yi, Zhang; Pu, Xiaorong


    This paper proposes a new approach to analyze high-dimensional data set using low-dimensional manifold. This manifold-based approach provides a unified formulation for both learning from and synthesis back to the input space. The manifold learning method desires to solve two problems in many existing algorithms. The first problem is the local manifold distortion caused by the cost averaging of the global cost optimization during the manifold learning. The second problem results from the unit variance constraint generally used in those spectral embedding methods where global metric information is lost. For the out-of-sample data points, the proposed approach gives simple solutions to transverse between the input space and the feature space. In addition, this method can be used to estimate the underlying dimension and is robust to the number of neighbors. Experiments on both low-dimensional data and real image data are performed to illustrate the theory.

  6. Heterotic model building: 16 special manifolds

    He, Yang-Hui [Department of Mathematics, City University,London, EC1V 0HB (United Kingdom); School of Physics, NanKai University,Tianjin, 300071 (China); Merton College, University of Oxford,Oxford OX14JD (United Kingdom); Lee, Seung-Joo [School of Physics, Korea Institute for Advanced Study,Seoul 130-722 (Korea, Republic of); Lukas, Andre; Sun, Chuang [Rudolf Peierls Centre for Theoretical Physics, University of Oxford,1 Keble Road, Oxford OX1 3NP (United Kingdom)


    We study heterotic model building on 16 specific Calabi-Yau manifolds constructed as hypersurfaces in toric four-folds. These 16 manifolds are the only ones among the more than half a billion manifolds in the Kreuzer-Skarke list with a non-trivial first fundamental group. We classify the line bundle models on these manifolds, both for SU(5) and SO(10) GUTs, which lead to consistent supersymmetric string vacua and have three chiral families. A total of about 29000 models is found, most of them corresponding to SO(10) GUTs. These models constitute a starting point for detailed heterotic model building on Calabi-Yau manifolds in the Kreuzer-Skarke list. The data for these models can be downloaded

  7. Method for Determining Optimum Injector Inlet Geometry

    Trinh, Huu P. (Inventor); Myers, W. Neill (Inventor)


    A method for determining the optimum inlet geometry of a liquid rocket engine swirl injector includes obtaining a throttleable level phase value, volume flow rate, chamber pressure, liquid propellant density, inlet injector pressure, desired target spray angle and desired target optimum delta pressure value between an inlet and a chamber for a plurality of engine stages. The method calculates the tangential inlet area for each throttleable stage. The method also uses correlation between the tangential inlet areas and delta pressure values to calculate the spring displacement and variable inlet geometry of a liquid rocket engine swirl injector.

  8. Centrifugal pump inlet pressure site affects measurement.

    Augustin, Simon; Horton, Alison; Butt, Warwick; Bennett, Martin; Horton, Stephen


    During extracorporeal life support (ECLS), blood is exposed to a myriad of unphysiological factors that can affect outcome. One aspect of this is the sub-atmospheric pressure generated by the ECLS pump and imparted to blood elements along the pump inlet line. This pressure can be measured on the inlet line close to the pump head by adding a connector, or at the venous cannula connection site. We compared the two measurement sites located at both points; between the venous cannula-inlet tubing and inlet tubing-pump, with a range of cannulae and flows. We also investigated the effects on inlet pressure from pump afterload and increasing inlet tubing length.

  9. Heisenberg symmetry and hypermultiplet manifolds

    Antoniadis, Ignatios; Petropoulos, P Marios; Siampos, Konstantinos


    We study the emergence of Heisenberg (Bianchi II) algebra in hyper-K\\"ahler and quaternionic spaces. This is motivated by the r\\^ole these spaces with this symmetry play in $\\mathcal{N}=2$ hypermultiplet scalar manifolds. We show how to construct related pairs of hyper-K\\"ahler and quaternionic spaces under general symmetry assumptions, the former being a zooming-in limit of the latter at vanishing cosmological constant. We further apply this method for the two hyper-K\\"ahler spaces with Heisenberg algebra, which is reduced to $U(1)\\times U(1)$ at the quaternionic level. We also show that no quaternionic spaces exist with a strict Heisenberg symmetry -- as opposed to $\\text{Heisenberg} \\ltimes U(1)$. We finally discuss the realization of the latter by gauging appropriate $Sp(2,4)$ generators in $\\mathcal{N}=2$ conformal supergravity.

  10. Moving Manifolds in Electromagnetic Fields

    David V. Svintradze


    Full Text Available We propose dynamic non-linear equations for moving surfaces in an electromagnetic field. The field is induced by a material body with a boundary of the surface. Correspondingly the potential energy, set by the field at the boundary can be written as an addition of four-potential times four-current to a contraction of the electromagnetic tensor. Proper application of the minimal action principle to the system Lagrangian yields dynamic non-linear equations for moving three dimensional manifolds in electromagnetic fields. The equations in different conditions simplify to Maxwell equations for massless three surfaces, to Euler equations for a dynamic fluid, to magneto-hydrodynamic equations and to the Poisson-Boltzmann equation.

  11. Heisenberg symmetry and hypermultiplet manifolds

    Ignatios Antoniadis


    Full Text Available We study the emergence of Heisenberg (Bianchi II algebra in hyper-Kähler and quaternionic spaces. This is motivated by the rôle these spaces with this symmetry play in N=2 hypermultiplet scalar manifolds. We show how to construct related pairs of hyper-Kähler and quaternionic spaces under general symmetry assumptions, the former being a zooming-in limit of the latter at vanishing scalar curvature. We further apply this method for the two hyper-Kähler spaces with Heisenberg algebra, which is reduced to U(1×U(1 at the quaternionic level. We also show that no quaternionic spaces exist with a strict Heisenberg symmetry – as opposed to Heisenberg⋉U(1. We finally discuss the realization of the latter by gauging appropriate Sp(2,4 generators in N=2 conformal supergravity.

  12. Function theory on symplectic manifolds

    Polterovich, Leonid


    This is a book on symplectic topology, a rapidly developing field of mathematics which originated as a geometric tool for problems of classical mechanics. Since the 1980s, powerful methods such as Gromov's pseudo-holomorphic curves and Morse-Floer theory on loop spaces gave rise to the discovery of unexpected symplectic phenomena. The present book focuses on function spaces associated with a symplectic manifold. A number of recent advances show that these spaces exhibit intriguing properties and structures, giving rise to an alternative intuition and new tools in symplectic topology. The book provides an essentially self-contained introduction into these developments along with applications to symplectic topology, algebra and geometry of symplectomorphism groups, Hamiltonian dynamics and quantum mechanics. It will appeal to researchers and students from the graduate level onwards. I like the spirit of this book. It formulates concepts clearly and explains the relationship between them. The subject matter is i...

  13. Harmonic space and quaternionic manifolds

    Galperin, A; Ogievetsky, O V


    We find a principle of harmonic analyticity underlying the quaternionic (quaternion-K\\"ahler) geometry and solve the differential constraints which define this geometry. To this end the original $4n$-dimensional quaternionic manifold is extended to a bi-harmonic space. The latter includes additional harmonic coordinates associated with both the tangent local $Sp(1)$ group and an extra rigid $SU(2)$ group rotating the complex structures. Then the constraints can be rewritten as integrability conditions for the existence of an analytic subspace in the bi-harmonic space and solved in terms of two unconstrained potentials on the analytic subspace. Geometrically, the potentials have the meaning of vielbeins associated with the harmonic coordinates. We also establish a one-to-one correspondence between the quaternionic spaces and off-shell $N=2$ supersymmetric sigma-models coupled to $N=2$ supergravity. The general $N=2$ sigma-model Lagrangian when written in the harmonic superspace is composed of the quaternionic ...

  14. Manifold Matching for High-Dimensional Pattern Recognition

    HOTTA, Seiji


    In this chapter manifold matching for high-dimensional pattern classification was described. The topics described in this chapter were summarized as follows: The meaning and effectiveness of manifold matching The similarity between various classifiers from the point of view of manifold matching Accuracy improvement for manifold matching Learning rules for manifold matching Experimental results on handwritten digit datasets showed that manifold matching achieved lower error rates than other cl...

  15. Harmonic Riemannian Maps on Locally Conformal Kaehler Manifolds

    Bayram Sahin


    We study harmonic Riemannian maps on locally conformal Kaehler manifolds ($lcK$ manifolds). We show that if a Riemannian holomorphic map between $lcK$ manifolds is harmonic, then the Lee vector field of the domain belongs to the kernel of the Riemannian map under a condition. When the domain is Kaehler, we prove that a Riemannian holomorphic map is harmonic if and only if the $lcK$ manifold is Kaehler. Then we find similar results for Riemannian maps between $lcK$ manifolds and Sasakian manifolds. Finally, we check the constancy of some maps between almost complex (or almost contact) manifolds and almost product manifolds.

  16. Discriminative sparse coding on multi-manifolds

    Wang, J.J.-Y.


    Sparse coding has been popularly used as an effective data representation method in various applications, such as computer vision, medical imaging and bioinformatics. However, the conventional sparse coding algorithms and their manifold-regularized variants (graph sparse coding and Laplacian sparse coding), learn codebooks and codes in an unsupervised manner and neglect class information that is available in the training set. To address this problem, we propose a novel discriminative sparse coding method based on multi-manifolds, that learns discriminative class-conditioned codebooks and sparse codes from both data feature spaces and class labels. First, the entire training set is partitioned into multiple manifolds according to the class labels. Then, we formulate the sparse coding as a manifold-manifold matching problem and learn class-conditioned codebooks and codes to maximize the manifold margins of different classes. Lastly, we present a data sample-manifold matching-based strategy to classify the unlabeled data samples. Experimental results on somatic mutations identification and breast tumor classification based on ultrasonic images demonstrate the efficacy of the proposed data representation and classification approach. 2013 The Authors. All rights reserved.

  17. Does the presence of bacteria effect basaltic glass dissolution rates? 1: Dead Pseudomonas reactants

    Stockmann, Gabrielle J.; Shirokova, Liudmila S.; Pokrovsky, Oleg S.; Oelkers, Eric H.; Benezeth, Pascale


    Basaltic glass and crystalline basalt formations in Iceland have been suggested for industrial CO2 storage due to their porous and permeable properties and high reactivity. Acid CO2-saturated waters in contact with basaltic glass will lead to rapid dissolution of the glass and release of divalent cations, (Ca2+, Mg2+, Fe2+) that can react to form stable carbonates and thereby trap the CO2. However, the basalt formations in Iceland not only contains glass and mineral assemblages, but also host microbiological communities that either by their presence or by active involvement in chemical reactions could affect the amount of basaltic glass being dissolved and CO2 being trapped. Samples of natural bacteria communities from the CO2 storage grounds in Iceland were collected, separated, and purified using agar plate technique and cultured under laboratory conditions in nutrient broth-rich media. Heterotrophic aerobic Gram-negative strain of Pseudomonas reactants was selected for a series of flow-through experiments aimed at evaluation of basaltic glass dissolution rate in the presense of increasing amounts of dead bacteria and their lysis products. The experiments were carried out using mixed-flow reactors at pH 4, 6, 8 and 10 at 25 °C. Each of the four reactors contained 1 gram of basaltic glass of the size fraction 45-125 μm. This glass was dissolved in ~ 0.01 M buffer solutions (acetate, MES, bicarbonate and carbonate+bicarbonate mixture) of the desired pH. All experiments ran 2 months, keeping the flowrate and temperature stable and only changing the concentration of dead bacteria in the inlet solutions (from 0 to 430 mg/L). Experiments were performed in sterile conditions, and bacterial growth was prevented by adding NaN3 to the inlet solutions. Routine culturing of bacteria on the agar plates confirmed the sterility of experiments. Samples of outlet solutions were analyzed for major cations and trace elements by ICP-MS. Results demonstrate a slight decrease in the

  18. Calculating fusion neutron energy spectra from arbitrary reactant distributions

    Eriksson, J.; Conroy, S.; Andersson Sundén, E.; Hellesen, C.


    The Directional Relativistic Spectrum Simulator (DRESS) code can perform Monte-Carlo calculations of reaction product spectra from arbitrary reactant distributions, using fully relativistic kinematics. The code is set up to calculate energy spectra from neutrons and alpha particles produced in the D(d, n)3He and T(d, n)4He fusion reactions, but any two-body reaction can be simulated by including the corresponding cross section. The code has been thoroughly tested. The kinematics calculations have been benchmarked against the kinematics module of the ROOT Data Analysis Framework. Calculated neutron energy spectra have been validated against tabulated fusion reactivities and against an exact analytical expression for the thermonuclear fusion neutron spectrum, with good agreement. The DRESS code will be used as the core of a detailed synthetic diagnostic framework for neutron measurements at the JET and MAST tokamaks.

  19. Space time manifolds and contact structures

    K. L. Duggal


    Full Text Available A new class of contact manifolds (carring a global non-vanishing timelike vector field is introduced to establish a relation between spacetime manifolds and contact structures. We show that odd dimensional strongly causal (in particular, globally hyperbolic spacetimes can carry a regular contact structure. As examples, we present a causal spacetime with a non regular contact structure and a physical model [Gödel Universe] of Homogeneous contact manifold. Finally, we construct a model of 4-dimensional spacetime of general relativity as a contact CR-submanifold.

  20. Higher Order Hessian Structures on Manifolds

    R David Kumar


    In this paper we define th order Hessian structures on manifolds and study them. In particular, when =3, we make a detailed study and establish a one-to-one correspondence between third-order Hessian structures and a certain class of connections on the second-order tangent bundle of a manifold. Further, we show that a connection on the tangent bundle of a manifold induces a connection on the second-order tangent bundle. Also we define second-order geodesics of special second-order connection which gives a geometric characterization of symmetric third-order Hessian structures.

  1. Loops in Reeb Graphs of 2-Manifolds

    Cole-McLaughlin, K; Edelsbrunner, H; Harer, J; Natarajan, V; Pascucci, V


    Given a Morse function f over a 2-manifold with or without boundary, the Reeb graph is obtained by contracting the connected components of the level sets to points. We prove tight upper and lower bounds on the number of loops in the Reeb graph that depend on the genus, the number of boundary components, and whether or not the 2-manifold is orientable. We also give an algorithm that constructs the Reeb graph in time O(n log n), where n is the number of edges in the triangulation used to represent the 2-manifold and the Morse function.

  2. Loops in Reeb Graphs of 2-Manifolds

    Cole-McLaughlin, K; Edelsbrunner, H; Harer, J; Natarajan, V; Pascucci, V


    Given a Morse function f over a 2-manifold with or without boundary, the Reeb graph is obtained by contracting the connected components of the level sets to points. We prove tight upper and lower bounds on the number of loops in the Reeb graph that depend on the genus, the number of boundary components, and whether or not the 2-manifold is orientable. We also give an algorithm that constructs the Reeb graph in time O(n log n), where n is the number of edges in the triangulation used to represent the 2-manifold and the Morse function.

  3. The impact of reactants composition and temperature on the flow structure in a wake stabilized laminar lean premixed CH4/H2/air flames; mechanism and scaling

    Michaels, D.


    In this paper we investigate the role of reactants composition and temperature in defining the steady flow structure in bluff body stabilized premixed flames. The study was motivated by experiments which showed that the flow structure and stability map for different fuels and inlet conditions collapse using the extinction strain rate as the chemical time scale. The investigation is conducted using a laminar lean premixed flame stabilized on a heat conducting bluff-body. Calculations are performed for a wide range of mixtures of CH4/H2/air (0.35 ≤ ϕ ≤ 0.75, 0 ≤ %H2 ≤ 40, 300 ≤ Tin [K] ≤ 500) in order to systematically vary the burning velocity (2.0–35.6 cm/s), dilatation ratio (2.7–6.4), and extinction strain rate (106–2924 1/s). The model is based on a fully resolved unsteady two-dimensional flow with detailed chemistry and species transport, and with no artificial flame anchoring boundary conditions. Calculations reveal that the recirculation zone length correlates with a chemical time scale based on the flame extinction strain rate corresponding to the inlet fuel composition, stoichiometry, pressure and temperature; and are consistent with experimental data in literature. It was found that in the wake region the flame is highly stretched and its location and interaction with the flow is governed by the reactants combustion characteristics under high strain.

  4. The Hodge theory of projective manifolds

    de Cataldo, Mark Andrea


    This book is a written-up and expanded version of eight lectures on the Hodge theory of projective manifolds. It assumes very little background and aims at describing how the theory becomes progressively richer and more beautiful as one specializes from Riemannian, to Kähler, to complex projective manifolds. Though the proof of the Hodge Theorem is omitted, its consequences - topological, geometrical and algebraic - are discussed at some length. The special properties of complex projective manifolds constitute an important body of knowledge and readers are guided through it with the help of selected exercises. Despite starting with very few prerequisites, the concluding chapter works out, in the meaningful special case of surfaces, the proof of a special property of maps between complex projective manifolds, which was discovered only quite recently.

  5. A Class of Homogeneous Einstein Manifolds

    Yifang KANG; Ke LIANG


    A Riemannian manifold (M,g) is called Einstein manifold if its Ricci tensor satisfies r=c·g for some constant c. General existence results are hard to obtain,e.g., it is as yet unknown whether every compact manifold admits an Einstein metric. A natural approach is to impose additional homogeneous assumptions. M. Y. Wang and W. Ziller have got some results on compact homogeneous space G/H. They investigate standard homogeneous metrics, the metric induced by Killing form on G/H, and get some classification results. In this paper some more general homogeneous metrics on some homogeneous space G/H are studies, and a necessary and sufficient condition for this metric to be Einstein is given. The authors also give some examples of Einstein manifolds with non-standard homogeneous metrics.

  6. Branched standard spines of 3-manifolds

    Benedetti, Riccardo


    This book provides a unified combinatorial realization of the categroies of (closed, oriented) 3-manifolds, combed 3-manifolds, framed 3-manifolds and spin 3-manifolds. In all four cases the objects of the realization are finite enhanced graphs, and only finitely many local moves have to be taken into account. These realizations are based on the notion of branched standard spine, introduced in the book as a combination of the notion of branched surface with that of standard spine. The book is intended for readers interested in low-dimensional topology, and some familiarity with the basics is assumed. A list of questions, some of which concerning relations with the theory of quantum invariants, is enclosed.


    Guo-liang Xu; Chandrajit L. Bajaj


    In this paper, we provide simple and explicit formulas for computing Riemannian cur-vatures, mean curvature vectors, principal curvatures and principal directions for a 2-dimensional Riemannian manifold embedded in IRk with k ≥ 3.

  8. 3-manifold groups are virtually residually p

    Aschenbrenner, Matthias


    Given a prime $p$, a group is called residually $p$ if the intersection of its $p$-power index normal subgroups is trivial. A group is called virtually residually $p$ if it has a finite index subgroup which is residually $p$. It is well-known that finitely generated linear groups over fields of characteristic zero are virtually residually $p$ for all but finitely many $p$. In particular, fundamental groups of hyperbolic $3$-manifolds are virtually residually $p$. It is also well-known that fundamental groups of $3$-manifolds are residually finite. In this paper we prove a common generalization of these results: every $3$-manifold group is virtually residually $p$ for all but finitely many~$p$. This gives evidence for the conjecture (Thurston) that fundamental groups of $3$-manifolds are linear groups.

  9. Hierarchical manifold learning for regional image analysis.

    Bhatia, Kanwal K; Rao, Anil; Price, Anthony N; Wolz, Robin; Hajnal, Joseph V; Rueckert, Daniel


    We present a novel method of hierarchical manifold learning which aims to automatically discover regional properties of image datasets. While traditional manifold learning methods have become widely used for dimensionality reduction in medical imaging, they suffer from only being able to consider whole images as single data points. We extend conventional techniques by additionally examining local variations, in order to produce spatially-varying manifold embeddings that characterize a given dataset. This involves constructing manifolds in a hierarchy of image patches of increasing granularity, while ensuring consistency between hierarchy levels. We demonstrate the utility of our method in two very different settings: 1) to learn the regional correlations in motion within a sequence of time-resolved MR images of the thoracic cavity; 2) to find discriminative regions of 3-D brain MR images associated with neurodegenerative disease.

  10. Regional manifold learning for disease classification.

    Ye, Dong Hye; Desjardins, Benoit; Hamm, Jihun; Litt, Harold; Pohl, Kilian M


    While manifold learning from images itself has become widely used in medical image analysis, the accuracy of existing implementations suffers from viewing each image as a single data point. To address this issue, we parcellate images into regions and then separately learn the manifold for each region. We use the regional manifolds as low-dimensional descriptors of high-dimensional morphological image features, which are then fed into a classifier to identify regions affected by disease. We produce a single ensemble decision for each scan by the weighted combination of these regional classification results. Each weight is determined by the regional accuracy of detecting the disease. When applied to cardiac magnetic resonance imaging of 50 normal controls and 50 patients with reconstructive surgery of Tetralogy of Fallot, our method achieves significantly better classification accuracy than approaches learning a single manifold across the entire image domain.

  11. Particle Filtering on the Audio Localization Manifold

    Ettinger, Evan


    We present a novel particle filtering algorithm for tracking a moving sound source using a microphone array. If there are N microphones in the array, we track all $N \\choose 2$ delays with a single particle filter over time. Since it is known that tracking in high dimensions is rife with difficulties, we instead integrate into our particle filter a model of the low dimensional manifold that these delays lie on. Our manifold model is based off of work on modeling low dimensional manifolds via random projection trees [1]. In addition, we also introduce a new weighting scheme to our particle filtering algorithm based on recent advancements in online learning. We show that our novel TDOA tracking algorithm that integrates a manifold model can greatly outperform standard particle filters on this audio tracking task.

  12. Polynomial chaos representation of databases on manifolds

    Soize, C., E-mail: [Université Paris-Est, Laboratoire Modélisation et Simulation Multi-Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-La-Vallée, Cedex 2 (France); Ghanem, R., E-mail: [University of Southern California, 210 KAP Hall, Los Angeles, CA 90089 (United States)


    Characterizing the polynomial chaos expansion (PCE) of a vector-valued random variable with probability distribution concentrated on a manifold is a relevant problem in data-driven settings. The probability distribution of such random vectors is multimodal in general, leading to potentially very slow convergence of the PCE. In this paper, we build on a recent development for estimating and sampling from probabilities concentrated on a diffusion manifold. The proposed methodology constructs a PCE of the random vector together with an associated generator that samples from the target probability distribution which is estimated from data concentrated in the neighborhood of the manifold. The method is robust and remains efficient for high dimension and large datasets. The resulting polynomial chaos construction on manifolds permits the adaptation of many uncertainty quantification and statistical tools to emerging questions motivated by data-driven queries.

  13. Cohomogeneity Two Actions on Flat Riemannian Manifolds



    In this paper, we study fiat Riemannian manifolds which have codimension two orbits,under the action of a closed and connected Lie group G of isometries. We assume that G has fixedpoints, then characterize M and orbits of M.

  14. Tidal Motion in a Complex Inlet and Bay System, Ponce de Leon Inlet, Florida


    REPORT TYPE N/A 3. DATES COVERED - 4. TITLE AND SUBTITLE Tidal Motion in a Complex Inlet and Bay System, Ponce de Leon Inlet, Florida 5a...investigated in Ponce de Leon (Ponce) Inlet, Florida, and its bay channels through a 10-week data-collection campaign and two-dimensional numerical...Beach, Florida Summer 2000 Tidal Motion in a Complex Inlet and Bay System, Ponce de Leon Inlet, Florida Adele Militellot and Gary A. Zarillo:j: t

  15. Mathematical Background of Formalism of Operator Manifold

    Ter-Kazarian, G T


    The analysis of mathematical structure of the method of operator manifold guides our discussion. The latter is a still wider generalization of the method of secondary quantization with appropriate expansion over the geometric objects. The nature of operator manifold provides its elements with both quantum field and geometry aspects, a detailed study of which is a subject of present paper. It yields a quantization of geometry differing in principle from all earlier suggested schemes.

  16. The convexity radius of a Riemannian manifold

    Dibble, James


    The ratio of convexity radius over injectivity radius may be made arbitrarily small within the class of compact Riemannian manifolds of any fixed dimension at least two. This is proved using Gulliver's method of constructing manifolds with focal points but no conjugate points. The approach is suggested by a characterization of the convexity radius that resembles a classical result of Klingenberg about the injectivity radius.

  17. Multiply manifolded molten carbonate fuel cells

    Krumpelt, M.; Roche, M.F.; Geyer, H.K.; Johnson, S.A.


    This study consists of research and development activities related to the concept of a molten carbonate fuel cell (MCFC) with multiple manifolds. Objective is to develop an MCFC having a higher power density and a longer life than other MCFC designs. The higher power density will result from thinner gas flow channels; the extended life will result from reduced temperature gradients. Simplification of the gas flow channels and current collectors may also significantly reduce cost for the multiply manifolded MCFC.

  18. Blowing up generalized Kahler 4-manifolds

    Cavalcanti, Gil R


    We show that the blow-up of a generalized Kahler 4-manifold in a nondegenerate complex point admits a generalized Kahler metric. As with the blow-up of complex surfaces, this metric may be chosen to coincide with the original outside a tubular neighbourhood of the exceptional divisor. To accomplish this, we develop a blow-up operation for bi-Hermitian manifolds.

  19. On some applications of invariant manifolds

    Xi-Yun Hou; Lin Liu; Yu-Hui Zhao


    Taking transfer orbits of a collinear libration point probe, a lunar probe and an interplanetary probe as examples, some applications of stable and unstable invariant manifolds of the restricted three-body problem are discussed. Research shows that transfer energy is not necessarily conserved when invariant manifolds are used. For the cases in which the transfer energy is conserved, the cost is a much longer transfer time.

  20. Quaternionic-like manifolds and homogeneous twistor spaces.

    Pantilie, Radu


    Motivated by the quaternionic geometry corresponding to the homogeneous complex manifolds endowed with (holomorphically) embedded spheres, we introduce and initiate the study of the 'quaternionic-like manifolds'. These contain, as particular subclasses, the CR quaternionic and the ρ-quaternionic manifolds. Moreover, the notion of 'heaven space' finds its adequate level of generality in this setting: (essentially) any real analytic quaternionic-like manifold admits a (germ) unique heaven space, which is a ρ-quaternionic manifold. We, also, give a natural construction of homogeneous complex manifolds endowed with embedded spheres, thus, emphasizing the abundance of the quaternionic-like manifolds.

  1. Robinson manifolds and Cauchy-Riemann spaces

    Trautman, A


    A Robinson manifold is defined as a Lorentz manifold (M, g) of dimension 2n >= 4 with a bundle N subset of C centre dot TM such that the fibres of N are maximal totally null and there holds the integrability condition [Sec N, Sec N] subset of Sec N. The real part of N intersection N-bar is a bundle of null directions tangent to a congruence of null geodesics. This generalizes the notion of a shear-free congruence of null geodesics (SNG) in dimension 4. Under a natural regularity assumption, the set M of all these geodesics has the structure of a Cauchy-Riemann manifold of dimension 2n - 1. Conversely, every such CR manifold lifts to many Robinson manifolds. Three definitions of a CR manifold are described here in considerable detail; they are equivalent under the assumption of real analyticity, but not in the smooth category. The distinctions between these definitions have a bearing on the validity of the Robinson theorem on the existence of null Maxwell fields associated with SNGs. This paper is largely a re...

  2. Very high frequency plasma reactant for atomic layer deposition

    Oh, Il-Kwon; Yoo, Gilsang; Yoon, Chang Mo; Kim, Tae Hyung; Yeom, Geun Young; Kim, Kangsik; Lee, Zonghoon; Jung, Hanearl; Lee, Chang Wan; Kim, Hyungjun; Lee, Han-Bo-Ram


    Although plasma-enhanced atomic layer deposition (PE-ALD) results in several benefits in the formation of high-k dielectrics, including a low processing temperature and improved film properties compared to conventional thermal ALD, energetic radicals and ions in the plasma cause damage to layer stacks, leading to the deterioration of electrical properties. In this study, the growth characteristics and film properties of PE-ALD Al2O3 were investigated using a very-high-frequency (VHF) plasma reactant. Because VHF plasma features a lower electron temperature and higher plasma density than conventional radio frequency (RF) plasma, it has a larger number of less energetic reaction species, such as radicals and ions. VHF PE-ALD Al2O3 shows superior physical and electrical properties over RF PE-ALD Al2O3, including high growth per cycle, excellent conformality, low roughness, high dielectric constant, low leakage current, and low interface trap density. In addition, interlayer-free Al2O3 on Si was achieved in VHF PE-ALD via a significant reduction in plasma damage. VHF PE-ALD will be an essential process to realize nanoscale devices that require precise control of interfaces and electrical properties.

  3. Very high frequency plasma reactant for atomic layer deposition

    Oh, Il-Kwon; Yoo, Gilsang; Yoon, Chang Mo [School of Electrical and Electronic Engineering, Yonsei University, Seoul 120-749 (Korea, Republic of); Kim, Tae Hyung; Yeom, Geun Young [Department of Advanced Materials Engineering, Sungkyunkwan University, Suwon 440-746 (Korea, Republic of); Kim, Kangsik; Lee, Zonghoon [School Materials Science and Engineering, Ulsan National Institute of Science and Technology (UNIST), Ulsan 44919 (Korea, Republic of); Jung, Hanearl; Lee, Chang Wan [School of Electrical and Electronic Engineering, Yonsei University, Seoul 120-749 (Korea, Republic of); Kim, Hyungjun, E-mail: [School of Electrical and Electronic Engineering, Yonsei University, Seoul 120-749 (Korea, Republic of); Lee, Han-Bo-Ram, E-mail: [Department of Materials Science and Engineering, Incheon National University, 406-840 Incheon (Korea, Republic of)


    Highlights: • Fundamental research plasma process for thin film deposition is presented. • VHF plasma source for PE-ALD Al{sub 2}O{sub 3} was employed to reduce plasma damage. • The use of VHF plasma improved all of the film qualities and growth characteristics. - Abstract: Although plasma-enhanced atomic layer deposition (PE-ALD) results in several benefits in the formation of high-k dielectrics, including a low processing temperature and improved film properties compared to conventional thermal ALD, energetic radicals and ions in the plasma cause damage to layer stacks, leading to the deterioration of electrical properties. In this study, the growth characteristics and film properties of PE-ALD Al{sub 2}O{sub 3} were investigated using a very-high-frequency (VHF) plasma reactant. Because VHF plasma features a lower electron temperature and higher plasma density than conventional radio frequency (RF) plasma, it has a larger number of less energetic reaction species, such as radicals and ions. VHF PE-ALD Al{sub 2}O{sub 3} shows superior physical and electrical properties over RF PE-ALD Al{sub 2}O{sub 3}, including high growth per cycle, excellent conformality, low roughness, high dielectric constant, low leakage current, and low interface trap density. In addition, interlayer-free Al{sub 2}O{sub 3} on Si was achieved in VHF PE-ALD via a significant reduction in plasma damage. VHF PE-ALD will be an essential process to realize nanoscale devices that require precise control of interfaces and electrical properties.

  4. Planar Inlet Design and Analysis Process (PINDAP)

    Slater, John W.; Gruber, Christopher R.


    The Planar Inlet Design and Analysis Process (PINDAP) is a collection of software tools that allow the efficient aerodynamic design and analysis of planar (two-dimensional and axisymmetric) inlets. The aerodynamic analysis is performed using the Wind-US computational fluid dynamics (CFD) program. A major element in PINDAP is a Fortran 90 code named PINDAP that can establish the parametric design of the inlet and efficiently model the geometry and generate the grid for CFD analysis with design changes to those parameters. The use of PINDAP is demonstrated for subsonic, supersonic, and hypersonic inlets.

  5. Cold-air performance of compressor-drive turbine of Department of Energy upgraded automobile gas turbine engine. 1: Volute-manifold and stator performance

    Roelke, R. J.; Haas, J. E.


    The aerodynamic performance of the inlet manifold and stator assembly of the compressor drive turbine was experimentally determined with cold air as the working fluid. The investigation included measurements of mass flow and stator-exit fluid torque as well as radial surveys of total pressure and flow angle at the stator inlet and annulus surveys of total pressure and flow angle at the stator exit. The stator-exit aftermixed flow conditions and overall stator efficiency were obtained and compared with their design values and the experimental results from three other stators. In addition, an analysis was made to determine the constituent aerodynamic losses that made up the stator kinetic energy loss.

  6. Lattice QCD on Non-Orientable Manifolds

    Mages, Simon; Borsanyi, Szabolcs; Fodor, Zoltan; Katz, Sandor; Szabo, Kalman K


    A common problem in lattice QCD simulations on the torus is the extremely long autocorrelation time of the topological charge, when one approaches the continuum limit. The reason is the suppressed tunneling between topological sectors. The problem can be circumvented by replacing the torus with a different manifold, so that the field configuration space becomes connected. This can be achieved by using open boundary conditions on the fields, as proposed earlier. It has the side effect of breaking translational invariance completely. Here we propose to use a non-orientable manifold, and show how to define and simulate lattice QCD on it. We demonstrate in quenched simulations that this leads to a drastic reduction of the autocorrelation time. A feature of the new proposal is, that translational invariance is preserved up to exponentially small corrections. A Dirac-fermion on a non-orientable manifold poses a challenge to numerical simulations: the fermion determinant becomes complex. We propose two approaches to...

  7. New Spinor Fields on Lorentzian 7-Manifolds

    Bonora, L


    This paper deals with the classification of spinor fields according to the bilinear covariants in 7 dimensions. It extends to higher dimensions the so-called Lounesto spinor fields classification in Minkowski spacetime, which encompasses Dirac, Weyl, Majorana, and more generally flagpoles, flag-dipoles and dipole spinor fields. A generalized classification according to the bilinear covariants was previously studied on Euclidean 7-manifolds. It presents either just one spinor field class, in the real case of Majorana spinors, or three non-trivial classes in the most general case. In this paper we show that by imposing appropriate conditions on spinor fields in 7d manifolds with Lorentzian metric, the formerly obtained obstructions for new classes of spinor fields can be circumvented. New spinor fields classes are then explicitly constructed. In particular, on 7-manifolds with asymptotically flat black hole background, by means of such spinors one can introduce a generalized current density which further serves...

  8. Cork twisting exotic Stein 4-manifolds

    Akbulut, Selman


    From any 4-dimensional oriented handlebody X without 3- and 4-handles and with $b_2\\geq 1$, we construct arbitrary many compact Stein 4-manifolds which are mutually homeomorphic but not diffeomorphic to each other, so that their topological invariants (their fundamental groups, homology groups, boundary homology groups, and intersection forms) coincide with those of X. We also discuss the induced contact structures on their boundaries. Furthermore, for any smooth 4-manifold pair (Z,Y) such that the complement $Z-\\textnormal{int}\\,Y$ is a handlebody without 3- and 4-handles and with $b_2\\geq 1$, we construct arbitrary many exotic embeddings of a compact 4-manifold Y' into Z, such that Y' has the same topological invariants as Y.

  9. Unknotting tunnels in hyperbolic 3-manifolds

    Adams, Colin


    An unknotting tunnel in a 3-manifold with boundary is a properly embedded arc, the complement of an open neighborhood of which is a handlebody. A geodesic with endpoints on the cusp boundary of a hyperbolic 3-manifold and perpendicular to the cusp boundary is called a vertical geodesic. Given a vertical geodesic in a hyperbolic 3-manifold M, we find sufficient conditions for it to be an unknotting tunnel. In particular, if the vertical geodesic corresponds to a 4-bracelet, 5-bracelet or 6-bracelet in the universal cover and has short enough length, it must be an unknotting tunnel. Furthermore, we consider a vertical geodesic that satisfies the elder sibling property, which means that in the universal cover, every horoball except the one centered at infinity is connected to a larger horoball by a lift of the vertical geodesic. Such a vertical geodesic with length less than ln(2) is then shown to be an unknotting tunnel.

  10. Duality constructions from quantum state manifolds

    Kriel, J N; Scholtz, F G


    The formalism of quantum state space geometry on manifolds of generalised coherent states is proposed as a natural setting for the construction of geometric dual descriptions of non-relativistic quantum systems. These state manifolds are equipped with natural Riemannian and symplectic structures derived from the Hilbert space inner product. This approach allows for the systematic construction of geometries which reflect the dynamical symmetries of the quantum system under consideration. We analyse here in detail the two dimensional case and demonstrate how existing results in the AdS_2/CFT_1 context can be understood within this framework. We show how the radial/bulk coordinate emerges as an energy scale associated with a regularisation procedure and find that, under quite general conditions, these state manifolds are asymptotically anti-de Sitter solutions of a class of classical dilaton gravity models. For the model of conformal quantum mechanics proposed by de Alfaro et. al. the corresponding state manifol...

  11. Roughly isometric minimal immersions into Riemannian manifolds

    Markvorsen, Steen

    A given metric (length-) space $X$ (whether compact or not) is roughly isometric to any one of its Kanai graphs $G$, which in turn can be {\\em{geometrized}} by considering each edge of $G$ as a 1-dimensional manifold with an associated metric $g$ giving the 'correct' length of the edge. In this t......A given metric (length-) space $X$ (whether compact or not) is roughly isometric to any one of its Kanai graphs $G$, which in turn can be {\\em{geometrized}} by considering each edge of $G$ as a 1-dimensional manifold with an associated metric $g$ giving the 'correct' length of the edge....... In this talk we will mainly be concerned with {\\em{minimal}} isometric immersions of such geometrized approximations $(G, g)$ of $X$ into Riemannian manifolds $N$ with bounded curvature. When such an immersion exists, we will call it an $X$-web in $N$. Such webs admit a natural 'geometric' extension...

  12. Burning invariant manifolds in reactive front propagation

    Mahoney, John; Mitchell, Kevin; Solomon, Tom


    We present theory and experiments on the dynamics of reaction fronts in a two-dimensional flow composed of a chain of alternating vortices. Inspired by the organization of passive transport by invariant manifolds, we introduce burning invariant manifolds (BIMs), which act as one-sided barriers to front propagation. The BIMs emerge from the theory when the advection-reaction- diffusion system is recast as an ODE for reaction front elements. Experimentally, we demonstrate how these BIMs can be measured and compare their behavior with simulation. Finally, a topological BIM formalism yields a maximum front propagation speed.

  13. Radio Interferometric Calibration Using a Riemannian Manifold

    Yatawatta, Sarod


    In order to cope with the increased data volumes generated by modern radio interferometers such as LOFAR (Low Frequency Array) or SKA (Square Kilometre Array), fast and efficient calibration algorithms are essential. Traditional radio interferometric calibration is performed using nonlinear optimization techniques such as the Levenberg-Marquardt algorithm in Euclidean space. In this paper, we reformulate radio interferometric calibration as a nonlinear optimization problem on a Riemannian manifold. The reformulated calibration problem is solved using the Riemannian trust-region method. We show that calibration on a Riemannian manifold has faster convergence with reduced computational cost compared to conventional calibration in Euclidean space.

  14. The "Parity" Anomaly On An Unorientable Manifold

    Witten, Edward


    The "parity" anomaly -- more accurately described as an anomaly in time-reversal or reflection symmetry -- arises in certain theories of fermions coupled to gauge fields and/or gravity in a spacetime of odd dimension. The "parity" anomaly has traditionally been studied on orientable manifolds only, but recent developments involving topological superconductors have made it clear that one can get more information by asking what happens on an unorientable manifold. In this paper, we analyze the "parity" anomaly for fermions coupled to gauge fields and gravity in $2+1$ dimensions. We consider applications to gapped boundary states of a topological superconductor and to M2-branes in string/M-theory.

  15. Wilson Fermions on a Randomly Triangulated Manifold

    Burda, Z; Krzywicki, A


    A general method of constructing the Dirac operator for a randomly triangulated manifold is proposed. The fermion field and the spin connection live, respectively, on the nodes and on the links of the corresponding dual graph. The construction is carried out explicitly in 2-d, on an arbitrary orientable manifold without boundary. It can be easily converted into a computer code. The equivalence, on a sphere, of Majorana fermions and Ising spins in 2-d is rederived. The method can, in principle, be extended to higher dimensions.

  16. Unraveling flow patterns through nonlinear manifold learning.

    Tauro, Flavia; Grimaldi, Salvatore; Porfiri, Maurizio


    From climatology to biofluidics, the characterization of complex flows relies on computationally expensive kinematic and kinetic measurements. In addition, such big data are difficult to handle in real time, thereby hampering advancements in the area of flow control and distributed sensing. Here, we propose a novel framework for unsupervised characterization of flow patterns through nonlinear manifold learning. Specifically, we apply the isometric feature mapping (Isomap) to experimental video data of the wake past a circular cylinder from steady to turbulent flows. Without direct velocity measurements, we show that manifold topology is intrinsically related to flow regime and that Isomap global coordinates can unravel salient flow features.

  17. Unraveling flow patterns through nonlinear manifold learning.

    Flavia Tauro

    Full Text Available From climatology to biofluidics, the characterization of complex flows relies on computationally expensive kinematic and kinetic measurements. In addition, such big data are difficult to handle in real time, thereby hampering advancements in the area of flow control and distributed sensing. Here, we propose a novel framework for unsupervised characterization of flow patterns through nonlinear manifold learning. Specifically, we apply the isometric feature mapping (Isomap to experimental video data of the wake past a circular cylinder from steady to turbulent flows. Without direct velocity measurements, we show that manifold topology is intrinsically related to flow regime and that Isomap global coordinates can unravel salient flow features.

  18. Inertial manifold of the atmospheric equations

    李建平; 丑纪范


    For a class of nonlinear evolution equations, their global attractors are studied and the existence of their inertial manifolds is discussed using the truncated method. Then, on the basis of the properties of operators of the atmospheric equations, it is proved that the operator equation of the atmospheric motion with dissipation and external forcing belongs to the class of nonlinear evolution equations. Therefore, it is known that there exists an inertial manifold of the atmospheric equations if the spectral gap condition for the dissipation operator is satisfied. These results furnish a basis for further studying the dynamical properties of global attractor of the atmospheric equations and for designing better numerical scheme.

  19. Tangent bundles of Hantzsche-Wendt manifolds

    Gaşior, A.; Szczepański, A.


    We formulate a condition for the existence of a SpinC-structure on an oriented flat manifold Mn with H2(Mn,R)=0. We prove that Mn has a SpinC-structure if and only if there exists a homomorphism ɛ:π1(Mn)→SpinC(n) such that λ∘ɛ=h, where h:π1(Mn)→SO(n) is a holonomy homomorphism and λ:SpinC(n)→SO(n) is a standard homomorphism defined. As an application we shall prove that all cyclic Hantzsche-Wendt manifolds do not have the SpinC-structure.

  20. Beyond Sentiment: The Manifold of Human Emotions

    Kim, Seungyeon; Lebanon, Guy; Essa, Irfan


    Sentiment analysis predicts the presence of positive or negative emotions in a text document. In this paper we consider higher dimensional extensions of the sentiment concept, which represent a richer set of human emotions. Our approach goes beyond previous work in that our model contains a continuous manifold rather than a finite set of human emotions. We investigate the resulting model, compare it to psychological observations, and explore its predictive capabilities. Besides obtaining significant improvements over a baseline without manifold, we are also able to visualize different notions of positive sentiment in different domains.

  1. Generalized nonuniform dichotomies and local stable manifolds

    Bento, António J G


    We establish the existence of local stable manifolds for semiflows generated by nonlinear perturbations of nonautonomous ordinary linear differential equations in Banach spaces, assuming the existence of a general type of nonuniform dichotomy for the evolution operator that contains the nonuniform exponential and polynomial dichotomies as a very particular case. The family of dichotomies considered allow situations for which the classical Lyapunov exponents are zero. Additionally, we give new examples of application of our stable manifold theorem and study the behavior of the dynamics under perturbations.

  2. Aerosol Inlet Characterization Experiment Report

    Bullard, Robert L. [Brookhaven National Lab. (BNL), Upton, NY (United States); Kuang, Chongai [Brookhaven National Lab. (BNL), Upton, NY (United States); Uin, Janek [Brookhaven National Lab. (BNL), Upton, NY (United States); Smith, Scott [Brookhaven National Lab. (BNL), Upton, NY (United States); Springston, Stephen R. [Brookhaven National Lab. (BNL), Upton, NY (United States)


    The U.S. Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) Climate Research Facility Aerosol Observation System inlet stack was characterized for particle penetration efficiency from 10 nm to 20 μm in diameter using duplicate scanning mobility particle sizers (10 nm-450 nm), ultra-high-sensitivity aerosol spectrometers (60 nm-μm), and aerodynamic particle sizers (0.5 μm-20 μm). Results show good model-measurement agreement and unit transmission efficiency of aerosols from 10 nm to 4 μm in diameter. Large uncertainties in the measured transmission efficiency exist above 4 μm due to low ambient aerosol signal in that size range.

  3. External-Compression Supersonic Inlet Design Code

    Slater, John W.


    A computer code named SUPIN has been developed to perform aerodynamic design and analysis of external-compression, supersonic inlets. The baseline set of inlets include axisymmetric pitot, two-dimensional single-duct, axisymmetric outward-turning, and two-dimensional bifurcated-duct inlets. The aerodynamic methods are based on low-fidelity analytical and numerical procedures. The geometric methods are based on planar geometry elements. SUPIN has three modes of operation: 1) generate the inlet geometry from a explicit set of geometry information, 2) size and design the inlet geometry and analyze the aerodynamic performance, and 3) compute the aerodynamic performance of a specified inlet geometry. The aerodynamic performance quantities includes inlet flow rates, total pressure recovery, and drag. The geometry output from SUPIN includes inlet dimensions, cross-sectional areas, coordinates of planar profiles, and surface grids suitable for input to grid generators for analysis by computational fluid dynamics (CFD) methods. The input data file for SUPIN and the output file from SUPIN are text (ASCII) files. The surface grid files are output as formatted Plot3D or stereolithography (STL) files. SUPIN executes in batch mode and is available as a Microsoft Windows executable and Fortran95 source code with a makefile for Linux.

  4. On Kähler–Norden Manifolds-Erratum

    M Iscan; A A Salimov


    This paper is concerned with the problem of the geometry of Norden manifolds. Some properties of Riemannian curvature tensors and curvature scalars of Kähler–Norden manifolds using the theory of Tachibana operators is presented.

  5. Modeling of EGR Mixing in an Engine Intake Manifold Using LES

    Sakowitz A.


    Full Text Available We investigate the mixing process of exhaust gases with fresh air in Internal Combustion Engines (ICE. For this purpose, the flow in an inlet manifold of a six-cylinder heavy-duty Diesel engine is computed using compressible Large Eddy Simulations (LES. The Exhaust Gas Recirculation (EGR concentration is modeled as a passive scalar. The results are validated by on-engine measurements of the EGR concentration using COZ probes. The boundary conditions for the highly pulsating flow are taken partly from one-dimensional simulations, partly from pressure measurements on the engine. In order to assess the sensitivity to the boundary conditions, changes are applied to the base-line case. The mixing quality is evaluated in terms of cylinder-to-cylinder distribution and the spatial RMS over the outlet cross- sections. Different averaging techniques are applied. It was found that the temporal and spatial EGR distribution is different among the cylinders. The EGR distribution within the cylinder inlet is non-uniform. These factors imply that one should not use a time-averaged EGR value as indicator for the EGR content. Furthermore, it was found that the flow pulsations at the EGR inlet have a large influence on the EGR distribution. By comparing the LES results with measurements, it was shown that LES gives a better and deeper insight into the mixing in such turbulent, pulsating flow situations.

  6. $\\rm G_2$ holonomy manifolds are superconformal

    Díaz, Lázaro O Rodríguez


    We study the chiral de Rham complex (CDR) over a manifold $M$ with holonomy $\\rm G_2$. We prove that the vertex algebra of global sections of the CDR associated to $M$ contains two commuting copies of the Shatashvili-Vafa $\\rm G_2$ superconformal algebra. Our proof is a tour de force, based on explicit computations.

  7. Four-manifolds, geometries and knots

    Hillman, Jonathan A


    The goal of this book is to characterize algebraically the closed 4-manifolds that fibre nontrivially or admit geometries in the sense of Thurston, or which are obtained by surgery on 2-knots, and to provide a reference for the topology of such manifolds and knots. The first chapter is purely algebraic. The rest of the book may be divided into three parts: general results on homotopy and surgery (Chapters 2-6), geometries and geometric decompositions (Chapters 7-13), and 2-knots (Chapters 14-18). In many cases the Euler characteristic, fundamental group and Stiefel-Whitney classes together form a complete system of invariants for the homotopy type of such manifolds, and the possible values of the invariants can be described explicitly. The strongest results are characterizations of manifolds which fibre homotopically over S^1 or an aspherical surface (up to homotopy equivalence) and infrasolvmanifolds (up to homeomorphism). As a consequence 2-knots whose groups are poly-Z are determined up to Gluck reconstruc...

  8. Einstein constraints on n dimensional compact manifolds

    Choquet-Bruhat, Y


    We give a general survey of the solution of the Einstein constraints by the conformal method on n dimensional compact manifolds. We prove some new results about solutions with low regularity (solutions in $H_{2}$ when n=3), and solutions with unscaled sources.

  9. M-theory and G_2 Manifolds

    Becker, Katrin; Robbins, Daniel


    In this talk we report on recent progress in describing compactifications of string theory and M-theory on G_2 and Spin(7) manifolds. We include the infinite set of alpha'-corrections and describe the entire tower of massless and massive Kaluza-Klein modes resulting from such compactifications.

  10. Remarks on homogeneous manifolds satisfying Levi conditions

    Huckleberry, Alan


    Homogeneous complex manifolds satisfying various types of Levi conditions are considered. Classical results which were of particular interest to Andreotti are recalled. Convexity and concavity properties of flag domains are discussed in some detail. A precise classification of pseudoconvex flag domains is given. It is shown that flag domains which are in a certain sense generic are pseudoconcave.

  11. Exponential estimates of symplectic slow manifolds

    Kristiansen, Kristian Uldall; Wulff, C.


    is motivated by a paper of MacKay from 2004. The method does not notice resonances, and therefore we do not pose any restrictions on the motion normal to the slow manifold other than it being fast and analytic. We also present a stability result and obtain a generalization of a result of Gelfreich and Lerman...

  12. Modelling of the Manifold Filling Dynamics

    Hendricks, Elbert; Chevalier, Alain Marie Roger; Jensen, Michael


    Mean Value Engine Models (MVEMs) are dynamic models which describe dynamic engine variable (or state) responses on time scales slightly longer than an engine event. This paper describes a new model of the intake manifold filling dynamics which is simple and easy to calibrate for use in engine con...

  13. Duality constructions from quantum state manifolds

    Kriel, J. N.; van Zyl, H. J. R.; Scholtz, F. G.


    The formalism of quantum state space geometry on manifolds of generalised coherent states is proposed as a natural setting for the construction of geometric dual descriptions of non-relativistic quantum systems. These state manifolds are equipped with natural Riemannian and symplectic structures derived from the Hilbert space inner product. This approach allows for the systematic construction of geometries which reflect the dynamical symmetries of the quantum system under consideration. We analyse here in detail the two dimensional case and demonstrate how existing results in the AdS 2 /CF T 1 context can be understood within this framework. We show how the radial/bulk coordinate emerges as an energy scale associated with a regularisation procedure and find that, under quite general conditions, these state manifolds are asymptotically anti-de Sitter solutions of a class of classical dilaton gravity models. For the model of conformal quantum mechanics proposed by de Alfaro et al. [1] the corresponding state manifold is seen to be exactly AdS 2 with a scalar curvature determined by the representation of the symmetry algebra. It is also shown that the dilaton field itself is given by the quantum mechanical expectation values of the dynamical symmetry generators and as a result exhibits dynamics equivalent to that of a conformal mechanical system.

  14. Heat Kernel Renormalization on Manifolds with Boundary

    Albert, Benjamin I.


    In the monograph Renormalization and Effective Field Theory, Costello gave an inductive position space renormalization procedure for constructing an effective field theory that is based on heat kernel regularization of the propagator. In this paper, we extend Costello's renormalization procedure to a class of manifolds with boundary. In addition, we reorganize the presentation of the preexisting material, filling in details and strengthening the results.

  15. Geometrical description of denormalized thermodynamic manifold

    Wu Li-Ping; Sun Hua-Fei; Cao Li-Mei


    In view of differential geometry,the state space of thermodynamic parameters is investigated. Here the geometrical structures of the denormalized thermodynamic manifold are considered. The relation of their geometrical metrics is obtained. Moreover an example is used to illustrate our conclusions.

  16. On homological stability for configuration spaces on closed background manifolds

    Cantero, Federico; Palmer, Martin


    We introduce a new map between configuration spaces of points in a background manifold - the replication map - and prove that it is a homology isomorphism in a range with certain coefficients. This is particularly of interest when the background manifold is closed, in which case the classical stabilisation map does not exist. We then establish conditions on the manifold and on the coefficients under which homological stability holds for configuration spaces on closed manifolds. These conditio...

  17. Royden's lemma in infinite dimensions and Hilbert-Hartogs manifolds

    Ivashkovich, S


    We prove the Royden's Lemma for complex Hilbert manifolds, i.e., that a holomorphic imbedding of the closure of a finite dimensional, strictly pseudoconvex domain into a complex Hilbert manifold extends to a biholomorphic mapping onto a product of this domain with the unit ball in Hilbert space. This reduces several problems concerning complex Hilbert manifolds to open subsets of a Hilbert space. As an illustration we prove some results on generalized loop spaces of complex manifolds.

  18. Fluid manifold design for a solar energy storage tank

    Humphries, W. R.; Hewitt, H. C.; Griggs, E. I.


    A design technique for a fluid manifold for use in a solar energy storage tank is given. This analytical treatment generalizes the fluid equations pertinent to manifold design, giving manifold pressures, velocities, and orifice pressure differentials in terms of appropriate fluid and manifold geometry parameters. Experimental results used to corroborate analytical predictions are presented. These data indicate that variations in discharge coefficients due to variations in orifices can cause deviations between analytical predictions and actual performance values.

  19. On Self-Mapping Degrees of S3- Geometry Manifolds

    Xiao Ming DU


    In this paper we determined all of the possible self-mapping degrees of the manifolds with S3-geometry, which are supposed to be all 3-manifolds with finite fundamental groups. This is a part of a project to determine all possible self-mapping degrees of all closed orientable 3-manifold in Thurston's picture.

  20. Canonical connection on a class of Riemannian almost product manifolds

    Mekerov, Dimitar


    The canonical connection on a Riemannian almost product manifolds is an analogue to the Hermitian connection on an almost Hermitian manifold. In this paper we consider the canonical connection on a class of Riemannian almost product manifolds with nonintegrable almost product structure.


    王芝银; 李云鹏


    A brief introduction is made for the Numerical Manifold Method and its analysingprocess in rock mechanics. Some aspects of the manifold method are improved in implementingprocess according to the practice of excavating underground openings. Corresponding formulasare given and a computer program of the Numerical Manifold Method has been completed in thispaper.

  2. Holomorphic Cartan geometries, Calabi--Yau manifolds and rational curves

    Biswas, Indranil; 10.1016/j.difgeo.2009.09.003


    We prove that if a Calabi--Yau manifold $M$ admits a holomorphic Cartan geometry, then $M$ is covered by a complex torus. This is done by establishing the Bogomolov inequality for semistable sheaves on compact K\\"ahler manifolds. We also classify all holomorphic Cartan geometries on rationally connected complex projective manifolds.

  3. Wave equations on anti self dual (ASD) manifolds

    Bashingwa, Jean-Juste; Kara, A. H.


    In this paper, we study and perform analyses of the wave equation on some manifolds with non diagonal metric g_{ij} which are of neutral signatures. These include the invariance properties, variational symmetries and conservation laws. In the recent past, wave equations on the standard (space time) Lorentzian manifolds have been performed but not on the manifolds from metrics of neutral signatures.

  4. Poisson Manifolds, Lie Algebroids, Modular Classes: a Survey

    Yvette Kosmann-Schwarzbach


    Full Text Available After a brief summary of the main properties of Poisson manifolds and Lie algebroids in general, we survey recent work on the modular classes of Poisson and twisted Poisson manifolds, of Lie algebroids with a Poisson or twisted Poisson structure, and of Poisson-Nijenhuis manifolds. A review of the spinor approach to the modular class concludes the paper.

  5. Local topology in deformation spaces of hyperbolic 3-manifolds

    Brock, Jeffrey F; Canary, Richard D; Minsky, Yair N


    We prove that the deformation space AH(M) of marked hyperbolic 3-manifolds homotopy equivalent to a fixed compact 3-manifold M with incompressible boundary is locally connected at minimally parabolic points. Moreover, spaces of Kleinian surface groups are locally connected at quasiconformally rigid points. Similar results are obtained for deformation spaces of acylindrical 3-manifolds and Bers slices.

  6. On the conformal geometry of transverse Riemann Lorentz manifolds

    Aguirre, E.; Fernández, V.; Lafuente, J.


    Physical reasons suggested in [J.B. Hartle, S.W. Hawking, Wave function of the universe, Phys. Rev. D41 (1990) 1815-1834] for the Quantum Gravity Problem lead us to study type-changing metrics on a manifold. The most interesting cases are Transverse Riemann-Lorentz Manifolds. Here we study the conformal geometry of such manifolds.

  7. Einstein Metrics, Four-Manifolds, and Differential Topology


    This article presents a new and more elementary proof of the main Seiberg-Witten-based obstruction to the existence of Einstein metrics on smooth compact 4-manifolds. It also introduces a new smooth manifold invariant which conveniently encapsulates those aspects of Seiberg-Witten theory most relevant to the study of Riemannian variational problems on 4-manifolds.

  8. Gleason grading of prostate histology utilizing manifold regularization via statistical shape model of manifolds

    Sparks, Rachel; Madabhushi, Anant


    Gleason patterns of prostate cancer histopathology, characterized primarily by morphological and architectural attributes of histological structures (glands and nuclei), have been found to be highly correlated with disease aggressiveness and patient outcome. Gleason patterns 4 and 5 are highly correlated with more aggressive disease and poorer patient outcome, while Gleason patterns 1-3 tend to reflect more favorable patient outcome. Because Gleason grading is done manually by a pathologist visually examining glass (or digital) slides, subtle morphologic and architectural differences of histological attributes may result in grading errors and hence cause high inter-observer variability. Recently some researchers have proposed computerized decision support systems to automatically grade Gleason patterns by using features pertaining to nuclear architecture, gland morphology, as well as tissue texture. Automated characterization of gland morphology has been shown to distinguish between intermediate Gleason patterns 3 and 4 with high accuracy. Manifold learning (ML) schemes attempt to generate a low dimensional manifold representation of a higher dimensional feature space while simultaneously preserving nonlinear relationships between object instances. Classification can then be performed in the low dimensional space with high accuracy. However ML is sensitive to the samples contained in the dataset; changes in the dataset may alter the manifold structure. In this paper we present a manifold regularization technique to constrain the low dimensional manifold to a specific range of possible manifold shapes, the range being determined via a statistical shape model of manifolds (SSMM). In this work we demonstrate applications of the SSMM in (1) identifying samples on the manifold which contain noise, defined as those samples which deviate from the SSMM, and (2) accurate out-of-sample extrapolation (OSE) of newly acquired samples onto a manifold constrained by the SSMM. We

  9. Local Schrodinger flow into Kahler manifolds

    DlNG; Weiyue(


    [1]Ding, W. Y. , Wang, Y. D. , Schrodinger flows of maps into symplectic manifolds, Science in China, Ser. A, 1998, 41(7): 746.[2]Landau, L. D., Lifshitz, E. M., On the theory of the dispersion of magnetic permeability in ferromagnetic bodies, Phys. Z.Sowj., 1935, 8: 153; reproduced in Collected Papers of L. D. Landau, New York: Pergaman Press, 1965, 101-114.[3]Faddeev, L., Takhtajan, L. A. , Hamiltonian Methods in the Theory of Solitons, Berlin-Heidelberg-New York: Springer-Verlag, 1987.[4]Nakamura, K., Sasada, T., Soliton and wave trains in ferromagnets, Phys. Lett. A, 1974, 48: 321.[5]Zhou, Y. , Guo, B. , Tan, S. , Existence and uniqueness of smooth solution for system of ferromagnetic chain, Science in China, Ser. A, 1991, 34(3): 257.[6]Pang, P. , Wang, H. , Wang, Y. D. , Schrodinger flow of maps into Kahler manifolds, Asian J. of Math. , in press.[7]Wang, H. , Wang, Y. D. , Global inhomogeneous Schrodinger flow, Int. J. Math., 2000, 11: 1079.[8]Pang, P., Wang, H., Wang, Y. D., Local existence for inhomogeneous Schrodinger flow of maps into Kahler manifolds,Acta Math. Sinica, English Series, 2000, 16: 487.[9]Temg, C. L., Uhlenbeck, K., Schrodinger flows on Grassmannians, in Integrable Systems, Geometry and Topology,Somervi11e, MA: International Press, in press.[10]Chang, N., Shatah, J., Uhlenbeck, K., Schrodinger maps, Commun. Pure Appl. Math., 2000, 53: 157.[11]Wang, Y. D., Ferromagnetic chain equation from a closed Riemannian manifold into S2, Int. J. Math., 1995, 6: 93.[12]Wang, Y. D., Heisenberg chain systems from compact manifolds into S2, J. Math. Phys., 1998, 39(1): 363.[13]Sulem, P., Sulem, C., Bardos, C., On the continuous limit for a system of classical spins, Commun. Math. Phys., 1986,107: 431.[14]Aubin, T., Nonlinear Analysis on Manifolds, Monge-Ampère Equations, Berlin-Heidelberg-New York: Springer-Verlag,1982.[15]Eells, J. , Lemaire, L. , Another report on harmonic maps, Bull. London

  10. Lower bounds on volumes of hyperbolic Haken 3-manifolds

    Agol, Ian; Storm, Peter A.; Thurston, William P.


    We prove a volume inequality for 3-manifolds having C^{0} metrics ``bent'' along a surface and satisfying certain curvature conditions. The result makes use of Perelman's work on the Ricci flow and geometrization of closed 3-manifolds. Corollaries include a new proof of a conjecture of Bonahon about volumes of convex cores of Kleinian groups, improved volume estimates for certain Haken hyperbolic 3-manifolds, and a lower bound on the minimal volume of orientable hyperbolic 3-manifolds. An appendix compares estimates of volumes of hyperbolic 3-manifolds drilled along a closed embedded geodesic with experimental data.


    LUO Shao-ming; ZHANG Xiang-wei; L(U) Wen-ge; JIANG Dong-ru


    The three-dimensional numerical manifold method(NMM) is studied on the basis of two-dimensional numerical manifold method. The three-dimensional cover displacement function is studied. The mechanical analysis and Hammer integral method of three-dimensional numerical manifold method are put forward. The stiffness matrix of three-dimensional manifold element is derived and the dissection rules are given. The theoretical system and the numerical realizing method of three-dimensional numerical manifold method are systematically studied. As an example, the cantilever with load on the end is calculated, and the results show that the precision and efficiency are agreeable.

  12. Gas Turbine Engine Inlet Wall Design

    Florea, Razvan Virgil (Inventor); Matalanis, Claude G. (Inventor); Stucky, Mark B. (Inventor)


    A gas turbine engine has an inlet duct formed to have a shape with a first ellipse in one half and a second ellipse in a second half. The second half has an upstream most end which is smaller than the first ellipse. The inlet duct has a surface defining the second ellipse which curves away from the first ellipse, such that the second ellipse is larger at an intermediate location. The second ellipse is even larger at a downstream end of the inlet duct leading into a fan.

  13. Reactant ion chemistry for detection of TNT, RDX, and PETN using an ion mobility spectrometer

    Klassen, S.E.; Rodacy, P.; Silva, R.


    This report describes the responses of three energetic materials (TNT, RDX, and PETN) to varying reactant ion chemistries and IMS cell temperatures. The following reactant ion chemistries were evaluated; air-dry; air-wet; methylene chloride-dry; methylene chloride-wet; methylene bromide-dry; nitrogen dioxide-wet; sulfur dioxide-wet. The temperature was varied between 160 - 220{degrees}C.

  14. New Calabi-Yau Manifolds with Small Hodge Numbers

    Candelas, Philip


    It is known that many Calabi-Yau manifolds form a connected web. The question of whether all Calabi-Yau manifolds form a single web depends on the degree of singularity that is permitted for the varieties that connect the distinct families of smooth manifolds. If only conifolds are allowed then, since shrinking two-spheres and three-spheres to points cannot affect the fundamental group, manifolds with different fundamental groups will form disconnected webs. We examine these webs for the tip of the distribution of Calabi-Yau manifolds where the Hodge numbers (h^{11}, h^{21}) are both small. In the tip of the distribution the quotient manifolds play an important role. We generate via conifold transitions from these quotients a number of new manifolds. These include a manifold with \\chi =-6 that is an analogue of the Tian-Yau manifold and manifolds with an attractive structure that may prove of interest for string phenomenology. We also examine the relation of some of these manifolds to the remarkable Gross-Pop...

  15. A non-permselective membrane reactor for chemical processes normally requiring strict stoichiometric feed rates of reactants

    Sloot, H.J.; Versteeg, G.F.; Swaaij, W.P.M. van


    A novel type of membrane reactor with separated feeding of the reactants is presented for chemical processes normally requiring strict stoichiometric feed rates of premixed reactants. The reactants are fed in the reactor to the different sides of a porous membrane which is impregnated with a catalys

  16. A non-permselective membrane reactor for chemical processes normally requiring strict stoichiometric feed rates of reactants

    Sloot, H.J.; Versteeg, G.F.; Swaaij, W.P.M. van


    A novel type of membrane reactor with separated feeding of the reactants is presented for chemical processes normally requiring strict stoichiometric feed rates of premixed reactants. The reactants are fed in the reactor to the different sides of a porous membrane which is impregnated with a

  17. Manifold learning-based subspace distance for machinery damage assessment

    Sun, Chuang; Zhang, Zhousuo; He, Zhengjia; Shen, Zhongjie; Chen, Binqiang


    Damage assessment is very meaningful to keep safety and reliability of machinery components, and vibration analysis is an effective way to carry out the damage assessment. In this paper, a damage index is designed by performing manifold distance analysis on vibration signal. To calculate the index, vibration signal is collected firstly, and feature extraction is carried out to obtain statistical features that can capture signal characteristics comprehensively. Then, manifold learning algorithm is utilized to decompose feature matrix to be a subspace, that is, manifold subspace. The manifold learning algorithm seeks to keep local relationship of the feature matrix, which is more meaningful for damage assessment. Finally, Grassmann distance between manifold subspaces is defined as a damage index. The Grassmann distance reflecting manifold structure is a suitable metric to measure distance between subspaces in the manifold. The defined damage index is applied to damage assessment of a rotor and the bearing, and the result validates its effectiveness for damage assessment of machinery component.

  18. Calabi-Yau Manifolds Over Finite Fields, 1

    Candelas, Philip; Rodríguez-Villegas, F; Candelas, Philip; Ossa, Xenia de la; Rodriguez-Villegas, Fernando


    We study Calabi-Yau manifolds defined over finite fields. These manifolds have parameters, which now also take values in the field and we compute the number of rational points of the manifold as a function of the parameters. The intriguing result is that it is possible to give explicit expressions for the number of rational points in terms of the periods of the holomorphic three-form. We show also, for a one parameter family of quintic threefolds, that the number of rational points of the manifold is closely related to as the number of rational points of the mirror manifold. Our interest is primarily with Calabi-Yau threefolds however we consider also the interesting case of elliptic curves and even the case of a quadric in CP_1 which is a zero dimensional Calabi-Yau manifold. This zero dimensional manifold has trivial dependence on the parameter over C but a not trivial arithmetic structure.

  19. Quaternionic Kahler Manifolds, Constrained Instantons and the Magic Square: I

    Dasgupta, Keshav; Wissanji, Alisha


    The classification of homogeneous quaternionic manifolds has been done by Alekseevskii, Wolf et al using transitive solvable group of isometries. These manifolds are not generically symmetric, but there is a subset of quaternionic manifolds that are symmetric and Einstein. A further subset of these manifolds are the magic square manifolds. We show that all the symmetric quaternionic manifolds including the magic square can be succinctly classified by constrained instantons. These instantons are mostly semilocal, and their constructions for the magic square can be done from the corresponding Seiberg-Witten curves for certain N = 2 gauge theories that are in general not asymptotically free. Using these, we give possible constructions, such as the classical moduli space metrics, of constrained instantons with exceptional global symmetries. We also discuss the possibility of realising the Kahler manifolds in the magic square using other solitonic configurations in the theory, and point out an interesting new sequ...

  20. Monte Carlo simulations for a Lotka-type model with reactant surface diffusion and interactions.

    Zvejnieks, G; Kuzovkov, V N


    The standard Lotka-type model, which was introduced for the first time by Mai et al. [J. Phys. A 30, 4171 (1997)] for a simplified description of autocatalytic surface reactions, is generalized here for a case of mobile and energetically interacting reactants. The mathematical formalism is proposed for determining the dependence of transition rates on the interaction energy (and temperature) for the general mathematical model, and the Lotka-type model, in particular. By means of Monte Carlo computer simulations, we have studied the impact of diffusion (with and without energetic interactions between reactants) on oscillatory properties of the A+B-->2B reaction. The diffusion leads to a desynchronization of oscillations and a subsequent decrease of oscillation amplitude. The energetic interaction between reactants has a dual effect depending on the type of mobile reactants. In the limiting case of mobile reactants B the repulsion results in a decrease of amplitudes. However, these amplitudes increase if reactants A are mobile and repulse each other. A simplified interpretation of the obtained results is given.

  1. Constructing Dualities from Quantum State Manifolds

    van Zyl, H J R


    The thesis develops a systematic procedure to construct semi-classical gravitational duals from quantum state manifolds. Though the systems investigated are simple quantum mechanical systems without gauge symmetry many familiar concepts from the conventional gauge/gravity duality come about in a very natural way. The investigation of the low-dimensional manifolds link existing results in the $AdS_2/CFT_1$ literature. We are able to extend these in various ways and provide an explicit dictionary. The higher dimensional investigation is also concluded with a simple dictionary, but this dictionary requires the inclusion of many bulk coordinates. Consequently further work is needed to relate these results to existing literature. Possible ways to achieve this are discussed.

  2. Dynamical systems on 2- and 3-manifolds

    Grines, Viacheslav Z; Pochinka, Olga V


    This book provides an introduction to the topological classification of smooth structurally stable diffeomorphisms on closed orientable 2- and 3-manifolds.The topological classification is one of the main problems of the theory of dynamical systems and the results presented in this book are mostly for dynamical systems satisfying Smale's Axiom A. The main results on the topological classification of discrete dynamical systems are widely scattered among many papers and surveys. This book presents these results fluidly, systematically, and for the first time in one publication. Additionally, this book discusses the recent results on the topological classification of Axiom A diffeomorphisms focusing on the nontrivial effects of the dynamical systems on 2- and 3-manifolds. The classical methods and approaches which are considered to be promising for the further research are also discussed. < The reader needs to be familiar with the basic concepts of the qualitative theory of dynamical systems which are present...

  3. New spinor fields on Lorentzian 7-manifolds

    Bonora, L. [International School for Advanced Studies (SISSA),Via Bonomea 265, 34136 Trieste (Italy); Rocha, Roldão da [Centro de Matemática, Computação e Cognição, Universidade Federal do ABC,Avenida dos Estados, 5001, Santo André (Brazil)


    This paper deals with the classification of spinor fields according to the bilinear covariants in 7 dimensions. The previously investigated Riemannian case is characterized by either one spinor field class, in the real case of Majorana spinors, or three non-trivial classes in the most general complex case. In this paper we show that by imposing appropriate conditions on spinor fields in 7d manifolds with Lorentzian metric, the formerly obtained obstructions for new classes of spinor fields can be circumvented. New spinor fields classes are then explicitly constructed. In particular, on 7-manifolds with asymptotically flat black hole background, these spinors can define a generalized current density which further defines a time Killing vector at the spatial infinity.

  4. Manifold Learning by Preserving Distance Orders.

    Ataer-Cansizoglu, Esra; Akcakaya, Murat; Orhan, Umut; Erdogmus, Deniz


    Nonlinear dimensionality reduction is essential for the analysis and the interpretation of high dimensional data sets. In this manuscript, we propose a distance order preserving manifold learning algorithm that extends the basic mean-squared error cost function used mainly in multidimensional scaling (MDS)-based methods. We develop a constrained optimization problem by assuming explicit constraints on the order of distances in the low-dimensional space. In this optimization problem, as a generalization of MDS, instead of forcing a linear relationship between the distances in the high-dimensional original and low-dimensional projection space, we learn a non-decreasing relation approximated by radial basis functions. We compare the proposed method with existing manifold learning algorithms using synthetic datasets based on the commonly used residual variance and proposed percentage of violated distance orders metrics. We also perform experiments on a retinal image dataset used in Retinopathy of Prematurity (ROP) diagnosis.

  5. Adaptive graph construction for Isomap manifold learning

    Tran, Loc; Zheng, Zezhong; Zhou, Guoqing; Li, Jiang


    Isomap is a classical manifold learning approach that preserves geodesic distance of nonlinear data sets. One of the main drawbacks of this method is that it is susceptible to leaking, where a shortcut appears between normally separated portions of a manifold. We propose an adaptive graph construction approach that is based upon the sparsity property of the l1 norm. The l1 enhanced graph construction method replaces k-nearest neighbors in the classical approach. The proposed algorithm is first tested on the data sets from the UCI data base repository which showed that the proposed approach performs better than the classical approach. Next, the proposed approach is applied to two image data sets and achieved improved performances over standard Isomap.

  6. Cosmic Topology of Double Action Manifolds

    Aurich, Ralf


    The cosmic microwave background (CMB) anisotropies in spherical 3-spaces with a non-trivial topology are studied. This paper discusses the special class of the so-called double action manifolds, which are for the first time analysed with respect to their CMB anisotropies. The CMB anisotropies are computed for all double action manifolds generated by a dihedral and a cyclic group with a group order of up to 180 leading to 33 different topologies. Several spaces are found which show a suppression of the CMB anisotropies on large angular distances as it is found on the real CMB sky. It turns out that these spaces possess fundamental cells defined as Voronoi domains which are close to highly symmetric polyhedra like Platonic or Archimedean ones.

  7. Geometry of manifolds with area metric

    Schuller, F P


    We construct the differential geometry of smooth manifolds equipped with an algebraic curvature map acting as an area measure. Area metric geometry provides a spacetime structure suitable for the discussion of gauge theories and strings, and is considerably more general than Lorentzian geometry. Our construction of geometrically relevant objects, such as an area metric compatible connection and derived tensors, makes essential use of a decomposition theorem due to Gilkey, showing that a general area metric is generated by a finite collection of metrics rather than by a single one. Employing curvature invariants for area metric manifolds we devise an entirely new class of gravity theories with inherently stringy character, and discuss gauge matter actions.


    钟同德; 钟春平


    Using non-linear connection of Finsler manifold M, the existence of localcoordinates which is normalized at a point x is proved, and the Laplace operator △ on1-form of M is defined by non-linear connection and its curvature tensor. After proving themaximum principle theorem of Hopf-Bochner on M, the Bochner type vanishing theoremof Killing vectors and harmonic 1-form are obtained.

  9. Lightlike Submanifolds of Indefinite Sasakian Manifolds

    K. L. Duggal


    submanifolds of indefinite Sasakian manifolds. Then, we introduce a general notion of contact Cauchy-Riemann (CR lightlike submanifolds and study the geometry of leaves of their distributions. We also study a class, namely, contact screen Cauchy-Riemann (SCR lightlike submanifolds which include invariant and screen real subcases. Finally, we prove characterization theorems on the existence of contact SCR, screen real, invariant, and contact CR minimal lightlike submanifolds.

  10. Proper holomorphic mappings between hyperbolic product manifolds

    Janardhanan, Jaikrishnan


    We generalize a result of Remmert and Stein, on proper holomorphic mappings between domains that are products of certain planar domains, to finite proper holomorphic mappings between complex manifolds that are products of hyper- bolic Riemann surfaces. While an important special case of our result follows from the ideas developed by Remmert and Stein, our proof of the full result relies on the interplay of the latter ideas and a finiteness theorem for Riemann surfaces.

  11. Symplectic Manifolds, Coherent States and Semiclassical Approximation

    Rajeev, S G; Sen, S; Sen, Siddhartha


    We describe the symplectic structure and Hamiltonian dynamics for a class of Grassmannian manifolds. Using the two dimensional sphere ($S^2$) and disc ($D^2$) as illustrative cases, we write their path integral representations using coherent state techniques. These path integrals can be evaluated exactly by semiclassical methods, thus providing examples of localisation formula. Along the way, we also give a local coordinate description for a class of Grassmannians.

  12. Nonsmoothable Involutions on Spin 4-Manifolds

    Changtao Xue; Ximin Liu


    Let be a closed, simply-connected, smooth, spin 4-manifold whose intersection form is isomorphic to $n(-E_8)\\oplus mH$, where is the hyperbolic form. In this paper, we prove that for such that $n≡ 2\\mathrm{mod} 4$, there exists a locally linear pseudofree $\\mathbb{Z}_2$-action on which is nonsmoothable with respect to any possible smooth structure on .

  13. Annual report, Cook Inlet District, 1958 season

    US Fish and Wildlife Service, Department of the Interior — Commercial fishery management activities for Cook Inlet and Resurrection Bay for 1958, including lists of operators and extensive statistics.

  14. Annual report, Cook Inlet District, 1956 season

    US Fish and Wildlife Service, Department of the Interior — Commercial fishery management activities for Cook Inlet and Resurrection Bay for 1956, including lists of operators and extensive statistics.

  15. Annual report, Cook Inlet District, 1954 season

    US Fish and Wildlife Service, Department of the Interior — Commercial fishery management activities for Cook Inlet and Resurrection Bay for 1954, including lists of operators and extensive statistics.

  16. Annual report, Cook Inlet District, 1957 season

    US Fish and Wildlife Service, Department of the Interior — Commercial fishery management activities for Cook Inlet and Resurrection Bay for 1957, including lists of operators and extensive statistics.

  17. Annual report, Cook Inlet District, 1959 season

    US Fish and Wildlife Service, Department of the Interior — Commercial fishery management activities for Cook Inlet and Resurrection Bay for 1959, including lists of operators and extensive statistics.

  18. Interactions Between Wetlands and Tidal Inlets


    Madre, TX), (3) fjord-type (e.g., Penobscot Bay , ME), and (4) tectonically created estuaries (e.g., San Francisco Bay , CA) (Pritchard 1967). This CHETN...small marsh island in San Francisco Bay , CA. Wolaver et al. (1988) measured suspended sediment flux of 827 g/m2/year into a marsh in North Inlet, SC...permanent or ephemeral inlets. Conversely, the development or construction of wetlands within an estuary reduces bay area and the tidal prism, which will

  19. A parametric design of compact exhaust manifold junction in heavy duty diesel engine using CFD

    Naeimi Hessamedin


    Full Text Available Nowadays, computational fluid dynamics codes (CFD are prevalently used to simulate the gas dynamics in many fluid piping systems such as steam and gas turbines, inlet and exhaust in internal combustion engines. In this paper, a CFD software is used to obtain the total energy losses in adiabatic compressible flow at compact exhaust manifold junction. A steady state onedimensional adiabatic compressible flow with friction model has been applied to subtract the straight pipe friction losses from the total energy losses. The total pressure loss coefficient has been related to the extrapolated Mach number in the common branch and to the mass flow rate ratio between branches at different flow configurations, in both combining and dividing flows. The study indicate that the numerical results were generally in good agreement with those of experimental data from the literature and will be applied as a boundary condition in one-dimensional global simulation models of fluid systems in which these components are present.

  20. Three-manifolds class field theory (Homology of coverings for a non-virtually Haken manifold)

    Reznikov, A G


    This is a first in a series of papers, devoted to the relation betwwen three-manifolds and number fields. The present paper studies first homology of finite coverings of a three-manifold with primary interest in the Thurston $b_1$ conjecture.The main result reads: if $M$ does not yield the Thurston conjecture, then the pro-p completion of its fundamental group is a Poincaré duality pro-p group. Conceptually, it means that we have a ``p-adic'' three-manifold. We develop several algebraic techniques, including a new powerful specral seguence, to actually compute homology of coverings, assumong only information on homology of $M$, a thing never done before.A number of applications to the structure of finite group cohomology rings is also given.

  1. Generalized Calabi-Yau manifolds and the mirror of a rigid manifold

    Candelas, Philip; Parkes, L


    We describe the mirror of the Z orbifold as a representation of a class of generalized Calabi-Yau manifolds that can be realized as manifolds of dimension five and seven. Despite their dimension these correspond to superconformal theories with $c=9$ and so are perfectly good for compactifying the heterotic string to the four dimensions of space-time. As a check of mirror symmetry we compute the structure of the space of complex structures of the mirror and check that this reproduces the known results for the Yukawa couplings and metric appropriate to the Kahler class parameters on the Z orbifold together with their instanton corrections.

  2. Acceleration of disproportionation of aromatic alcohols through self-emulsification of reactants in water.

    Zhang, Binbin; Song, Jinliang; Liu, Huizhen; Han, Buxing; Jiang, Tao; Fan, Honglei; Zhang, Zhaofu; Wu, Tianbin


    Exploration of new and effective routes to conduct organic reactions in water using the special properties of water/organics is of great importance. In this work, we performed the disproportionation of various aromatic alcohols in water and in different organic solvents. It was demonstrated that the disproportionation reactions of the alcohols were accelerated more effectively in water than organic-solvent-based or solvent-free reactions. A series of control experiments were conducted to study the mechanism of the accelerated reaction rate in water. It was shown that the reactants could emulsify the reactant/water systems at the reaction conditions owing to their amphiphilic nature. The regularly orientated reactant molecules at the water/reactant droplet interface improved the contact probability of the reactive groups and the Pd nanocatalysts, which is one of the main reasons for the enhanced reaction rate in water. Controlling the self-emulsification of amphiphilic reactant/water systems has great application potential for optimizing the rate and/or selectivity of many organic reactions.

  3. The Ricci Curvature of Half-flat Manifolds

    Ali, T; Ali, Tibra; Cleaver, Gerald B.


    We derive expressions for the Ricci curvature tensor and scalar in terms of intrinsic torsion classes of half-flat manifolds by exploiting the relationship between half-flat manifolds and non-compact $G_2$ holonomy manifolds. Our expressions are tested for Iwasawa and more general nilpotent manifolds. We also derive expressions, in the language of Calabi-Yau moduli spaces, for the torsion classes and the Ricci curvature of the \\emph{particular} half-flat manifolds that arise naturally via mirror symmetry in flux compactifications. Using these expressions we then derive a constraint on the K\\"ahler moduli space of type II string theory on these half-flat manifolds.

  4. Complex synchronization manifold in coupled time-delayed systems

    Hoang, Thang Manh, E-mail: [Signal and Information Processing Laboratory, Faculty of Electronics and Telecommunications, Hanoi University of Science and Technology, 1 Dai Co Viet, Hanoi (Viet Nam)


    Research highlights: The complex synchronization manifold in coupled multiple time delay systems is demonstrated for the first time. The complex synchronization manifold is in the form of sum of multiple simple manifolds. The equation for driving signal is the sum of nonlinearly transformed components of delayed state variable. - Abstract: In the present paper, the complex synchronization manifold generated in coupled multiple time delay systems is demonstrated for the first time. There, the manifold is in the form of sum of multiple simple manifolds. The structure of master is identical to that of slave. The equation for driving signal is the sum of nonlinearly transformed components of delayed state variable. The specific examples will demonstrate and verify the effectiveness of the proposed model.

  5. Regional manifold learning for deformable registration of brain MR images.

    Ye, Dong Hye; Hamm, Jihun; Kwon, Dongjin; Davatzikos, Christos; Pohl, Kilian M


    We propose a method for deformable registration based on learning the manifolds of individual brain regions. Recent publications on registration of medical images advocate the use of manifold learning in order to confine the search space to anatomically plausible deformations. Existing methods construct manifolds based on a single metric over the entire image domain thus frequently miss regional brain variations. We address this issue by first learning manifolds for specific regions and then computing region-specific deformations from these manifolds. We then determine deformations for the entire image domain by learning the global manifold in such a way that it preserves the region-specific deformations. We evaluate the accuracy of our method by applying it to the LPBA40 dataset and measuring the overlap of the deformed segmentations. The result shows significant improvement in registration accuracy on cortex regions compared to other state of the art methods.

  6. How to Find the Holonomy Algebra of a Lorentzian Manifold

    Galaev, Anton S.


    Manifolds with exceptional holonomy play an important role in string theory, supergravity and M-theory. It is explained how one can find the holonomy algebra of an arbitrary Riemannian or Lorentzian manifold. Using the de Rham and Wu decompositions, this problem is reduced to the case of locally indecomposable manifolds. In the case of locally indecomposable Riemannian manifolds, it is known that the holonomy algebra can be found from the analysis of special geometric structures on the manifold. If the holonomy algebra of a locally indecomposable Lorentzian manifold ( M, g) of dimension n is different from , then it is contained in the similitude algebra . There are four types of such holonomy algebras. Criterion to find the type of is given, and special geometric structures corresponding to each type are described. To each there is a canonically associated subalgebra . An algorithm to find is provided.

  7. The Structure of some Classes of -Contact Manifolds

    Mukut Mani Tripathi; Mohit Kumar Dwivedi


    We study projective curvature tensor in -contact and Sasakian manifolds. We prove that (1) if a -contact manifold is quasi projectively flat then it is Einstein and (2) a -contact manifold is -projectively flat if and only if it is Einstein Sasakian. Necessary and sufficient conditions for a -contact manifold to be quasi projectively flat and -projectively flat are obtained. We also prove that for a (2+1)-dimensional Sasakian manifold the conditions of being quasi projectively flat, -projectively flat and locally isometric to the unit sphere $S^{2n+1}(1)$ are equivalent. Finally, we prove that a compact -projectively flat -contact manifold with regular contact vector field is a principal $S^1$-bundle over an almost Kaehler space of constant holomorphic sectional curvature 4.

  8. Two-phase Flow Distribution in Heat Exchanger Manifolds

    Vist, Sivert


    The current study has investigated two-phase refrigerant flow distribution in heat exchange manifolds. Experimental data have been acquired in a heat exchanger test rig specially made for measurement of mass flow rate and gas and liquid distribution in the manifolds of compact heat exchangers. Twelve different manifold designs were used in the experiments, and CO2 and HFC-134a were used as refrigerants.

  9. P-connection on Riemannian almost product manifolds

    Mekerov, Dimitar


    In the present work, we introduce a linear connection (preserving the almost product structure and the Riemannian metric) on Riemannian almost product manifolds. This connection, called P-connection, is an analogue of the first canonical connection of Lichnerowicz in the Hermitian geometry and the B-connection in the geometry of the almost complex manifolds with Norden metric. Particularly, we consider the P-connection on a the class of manifolds with nonintegrable almost product structure.

  10. Some hyperbolic three-manifolds that bound geometrically

    KOLPAKOV, Alexander; Martelli, Bruno; Tschantz, Steven


    A closed connected hyperbolic $n$-manifold bounds geometrically if it is isometric to the geodesic boundary of a compact hyperbolic $(n+1)$-manifold. A. Reid and D. Long have shown by arithmetic methods the existence of infinitely many manifolds that bound geometrically in every dimension. We construct here infinitely many explicit examples in dimension $n=3$ using right-angled dodecahedra and $120$-cells and a simple colouring technique introduced by M. Davis and T. Januszkiewicz. Namely, fo...

  11. Equivariant Gromov-Witten Invariants of Algebraic GKM Manifolds

    Liu, Chiu-Chu Melissa; Sheshmani, Artan


    An algebraic GKM manifold is a non-singular algebraic variety equipped with an algebraic action of an algebraic torus, with only finitely many torus fixed points and finitely many 1-dimensional orbits. In this expository article, we use virtual localization to express equivariant Gromov-Witten invariants of any algebraic GKM manifold (which is not necessarily compact) in terms of Hodge integrals over moduli stacks of stable curves and the GKM graph of the GKM manifold.

  12. Notes on holonomy matrices of hyperbolic 3-manifolds with cusps

    Fukui, Fumitaka


    In this paper, we give a method to construct holonomy matrices of hyperbolic 3-manifolds by extending the known method of hyperbolic 2-manifolds. It enables us to consider hyperbolic 3-manifolds with nontrivial holonomies. We apply our method to an ideal tetrahedron and succeed in making the holonomies nontrivial. We also derive the partition function of the ideal tetrahedron with nontrivial holonomies by using the duality proposed by Dimofte, Gaiotto and Gukov.

  13. Frobenius manifolds, quantum cohomology, and moduli spaces

    Manin, Yuri I


    This is the first monograph dedicated to the systematic exposition of the whole variety of topics related to quantum cohomology. The subject first originated in theoretical physics (quantum string theory) and has continued to develop extensively over the last decade. The author's approach to quantum cohomology is based on the notion of the Frobenius manifold. The first part of the book is devoted to this notion and its extensive interconnections with algebraic formalism of operads, differential equations, perturbations, and geometry. In the second part of the book, the author describes the con

  14. M-theory and G2 manifolds

    Becker, Katrin; Becker, Melanie; Robbins, Daniel


    In this talk we report on recent progress in describing compactifications of string theory and M-theory on G2 and Spin(7) manifolds. We include the infinite set of α’-corrections and describe the entire tower of massless and massive Kaluza-Klein modes resulting from such compactifications. Contribution to the ‘Focus Issue on Gravity, Supergravity and Fundamental Physics: the Richard Arnowitt Symposium’, to be published in Physica Scripta. Based on a talk delivered by Becker at the workshop ‘Superstring Perturbation Theory’ at the Perimeter Institute, 22-24 April 2015.

  15. Semiclassical Asymptotics on Manifolds with Boundary

    Koldan, Nilufer; Shubin, Mikhail


    We discuss semiclassical asymptotics for the eigenvalues of the Witten Laplacian for compact manifolds with boundary in the presence of a general Riemannian metric. To this end, we modify and use the variational method suggested by Kordyukov, Mathai and Shubin (2005), with a more extended use of quadratic forms instead of the operators. We also utilize some important ideas and technical elements from Helffer and Nier (2006), who were the first to supply a complete proof of the full semi-classical asymptotic expansions for the eigenvalues with fixed numbers.

  16. Lefschetz Fibrations on Compact Stein Manifolds

    Akbulut, Selman


    Here we prove that a compact Stein manifold W of dimension 2n+2>4 admits a Lefschetz fibration over the 2-disk with Stein fibers, such that the monodromy of the fibration is a symplectomorphism induced by compositions of "generalized Dehn twists" along imbedded n-spheres on the generic fiber. Also, the open book on the boundary of W, which is determined by the fibration, is compatible with the contact structure induced by the Stein structure. This generalizes the Stein surface case of n=1, previously proven by Loi-Piergallini and Akbulut-Ozbagci.

  17. Manifold parameter space and its applications

    Sato, Atsushi


    We review the several features of the new parameter space which we presented in the previous paper, and show the differentiable manifold properties of this parameter space coordinate. Using this parameter coordinate we calculate three Feynman amplitudes of the vacuum polarization with a gluon loop, a quark loop and a ghost loop in QCD and show that the results are perfectly equal to those of the usual calculations by the Feynman parametrization technique in the scheme of the dimensional regularization. Then we try to calculate the anomalous magnetic moment of an on-shell quark in QCD by using the dimensional regularization, our new parametrization and integral method.

  18. Laplacian embedded regression for scalable manifold regularization.

    Chen, Lin; Tsang, Ivor W; Xu, Dong


    Semi-supervised learning (SSL), as a powerful tool to learn from a limited number of labeled data and a large number of unlabeled data, has been attracting increasing attention in the machine learning community. In particular, the manifold regularization framework has laid solid theoretical foundations for a large family of SSL algorithms, such as Laplacian support vector machine (LapSVM) and Laplacian regularized least squares (LapRLS). However, most of these algorithms are limited to small scale problems due to the high computational cost of the matrix inversion operation involved in the optimization problem. In this paper, we propose a novel framework called Laplacian embedded regression by introducing an intermediate decision variable into the manifold regularization framework. By using ∈-insensitive loss, we obtain the Laplacian embedded support vector regression (LapESVR) algorithm, which inherits the sparse solution from SVR. Also, we derive Laplacian embedded RLS (LapERLS) corresponding to RLS under the proposed framework. Both LapESVR and LapERLS possess a simpler form of a transformed kernel, which is the summation of the original kernel and a graph kernel that captures the manifold structure. The benefits of the transformed kernel are two-fold: (1) we can deal with the original kernel matrix and the graph Laplacian matrix in the graph kernel separately and (2) if the graph Laplacian matrix is sparse, we only need to perform the inverse operation for a sparse matrix, which is much more efficient when compared with that for a dense one. Inspired by kernel principal component analysis, we further propose to project the introduced decision variable into a subspace spanned by a few eigenvectors of the graph Laplacian matrix in order to better reflect the data manifold, as well as accelerate the calculation of the graph kernel, allowing our methods to efficiently and effectively cope with large scale SSL problems. Extensive experiments on both toy and real

  19. Optical manifold for light-emitting diodes

    Chaves, Julio C.; Falicoff, Waqidi; Minano, Juan C.; Benitez, Pablo; Parkyn, Jr., William A.; Alvarez, Roberto; Dross, Oliver


    An optical manifold for efficiently combining a plurality of blue LED outputs to illuminate a phosphor for a single, substantially homogeneous output, in a small, cost-effective package. Embodiments are disclosed that use a single or multiple LEDs and a remote phosphor, and an intermediate wavelength-selective filter arranged so that backscattered photoluminescence is recycled to boost the luminance and flux of the output aperture. A further aperture mask is used to boost phosphor luminance with only modest loss of luminosity. Alternative non-recycling embodiments provide blue and yellow light in collimated beams, either separately or combined into white.

  20. 3-manifolds with(out) metrics of nonpositive curvature

    Leeb, B


    In the context of Thurstons geometrisation program we address the question which compact aspherical 3-manifolds admit Riemannian metrics of nonpositive curvature. We show that non-geometric Haken manifolds generically, but not always, admit such metrics. More precisely, we prove that a Haken manifold with, possibly empty, boundary of zero Euler characteristic admits metrics of nonpositive curvature if the boundary is non-empty or if at least one atoroidal component occurs in its canonical topological decomposition. Our arguments are based on Thurstons Hyperbolisation Theorem. We give examples of closed graph-manifolds with linear gluing graph and arbitrarily many Seifert components which do not admit metrics of nonpositive curvature.

  1. Blow-up of generalized complex 4-manifolds

    Cavalcanti, Gil R


    We introduce blow-up and blow-down operations for generalized complex 4-manifolds. Combining these with a surgery analogous to the logarithmic transform, we then construct generalized complex structures on nCP2 # m \\bar{CP2} for n odd, a family of 4-manifolds which admit neither complex nor symplectic structures unless n=1. We also extend the notion of a symplectic elliptic Lefschetz fibration, so that it expresses a generalized complex 4-manifold as a fibration over a two-dimensional manifold with boundary.

  2. Noncommutative Deformations of Locally Symmetric K\\"ahler manifolds

    Hara, Kentaro


    We derive algebraic recurrence relations to obtain a deformation quantization with separation of variables for a locally symmetric K\\"ahler manifold. This quantization method is one of the ways to perform a deformation quantization of K\\"ahler manifolds, which is introduced by Karabegov. From the recurrence relations, concrete expressions of star products for one-dimensional local symmetric K\\"ahler manifolds and ${\\mathbb C}P^N$ are constructed. The recurrence relations for a Grassmann manifold $G_{2,2}$ are closely studied too.


    The life cycle design methodology was applied to the design analysis of three alternatives for the lower plehum of the air intake manifold for us with a 5.4L F-250 truck engine: a sand cast aluminum, a lost core molded nylon composite, and a vibration welded nylon composite. The ...

  4. On the trace-manifold generated by the deformations of a body-manifold

    Boja Nicolae


    Full Text Available In this paper, concerned to the study of continuous deformations of material media using some tools of modem differential geometry, a moving frame of Frenet type along the orbits of an one-parameter group acting on a so-called "trace-manifold", M, associated to the deformations, is constructed. The manifold M is defined as an infinite union of non-disjoint compact manifolds, generated by the consecutive positions in the Euclidean affine 3-space of a body-manifold under deformations in a closed time interval. We put in evidence a skew-symmetric band tensor of second order, ω, which describes the deformation in a small neighborhood of any point along the orbits. The non-null components ωi,i+i, (i =1,2, of ω are assimilated as like curvatures at each point of an orbit in the planes generated by the pairs of vectors (ĕi,ĕi+i of a moving frame in M associated to the orbit in a similar way as the Frenet's frame is. Also a formula for the energy of the orbits is given and its relationship with some stiffness matrices is established.

  5. Enhanced bactericidal action of acidified sodium chlorite caused by the saturation of reactants.

    Kim, N H; Park, T H; Rhee, M S


    Factors affecting the antibacterial action of acidified sodium chlorite (ASC), a widely used disinfectant, have not been determined. This study investigated the significant factors suggesting efficient production method to maximize bactericidal action of ASC. The effects of (i) preparation procedures (total three methods); (ii) initial concentrations of reactants: sodium chlorite (SC) and citric acid (CTA) (up to maximum solubility of each reactant) and (iii) final pH values (3·0 and 2·5) to the bactericidal action of ASC were investigated with a fixed final concentration of SC (10 ppm) using various foodborne pathogens (Escherichia coli O157:H7, Listeria monocytogenes, Salmonella Typhimurium and Staphylococcus aureus). The antimicrobial compounds produced and the bactericidal effects depended on the preparation procedure and the initial concentrations of the reactants. The ASC prepared by premixing highly concentrated reactants (in particular > 40%) followed by dilution (dilution after reaction, DAR) was more effective in inactivating foodborne pathogens, and it produced higher antimicrobial compound (Cl(2) and ClO(2)) yields than the other procedures. A 5-min treatment with ASC, produced using the other procedures, resulted in a reduction of < 3·5 log CFU ml(-1) (Gram positive = 0·18-0·78; Gram negative = 0·03-3·49 log CFU ml(-1)), whereas ASC produced with the DAR procedure using the saturated reactants completely inactivated all of the test pathogens within 5 min without recovery (initial concentration = 6·94-7·08 log CFU ml(-1)). The ASC production with the DAR procedure using the saturated reactants maximizes both the antimicrobial compound yields and bactericidal effects of the ASC solutions. This study will contribute to increase the efficiency of ASC treatments for disinfections reducing the effective SC concentrations for industrial use. © 2014 The Society for Applied Microbiology.

  6. Influences of flow loss and inlet distortions from radial inlets on the performances of centrifugal compressor stages

    Han, Feng Hui; Mao, Yi Jun [School of Energy and Power Engineering, Xi' an Jiaotong University, Xi' an (China); Tan, Ji Jian [Dept. of Research and Development, Shenyang Blower Works Group Co., Ltd., Shenyang (China)


    Radial inlets are typical upstream components of multistage centrifugal compressors. Unlike axial inlets, radial inlets generate additional flow loss and introduce flow distortions at impeller inlets. Such distortions negatively affect the aerodynamic performance of compressor stages. In this study, industrial centrifugal compressor stages with different radial inlets are investigated via numerical simulations. Two reference models were built, simulated, and compared with each original compressor stage to analyze the respective and coupling influences of flow loss and inlet distortions caused by radial inlets on the performances of the compressor stage and downstream components. Flow loss and inlet distortions are validated as the main factors through which radial inlets negatively affect compressor performance. Results indicate that flow loss inside radial inlets decreases the performance of the whole compressor stage but exerts minimal effect on downstream components. By contrast, inlet distortions induced by radial inlets negatively influence the performance of the whole compressor stage and exert significant effects on downstream components. Therefore, when optimizing radial inlets, the reduction of inlet distortions might be more effective than the reduction of flow loss. This research provides references and suggestions for the design and improvement of radial inlets.

  7. Willmore Spheres in Compact Riemannian Manifolds

    Mondino, Andrea


    The paper is devoted to the variational analysis of the Willmore, and other L^2 curvature functionals, among immersions of 2-dimensional surfaces into a compact riemannian m-manifold (M^m,h) with m>2. The goal of the paper is twofold, on one hand, we give the right setting for doing the calculus of variations (including min max methods) of such functionals for immersions into manifolds and, on the other hand, we prove existence results for possibly branched Willmore spheres under various constraints (prescribed homotopy class, prescribed area) or under curvature assumptions for M^m. To this aim, using the integrability by compensation, we develop first the regularity theory for the critical points of such functionals. We then prove a rigidity theorem concerning the relation between CMC and Willmore spheres. Then we prove that, for every non null 2-homotopy class, there exists a representative given by a Lipschitz map from the 2-sphere into M^m realizing a connected family of conformal smooth (possibly branche...

  8. Real group orbits on flag manifolds

    Akhiezer, Dmitri


    In this survey, we gather together various results on the action of a real form of a complex semisimple Lie group on its flag manifolds. We start with the finiteness theorem of J.Wolf implying that at least one of the orbits is open. We give a new proof of the converse statement for real forms of inner type, essentially due to F.M.Malyshev. Namely, if a real semisimple Lie group of inner type has an open orbit on an algebraic homogeneous space of the complexified group then the homogeneous space is a flag manifold. To prove this, we recall, partly with proofs, some results of A.L.Onishchik on the factorizations of reductive groups. Finally, we discuss the cycle spaces of open orbits and define the crown of a symmetric space of non-compact type. With some exceptions, the cycle space agrees with the crown. We sketch a complex analytic proof of this result, due to G.Fels, A.Huckleberry and J.Wolf.



    Abstract The geometry of hypersurfaces of a Kaehler manifold are studied. Some wellknown formulas and theorems in theory of surfaces of Euclidean 3-space are generalized to the hypersurfaces in a Kaehler manifold, such as Gauss's formulae, second fundamental form, the equation of Gauss and Codazzi and so forth.



    Using the mechanical principle, the theory of modern geometry and advanced calculus, Hamiltonian mechanics was generalized to Kahler manifolds, and the Hamiltonian mechanics on Kahler manifolds was established. Then the complex mathematical aspect of Hamiltonian vector field and Hamilton's equations was obtained, and so on.

  11. The quantum equivariant cohomology of toric manifolds through mirror symmetry

    Baptista, J.M.


    Using mirror symmetry as described by Hori and Vafa, we compute the quantum equivariant cohomology ring of toric manifolds. This ring arises naturally in topological gauged sigma-models and is related to the Hamiltonian Gromov-Witten invariants of the target manifold.

  12. Manifold mapping: a two-level optimization technique

    Echeverria, D.; Hemker, P.W.


    In this paper, we analyze in some detail the manifold-mapping optimization technique introduced recently [Echeverría and Hemker in space mapping and defect correction. Comput Methods Appl Math 5(2): 107-–136, 2005]. Manifold mapping aims at accelerating optimal design procedures that otherwise requi

  13. Deformations of log-Lagrangian submanifolds of Poisson manifolds


    We consider Lagrangian-like submanifolds in certain even-dimensional 'symplectic-like' Poisson manifolds. We show, under suitable transversality hypotheses, that the pair consisting of the ambient Poisson manifold and the submanifold has unobstructed deformations and that the deformations automatically preserve the Lagrangian-like property.

  14. Approximate Inertial Manifolds for Chemotaxis-Growth System

    Hong LUO; Zhilin PU


    The long-time behaviour of solution to chemotaxis-growth system with Neumann condition is considered in this paper.The approximate inertial manifolds of such equations are constructed based on the contraction principle,and the orders of approximations of the manifolds to the global attractor are derived.

  15. Embedding universal covers of graph manifolds in products of trees

    Hume, David


    We prove that the universal cover of any graph manifold quasi-isometrically embeds into a product of three trees. In particular we show that the Assouad-Nagata dimension of the universal cover of any closed graph manifold is 3, proving a conjecture of Smirnov.

  16. Spectral invariants of operators of Dirac type on partitioned manifolds

    Booss-Bavnbek, Bernhelm; Bleecker, D.


    We review the concepts of the index of a Fredholm operator, the spectral flow of a curve of self-adjoint Fredholm operators, the Maslov index of a curve of Lagrangian subspaces in symplectic Hilbert space, and the eta invariant of operators of Dirac type on closed manifolds and manifolds with bou...

  17. Existence and bifurcation of integral manifolds with applications

    HAN; Mao'an; CHEN; Xianfeng


    In this paper a bifurcation theorem on the existence of integral manifolds is obtained by using contracting principle. As an application, sufficient conditions for a higher dimensional system to have an integral manifold are given. Especially the existence and uniqueness of a 3-dimensional invariant torus appearing in a 4-dimensional autonomous system with singularity of codimension two are proved.

  18. Variable volume combustor with nested fuel manifold system

    McConnaughhay, Johnie Franklin; Keener, Christopher Paul; Johnson, Thomas Edward; Ostebee, Heath Michael


    The present application provides a combustor for use with a gas turbine engine. The combustor may include a number of micro-mixer fuel nozzles, a fuel manifold system in communication with the micro-mixer fuel nozzles to deliver a flow of fuel thereto, and a linear actuator to maneuver the micro-mixer fuel nozzles and the fuel manifold system.

  19. Characterizing pathological deviations from normality using constrained manifold-learning.

    Duchateau, Nicolas; De Craene, Mathieu; Piella, Gemma; Frangi, Alejandro F


    We propose a technique to represent a pathological pattern as a deviation from normality along a manifold structure. Each subject is represented by a map of local motion abnormalities, obtained from a statistical atlas of motion built from a healthy population. The algorithm learns a manifold from a set of patients with varying degrees of the same pathology. The approach extends recent manifold-learning techniques by constraining the manifold to pass by a physiologically meaningful origin representing a normal motion pattern. Individuals are compared to the manifold population through a distance that combines a mapping to the manifold and the path along the manifold to reach its origin. The method is applied in the context of cardiac resynchronization therapy (CRT), focusing on a specific motion pattern of intra-ventricular dyssynchrony called septal flash (SF). We estimate the manifold from 50 CRT candidates with SF and test it on 38 CRT candidates and 21 healthy volunteers. Experiments highlight the need of nonlinear techniques to learn the studied data, and the relevance of the computed distance for comparing individuals to a specific pathological pattern.

  20. Hetero-manifold Regularisation for Cross-modal Hashing.

    Zheng, Feng; Tang, Yi; Shao, Ling


    Recently, cross-modal search has attracted considerable attention but remains a very challenging task because of the integration complexity and heterogeneity of the multi-modal data. To address both challenges, in this paper, we propose a novel method termed hetero-manifold regularisation (HMR) to supervise the learning of hash functions for efficient cross-modal search. A hetero-manifold integrates multiple sub-manifolds defined by homogeneous data with the help of cross-modal supervision information. Taking advantages of the hetero-manifold, the similarity between each pair of heterogeneous data could be naturally measured by three order random walks on this hetero-manifold. Furthermore, a novel cumulative distance inequality defined on the hetero-manifold is introduced to avoid the computational difficulty induced by the discreteness of hash codes. By using the inequality, cross-modal hashing is transformed into a problem of hetero-manifold regularised support vector learning. Therefore, the performance of cross-modal search can be significantly improved by seamlessly combining the integrated information of the hetero-manifold and the strong generalisation of the support vector machine. Comprehensive experiments show that the proposed HMR achieve advantageous results over the state-of-the-art methods in several challenging cross-modal tasks.

  1. Manifold mapping: a two-level optimization technique

    Echeverría, D.; Hemker, P.W.


    In this paper, we analyze in some detail the manifold-mapping optimization technique introduced recently [Echeverría and Hemker in space mapping and defect correction. Comput Methods Appl Math 5(2): 107--136, 2005]. Manifold mapping aims at accelerating optimal design procedures that otherwise requi

  2. 4-manifolds and intersection forms with local coefficients

    Frøyshov, Kim Anders


    We extend Donaldson's diagonalization theorem to intersection forms with certain local coefficients, under some constraints. This provides new examples of non-smoothable topological 4-manifolds.......We extend Donaldson's diagonalization theorem to intersection forms with certain local coefficients, under some constraints. This provides new examples of non-smoothable topological 4-manifolds....

  3. Hilbert manifold structure for asymptotically hyperbolic relativistic initial data

    Fougeirol, Jérémie


    We provide a Hilbert manifold structure {\\`a} la Bartnik for the space of asymptotically hyperbolic initial data for the vacuum constraint equations. The adaptation led us to prove new weighted Poincar{\\'e} and Korn type inequalities for AH manifolds with inner boundary and weakly regular metric.

  4. Dynamical systems on a Riemannian manifold that admit normal shift

    Boldin, A.Yu.; Dmitrieva, V.V.; Safin, S.S.; Sharipov, R.A. [Bashkir State Univ. (Russian Federation)


    Newtonian dynamical systems that admit normal shift on an arbitrary Riemannian manifold are considered. The determining equations for these systems, which constitute the condition of weak normality, are derived. The extension of the algebra of tensor fields to manifolds is considered.

  5. Solid oxide fuel cell systems with hot zones having improved reactant distribution

    Poshusta, Joseph C.; Booten, Charles W.; Martin, Jerry L.


    A Solid Oxide Fuel Cell (SOFC) system having a hot zone with a center cathode air feed tube for improved reactant distribution, a CPOX reactor attached at the anode feed end of the hot zone with a tail gas combustor at the opposing end for more uniform heat distribution, and a counter-flow heat exchanger for efficient heat retention.

  6. The catalytic combustion of natural gas in a membrane reactor with separate feed of reactants

    Neomagus, H.W.J.P.; Saracco, G.; Wessel, H.F.W.; Versteeg, G.F.


    This paper provides an experimental and modelling analysis of the performance of a membrane reactor with separate feed of reactants for the combustion of methane. In this reactor concept methane and air streams are fed at opposite sides of a Pt/γ-Al2O3-activated porous membrane which hosts their

  7. The catalytic combustion of natural gas in a membrane reactor with separate feed of reactants

    Neomagus, H.W.J.P.; Saracco, G.; Wessel, H.F.W.; Versteeg, G.F.


    This paper provides an experimental and modelling analysis of the performance of a membrane reactor with separate feed of reactants for the combustion of methane. In this reactor concept methane and air streams are fed at opposite sides of a Pt/γ-Al2O3-activated porous membrane which hosts their rea

  8. Catalytic membrane in denitrification of water: a means to facilitate intraporous diffusion of reactants

    Ilinich, O.M.; Cuperus, F.P.; Gemert, van R.W.; Gribov, E.N.; Nosova, L.V.


    The series of mono- and bi-metallic catalysts with Pd and/or Cu supported over γ-Al 2O 3 was investigated with respect to reduction of nitrate and nitrite ions in water by hydrogen. Pronounced limitations of catalytic performance due to intraporous diffusion of the reactants were observed in the rea

  9. Isolation of a lipopolysaccharide-binding acute phase reactant from rabbit serum.

    Tobias, P S; Soldau, K; Ulevitch, R J


    This report describes the purification of an acute phase reactant from acute phase rabbit serum, which endows normal serum with the properties of acute phase serum, insofar as LPS is concerned. The acute phase reactant is referred to as LPS-binding protein, or LBP. LBP was purified approximately 2,000-fold by chromatography of acute phase serum on Bio-Rex 70 and Mono-Q resins. The resulting preparation consisted of two glycoproteins having molecular weights of 60,500 and 58,000; the two were obtained in a variable ratio, usually near 10:1, respectively. After separation by SDS-PAGE, the N-terminal 36 amino acid sequences of the two proteins were identical. From the N-terminal sequence, as well as other properties of LBP, LBP appears to be unrelated to any known acute phase reactants. The direct interaction of LPS and LBP was inferred from two types of evidence: first, immunoprecipitation of [3H]LPS from APRS by anti-LBP sera; and second, by the 125I-labeling of LBP when APRS-containing 125I-labeled 2-(p-azidosalicylamido)ethyl 1,3'-dithiopropionyl-LPS was photolysed. The data presented here support the concept that the 60-kD glycoprotein we have termed LBP is a newly recognized acute phase reactant that may modulate the biochemical and biologic properties of LPS in vivo.

  10. 共反应剂TPPD的制备%Synthesis of a nevol co-reactant TPPD

    冉红; 梁艳霞; 刘娟娟; 肖丹


    本实验合成了一种共反应剂N,N,N’,N’-4-丙基-戊二胺(TPPD),它的分子中含有两个叔氨基,与传统的共反应剂三丙胺(TPA)相比增加了一个氮的活性位点.并且分子中的碳碳长链使得TPPD的疏水性增加,因此能与钌配合物[Ru(bpy)3] [4-(Clph)4B]2同时固定到ITO电极上,减少了ECL过程中的共反应剂的消耗.%In this work,a new organic-soluble co-reactant N,N,N',N'-tetrakis(propyl)-pentanediamine(TPPD) was synthesized. It contains two tertiary amines. Compared with the traditional co-reactant, such as tripropylamine (TPA) it has two nitrogen active sites. The new co-reactant is very hydrophobic and thus could be co-immobilized with tris(2,2'-bipyridine)ruthenium(II)ditetrakis (4-chlorophenyl)borate[Ru(bpy)3] [4-(Clph)4B]2 on an indium tin oxide(ITO) electrode. So the consumption of co-reactant is greatly reduced in the electrochemiluminescent(ECL) process.

  11. Catalytic membrane in denitrification of water: a means to facilitate intraporous diffusion of reactants

    Ilinich, O.M.; Cuperus, F.P.; Gemert, van R.W.; Gribov, E.N.; Nosova, L.V.


    The series of mono- and bi-metallic catalysts with Pd and/or Cu supported over γ-Al 2O 3 was investigated with respect to reduction of nitrate and nitrite ions in water by hydrogen. Pronounced limitations of catalytic performance due to intraporous diffusion of the reactants were observed in the

  12. The catalytic combustion of natural gas in a membrane reactor with separate feed of reactants

    Neomagus, H.W.J.P.; Saracco, G.; Wessel, H.F.W.; Versteeg, G.F.


    This paper provides an experimental and modelling analysis of the performance of a membrane reactor with separate feed of reactants for the combustion of methane. In this reactor concept methane and air streams are fed at opposite sides of a Pt/γ-Al2O3-activated porous membrane which hosts their rea

  13. Cold water inlet in solar tanks - valuation

    Andersen, Elsa


    The aim of the project is to make a proposal for how to value a storage tank with a poor design of the cold water inlet. Based on measurements and calculations a number of curves, which are valid for this valuation, are worked out. Based on a simple test with a uniform heated storage tank the ratio...

  14. Miniature piezo electric vacuum inlet valve

    Keville, Robert F.; Dietrich, Daniel D.


    A miniature piezo electric vacuum inlet valve having a fast pulse rate and is battery operated with variable flow capability. The low power (piezo electric valves which require preloading of the crystal drive mechanism and 120 Vac, thus the valve of the present invention is smaller by a factor of three.

  15. Manifold learning based feature extraction for classification of hyper-spectral data

    Lunga, D


    Full Text Available often lie on sparse, nonlinear manifolds whose geometric and topological structures can be exploited via manifold learning techniques. In this article, we focused on demonstrating the opportunities provided by manifold learning for classification...

  16. Investigating performance of microchannel evaporators with different manifold structures

    Shi, Junye; Qu, Xiaohua; Qi, Zhaogang; Chen, Jiangping [Institute of Refrigeration and Cryogenics, Shanghai Jiao Tong University, No. 800, Dongchuan Rd, Shanghai 200240 (China)


    In this paper, the performances of microchannel evaporators with different manifold structures are experimentally investigated. Eight evaporator samples with 7 different designs of the I/O manifold and 5 different designs of the return manifold are made for this study. The performances of the evaporator samples are tested on a psychometric calorimeter test bench with the refrigerant 134A at a real automotive AC condition. The results on the variations of the cooling capacity and air temperature distribution of the evaporator due to the deflector designs in the I/O manifold and flow hole arrangements in the return manifold are presented and analyzed. By studying the KPI's for the performance of an evaporator, the design trade-off for an evaporator designer is summarized and discussed. (author)

  17. Natural connections on conformal Riemannian P-manifolds

    Gribacheva, Dobrinka


    The class of conformal Riemannian P-manifolds is the largest class of Riemannian almost product manifolds, which is closed with respect to the group of the conformal transformations of the Riemannian metric. This class is an analogue of the class of conformal Kaehler manifolds in almost Hermitian geometry. In the present work we study on a conformal Riemannian P-manifold (M, P, g) the natural linear connections, i.e. the linear connections preserving the almost product structure P and the Riemannian metric g. We find necessary and sufficient conditions the curvature tensor of such a connection to have similar properties like the ones of the Kaehler tensor in Hermitian geometry. We determine the type of the manifolds admitting a natural connection with a parallel torsion.

  18. MOCVD manifold switching effects on growth and characterization

    Clark, Ivan O.; Fripp, Archibald L.; Jesser, William A.


    A combined modeling and experimental approach is used to quantify the effects of various manifold components on the switching speed in metalorganic chemical vapor deposition (MOCVD). In particular, two alternative vent-run high-speed switching manifold designs suitable for either continuous or interrupted growth have been investigated. Both designs are incorporated in a common manifold, instrumented with a mass spectrometer. The experiments have been performed using nitrogen as the transport gas and argon as the simulated source gas. The advantages and limitations of two designs are discussed. It is found that while constant flow manifold switching systems may have fluid dynamic advantages, care must be taken to minimize sections of the supply manifold with low flow rates if rapid changes in alloy composition are required.

  19. Some conformally flat spin manifolds, Dirac operators and automorphic forms

    Krau[Ss]Har, R. S.; Ryan, John


    In this paper we study Clifford and harmonic analysis on some examples of conformal flat manifolds that have a spinor structure, or more generally, at least a pin structure. The examples treated here are manifolds that can be parametrized by U/[Gamma] where U is a subdomain of either Sn or Rn and [Gamma] is a Kleinian group acting discontinuously on U. The examples studied here include RPn and the Hopf manifolds S1xSn-1. Also some hyperbolic manifolds will be treated. Special kinds of Clifford-analytic automorphic forms associated to the different choices of [Gamma] are used to construct explicit Cauchy kernels, Cauchy integral formulas, Green's kernels and formulas together with Hardy spaces and Plemelj projection operators for Lp spaces of hypersurfaces lying in these manifolds.

  20. Local Linear Regression on Manifolds and its Geometric Interpretation

    Cheng, Ming-Yen


    We study nonparametric regression with high-dimensional data, when the predictors lie on an unknown, lower-dimensional manifold. In this context, recently \\cite{aswani_bickel:2011} suggested performing the conventional local linear regression (LLR) in the ambient space and regularizing the estimation problem using information obtained from learning the manifold locally. By contrast, our approach is to reduce the dimensionality first and then construct the LLR directly on a tangent plane approximation to the manifold. Under mild conditions, asymptotic expressions for the conditional mean squared error of the proposed estimator are derived for both the interior and the boundary cases. One implication of these results is that the optimal convergence rate depends only on the intrinsic dimension $d$ of the manifold, but not on the ambient space dimension $p$. Another implication is that the estimator is design adaptive and automatically adapts to the boundary of the unknown manifold. The bias and variance expressi...

  1. Convex functions and optimization methods on Riemannian manifolds

    Udrişte, Constantin


    This unique monograph discusses the interaction between Riemannian geometry, convex programming, numerical analysis, dynamical systems and mathematical modelling. The book is the first account of the development of this subject as it emerged at the beginning of the 'seventies. A unified theory of convexity of functions, dynamical systems and optimization methods on Riemannian manifolds is also presented. Topics covered include geodesics and completeness of Riemannian manifolds, variations of the p-energy of a curve and Jacobi fields, convex programs on Riemannian manifolds, geometrical constructions of convex functions, flows and energies, applications of convexity, descent algorithms on Riemannian manifolds, TC and TP programs for calculations and plots, all allowing the user to explore and experiment interactively with real life problems in the language of Riemannian geometry. An appendix is devoted to convexity and completeness in Finsler manifolds. For students and researchers in such diverse fields as pu...

  2. Noninvariant Hypersurfaces of a Nearly Trans-Sasakian Manifolds

    Satya Prakash Yadav


    Full Text Available The present paper focuses on the study of noninvariant hypersurfaces of a nearly trans-Sasakian manifold equipped with (f,g,u,v,λ-structure. Initially some properties of this structure have been discussed. Further, the second fundamental forms of noninvariant hypersurfaces of nearly trans-Sasakian manifolds and nearly cosymplectic manifolds with (f,g,u,v,λ-structure have been calculated provided f is parallel. In addition, the eigenvalues of f have been found and proved that a noninvariant hypersurface with (f,g,u,v,λ-structure of nearly cosymplectic manifold with contact structure becomes totally geodesic. Finally the paper has been concluded by investigating the necessary condition for totally geodesic or totally umbilical noninvariant hypersurface with (f,g,u,v,λ-structure of a nearly trans-Sasakian manifold.

  3. Model Transport: Towards Scalable Transfer Learning on Manifolds

    Freifeld, Oren; Hauberg, Søren; Black, Michael J.


    “commutes” with learning. Consequently, our compact framework, applicable to a large class of manifolds, is not restricted by the size of either the training or test sets. We demonstrate the approach by transferring PCA and logistic-regression models of real-world data involving 3D shapes and image......We consider the intersection of two research fields: transfer learning and statistics on manifolds. In particular, we consider, for manifold-valued data, transfer learning of tangent-space models such as Gaussians distributions, PCA, regression, or classifiers. Though one would hope to simply use...... ordinary Rn-transfer learning ideas, the manifold structure prevents it. We overcome this by basing our method on inner-product-preserving parallel transport, a well-known tool widely used in other problems of statistics on manifolds in computer vision. At first, this straightforward idea seems to suffer...

  4. Novel Adsorbent-Reactants for Treatment of Ash and Scrubber Pond Effluents

    Bill Batchelor; Dong Suk Han; Eun Jung Kim


    The overall goal of this project was to evaluate the ability of novel adsorbent/reactants to remove specific toxic target chemicals from ash and scrubber pond effluents while producing stable residuals for ultimate disposal. The target chemicals studied were arsenic (As(III) and As(V)), mercury (Hg(II)) and selenium (Se(IV) and Se(VI)). The adsorbent/reactants that were evaluated are iron sulfide (FeS) and pyrite (FeS{sub 2}). Procedures for measuring concentrations of target compounds and characterizing the surfaces of adsorbent-reactants were developed. Effects of contact time, pH (7, 8, 9, 10) and sulfate concentration (0, 1, 10 mM) on removal of all target compounds on both adsorbent-reactants were determined. Stability tests were conducted to evaluate the extent to which target compounds were released from the adsorbent-reactants when pH changed. Surface characterization was conducted with x-ray photoelectron spectroscopy (XPS) to identify reactions occurring on the surface between the target compounds and surface iron and sulfur. Results indicated that target compounds could be removed by FeS{sub 2} and FeS and that removal was affected by time, pH and surface reactions. Stability of residuals was generally good and appeared to be affected by the extent of surface reactions. Synthesized pyrite and mackinawite appear to have the required characteristics for removing the target compounds from wastewaters from ash ponds and scrubber ponds and producing stable residuals.

  5. Evolutionary global optimization, manifolds and applications

    Aguiar e Oliveira Junior, Hime


    This book presents powerful techniques for solving global optimization problems on manifolds by means of evolutionary algorithms, and shows in practice how these techniques can be applied to solve real-world problems. It describes recent findings and well-known key facts in general and differential topology, revisiting them all in the context of application to current optimization problems. Special emphasis is put on game theory problems. Here, these problems are reformulated as constrained global optimization tasks and solved with the help of Fuzzy ASA. In addition, more abstract examples, including minimizations of well-known functions, are also included. Although the Fuzzy ASA approach has been chosen as the main optimizing paradigm, the book suggests that other metaheuristic methods could be used as well. Some of them are introduced, together with their advantages and disadvantages. Readers should possess some knowledge of linear algebra, and of basic concepts of numerical analysis and probability theory....

  6. Geometric solitons of Hamiltonian flows on manifolds

    Song, Chong, E-mail: [School of Mathematical Sciences, Xiamen University, Xiamen 361005 (China); Sun, Xiaowei, E-mail: [School of Applied Mathematics, Central University of Finance and Economics, Beijing 100081 (China); Wang, Youde, E-mail: [Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190 (China)


    It is well-known that the LIE (Locally Induction Equation) admit soliton-type solutions and same soliton solutions arise from different and apparently irrelevant physical models. By comparing the solitons of LIE and Killing magnetic geodesics, we observe that these solitons are essentially decided by two families of isometries of the domain and the target space, respectively. With this insight, we propose the new concept of geometric solitons of Hamiltonian flows on manifolds, such as geometric Schrödinger flows and KdV flows for maps. Moreover, we give several examples of geometric solitons of the Schrödinger flow and geometric KdV flow, including magnetic curves as geometric Schrödinger solitons and explicit geometric KdV solitons on surfaces of revolution.

  7. The Operator Manifold Formalism; 2, Physical Applications

    Ter-Kazarian, G T


    Within the operator manifold approach (part I, hep-th/9812181) we derive the Gell-Mann-Nishijima relation and flavour group, whereas the leptons are particles with integer electric and leptonic charges and free of confinement, while quarks carry fractional electric and baryonic charges and imply the confinement. We consider the unified electroweak interactions with small number of free parameters, exploit the background of the local expanded symmetry $SU(2)\\otimes U(1)$ and P-violation. The Weinberg mixing angle is shown to have fixed value at $30^{o}$. The Higgs bosons arise on an analogy of the Cooper pairs in superconductivity. Within the present microscopic approach we predict the Kobayashi-Maskawa quark flavour mixing; the appearance of the CP-violation phase; derive the mass-spectrum of leptons and quarks, as well as other emerging particles, and also some useful relations between their masses.

  8. Killing superalgebras for Lorentzian four-manifolds

    de Medeiros, Paul; Santi, Andrea


    We determine the Killing superalgebras underpinning field theories with rigid unextended supersymmetry on Lorentzian four-manifolds by re-interpreting them as filtered deformations of $\\mathbb{Z}$-graded subalgebras with maximum odd dimension of the $N{=}1$ Poincar\\'e superalgebra in four dimensions. Part of this calculation involves computing a Spencer cohomology group which, by analogy with a similar result in eleven dimensions, prescribes a notion of Killing spinor, which we identify with the defining condition for bosonic supersymmetric backgrounds of minimal off-shell supergravity in four dimensions. We prove that such Killing spinors always generate a Lie superalgebra, and that this Lie superalgebra is a filtered deformation of a subalgebra of the $N{=}1$ Poincar\\'e superalgebra in four dimensions. Demanding the flatness of the connection defining the Killing spinors, we obtain equations satisfied by the maximally supersymmetric backgrounds. We solve these equations, arriving at the classification of ma...

  9. An Underlying Geometrical Manifold for Hamiltonian Mechanics

    Horwitz, L P; Levitan, J; Lewkowicz, M


    We show that there exists an underlying manifold with a conformal metric and compatible connection form, and a metric type Hamiltonian (which we call the geometrical picture) that can be put into correspondence with the usual Hamilton-Lagrange mechanics. The requirement of dynamical equivalence of the two types of Hamiltonians, that the momenta generated by the two pictures be equal for all times, is sufficient to determine an expansion of the conformal factor, defined on the geometrical coordinate representation, in its domain of analyticity with coefficients to all orders determined by functions of the potential of the Hamilton-Lagrange picture, defined on the Hamilton-Lagrange coordinate representation, and its derivatives. Conversely, if the conformal function is known, the potential of a Hamilton-Lagrange picture can be determined in a similar way. We show that arbitrary local variations of the orbits in the Hamilton-Lagrange picture can be generated by variations along geodesics in the geometrical pictu...

  10. On timelike surfaces in Lorentzian manifolds

    Hasse, Wolfgang


    We discuss the geometry of timelike surfaces (two-dimensional submanifolds) in a Lorentzian manifold and its interpretation in terms of general relativity. A classification of such surfaces is presented which distinguishes four cases of special algebraic properties of the second fundamental form from the generic case. In the physical interpretation a timelike surface can be viewed as the worldsheet of a ``track'', and timelike curves in this surface can be viewed as the worldlines of observers who are bound to the track, like someone sitting in a roller-coaster car. With this interpretation, our classification turns out to be closely related to (i) the visual appearance of the track, (ii) gyroscopic transport along the track, and (iii) inertial forces perpendicular to the track. We illustrate our general results with timelike surfaces in the Kerr-Newman spacetime.

  11. Cusp geometry of fibered 3-manifolds

    Futer, David


    Let F be a surface and suppose that \\phi: F -> F is a pseudo-Anosov homeomorphism fixing a puncture p of F. The mapping torus M = M_\\phi\\ is hyperbolic and contains a maximal cusp C about the puncture p. We show that the area and height of the cusp torus bounding C are equal, up to explicit multiplicative error, to the stable translation distance of \\phi\\ acting on the arc complex A(F,p). Our proofs rely on elementary facts about the hyperbolic geometry of pleated surfaces. In particular, we do not use any deep results in Teichmueller theory, Kleinian group theory, or the coarse geometry of A(F,p). A similar result holds for quasi-Fuchsian manifolds N = (F x R). In that setting, we prove a combinatorial estimate on the area and height of the cusp annulus in the convex core of N and give explicit multiplicative and additive errors.

  12. Biomedical data analysis by supervised manifold learning.

    Alvarez-Meza, A M; Daza-Santacoloma, G; Castellanos-Dominguez, G


    Biomedical data analysis is usually carried out by assuming that the information structure embedded into the biomedical recordings is linear, but that statement actually does not corresponds to the real behavior of the extracted features. In order to improve the accuracy of an automatic system to diagnostic support, and to reduce the computational complexity of the employed classifiers, we propose a nonlinear dimensionality reduction methodology based on manifold learning with multiple kernel representations, which learns the underlying data structure of biomedical information. Moreover, our approach can be used as a tool that allows the specialist to do a visual analysis and interpretation about the studied variables describing the health condition. Obtained results show how our approach maps the original high dimensional features into an embedding space where simple and straightforward classification strategies achieve a suitable system performance.

  13. Stochastic gradient descent on Riemannian manifolds

    Bonnabel, Silvere


    Stochastic gradient descent is a simple appproach to find the local minima of a function whose evaluations are corrupted by noise. In this paper, mostly motivated by machine learning applications, we develop a procedure extending stochastic gradient descent algorithms to the case where the function is defined on a Riemannian manifold. We prove that, as in the Euclidian case, the descent algorithm converges to a critical point of the cost function. The algorithm has numerous potential applications, and we show several well-known algorithms can be cast in our versatile geometric framework. We also address the gain tuning issue in connection with the tools of the recent theory of symmetry-preserving observers.

  14. Classification of Framed Links in 3-Manifolds

    Matija Cencelj; Dušan Repovš; Mikhail B Skopenkov


    We present a short and complete proof of the following Pontryagin theorem, whose original proof was complicated and has never been published in detail. Let be a connected oriented closed smooth 3-manifold, $L_1(M)$ be the set of framed links in up to a framed cobordism, and $\\deg: L_1(M)→ H_1(M;\\mathbb{Z})$ be the map taking a framed link to its homology class. Then for each $\\in H_1(M;\\mathbb{Z})$ there is a one-to-one correspondence between the set $\\deg^{-1}$ and the group $\\mathbb{Z}_{2d()}$, where () is the divisibility of the projection of to the free part of $H_1(M;\\mathbb{Z})$.

  15. Diffusion Harmonics and Dual Geometry on Carnot Manifolds

    Constantin, Sarah

    The "curse of dimensionality" motivates the importance of techniques for computing low-dimensional approximations of high-dimensional data. It is often necessary to use nonlinear techniques to recover a low-dimensional manifold embedded via a nonlinear map in a high-dimensional space; this family of techniques is referred to as "manifold learning." The accuracy of manifold-learning-based approximations is founded on asymptotic results that assume the data is drawn from a low-dimensional Riemannian manifold. However, in natural datasets, this assumption is often overly restrictive. In the first part of this thesis we examine a more general class of manifolds known as Carnot manifolds, a type of sub-Riemannian manifold that governs natural phenomena such as chemical kinetics and configuration spaces of jointed objects. We find that diffusion maps can be generalized to Carnot manifolds and that the projection onto diffusion harmonics gives an almost isometric embedding; as a side effect, the diffusion distance is a computationally fast estimate for the shortest distance between two points on a Carnot manifold. We apply this theory to biochemical network data and observe that the chemical kinetics of the EGFR network are governed by a Carnot, but not Riemannian, manifold. In the second part of this thesis we examine the Heisenberg group, a classical example of a Carnot manifold. We obtain a representation-theoretic proof that the eigenfunctions of the sub-Laplacian on SU(2) approach the eigenfunctions of the sub-Laplacian on the Heisenberg group, in the limit as the radius of the sphere becomes large, in analogy with the limiting relationship between the Fourier series on the circle and the Fourier transform on the line. This result also illustrates how projecting onto the sub-Laplacian eigenfunctions of a non-compact Carnot manifold can be locally approximated by projecting onto the sub-Laplacian eigenfunctions of a tangent compact Carnot manifold. In the third part

  16. Flow Control in a Compact Inlet

    Vaccaro, John C.


    An experimental investigation of flow control, via various control jets actuators, was undertaken to eliminate separation and secondary flows in a compact inlet. The compact inlet studied was highly aggressive with a length-to-diameter ratio of 1.5. A brand new facility was designed and built to enable various actuation methodologies as well as multiple measurement techniques. Techniques included static surface pressure, total pressure, and stereoscopic particle image velocimetry. Experimental data were supplemented with numerical simulations courtesy of Prof. Kenneth Jansen, Dr. Onkar Sahni, and Yi Chen. The baseline flow field was found to be dominated by two massive separations and secondary flow structures. These secondary structures were present at the aerodynamic interface plane in the form of two counter-rotating vortices inducing upwash along centerline. A dominant shedding frequency of 350 Hz was measured both at the aerodynamic interface plane and along the lower surface of the inlet. Flow control experiments started utilizing a pair of control jets placed in streamwise locations where flow was found to separate. Tests were performed for a range of inlet Mach numbers from 0.2 to 0.44. Steady and unsteady static pressure measurements along the upper and lower walls of the duct were performed for various combinations of actuation. The parameters that were tested include the control jets momentum coefficient, their blowing ratio, the actuation frequency, as well as different combinations of jets. It was shown that using mass flux ratio as a criterion to define flow control is not sufficient, and one needs to provide both the momentum coefficient and the blowing ratio to quantify the flow control performance. A detailed study was undertaken on controlling the upstream separation point for an inlet Mach number of 0.44. Similar to the baseline flow field, the flow field associated with the activation of a two-dimensional control jet actuator was dominated by

  17. On the mechanism of effective chemical reactions with turbulent mixing of reactants and finite rate of molecular reactions

    Vorotilin, V. P.


    A generalization of the theory of chemical transformation processes under turbulent mixing of reactants and arbitrary values of the rate of molecular reactions is presented that was previously developed for the variant of an instantaneous reaction [13]. The use of the features of instantaneous reactions when considering the general case, namely, the introduction of the concept of effective reaction for the reactant volumes and writing a closing conservation equation for these volumes, became possible due to the partition of the whole amount of reactants into "active" and "passive" classes; the reactants of the first class are not mixed and react by the mechanism of instantaneous reactions, while the reactants of the second class approach each other only through molecular diffusion, and therefore their contribution to the reaction process can be neglected. The physical mechanism of reaction for the limit regime of an ideal mixing reactor (IMR) is revealed and described. Although formally the reaction rate in this regime depends on the concentration of passive fractions of the reactants, according to the theory presented, the true (hidden) mechanism of the reaction is associated only with the reaction of the active fractions of the reactants with vanishingly small concentration in the volume of the reactor. It is shown that the rate constant of fast chemical reactions can be evaluated when the mixing intensity of reactants is much less than that needed to reach the mixing conditions in an IMR.

  18. The catalytic oxidation of H2S in a stainless steel membrane reactor with separate feed of reactants.

    Neomagus, H.W.J.P.; van Swaaij, Willibrordus Petrus Maria; Versteeg, Geert


    The oxidation of H2S is studied in a membrane reactor with separate feed of reactants. As a novelty in the concept of separate introduction of the reactants, a sintered stainless steel membrane is used, because this type of material is easy to integrate into the reactor, and the catalytic properties

  19. The catalytic oxidation of H2S in a stainless steel membrane reactor with separate feed of reactants

    Neomagus, H.W.J.P.; Swaaij, W.P.M. van; Versteeg, G.F.


    The oxidation of H2S is studied in a membrane reactor with separate feed of reactants. As a novelty in the concept of separate introduction of the reactants, a sintered stainless steel membrane is used, because this type of material is easy to integrate into the reactor, and the catalytic properties

  20. Piping structural design for the ITER thermal shield manifold

    Noh, Chang Hyun, E-mail: [ITER Korea, National Fusion Research Institute, Daejeon 305-333 (Korea, Republic of); Chung, Wooho, E-mail: [ITER Korea, National Fusion Research Institute, Daejeon 305-333 (Korea, Republic of); Nam, Kwanwoo; Kang, Kyoung-O. [ITER Korea, National Fusion Research Institute, Daejeon 305-333 (Korea, Republic of); Bae, Jing Do; Cha, Jong Kook [Korea Marine Equipment Research Institute, Busan 606-806 (Korea, Republic of); Kim, Kyoung-Kyu [Mecha T& S, Jinju-si 660-843 (Korea, Republic of); Hamlyn-Harris, Craig; Hicks, Robby; Her, Namil; Jun, Chang-Hoon [ITER Organization, Route de Vinon-sur-Verdon, CS 90 046, 13067 St. Paul Lez Durance Cedex (France)


    Highlights: • We finalized piping design of ITER thermal shield manifold for procurement. • Support span is determined by stress and deflection limitation. • SQP, which is design optimization method, is used for the pipe design. • Benchmark analysis is performed to verify the analysis software. • Pipe design is verified by structural analyses. - Abstract: The thermal shield (TS) provides the thermal barrier in the ITER tokamak to minimize heat load transferred by thermal radiation from the hot components to the superconducting magnets operating at 4.2 K. The TS is actively cooled by 80 K pressurized helium gas which flows from the cold valve box to the cooling tubes on the TS panels via manifold piping. This paper describes the manifold piping design and analysis for the ITER thermal shield. First, maximum allowable span for the manifold support is calculated based on the simple beam theory. In order to accommodate the thermal contraction in the manifold feeder, a contraction loop is designed and applied. Sequential Quadratic Programming (SQP) method is used to determine the optimized dimensions of the contraction loop to ensure adequate flexibility of manifold pipe. Global structural behavior of the manifold is investigated when the thermal movement of the redundant (un-cooled) pipe is large.

  1. Cohomological rigidity of manifolds defined by 3-dimensional polytopes

    Buchstaber, V. M.; Erokhovets, N. Yu.; Masuda, M.; Panov, T. E.; Park, S.


    A family of closed manifolds is said to be cohomologically rigid if a cohomology ring isomorphism implies a diffeomorphism for any two manifolds in the family. Cohomological rigidity is established here for large families of 3-dimensional and 6-dimensional manifolds defined by 3-dimensional polytopes. The class \\mathscr{P} of 3-dimensional combinatorial simple polytopes P different from tetrahedra and without facets forming 3- and 4-belts is studied. This class includes mathematical fullerenes, that is, simple 3- polytopes with only 5-gonal and 6-gonal facets. By a theorem of Pogorelov, any polytope in \\mathscr{P} admits in Lobachevsky 3-space a right-angled realisation which is unique up to isometry. Our families of smooth manifolds are associated with polytopes in the class \\mathscr{P}. The first family consists of 3-dimensional small covers of polytopes in \\mathscr{P}, or equivalently, hyperbolic 3-manifolds of Löbell type. The second family consists of 6-dimensional quasitoric manifolds over polytopes in \\mathscr{P}. Our main result is that both families are cohomologically rigid, that is, two manifolds M and M' from either family are diffeomorphic if and only if their cohomology rings are isomorphic. It is also proved that if M and M' are diffeomorphic, then their corresponding polytopes P and P' are combinatorially equivalent. These results are intertwined with classical subjects in geometry and topology such as the combinatorics of 3-polytopes, the Four Colour Theorem, aspherical manifolds, a diffeomorphism classification of 6-manifolds, and invariance of Pontryagin classes. The proofs use techniques of toric topology. Bibliography: 69 titles.

  2. New inlet nozzle assembly: C Reactor

    Calkin, J.F.


    The use of self-supported fuel elements in ribless Zircaloy-2 tubes at C-Reactor requires some inlet nozzle modification to allow charging of the larger overall diameter fuel pieces. A new nozzle assembly has been developed (by Equipment Development Operation -- IPD) which will allow use of the new fuel pieces and at the same time increase the reliability of the header-to-tube piping and reduce pumping power losses. Flow test data were requested for the new assembly and the results of these tests are presented herein. This report also presents a comparison of the header to tube energy losses for the various reactor inlet nozzle assemblies which are currently used on the Hanford production reactors.

  3. Modelling Complex Inlet Geometries in CFD

    Skovgaard, M.; Nielsen, Peter V.

    Modem inlet devices applied in the field of ventilation of rooms are getting more complex in terms of geometry in order to fulfil the occupants' demand for thermal comfort in the room and in order to decrease the energy consumption. This expresses the need for a more precise calculation of the fl...... and tested. The method is based upon threedimensional - and radial wall jet theory and upon diffuser specific experimental data....

  4. Persistence of noncompact normally hyperbolic invariant manifolds in bounded geometry

    Eldering, J


    We prove a persistence result for noncompact normally hyperbolic invariant manifolds in the setting of Riemannian manifolds of bounded geometry. Bounded geometry of the ambient manifold is a crucial assumption required to control the uniformity of all estimates throughout the proof. The $C^{k,\\alpha}$-smoothness result is optimal with respect to the spectral gap condition involved. The core of the persistence proof is based on the Perron method. In the process we derive new results on noncompact submanifolds in bounded geometry: a uniform tubular neighborhood theorem and uniform smooth approximation of a submanifold. The submanifolds considered are assumed to be uniformly $C^k$ bounded in an appropriate sense.

  5. 4-dimensional locally CAT(0)-manifolds with no Riemannian smoothings

    Davis, M; Lafont, J -F


    We construct examples of smooth 4-dimensional manifolds M supporting a locally CAT(0)-metric, whose universal cover X satisfy Hruska's isolated flats condition, and contain 2-dimensional flats F with the property that the boundary at infinity of F defines a nontrivial knot in the boundary at infinity of X. As a consequence, we obtain that the fundamental group of M cannot be isomorphic to the fundamental group of any Riemannian manifold of nonpositive sectional curvature. In particular, M is a locally CAT(0)-manifold which does not support any Riemannian metric of nonpositive sectional curvature.

  6. A global Torelli theorem for hyperkaehler manifolds (after Verbitsky)

    Huybrechts, Daniel


    Compact hyperkaehler manifolds are higher-dimensional generalizations of K3 surfaces. The classical Global Torelli theorem for K3 surfaces, however, does not hold in higher dimensions. More precisely, a compact hyperkaehler manifold is in general not determined by its natural weight-two Hodge structure. The text gives an account of a recent theorem of M. Verbitsky, which can be regarded as a weaker version of the Global Torelli theorem phrased in terms of the injectivity of the period map on the connected components of the moduli space of marked manifolds.

  7. Solving Einstein's Equation Numerically on Manifolds with Arbitrary Topologie

    Lindblom, Lee


    This talk will summarize some of the numerical methods we have developed for solving Einstein's equation numerically on manifolds with arbitrary spatial topologies. These methods include the use of multi-cube representations of arbitrary manifolds, a convenient new way to specify the differential structure on multi-cube representations, and a new fully covariant first-order symmetric hyperbolic representation of Einstein's equation. Progress on the problem of constructing the ``reference metrics'' (which are an essential element of our numerical method) for arbitrary manifolds will be described, and numerical results will be presented for some example simulations.

  8. Understanding 3-manifolds in the context of permutations

    Null, Karoline P


    We demonstrate how a 3-manifold, a Heegaard diagram, and a group presentation can each be interpreted as a pair of signed permutations in the symmetric group $S_d.$ We demonstrate the power of permutation data in programming and discuss an algorithm we have developed that takes the permutation data as input and determines whether the data represents a closed 3-manifold. We therefore have an invariant of groups, that is given any group presentation, we can determine if that presentation presents a closed 3-manifold.

  9. Dynamics and zeta functions on conformally compact manifolds

    Rowlett, Julie; Tapie, Samuel


    In this note, we study the dynamics and associated zeta functions of conformally compact manifolds with variable negative sectional curvatures. We begin with a discussion of a larger class of manifolds known as convex co-compact manifolds with variable negative curvature. Applying results from dynamics on these spaces, we obtain optimal meromorphic extensions of weighted dynamical zeta functions and asymptotic counting estimates for the number of weighted closed geodesics. A meromorphic extension of the standard dynamical zeta function and the prime orbit theorem follow as corollaries. Finally, we investigate interactions between the dynamics and spectral theory of these spaces.

  10. Optimal Design of a Subsonic Submerged Inlet

    Taskinoglu, Ezgi; Jovanovic, Vasilije; Elliott, Gregory; Knight, Doyle


    A multi-objective optimization study based on an epsilon-constraint method is conducted for the design optimization of a subsonic submerged air vehicle inlet. The multi-objective optimization problem is reformulated by minimizing one of the objectives and restricting the other objectives within user specified values. The figures of merits are the engine-face distortion and swirl that determines the inlet/engine compatibility. The distortion index is minimized while the feasible design space is determined by the swirl index. The design variables are the geometrical parameters defining the surface alteration. The design algorithm is driven by a gradient-based optimizer, and is constructed by integrating the optimizer with a solid modeller (Pro/Engineer), a mesh generator (Grid/Pro) and a flow solver (GASPex). The optimizer is CFSQP (C code for Feasible Sequential Quadratic Programming). Integration of the software packages is achieved by a Perl script. In order to verify the numerical results, an experimental setup for the same inlet geometry is prepared to run at the same flow conditions. The presentation will describe the numerical approach and summarize the results.

  11. A study of reactant interfaces in Ni+Al particle systems during shock wave propagation

    Austin, Ryan A.; McDowell, David L.; Horie, Yasuyuki; Benson, David J.


    Macro-scale responses of energetic materials during shock compression are influenced strongly by thermo-mechano-chemical processes occurring at the level of the microstructure. For example, it is believed that the propagation of chemical reactions in reactive particle systems is intimately linked to conditions at reactant interfaces such as surface temperature, phase changes, defect density, and mass mixing due to inelastic deformation. To provide explicit resolution of such interfacial conditions, numerical models are constructed. The finite element method is used to numerically solve the differential equations that govern the coupled thermomechanical response of micron-size particle mixtures of Ni and Al during shock wave propagation (interface chemistry is not yet modeled). The size and temperature distributions of contiguous reactant contact surfaces are quantified for a range of shock strengths. A parametric study of mixture attributes is undertaken to assess the sensitivity of the aforementioned distributions to variations of the microstructure.

  12. Rotational asymmetry of reactant concentration and its evolution in a circulating fluidized bed riser

    Dongbing Li; Ajay K. Ray; Madhumita B. Ray; Jesse Zhu


    Rotational asymmetric distribution of reactant (ozone) concentration and its evolution along with the gas-solid reactive flow were studied in a 76 mm i.d.,10.2 m high circulating fluidized bed (CFB) riser reactor.The superficial gas velocity ranged from 3 to 5 m/s and the solids circulation rates were 50 and 100kg/(m2 s).Experimental results show that the asymmetry of reactant distribution can extend to a height close to the length of flow developing zone of the CFB riser reactor and then disappears.Based on the hydrodynamics of the gas and solid phases in the solids entrance region,this asymmetry can be attributed to the effect of the solids entrance structure.

  13. Structure of silica xerogels synthesized with organoalkoxysilane co-reactants hints at multiple phase separation.

    Gommes, Cédric J; Basiura, Monika; Goderis, Bart; Pirard, Jean-Paul; Blacher, Silvia


    The microstructure of hybrid silica xerogels synthesized by the base-catalyzed polymerization of tetraethoxysilane (TEOS) in ethanol in the presence of 3-aminopropyltriethoxysilane (AES) and of 3-(2-aminoethylamino)propyltrimethoxysilane (EDAS) as co-reactants, and dried in subcritical conditions, is analyzed. A thorough structural characterization of the samples is performed combining nitrogen adsorption, small-angle X-ray scattering (SAXS), and transmission electron microscopy coupled with digital image analysis. The use of these methods shows that, for both co-reactants, the xerogels are made of macropores supported by filaments, with each filament being formed of smaller structures. The quantitative impact of the additive on each structural level is assessed. The data are compared with a previous time-resolved SAXS study conducted during the formation of the gels (J. Phys. Chem. B 2004, 108, 8983-8991). The results are analyzed in the framework of a double phase separation model.

  14. Acute-phase reactants in periodontal disease: current concepts and future implications.

    Archana, Vilasan; Ambili, Ranjith; Nisha, Krishnavilasam Jayakumary; Seba, Abraham; Preeja, Chandran


    Periodontal disease has been linked to adverse cardiovascular events by unknown mechanisms. C-reactive protein is a systemic marker released during the acute phase of an inflammatory response and is a prognostic marker for cardiovascular disease, with elevated serum levels being reported during periodontal disease. Studies also reported elevated levels of various other acute-phase reactants in periodontal disease. It has been reported extensively in the literature that treatment of periodontal infections can significantly lower serum levels of C-reactive protein. Therefore, an understanding of the relationship between acute-phase response and the progression of periodontal disease and other systemic health complications would have a profound effect on the periodontal treatment strategies. In view of this fact, the present review highlights an overview of acute-phase reactants and their role in periodontal disease. © 2014 Wiley Publishing Asia Pty Ltd.

  15. A mixed-reactants solid-polymer-electrolyte direct methanol fuel cell

    Scott, K.; Shukla, A. K.; Jackson, C. L.; Meuleman, W. R. A.

    Mixed-reactants solid-polymer-electrolyte direct methanol fuel cells (SPE-DMFCs) with a PtRu/C anode and a methanol-tolerant oxygen-reduction cathode catalyst have been assembled and have been subjected to galvanostatic polarisation studies. The oxygen-reduction cathode was either of the FeTMPP/C, CoTMPP/C, FeCoTMPP/C and RuSe/C. It was found that the SPE-DMFC with the RuSe/C cathode yielded the best performance. It has been possible to achieve power densities of approximately 50 and 20 mW/cm 2 while operating a mixed-reactants SPE-DMFC at 90 °C with oxygen and air fed cathodes, respectively. Interestingly, these SPE-DMFCs exhibit no parasitic oxidation of methanol with oxygen.

  16. Unsteady lubrication modeling of inlet zone in metal rolling processes

    毛明智; 谭建平


    An unsteady lubrication model of inlet zone in metal rolling was established. The simulation computations show that for the variation amplitude of the inlet film thickness, the variation of the inlet angle contributes the largest, the surface mean speed contributes the second and the back tension stress the least. The higher the input frequency is, the smaller the amplitude output of the inlet film thickness will be. For a sinusoidal input, the inlet film thickness varies periodically but is not a sine wave because the system is not linear.

  17. A continuous flow microfluidic calorimeter: 3-D numerical modeling with aqueous reactants

    Sen, Mehmet A.; Kowalski, Gregory J.; Fiering, Jason; Larson, Dale


    A computational analysis of the reacting flow field, species diffusion and heat transfer processes with thermal boundary layer effects in a microchannel reactor with a coflow configuration was performed. Two parallel adjacent streams of aqueous reactants flow along a wide, shallow, enclosed channel in contact with a substrate, which is affixed to a temperature controlled plate. The Fluent computational fluid dynamics package solved the Navier–Stokes, mass transport and energy equations. The e...

  18. Wet in situ transesterification of microalgae using ethyl acetate as a co-solvent and reactant.

    Park, Jeongseok; Kim, Bora; Chang, Yong Keun; Lee, Jae W


    This study addresses wet in situ transesterification of microalgae for the production of biodiesel by introducing ethyl acetate as both reactant and co-solvent. Ethyl acetate and acid catalyst are mixed with wet microalgae in one pot and the mixture is heated for simultaneous lipid extraction and transesterification. As a single reactant and co-solvent, ethyl acetate can provide higher FAEE yield and more saccharification of carbohydrates than the case of binary ethanol and chloroform as a reactant and a co-solvent. The optimal yield was 97.8wt% at 114°C and 4.06M catalyst with 6.67mlEtOAC/g dried algae based on experimental results and response surface methodology (RSM). This wet in situ transesterification of microalgae using ethyl acetate doesn't require an additional co-solvent and it also promises more economic benefit as combining extraction and transesterification in a single process. Copyright © 2017 Elsevier Ltd. All rights reserved.

  19. An efficient empirical model for microwave-induced average temperature of liquid cylindrical reactants.

    Yang, Chuqiao; Yakovlev, Vadim V


    Microwave-assisted chemical reactions have become very popular in preparative chemistry due to many advantages such as accelerated reaction rate, higher chemical yield and lower energy use. In dedicated equipment, however, the microwave units operate as "black boxes" keeping the role of the thermal effects in microwave-assisted chemical processes somewhat obscure. To address this issue, in this paper, we propose a simple mathematical model for computing microwave-induced temperature in a three-media cylindrical structure representing a core element of a typical microwave reactor with the reactant assumed to be stirred by convection flows. The model determines the average temperature of the reactant for the known absorbed microwave power and heating time. To illustrate its functionality, the model is used to compute time-temperature characteristics of water, ethanol, and methanol heated in the batch reactor MiniFlow 200SS. The curve calculated for water appears to be in an excellent agreement with an experiment. This confirms the hypothesis on temperature homogenization in liquid reactants in batch reactors due to convection and suggests that modeling can be helpful in clarifying and quantifying the details of microwave-assisted chemical processes.

  20. Unstart coupling mechanism analysis of multiple-modules hypersonic inlet.

    Hu, Jichao; Chang, Juntao; Wang, Lei; Cao, Shibin; Bao, Wen


    The combination of multiplemodules in parallel manner is an important way to achieve the much higher thrust of scramjet engine. For the multiple-modules scramjet engine, when inlet unstarted oscillatory flow appears in a single-module engine due to high backpressure, how to interact with each module by massflow spillage, and whether inlet unstart occurs in other modules are important issues. The unstarted flowfield and coupling characteristic for a three-module hypersonic inlet caused by center module II and side module III were, conducted respectively. The results indicate that the other two hypersonic inlets are forced into unstarted flow when unstarted phenomenon appears on a single-module hypersonic inlet due to high backpressure, and the reversed flow in the isolator dominates the formation, expansion, shrinkage, and disappearance of the vortexes, and thus, it is the major factor of unstart coupling of multiple-modules hypersonic inlet. The coupling effect among multiple modules makes hypersonic inlet be more likely unstarted.

  1. Altering symplectic manifolds by homologous recombination

    Abouzaid, Mohammed


    We use symplectic cohomology to study the non-uniqueness of symplectic structures on the smooth manifolds underlying affine varieties. Starting with a Lefschetz fibration on such a variety and a finite set of primes, the main new tool is a method, which we call homologous recombination, for constructing a Lefschetz fibration whose total space is smoothly equivalent to the original variety, but for which symplectic cohomology with coefficients in the given set of primes vanishes (there is also a simpler version that kills symplectic cohomology completely). Rather than relying on a geometric analysis of periodic orbits of a flow, the computation of symplectic cohomology depends on describing the Fukaya category associated to the new fibration. As a consequence we use a result of McLean to prove, for example, that an affine variety of real dimension greater than or equal to 4 supports infinitely many different (Wein)stein structures of finite type, and, assuming a mild cohomological condition, uncountably many d...

  2. An underlying geometrical manifold for Hamiltonian mechanics

    Horwitz, L. P.; Yahalom, A.; Levitan, J.; Lewkowicz, M.


    We show that there exists an underlying manifold with a conformal metric and compatible connection form, and a metric type Hamiltonian (which we call the geometrical picture), that can be put into correspondence with the usual Hamilton-Lagrange mechanics. The requirement of dynamical equivalence of the two types of Hamiltonians, that the momenta generated by the two pictures be equal for all times, is sufficient to determine an expansion of the conformal factor, defined on the geometrical coordinate representation, in its domain of analyticity with coefficients to all orders determined by functions of the potential of the Hamiltonian-Lagrange picture, defined on the Hamilton-Lagrange coordinate representation, and its derivatives. Conversely, if the conformal function is known, the potential of a Hamilton-Lagrange picture can be determined in a similar way. We show that arbitrary local variations of the orbits in the Hamilton-Lagrange picture can be generated by variations along geodesics in the geometrical picture and establish a correspondence which provides a basis for understanding how the instability in the geometrical picture is manifested in the instability of the the original Hamiltonian motion.

  3. Double Field Theory on Group Manifolds (Thesis)

    Hassler, Falk


    This thesis deals with Double Field Theory (DFT), an effective field theory capturing the low energy dynamics of closed strings on a torus. It renders T-duality on a torus manifest by adding $D$ winding coordinates in addition to the $D$ space time coordinates. An essential consistency constraint of the theory, the strong constraint, only allows for field configurations which depend on half of the coordinates of the arising doubled space. I derive DFT${}_\\mathrm{WZW}$, a generalization of the current formalism. It captures the low energy dynamics of a closed bosonic string propagating on a compact group manifold. Its classical action and the corresponding gauge transformations arise from Closed String Field Theory up to cubic order in the massless fields. These results are rewritten in terms of a generalized metric and extended to all orders in the fields. There is an explicit distinction between background and fluctuations. For the gauge algebra to close, the latter have to fulfill a modified strong constrai...

  4. Eignets for function approximation on manifolds

    Mhaskar, H N


    Let $\\XX$ be a compact, smooth, connected, Riemannian manifold without boundary, $G:\\XX\\times\\XX\\to \\RR$ be a kernel. Analogous to a radial basis function network, an eignet is an expression of the form $\\sum_{j=1}^M a_jG(\\circ,y_j)$, where $a_j\\in\\RR$, $y_j\\in\\XX$, $1\\le j\\le M$. We describe a deterministic, universal algorithm for constructing an eignet for approximating functions in $L^p(\\mu;\\XX)$ for a general class of measures $\\mu$ and kernels $G$. Our algorithm yields linear operators. Using the minimal separation amongst the centers $y_j$ as the cost of approximation, we give modulus of smoothness estimates for the degree of approximation by our eignets, and show by means of a converse theorem that these are the best possible for every \\emph{individual function}. We also give estimates on the coefficients $a_j$ in terms of the norm of the eignet. Finally, we demonstrate that if any sequence of eignets satisfies the optimal estimates for the degree of approximation of a smooth function, measured in ter...

  5. More on Cotton Flow on Three Manifolds

    Kilicarslan, Ercan; Tekin, Bayram


    Cotton flow tends to evolve a given initial metric on a three manifold to a conformally flat one. Here we expound upon the earlier work on Cotton flow and study the linearized version of it around a generic initial metric by employing a modified form of the DeTurck trick. We show that the flow around the flat space, as a critical point, reduces to an anisotropic generalization of linearized KdV equation with complex dispersion relations one of which is an unstable mode, rendering the the flat space unstable under small perturbations. We also show that Einstein spaces and some conformally flat non-Einstein spaces are linearly unstable. We refine the gradient flow formalism and compute the second variation of the entropy and show that generic critical points are extended Cotton solitons. We study some properties of these solutions and find a Topologically Massive soliton that is built from Cotton and Ricci solitons. In the Lorentzian signature, we also show that the pp-wave metrics are both Cotton and Ricci sol...

  6. On the scalar manifold of exceptional supergravity

    Cacciatori, S.L. [Dipartimento di Scienze ed Alta Tecnologia, Universita dell' Insubria, Via Valleggio, 11, 22100 Como (Italy); INFN, Sezione di Milano, Via Celoria, 16, 20133 Milano (Italy); Cerchiai, B.L. [INFN, Sezione di Milano, Via Celoria, 16, 20133 Milano (Italy); Dipartimento di Matematica, Universita degli Studi di Milano, Via Saldini, 50, 20133 Milano (Italy); Marrani, A. [Physics Department, Theory Unit, CERN, 1211, Geneva 23 (Switzerland)


    We construct two parametrizations of the non compact exceptional Lie group G = E{sub 7(-25)}, based on a fibration which has the maximal compact subgroup [(E{sub 6} x U(1))/Z{sub 3}] as a fiber. It is well known that G plays an important role in the N = 2 d = 4 magic exceptional supergravity, where it describes the U-duality of the theory and where the symmetric space M=G/K gives the vector multiplets' scalar manifold. First, by making use of the exponential map, we compute a realization of G/K, that is based on the E{sub 6} invariant d-tensor, and hence exhibits the maximal possible manifest [(E{sub 6} x U(1))/Z{sub 3}]-covariance. This provides a basis for the corresponding supergravity theory, which is the analogue of the Calabi-Vesentini coordinates. Then we study the Iwasawa decomposition. Its main feature is that it is SO(8)-covariant and therefore it highlights the role of triality. Along the way we analyze the relevant chain of maximal embeddings which leads to SO(8). It is worth noticing that being based on the properties of a ''mixed'' Freudenthal-Tits magic square, the whole procedure can be generalized to a broader class of groups of type E{sub 7}. (Copyright copyright 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  7. Learning the manifold of quality ultrasound acquisition.

    El-Zehiry, Noha; Yan, Michelle; Good, Sara; Fang, Tong; Zhou, S Kevin; Grady, Leo


    Ultrasound acquisition is a challenging task that requires simultaneous adjustment of several acquisition parameters (the depth, the focus, the frequency and its operation mode). If the acquisition parameters are not properly chosen, the resulting image will have a poor quality and will degrade the patient diagnosis and treatment workflow. Several hardware-based systems for autotuning the acquisition parameters have been previously proposed, but these solutions were largely abandoned because they failed to properly account for tissue inhomogeneity and other patient-specific characteristics. Consequently, in routine practice the clinician either uses population-based parameter presets or manually adjusts the acquisition parameters for each patient during the scan. In this paper, we revisit the problem of autotuning the acquisition parameters by taking a completely novel approach and producing a solution based on image analytics. Our solution is inspired by the autofocus capability of conventional digital cameras, but is significantly more challenging because the number of acquisition parameters is large and the determination of "good quality" images is more difficult to assess. Surprisingly, we show that the set of acquisition parameters which produce images that are favored by clinicians comprise a 1D manifold, allowing for a real-time optimization to maximize image quality. We demonstrate our method for acquisition parameter autotuning on several live patients, showing that our system can start with a poor initial set of parameters and automatically optimize the parameters to produce high quality images.

  8. Manifold Regularized Experimental Design for Active Learning.

    Zhang, Lining; Shum, Hubert P H; Shao, Ling


    Various machine learning and data mining tasks in classification require abundant data samples to be labeled for training. Conventional active learning methods aim at labeling the most informative samples for alleviating the labor of the user. Many previous studies in active learning select one sample after another in a greedy manner. However, this is not very effective because the classification models has to be retrained for each newly labeled sample. Moreover, many popular active learning approaches utilize the most uncertain samples by leveraging the classification hyperplane of the classifier, which is not appropriate since the classification hyperplane is inaccurate when the training data are small-sized. The problem of insufficient training data in real-world systems limits the potential applications of these approaches. This paper presents a novel method of active learning called manifold regularized experimental design (MRED), which can label multiple informative samples at one time for training. In addition, MRED gives an explicit geometric explanation for the selected samples to be labeled by the user. Different from existing active learning methods, our method avoids the intrinsic problems caused by insufficiently labeled samples in real-world applications. Various experiments on synthetic datasets, the Yale face database and the Corel image database have been carried out to show how MRED outperforms existing methods.

  9. Killing superalgebras for Lorentzian four-manifolds

    de Medeiros, Paul; Figueroa-O'Farrill, José; Santi, Andrea


    We determine the Killing superalgebras underpinning field theories with rigid unextended supersymmetry on Lorentzian four-manifolds by re-interpreting them as filtered deformations of mathbb{Z} -graded subalgebras with maximum odd dimension of the N = 1 Poincaré superalgebra in four dimensions. Part of this calculation involves computing a Spencer cohomology group which, by analogy with a similar result in eleven dimensions, prescribes a notion of Killing spinor, which we identify with the defining condition for bosonic supersymmetric backgrounds of minimal off-shell supergravity in four dimensions. We prove that such Killing spinors always generate a Lie superalgebra, and that this Lie superalgebra is a filtered deformation of a subalgebra of the N = 1 Poincaré superalgebra in four dimensions. Demanding the flatness of the connection defining the Killing spinors, we obtain equations satisfied by the maximally supersymmetric backgrounds. We solve these equations, arriving at the classification of maximally supersymmetric backgrounds whose associated Killing superalgebras are precisely the filtered deformations we classify in this paper.

  10. Lectures on four-manifolds and topological gauge theories

    Dijkgraaf, R. [Amsterdam Univ. (Netherlands). Dept. of Math.


    I give an elementary introduction to the theory of four-manifold invariants and its relation with topological field theory. I review the recent developments in the theory of Donaldson and Seiberg-Witten invariants. (orig.).

  11. Lectures on four-manifolds and topological gauge theories

    Dijkgraaf, Robbert


    I give an elementary introduction to the theory of four-manifold invariants and its relation with topological field theory. I review the recent developments in the theory of Donaldson and Seiberg-Witten invariants.

  12. The Banach-Tarski paradox for flag manifolds

    Komori, Yohei


    The famous Banach-Tarski paradox claims that the three dimensional rotation group acts on the two dimensional sphere paradoxically. In this paper, we generalize their result to show that the classical group acts on the flag manifold paradoxically.

  13. Geometry of almost-product Lorentzian manifolds and relativistic observer

    Borowiec, Andrzej


    The notion of relativistic observer is confronted with Naveira's classification of (pseudo-)Riemannian almost-product structures on space-time manifolds. Some physical properties and their geometrical counterparts are shortly discussed.

  14. Poincare duality angles for Riemannian manifolds with boundary

    Shonkwiler, Clayton


    On a compact Riemannian manifold with boundary, the absolute and relative cohomology groups appear as certain subspaces of harmonic forms. DeTurck and Gluck showed that these concrete realizations of the cohomology groups decompose into orthogonal subspaces corresponding to cohomology coming from the interior and boundary of the manifold. The principal angles between these interior subspaces are all acute and are called Poincare duality angles. This paper determines the Poincare duality angles of a collection of interesting manifolds with boundary derived from complex projective spaces and from Grassmannians, providing evidence that the Poincare duality angles measure, in some sense, how "close" a manifold is to being closed. This paper also elucidates a connection between the Poincare duality angles and the Dirichlet-to-Neumann operator for differential forms, which generalizes the classical Dirichlet-to-Neumann map arising in the problem of Electrical Impedance Tomography. Specifically, the Poincare duality...

  15. Kink manifolds in (1+1)-dimensional scalar field theory

    Alonso Izquierdo, A.; Gonzalez Leon, M.A. [Departamento de Estadistica y Matematica Aplicadas, Facultad de Ciencias, Universidad de Salamanca, Salamanca (Spain); Mateos Guilarte, J. [Departamento de Fisica, Facultad de Ciencias, Universidad de Salamanca, Salamanca (Spain)


    The general structure of kink manifolds in (1+1)-dimensional complex scalar field theory is described by analysing three special models. New solitary waves are reported. Kink energy sum rules arise between different types of solitary waves. (author)

  16. Manifold learning based feature extraction for classification of hyperspectral data

    Lunga, D


    Full Text Available Interest in manifold learning for representing the topology of large, high dimensional nonlinear data sets in lower, but still meaningful dimensions for visualization and classification has grown rapidly over the past decade, and particularly...

  17. Twisted Fock representations of noncommutative Kähler manifolds

    Sako, Akifumi; Umetsu, Hiroshi


    We introduce twisted Fock representations of noncommutative Kähler manifolds and give their explicit expressions. The twisted Fock representation is a representation of the Heisenberg like algebra whose states are constructed by applying creation operators to a vacuum state. "Twisted" means that creation operators are not Hermitian conjugate of annihilation operators in this representation. In deformation quantization of Kähler manifolds with separation of variables formulated by Karabegov, local complex coordinates and partial derivatives of the Kähler potential with respect to coordinates satisfy the commutation relations between the creation and annihilation operators. Based on these relations, we construct the twisted Fock representation of noncommutative Kähler manifolds and give a dictionary to translate between the twisted Fock representations and functions on noncommutative Kähler manifolds concretely.

  18. Linear approximation of the first eigenvalue on compact manifolds

    CHEN; Mufa(陈木法); E.; Scacciatelli; YAO; Liang(姚亮)


    For compact, connected Riemannian manifolds with Ricci curvature bounded below by a constant, what is the linear approximation of the first eigenvalue of Laplacian? The answer is presented with computer assisted proof and the result is optimal in certain sense.

  19. Manifold Elastic Net: A Unified Framework for Sparse Dimension Reduction

    Zhou, Tianyi; Wu, Xindong


    It is difficult to find the optimal sparse solution of a manifold learning based dimensionality reduction algorithm. The lasso or the elastic net penalized manifold learning based dimensionality reduction is not directly a lasso penalized least square problem and thus the least angle regression (LARS) (Efron et al. \\cite{LARS}), one of the most popular algorithms in sparse learning, cannot be applied. Therefore, most current approaches take indirect ways or have strict settings, which can be inconvenient for applications. In this paper, we proposed the manifold elastic net or MEN for short. MEN incorporates the merits of both the manifold learning based dimensionality reduction and the sparse learning based dimensionality reduction. By using a series of equivalent transformations, we show MEN is equivalent to the lasso penalized least square problem and thus LARS is adopted to obtain the optimal sparse solution of MEN. In particular, MEN has the following advantages for subsequent classification: 1) the local...

  20. Flat coordinates for Saito Frobenius manifolds and string theory

    Belavin, A. A.; Gepner, D.; Kononov, Ya. A.


    We investigate the connection between the models of topological conformal theory and noncritical string theory with Saito Frobenius manifolds. For this, we propose a new direct way to calculate the flat coordinates using the integral representation for solutions of the Gauss-Manin system connected with a given Saito Frobenius manifold. We present explicit calculations in the case of a singularity of type A n . We also discuss a possible generalization of our proposed approach to SU( N) k /( SU( N) k+1 × U(1)) Kazama-Suzuki theories. We prove a theorem that the potential connected with these models is an isolated singularity, which is a condition for the Frobenius manifold structure to emerge on its deformation manifold. This fact allows using the Dijkgraaf-Verlinde-Verlinde approach to solve similar Kazama-Suzuki models.

  1. Salient object detection: manifold-based similarity adaptation approach

    Zhou, Jingbo; Ren, Yongfeng; Yan, Yunyang; Gao, Shangbing


    A saliency detection algorithm based on manifold-based similarity adaptation is proposed. The proposed algorithm is divided into three steps. First, we segment an input image into superpixels, which are represented as the nodes in a graph. Second, a new similarity measurement is used in the proposed algorithm. The weight matrix of the graph, which indicates the similarities between the nodes, uses a similarity-based method. It also captures the manifold structure of the image patches, in which the graph edges are determined in a data adaptive manner in terms of both similarity and manifold structure. Then, we use local reconstruction method as a diffusion method to obtain the saliency maps. The objective function in the proposed method is based on local reconstruction, with which estimated weights capture the manifold structure. Experiments on four bench-mark databases demonstrate the accuracy and robustness of the proposed method.

  2. Supervised learning for neural manifold using spatiotemporal brain activity

    Kuo, Po-Chih; Chen, Yong-Sheng; Chen, Li-Fen


    Objective. Determining the means by which perceived stimuli are compactly represented in the human brain is a difficult task. This study aimed to develop techniques for the construction of the neural manifold as a representation of visual stimuli. Approach. We propose a supervised locally linear embedding method to construct the embedded manifold from brain activity, taking into account similarities between corresponding stimuli. In our experiments, photographic portraits were used as visual stimuli and brain activity was calculated from magnetoencephalographic data using a source localization method. Main results. The results of 10 × 10-fold cross-validation revealed a strong correlation between manifolds of brain activity and the orientation of faces in the presented images, suggesting that high-level information related to image content can be revealed in the brain responses represented in the manifold. Significance. Our experiments demonstrate that the proposed method is applicable to investigation into the inherent patterns of brain activity.

  3. Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment

    张振跃; 查宏远


    We present a new algorithm for manifold learning and nonlinear dimensionality reduction. Based on a set of unorganized da-ta points sampled with noise from a parameterized manifold, the local geometry of the manifold is learned by constructing an approxi-mation for the tangent space at each point, and those tangent spaces are then aligned to give the global coordinates of the data pointswith respect to the underlying manifold. We also present an error analysis of our algorithm showing that reconstruction errors can bequite small in some cases. We illustrate our algorithm using curves and surfaces both in 2D/3D Euclidean spaces and higher dimension-al Euclidean spaces. We also address several theoretical and algorithmic issues for further research and improvements.

  4. Manifold learning based registration algorithms applied to multimodal images.

    Azampour, Mohammad Farid; Ghaffari, Aboozar; Hamidinekoo, Azam; Fatemizadeh, Emad


    Manifold learning algorithms are proposed to be used in image processing based on their ability in preserving data structures while reducing the dimension and the exposure of data structure in lower dimension. Multi-modal images have the same structure and can be registered together as monomodal images if only structural information is shown. As a result, manifold learning is able to transform multi-modal images to mono-modal ones and subsequently do the registration using mono-modal methods. Based on this application, in this paper novel similarity measures are proposed for multi-modal images in which Laplacian eigenmaps are employed as manifold learning algorithm and are tested against rigid registration of PET/MR images. Results show the feasibility of using manifold learning as a way of calculating the similarity between multimodal images.

  5. A new embedding quality assessment method for manifold learning

    Zhang, Peng; Zhang, Bo


    Manifold learning is a hot research topic in the field of computer science. A crucial issue with current manifold learning methods is that they lack a natural quantitative measure to assess the quality of learned embeddings, which greatly limits their applications to real-world problems. In this paper, a new embedding quality assessment method for manifold learning, named as Normalization Independent Embedding Quality Assessment (NIEQA), is proposed. Compared with current assessment methods which are limited to isometric embeddings, the NIEQA method has a much larger application range due to two features. First, it is based on a new measure which can effectively evaluate how well local neighborhood geometry is preserved under normalization, hence it can be applied to both isometric and normalized embeddings. Second, it can provide both local and global evaluations to output an overall assessment. Therefore, NIEQA can serve as a natural tool in model selection and evaluation tasks for manifold learning. Experi...

  6. GrassmannOptim: An R Package for Grassmann Manifold Optimization

    Ko Placid Adragni


    Full Text Available The optimization of a real-valued objective function f(U, where U is a p X d,p > d, semi-orthogonal matrix such that UTU=Id, and f is invariant under right orthogonal transformation of U, is often referred to as a Grassmann manifold optimization. Manifold optimization appears in a wide variety of computational problems in the applied sciences. In this article, we present GrassmannOptim, an R package for Grassmann manifold optimization. The implementation uses gradient-based algorithms and embeds a stochastic gradient method for global search. We describe the algorithms, provide some illustrative examples on the relevance of manifold optimization and finally, show some practical usages of the package.

  7. A family quantization formula for symplectic manifolds with boundary


    his paper generalizes the family quantization formula of Zh angto the case of manifolds with boundary. As an application, Tian-Zhang's ana lytic version of the Guillemin-Kalkman-Martin residue formula is generalized to the family case.

  8. Kauffman polynomials of some links and invariants of 3-manifolds



    Kauffman bracket polynomials of the so-called generalized tree-like links are studied. An algorithm of Witten type invariants, which was defined by Blanchet and Habegger et al. of more general 3-manifolds is given.

  9. Spatial context driven manifold learning for hyperspectral image classification

    Zhang, Y


    Full Text Available Manifold learning techniques have demonstrated various levels of success in their ability to represent spectral signature characteristics in hyperspectral imagery. Such images consists of spectral features with very subtle differences and at times...

  10. Twisted Fock Representations of Noncommutative K\\"ahler Manifolds

    Sako, Akifumi


    We introduce twisted Fock representations of noncommutative K\\"ahler manifolds and give their explicit expressions. The twisted Fock representation is a representation of the Heisenberg like algebra whose states are constructed by acting creation operators on a vacuum state. "Twisted" means that creation operators are not hermitian conjugate of annihilation operators in this representation. In deformation quantization of K\\"ahler manifolds with separation of variables formulated by Karabegov, local complex coordinates and partial derivatives of the K\\"ahler potential with respect to coordinates satisfy the commutation relations between the creation and annihilation operators. Based on these relations, we construct the twisted Fock representation of noncommutative K\\"ahler manifolds and give a dictionary to translate between the twisted Fock representations and functions on noncommutative K\\"ahler manifolds concretely.

  11. MADMM: a generic algorithm for non-smooth optimization on manifolds

    Kovnatsky, Artiom; Glashoff, Klaus; Bronstein, Michael M.


    Numerous problems in machine learning are formulated as optimization with manifold constraints. In this paper, we propose the Manifold alternating directions method of multipliers (MADMM), an extension of the classical ADMM scheme for manifold-constrained non-smooth optimization problems and show its application to several challenging problems in dimensionality reduction, data analysis, and manifold learning.

  12. On the de Rham-Wu decomposition for Riemannian and Lorentzian manifolds

    Galaev, Anton S


    It is explained how to find the de~Rham decomposition of a Riemannian manifold and the Wu decomposition of a Lorentzian manifold. For that it is enough to find parallel symmetric bilinear forms on the manifold, and do some linear algebra. This result will allow to compute the connected holonomy group of an arbitrary Riemannian or Lorentzian manifold.

  13. Almost complex connections on almost complex manifolds with Norden metric

    Teofilova, Marta


    A four-parametric family of linear connections preserving the almost complex structure is defined on an almost complex manifold with Norden metric. Necessary and sufficient conditions for these connections to be natural are obtained. A two-parametric family of complex connections is studied on a conformal K\\"{a}hler manifold with Norden metric. The curvature tensors of these connections are proved to coincide.


    骆少明; 张湘伟; 蔡永昌


    The physical-cover-oriented variational principle of numerical manifold method (NMM) for the analysis of linear elastic static problems was put forward according to the displacement model and the characters of numerical manifold method. The theoretical calculating formulations and the controlling equation of NMM were derived. As an example,the plate with a hole in the center is calculated and the results show that the solution precision and efficiency of NMM are agreeable.

  15. A plug with infinite order and some exotic 4-manifolds

    Tange, Motoo


    Every exotic pair in 4-dimension is obtained each other by twisting a {\\it cork} or {\\it plug} which are codimension 0 submanifolds embedded in the 4-manifolds. The twist was an involution on the boundary of the submanifold. We define cork (or plug) with order $p\\in {\\Bbb N}\\cup \\{\\infty\\}$ and show there exists a plug with infinite order. Furthermore we show twisting $(P,\\varphi^2)$ gives to enlargements of $P$ compact exotic manifolds with boundary.

  16. Webs of Lagrangian Tori in Projective Symplectic Manifolds

    Hwang, Jun-Muk


    For a Lagrangian torus A in a simply-connected projective symplectic manifold M, we prove that M has a hypersurface disjoint from a deformation of A. This implies that a Lagrangian torus in a compact hyperk\\"ahler manifold is a fiber of an almost holomorphic Lagrangian fibration, giving an affirmative answer to a question of Beauville's. Our proof employs two different tools: the theory of action-angle variables for algebraically completely integrable Hamiltonian systems and Wielandt's theory of subnormal subgroups.

  17. The Identification of Convex Function on Riemannian Manifold

    Li Zou


    Full Text Available The necessary and sufficient condition of convex function is significant in nonlinear convex programming. This paper presents the identification of convex function on Riemannian manifold by use of Penot generalized directional derivative and the Clarke generalized gradient. This paper also presents a method for judging whether a point is the global minimum point in the inequality constraints. Our objective here is to extend the content and proof the necessary and sufficient condition of convex function to Riemannian manifolds.

  18. Characteristic varieties of quasi-projective manifolds and orbifolds

    Bartolo, Enrique Artal; Matei, Daniel


    We prove that the irreducible components of the characteristic varieties of quasi-projective manifolds are either pull-backs of such components for orbifolds, or torsion points. This gives an interpretation for the so-called \\emph{translated} components of the characteristic varieties, and shows that the zero-dimensional components are indeed torsion. The main result is used to derive further obstructions for a group to be the fundamental group of a quasi-projective manifold.

  19. Quasi-rigidity of hyperbolic 3-manifolds and scattering theory

    Borthwick, D; Taylor, E; Borthwick, David; Rae, Alan Mc; Taylor, Edward


    Take two isomorphic convex co-compact co-infinite volume Kleinian groups, whose regular sets are diffeomorphic. The quotient of hyperbolic 3-space by these groups gives two hyperbolic 3-manifolds whose scattering operators may be compared. We prove that the operator norm of the difference between the scattering operators is small, then the groups are related by a coorespondingly small quasi-conformal deformation. This in turn implies that the two hyperbolic 3-manifolds are quasi-isometric.

  20. Finite Time and Exact Time Controllability on Compact Manifolds

    Jouan, Philippe


    It is first shown that a smooth controllable system on a compact manifold is finite time controllable. The technique of proof is close to the one of Sussmann's orbit theorem, and no rank condition is required. This technique is also used to give a new and elementary proof of the equivalence between controllability for essentially bounded inputs and for piecewise constant ones. Two sufficient conditions for controllability at exact time on a compact manifold are then stated. Some applications,...

  1. A Note on Heegaard Splittings of Amalgamated 3-Manifolds

    Kun DU; Xutao GAO


    Let M be a compact orientable irreducible 3-manifold, and F be an essential connected closed surface in M which cuts M into two manifolds M1 and M2. If Mi has a minimal Heegaard splitting Mi = Vi ∪Hi Wi with d(H1) + d(H2) ≥ 2(g(M1) + g(M2) -g(F)) + 1, then g(M) = g(M1) + g(M2) - g(F).

  2. Solid state optical refrigeration using stark manifold resonances in crystals

    Seletskiy, Denis V.; Epstein, Richard; Hehlen, Markus P.; Sheik-Bahae, Mansoor


    A method and device for cooling electronics is disclosed. The device includes a doped crystal configured to resonate at a Stark manifold resonance capable of cooling the crystal to a temperature of from about 110K to about 170K. The crystal host resonates in response to input from an excitation laser tuned to exploit the Stark manifold resonance corresponding to the cooling of the crystal.

  3. Planetary Gearbox Fault Diagnosis Using Envelope Manifold Demodulation

    Weigang Wen; Gao, Robert X.; Weidong Cheng


    The important issue in planetary gear fault diagnosis is to extract the dependable fault characteristics from the noisy vibration signal of planetary gearbox. To address this critical problem, an envelope manifold demodulation method is proposed for planetary gear fault detection in the paper. This method combines complex wavelet, manifold learning, and frequency spectrogram to implement planetary gear fault characteristic extraction. The vibration signal of planetary gear is demodulated by w...

  4. Some properties of Fr\\'echet medians in Riemannian manifolds

    Yang, Le


    The consistency of Fr\\'echet medians is proved for probability measures in proper metric spaces. In the context of Riemannian manifolds, assuming that the probability measure has more than a half mass lying in a convex ball and verifies some concentration conditions, the positions of its Fr\\'echet medians are estimated. It is also shown that, in compact Riemannian manifolds, the Fr\\'echet sample medians of generic data points are always unique.

  5. Automorphisms and examples of compact non K\\"ahler manifolds

    Magnússon, Gunnar Þór


    Let $X$ be a compact K\\"ahler manifold with zero first Chern class and finite fundamental group. Folklore says that if an automorphism $f$ of $X$ fixes a K\\"ahler class, then its order is finite. We apply this result to construct a compact non K\\"ahler manifold $F$ as a fibration $X \\to F \\to B$ over a complex torus $B$.

  6. From integral manifolds and metrics to potential maps

    Udriste, C


    Full Text Available Our paper contains two main results: (1 the integral manifolds of a distribution together with two Riemann metrics produce potential maps which are in fact least squares approximations of the starting integral manifolds; (2 the least squares energy admits extremals satisfying periodic boundary conditions. Section 1 contains historical and bibliographical notes. Section 2 analyses some elements of the geometry produced on the jet bundle of order one by a semi-Riemann Sasaki-like metric. Section 3 describes the maximal integral manifolds of a distribution as solutions of a PDEs system of order one. Section 4 studies Poisson-like second-order prolongations of first order PDE systems and formulates the Lorentz-Udriste World-Force Law on a suitable semi-Riemann-Lagrange manifold (the base manifold of the jet bundle of order one. Section 5 exploits the idea of least squares Lagrangians, to include the integral manifolds of a distribution into a class of extremals. Section 6 gives conditions for the existence of extremals in conditions of multi-periodicity. Section 7 refers to the canonical forms of the vertical metric d-tensor produced by a density of energy on jet bundle of order one.

  7. Generalized Einstein Tensor for a Weyl Manifold and Its Applications

    Abdülkadir (O)ZDE(G)ER


    It is well known that the Einstein tensor G for a Piemannian manifold defined by Gβα =Rβα-1/2Rδα,Rβα =gβγRγα where Rγα and R are respectively the Ricci tensor and the scalar curvature of the manifold,plays an important part in Einstein's theory of gravitation as well as in proving some theorems in Riemannian geometry.In this work,we first obtain the generalized Einstein tensor for a Weyl manifold.Then,after studying some properties of generalized Einstein tensor,we prove that the conformed invariance of the generalized Einstein tensor implies the conformed invariance of the curvature tensor of the Weyl manifold and conversely.Moreover,we show that such Weyl manifolds admit a one-parameter family of hypersurfaces the orthogoned trajectories of which are geodesics.Finally,a necessary and sufficient condition in order that the generalized circles of a Weyl manifold be preserved by a conformal mapping is stated in terms of generalized Einstein tensors at corresponding points.

  8. Manifold learning of brain MRIs by deep learning.

    Brosch, Tom; Tam, Roger


    Manifold learning of medical images plays a potentially important role for modeling anatomical variability within a population with pplications that include segmentation, registration, and prediction of clinical parameters. This paper describes a novel method for learning the manifold of 3D brain images that, unlike most existing manifold learning methods, does not require the manifold space to be locally linear, and does not require a predefined similarity measure or a prebuilt proximity graph. Our manifold learning method is based on deep learning, a machine learning approach that uses layered networks (called deep belief networks, or DBNs) and has received much attention recently in the computer vision field due to their success in object recognition tasks. DBNs have traditionally been too computationally expensive for application to 3D images due to the large number of trainable parameters. Our primary contributions are (1) a much more computationally efficient training method for DBNs that makes training on 3D medical images with a resolution of up to 128 x 128 x 128 practical, and (2) the demonstration that DBNs can learn a low-dimensional manifold of brain volumes that detects modes of variations that correlate to demographic and disease parameters.

  9. Semisupervised Support Vector Machines With Tangent Space Intrinsic Manifold Regularization.

    Sun, Shiliang; Xie, Xijiong


    Semisupervised learning has been an active research topic in machine learning and data mining. One main reason is that labeling examples is expensive and time-consuming, while there are large numbers of unlabeled examples available in many practical problems. So far, Laplacian regularization has been widely used in semisupervised learning. In this paper, we propose a new regularization method called tangent space intrinsic manifold regularization. It is intrinsic to data manifold and favors linear functions on the manifold. Fundamental elements involved in the formulation of the regularization are local tangent space representations, which are estimated by local principal component analysis, and the connections that relate adjacent tangent spaces. Simultaneously, we explore its application to semisupervised classification and propose two new learning algorithms called tangent space intrinsic manifold regularized support vector machines (TiSVMs) and tangent space intrinsic manifold regularized twin SVMs (TiTSVMs). They effectively integrate the tangent space intrinsic manifold regularization consideration. The optimization of TiSVMs can be solved by a standard quadratic programming, while the optimization of TiTSVMs can be solved by a pair of standard quadratic programmings. The experimental results of semisupervised classification problems show the effectiveness of the proposed semisupervised learning algorithms.

  10. Dimensionality reduction of collective motion by principal manifolds

    Gajamannage, Kelum; Butail, Sachit; Porfiri, Maurizio; Bollt, Erik M.


    While the existence of low-dimensional embedding manifolds has been shown in patterns of collective motion, the current battery of nonlinear dimensionality reduction methods is not amenable to the analysis of such manifolds. This is mainly due to the necessary spectral decomposition step, which limits control over the mapping from the original high-dimensional space to the embedding space. Here, we propose an alternative approach that demands a two-dimensional embedding which topologically summarizes the high-dimensional data. In this sense, our approach is closely related to the construction of one-dimensional principal curves that minimize orthogonal error to data points subject to smoothness constraints. Specifically, we construct a two-dimensional principal manifold directly in the high-dimensional space using cubic smoothing splines, and define the embedding coordinates in terms of geodesic distances. Thus, the mapping from the high-dimensional data to the manifold is defined in terms of local coordinates. Through representative examples, we show that compared to existing nonlinear dimensionality reduction methods, the principal manifold retains the original structure even in noisy and sparse datasets. The principal manifold finding algorithm is applied to configurations obtained from a dynamical system of multiple agents simulating a complex maneuver called predator mobbing, and the resulting two-dimensional embedding is compared with that of a well-established nonlinear dimensionality reduction method.


    The project team applied the life cycle design methodology to the design analysis of three alternative air intake manifolds: a sand cast aluminum, brazed aluminum tubular, and nylon composite. The design analysis included a life cycle inventory analysis, environmental regulatory...

  12. Long-Term Morphological Modeling of Barrier Island Tidal Inlets

    Richard Styles


    Full Text Available The primary focus of this study is to apply a two-dimensional (2-D coupled flow-wave-sediment modeling system to simulate the development and growth of idealized barrier island tidal inlets. The idealized systems are drawn from nine U.S. coastal inlets representing Pacific Coast, Gulf Coast and Atlantic Coast geographical and climatological environments. A morphological factor is used to effectively model 100 years of inlet evolution and the resulting morphological state is gauged in terms of the driving hydrodynamic processes. Overall, the model performs within the range of established theoretically predicted inlet cross-sectional area. The model compares favorably to theoretical models of maximum inlet currents, which serve as a measure of inlet stability. Major morphological differences are linked to inlet geometry and tidal forcing. Narrower inlets develop channels that are more aligned with the inlet axis while wider inlets develop channels that appear as immature braided channel networks similar to tidal flats in regions with abundant sediment supply. Ebb shoals with strong tidal forcing extend further from shore and spread laterally, promoting multi-lobe development bisected by ebb shoal channels. Ebb shoals with moderate tidal forcing form crescent bars bracketing a single shore-normal channel. Longshore transport contributes to ebb shoal asymmetry and provides bed material to help maintain the sediment balance in the bay.

  13. Simulating triangulations. Graphs, manifolds and (quantum) spacetime

    Krueger, Benedikt


    Triangulations, which can intuitively be described as a tessellation of space into simplicial building blocks, are structures that arise in various different branches of physics: They can be used for describing complicated and curved objects in a discretized way, e.g., in foams, gels or porous media, or for discretizing curved boundaries for fluid simulations or dissipative systems. Interpreting triangulations as (maximal planar) graphs makes it possible to use them in graph theory or statistical physics, e.g., as small-world networks, as networks of spins or in biological physics as actin networks. Since one can find an analogue of the Einstein-Hilbert action on triangulations, they can even be used for formulating theories of quantum gravity. Triangulations have also important applications in mathematics, especially in discrete topology. Despite their wide occurrence in different branches of physics and mathematics, there are still some fundamental open questions about triangulations in general. It is a prior unknown how many triangulations there are for a given set of points or a given manifold, or even whether there are exponentially many triangulations or more, a question that relates to a well-defined behavior of certain quantum geometry models. Another major unknown question is whether elementary steps transforming triangulations into each other, which are used in computer simulations, are ergodic. Using triangulations as model for spacetime, it is not clear whether there is a meaningful continuum limit that can be identified with the usual and well-tested theory of general relativity. Within this thesis some of these fundamental questions about triangulations are answered by the use of Markov chain Monte Carlo simulations, which are a probabilistic method for calculating statistical expectation values, or more generally a tool for calculating high-dimensional integrals. Additionally, some details about the Wang-Landau algorithm, which is the primary used

  14. Cold water inlet in solar tanks - valuation

    Andersen, Elsa


    The aim of the project is to make a proposal for how to value a storage tank with a poor design of the cold water inlet. Based on measurements and calculations a number of curves, which are valid for this valuation, are worked out. Based on a simple test with a uniform heated storage tank the ratio...... between the energy tapped in one storage volume and the energy content in the tank before the tapping is measured. Afterwards the mixing factor, corresponding to the measured ratio, can be determined. It is proposed that the mixing factor is taken into consideration when the governmental subsidy for SDHW...

  15. Marine Ice Atlas for Cook Inlet, Alaska


    microwave/imager TDD thawing degree-day USACE U.S. Army Corps of Engineers USCB U.S. Census Bureau USCG U.S. Coast Guard USNO U.S. Naval Observatory WMO...large com- mercial fishing fleet based there. Homer, also a center for tourism , has a population of about 4,800. Marine facilities there include a deep...the importance of commercial navigation, fishing, and tourism access to remote sites around Cook Inlet, the practice continues today with even greater

  16. Low cost inlet filters for rainwater tanks

    Martinson, Brett; Thomas, T.


    Inlet filters are a common method for enhancing water quality in rainwater harvesting systems. They range from cheap cloth or gravel filters to complex and expensive multi-stage systems. Field experience has shown, however that filters often suffer from a lack of maintenance so self-cleaning is an advantage. Filters can clean themselves by dividing the water stream into two components; the first and largest is the clean water passed to the tank, the second much smaller component can be used t...

  17. Hydraulics and Stability of Five Texas Inlets.


    8217~~r 0.38 .. , q . P . I Pleasure Pier 7 Morgan’s Point 2 South Jetty 8 Railroad Causeway N 1. 3 Teuas City Dike 9 Chocolate Bayou A 4 Manna Reel 10 Son...Range and Level.............15 III HYDRAULICS AND STABILITY OF SPECIFIC INLETS...................... 15 1. Brazos River-Freeport Harbor Entrance...g acceleration of gravity K Keulegan repletion coefficient k wave number L channel length Le effective channel length n Manning’s coefficient P

  18. Influence of Inlet / Shoal Complex on Adjacent Shorelines via Inlet Sink Method


    placing dredged material onto adjacent beaches in moderate quantities (~200-500K cu yd) since the 1970 ’s (Dredging Information System (DIS...southward to Matanzas Inlet. Analysis of the ebb shoal volume change between surveys was made within a GIS framework using an area mask (Fig. 6

  19. Sub-Alfvenic inlet boundary conditions for axisymmetric MHD nozzles

    Cassibry, J T [Propulsion Research Center, University of Alabama in Huntsville, Huntsville, AL 35899 (United States); Wu, S T [Center for Space Plasma and Aeronomy Research, University of Alabama in Huntsville, Huntsville, AL 35899 (United States)


    There are numerous electromagnetic accelerator concepts which require plasma expansion through a magnetic nozzle. If the inlet flow is slower than one or all of the outgoing characteristics, namely, the Alfven, slow and fast magnetosonic speeds, then the number of inlet conditions which could be arbitrarily specified are reduced by the number of outgoing characteristics (up to three). We derive the axisymmetric compatibility equations using the method of projected characteristics for the inlet conditions in the z-plane to assure the boundary conditions being consistent with flow properties. We make simplifications to the equations assuming that the inlet Alfven speed is much faster than the sonic and slow magnetosonic speeds. We compare results for various inlet boundary conditions, including a modified Lax-Wendroff implementation of the compatibility equations, first order extrapolation and arbitrarily specifying the inlet conditions, in order to assess the stability and accuracy of various approaches.

  20. CFD numerical simulation of Archimedes spiral inlet hydrocyclone

    Zhang, L.; Wei, L.; Chang, B. H.; Xing, J. L.; Jia, K.


    For traditional linear type inlet, hydrocyclone has an unstable inner field, high turbulence intensity and low separation efficiency, this paper proposes an inlet mode that uses an Archimedes spiral hydrocyclone. A Mixture liquid-solid multiphase flow model combined with the kinetic theory of granular flow was used to simulate the high concentration water-sand-air three-phase flow in a hydrocyclone. We analyzed the pressure field, velocity field and turbulent kinetic energy and compared with traditional linear type inlet hydrocyclone inner field. The results show that Archimedes spiral inlet hydrocyclone's pressure field is evenly distributed. The Archimedes spiral inlet hydrocyclone can guide and accelerate the mixture flow and produce small forced vortex and less short circuit flow. The particles easily go to the outer vortex and are separated. The Archimedes spiral inlet hydrocyclone has effectively improved the stability of inner flow field and separation efficiency.

  1. [A new algorithm for NIR modeling based on manifold learning].

    Hong, Ming-Jian; Wen, Zhi-Yu; Zhang, Xiao-Hong; Wen, Quan


    Manifold learning is a new kind of algorithm originating from the field of machine learning to find the intrinsic dimensionality of numerous and complex data and to extract most important information from the raw data to develop a regression or classification model. The basic assumption of the manifold learning is that the high-dimensional data measured from the same object using some devices must reside on a manifold with much lower dimensions determined by a few properties of the object. While NIR spectra are characterized by their high dimensions and complicated band assignment, the authors may assume that the NIR spectra of the same kind of substances with different chemical concentrations should reside on a manifold with much lower dimensions determined by the concentrations, according to the above assumption. As one of the best known algorithms of manifold learning, locally linear embedding (LLE) further assumes that the underlying manifold is locally linear. So, every data point in the manifold should be a linear combination of its neighbors. Based on the above assumptions, the present paper proposes a new algorithm named least square locally weighted regression (LS-LWR), which is a kind of LWR with weights determined by the least squares instead of a predefined function. Then, the NIR spectra of glucose solutions with various concentrations are measured using a NIR spectrometer and LS-LWR is verified by predicting the concentrations of glucose solutions quantitatively. Compared with the existing algorithms such as principal component regression (PCR) and partial least squares regression (PLSR), the LS-LWR has better predictability measured by the standard error of prediction (SEP) and generates an elegant model with good stability and efficiency.

  2. An Experimental Investigation on Performance and Emissions of a Single Cylinder D.I Diesel Engine with Manifold Hydrogen Induction

    Haroun A.K. Shahad


    Full Text Available Hydrogen is a clean fuel for internal combustion engines as it produces only water vapor and nitrogen oxides when it burns. In this research, hydrogen is used as a blending fuel with diesel to reduce pollutants emission and to improve performance. It is inducted in the inlet manifold, (continuous manifold induction, which is of a single cylinder, four stroke, direct injection, variable compression ratio water cold diesel engine, type (Kirloskar. This technique of hydrogen blending is selected because of its simplicity and low cost. Hydrogen blending is built on the basis of energy replacement. A special electronic unit is designed and fabricated to control hydrogen blending ratio. The maximum achieved ratio is 30% of input energy and beyond that the engine operation becomes unsatisfactory. Tests are done with 17.5 compression ratio and 1500 rpm. The brake specific fuel consumption is reduced by 29% and the engine thermal efficiency increased by 16% at these operating conditions. The pollutant emissions of carbon oxides, UHC, and smoke opacity are dramatically decreased by 19.5%, 13%,and 45% respectively while NOx emission increased by 10%.

  3. Single cell performance studies on the Fe/Cr Redox Energy Storage System using mixed reactant solutions at elevated temperature

    Gahn, R. F.; Hagedorn, N. H.; Ling, J. S.

    Experimental studies in a 14.5 sq cm single cell system using mixed reactant solutions at 65 C are described. Systems were tested under isothermal conditions i.e., reactants and the cell were at the same temperature. Charging and discharging performance were evaluted by measuring watt-hour and coulombic efficiencies, voltage-current relationships, hydrogen evolution and membrane resistivity. Watt-hour efficiencies ranged from 86% at 43 ma/sq cm to 75% at 129 ma/sq cm with corresponding coulombic efficiencies of 92% and 97%, respectively. Hydrogen evolution was less than 1% of the charge coulombic capacity during charge-discharge cycling. Bismuth and bismuth-lead catalyzed chromium electrodes maintained reversible performance and low hydrogen evolution under normal and adverse cycling conditions. Reblending of the anode and cathode solutions was successfully demonstrated to compensate for osmotic volume changes. Improved performance was obtained with mixed reactant systems in comparison to the unmixed reactant systems.

  4. Long time durability tests of fabric inlet stratification pipes

    Andersen, Elsa; Furbo, Simon


    The long time durability of seven different two layer fabric inlet stratification pipes for enhancing thermal stratification in hot water stores is investigated experimentally. Accelerated durability tests are carried out with the inlet stratification pipes both in a domestic hot water tank...... and that this destroys the capability of building up thermal stratification for the fabric inlet stratification pipe. The results also show that although dirt, algae etc. are deposited in the fabric pipes in the space heating tank, the capability of the fabric inlet stratifiers to build up thermal stratification...

  5. The Geometry of Selected U.S. Tidal Inlets.


    Bodega Bay Inlet. Calif. 1931 NI C6GS S162 56 Humboldt Bay Inlet, Calif. 1859 NI CIGS 5710 57 Coos Bay Inlet. Oreg. 1885 NI USAE CB-I-18 58 Umpqua...Group 2 Group 3 Group 4 Group 5 Group 6 Outliers koriches Fripps Carolina Beach Lockwoods Folly Townsend Beaufort Hillsboro Stump St. Augustine Bodega ...Drakes Inlet, Calif. 1860 141 AlAN - -1 4-- * LtA94 LAND 0( -RAY 339 ft SECTON WDTHCHANNEL LENGTH 542. 626. Boo EGA BA 1931 C GS5162 BODEGA BAY 1931

  6. Hysteresis phenomenon of hypersonic inlet at high Mach number

    Jiao, Xiaoliang; Chang, Juntao; Wang, Zhongqi; Yu, Daren


    When the hypersonic inlet works at a Mach number higher than the design value, the hypersonic inlet is started with a regular reflection of the external compression shock at the cowl, whereas a Mach reflection will result in the shock propagating forwards to cause a shock detachment at the cowl lip, which is called "local unstart of inlet". As there are two operation modes of hypersonic inlet at high Mach number, the mode transition may occur with the operation condition of hypersonic inlet changing. A cowl-angle-variation-induced hysteresis and a downstream-pressure-variation-induced hysteresis in the hypersonic inlet start↔local unstart transition are obtained by viscous numerical simulations in this paper. The interaction of the external compression shock and boundary layer on the cowl plays a key role in the hysteresis phenomenon. Affected by the transition of external compression shock reflection at the cowl and the transition between separated and attached flow on the cowl, a hysteresis exists in the hypersonic inlet start↔local unstart transition. The hysteresis makes the operation of a hypersonic inlet very difficult to control. In order to avoid hysteresis phenomenon and keep the hypersonic inlet operating in a started mode, the control route should never pass through the local unstarted boundary.

  7. Effects of Flow Parameters and Inlet Geometry on Cyclone Efficiency



    A novel cyclone design, named converging symmetrical spiral inlet (CSSI) cyclone, is developed by improving the inlet geometry of conventional tangential single inlet (CTSI) cyclone for enhancing the physical performance of the cyclone.The collection efficiency of the CSSI cyclone is experimentally compared with the widely used CTSI cyclone. The results indicate that the CSSI cyclone provides higher collection efficiency by 5%~20% than that of the CTSI cyclone for a tested inlet velocity range of 11.99~23.85 m/s. In addition, the results of collection efficiency comparison between experimental data and theoretical model are also discussed.

  8. Electrochemiluminescence from tris(2,2′-bipyridyl) ruthenium (Ⅱ) in the presence of aminocarboxylic acid co-reactants


    Due to the highly sensitive electrochemiluminescence (ECL), tris(2,2′-bipyridyl) ruthenium(II) (Ru(bpy)32+) is often used in the field of bioarrays with the help of co-reactants. However, the generally used co-reactant, tripropylamine (TPA), is toxic, corrosive and volatile. Therefore, the search for safe, sensitive and economical co-reactants is critical. Herein, three aminocarboxylic acids, ethylenediamine-tetraacetic acid (EDTA), nitrilotriacetic acid (NTA), and 2-hydroxyethylethylene diaminetriacetic acid (HEDTA), have been investigated as potential co-reactants for promoting Ru(bpy)32+ ECL behaviour. A possible ECL mechanism is also presented. The experimental results suggested that the co-reactants have a different ECL behaviour compared to TPA, such as different pH- and surfactant-responses. The detection limits of Ru(bpy)32+ using NTA, EDTA and HEDTA as co-reactants are 1, 60 and 680 fmol·L-1, respectively. The results indicate that NTA has a much higher efficiency than TPA to excite Ru(bpy)3 2+ ECL under their own optimal conditions. NTA could be widely used in many fields because it is less toxic, corrosive and volatile than TPA. Moreover, using Ru(bpy)3 2+ ECL, a sensitive method for the detection of aminocarboxylic acids is also developed. An improvement of four orders of magnitude in detection limits is obtained for EDTA compared to the known Ru(bpy) 3 2+ chemiluminescent methods.

  9. Inlet and airframe compatibility for a V/STOL fighter/attack aircraft with top-mounted inlets

    Durston, D. A.; Smeltzer, D. B.


    Aerodynamic force and inlet pressure data are obtained for 9.5% force and pressure models of a V/STOL fighter/attack aircraft configuration with top mounted twin inlets. Data are presented from tests conducted in the Ames Unitary Wind Tunnels at Mach numbers of 0.6, 0.9, and 1.2 at angles of attack up to 27 deg. and angles of sideslip up to 12 deg. Trimmed aerodynamic characteristics and inlet performance are compared for three different leading edge extension (LEX) configurations. The effects of wing leading and trailing-edge flaps on the inlet are also determined. Maneuver perfromance is calculated form combined force and inlet pressure data. The largest of the three LEX sizes tested gives the best airplane maneuver performance. Wing flap deflections improved inlet recovery at all Mach numbers.

  10. Target detection performed on manifold approximations recovered from hyperspectral data

    Ziemann, Amanda K.; Messinger, David W.; Albano, James A.


    In high dimensional data, manifold learning seeks to identify the embedded lower-dimensional, non-linear mani- fold upon which the data lie. This is particularly useful in hyperspectral imagery where inherently m-dimensional data is often sparsely distributed throughout the d-dimensional spectral space, with m << d. By recovering the manifold, inherent structures and relationships within the data - which are not typically apparent otherwise - may be identified and exploited. The sparsity of data within the spectral space can prove challenging for many types of analysis, and in particular with target detection. In this paper, we propose using manifold recovery as a preprocessing step for spectral target detection algorithms. A graph structure is first built upon the data and the transformation into the manifold space is based upon that graph structure. Then, the Adaptive Co- sine/Coherence Estimator (ACE) algorithm is applied. We present an analysis of target detection performance in the manifold space using scene-derived target spectra from two different hyperspectral images.

  11. Compactifications of IIA supergravity on SU(2)-structure manifolds

    Spanjaard, B.


    In this thesis, we study compactifications of type IIA supergravity on six-dimensional manifolds with an SU(2)-structure. A general study of six-dimensional manifolds with SU(2)-structure shows that IIA supergravity compactified on such a manifold should yield a four-dimensional gauged N=4 supergravity. We explicitly derive the bosonic spectrum, gauge transformations and action for IIA supergravity compactified on two different manifolds with SU(2)-structure, one of which also has an H{sup (3)}{sub 10}-flux, and confirm that the resulting four-dimensional theories are indeed N=4 gauged supergravities. In the second chapter, we study an explicit construction of a set of SU(2)-structure manifolds. This construction involves a Scherk-Schwarz duality twist reduction of the half-maximal six-dimensional supergravity obtained by compactifying IIA supergravity on a K3. This reduction results in a gauged N=4 four-dimensional supergravity, where the gaugings can be divided into three classes of parameters. We relate two of the classes to parameters we found before, and argue that the third class of parameters could be interpreted as a mirror flux. (orig.)

  12. Physics on the adiabatically changed Finslerian manifold and cosmology

    Lipovka, Anton A


    In present paper we confirm our previous result [4] that Planck constant is adiabatic invariant of electromagnetic field propagating on the adiabatically changed Finslerian manifold. Direct calculation from cosmological parameters gives value h=6x10(-27) (erg s). We also confirm that Planck constant (and hence other fundamental constants which depend on h) is varied on time due to changing of geometry. As an example the variation of the fine structure constant is calculated. Its relative variation ((da/dt)/a) consist 1.0x10(-18) (1/s). We show that on the Finsler manifold characterized by adiabatically changed geometry, classical free electromagnetic field is quantized geometrically, from the properties of the manifold in such manner that adiabatic invariant of field is ET=6x10(-27)=h. Electrodynamic equations on the Finslerian manifold are suggested. It is stressed that quantization naturally appears from these equations and is provoked by adiabatically changed geometry of manifold. We consider in details tw...

  13. Hierarchical discriminant manifold learning for dimensionality reduction and image classification

    Chen, Weihai; Zhao, Changchen; Ding, Kai; Wu, Xingming; Chen, Peter C. Y.


    In the field of image classification, it has been a trend that in order to deliver a reliable classification performance, the feature extraction model becomes increasingly more complicated, leading to a high dimensionality of image representations. This, in turn, demands greater computation resources for image classification. Thus, it is desirable to apply dimensionality reduction (DR) methods for image classification. It is necessary to apply DR methods to relieve the computational burden as well as to improve the classification accuracy. However, traditional DR methods are not compatible with modern feature extraction methods. A framework that combines manifold learning based DR and feature extraction in a deeper way for image classification is proposed. A multiscale cell representation is extracted from the spatial pyramid to satisfy the locality constraints for a manifold learning method. A spectral weighted mean filtering is proposed to eliminate noise in the feature space. A hierarchical discriminant manifold learning is proposed which incorporates both category label and image scale information to guide the DR process. Finally, the image representation is generated by concatenating dimensionality reduced cell representations from the same image. Extensive experiments are conducted to test the proposed algorithm on both scene and object recognition datasets in comparison with several well-established and state-of-the-art methods with respect to classification precision and computational time. The results verify the effectiveness of incorporating manifold learning in the feature extraction procedure and imply that the multiscale cell representations may be distributed on a manifold.

  14. Enhanced manifold regularization for semi-supervised classification.

    Gan, Haitao; Luo, Zhizeng; Fan, Yingle; Sang, Nong


    Manifold regularization (MR) has become one of the most widely used approaches in the semi-supervised learning field. It has shown superiority by exploiting the local manifold structure of both labeled and unlabeled data. The manifold structure is modeled by constructing a Laplacian graph and then incorporated in learning through a smoothness regularization term. Hence the labels of labeled and unlabeled data vary smoothly along the geodesics on the manifold. However, MR has ignored the discriminative ability of the labeled and unlabeled data. To address the problem, we propose an enhanced MR framework for semi-supervised classification in which the local discriminative information of the labeled and unlabeled data is explicitly exploited. To make full use of labeled data, we firstly employ a semi-supervised clustering method to discover the underlying data space structure of the whole dataset. Then we construct a local discrimination graph to model the discriminative information of labeled and unlabeled data according to the discovered intrinsic structure. Therefore, the data points that may be from different clusters, though similar on the manifold, are enforced far away from each other. Finally, the discrimination graph is incorporated into the MR framework. In particular, we utilize semi-supervised fuzzy c-means and Laplacian regularized Kernel minimum squared error for semi-supervised clustering and classification, respectively. Experimental results on several benchmark datasets and face recognition demonstrate the effectiveness of our proposed method.

  15. Manifold Learning for Biomarker Discovery in MR Imaging

    Wolz, Robin; Aljabar, Paul; Hajnal, Joseph V.; Rueckert, Daniel

    We propose a framework for the extraction of biomarkers from low-dimensional manifolds representing inter- and intra-subject brain variation in MR image data. The coordinates of each image in such a low-dimensional space captures information about structural shape and appearance and, when a phenotype exists, about the subject's clinical state. A key contribution is that we propose a method for incorporating longitudinal image information in the learned manifold. In particular, we compare simultaneously embedding baseline and follow-up scans into a single manifold with the combination of separate manifold representations for inter-subject and intra-subject variation. We apply the proposed methods to 362 subjects enrolled in the Alzheimer's Disease Neuroimaging Initiative (ADNI) and classify healthy controls, subjects with Alzheimer's disease (AD) and subjects with mild cognitive impairment (MCI). Learning manifolds based on both the appearance and temporal change of the hippocampus, leads to correct classification rates comparable with those provided by state-of-the-art automatic segmentation estimates of hippocampal volume and atrophy. The biomarkers identified with the proposed method are data-driven and represent a potential alternative to a-priori defined biomarkers derived from manual or automated segmentations.

  16. Analysis on singular spaces: Lie manifolds and operator algebras

    Nistor, Victor


    We discuss and develop some connections between analysis on singular spaces and operator algebras, as presented in my sequence of four lectures at the conference Noncommutative geometry and applications, Frascati, Italy, June 16-21, 2014. Therefore this paper is mostly a survey paper, but the presentation is new, and there are included some new results as well. In particular, Sections 3 and 4 provide a complete short introduction to analysis on noncompact manifolds that is geared towards a class of manifolds-called "Lie manifolds" -that often appears in practice. Our interest in Lie manifolds is due to the fact that they provide the link between analysis on singular spaces and operator algebras. The groupoids integrating Lie manifolds play an important background role in establishing this link because they provide operator algebras whose structure is often well understood. The initial motivation for the work surveyed here-work that spans over close to two decades-was to develop the index theory of stratified singular spaces. Meanwhile, several other applications have emerged as well, including applications to Partial Differential Equations and Numerical Methods. These will be mentioned only briefly, however, due to the lack of space. Instead, we shall concentrate on the applications to Index theory.

  17. Hyperbolic normal forms and invariant manifolds: Astronomical applications

    Efthymiopoulos C.


    Full Text Available In recent years, the study of the dynamics induced by the invariant manifolds of unstable periodic orbits in nonlinear Hamiltonian dynamical systems has led to a number of applications in celestial mechanics and dynamical astronomy. Two applications of main current interest are i space manifold dynamics, i.e. the use of the manifolds in space mission design, and, in a quite different context, ii the study of spiral structure in galaxies. At present, most approaches to the computation of orbits associated with manifold dynamics (i.e. periodic or asymptotic orbits rely either on the use of the so-called Poincaré - Lindstedt method, or on purely numerical methods. In the present article we briefly review an analytic method of computation of invariant manifolds, first introduced by Moser (1958, and developed in the canonical framework by Giorgilli (2001. We use a simple example to demonstrate how hyperbolic normal form computations can be performed, and we refer to the analytic continuation method of Ozorio de Almeida and co-workers, by which we can considerably extend the initial domain of convergence of Moser’s normal form.

  18. Quasi-Newton Exploration of Implicitly Constrained Manifolds

    Tang, Chengcheng


    A family of methods for the efficient update of second order approximations of a constraint manifold is proposed in this thesis. The concept of such a constraint manifold corresponds to an abstract space prescribed by implicit nonlinear constraints, which can be a set of objects satisfying certain desired properties. This concept has a variety of applications, and it has been successfully introduced to fabrication-aware architectural design as a shape space consisting of all the implementable designs. The local approximation of such a manifold can be first order, in the tangent space, or second order, in the osculating surface, with higher precision. For a nonlinearly constrained manifold with rather high dimension and codimension, the computation of second order approximants (osculants) is time consuming. In this thesis, a type of so-called quasi-Newton manifold exploration methods which approximate the new osculants by updating the ones of a neighbor point by 1st-order information is introduced. The procedures are discussed in detail and the examples implemented to visually verify the methods are illustrated.

  19. Unsteady Diffusion Flames: Ignition, Travel, and Burnout (SUBCORE Project: Simplified Unsteady Burning of Contained Reactants)

    Fendell, Francis; Rungaldier, Harald


    An experimental apparatus for the examination of a planar, virtually strain-rate-free diffusion flame in microgravity has been designed and fabricated. Such a diffusion flame is characterized by relatively large spatial scale and high symmetry (to facilitate probing), and by relatively long fluid-residence time (to facilitate investigation of rates associated with sooting phenomena). Within the squat rectangular apparatus, with impervious, noncatalytic isothermal walls of stainless steel, a thin metallic splitter plate subdivides the contents into half-volumes. One half-volume initially contains fuel vapor diluted with an inert gas, and the other, oxidizer diluted with another inert gas-so that the two domains have equal pressure, density, and temperature. As the separator is removed, by translation in its own plane, through a tightly fitting slit in one side wall, a line ignitor in the opposite side wall initiates a triple-flame propagation across the narrow layer of combustible mixture formed near midheight in the chamber. The planar diffusion flame so emplaced is quickly disrupted in earth gravity. In microgravity, the planar flame persists, and travels ultimately into the half-volume containing the stoichiometrically deficient reactant; the flame eventually becomes extinguished owing to reactant depletion and heat loss to the walls.

  20. Time resolved FTIR study of the catalytic CO oxidation under periodic variation of the reactant concentration

    Kritzenberger, J.; Wokaun, A. [Paul Scherrer Inst. (PSI), Villigen (Switzerland)


    Oxidation of CO over palladium/zirconia catalyst obtained from an amorphous Pd{sub 25}Zr{sub 75} precursor was investigated by time resolved FTIR spectroscopy. Sine wave shaped modulation of the reactant concentration, i.e. variation of CO or O{sub 2} partial pressure, was used to induce variations of the IR signals of product (CO{sub 2}) and unconverted reactant (CO), which were detected in a multi-pass absorption cell. The phase shift {phi} between external perturbation and variation of the CO{sub 2} signal was examined in dependence on temperature (100{sup o}C{<=}T{<=}350{sup o}C) and modulation frequency (1.39x10{sup -4}Hz{<=}{omega}{<=}6.67x10{sup -2}Hz). From the phase shift values, a simple Eley-Rideal mechanism is excluded, and the rate limiting step of the Langmuir-Hinshelwood mechanism for the CO oxidation may be identified. Adsorption and possible surface movement of CO to the actual reaction site determine the rate of the CO oxidation on the palladium/zirconia catalyst used in our study. The introduction of an external perturbation is a first step towards the application of two-dimensional infrared spectroscopy to heterogeneous catalyzed reactions. (author) 3 figs., 4 refs.

  1. Inlet-engine matching for SCAR including application of a bicone variable geometry inlet. [Supersonic Cruise Aircraft Research

    Wasserbauer, J. F.; Gerstenmaier, W. H.


    Airflow characteristics of variable cycle engines (VCE) designed for Mach 2.32 can have transonic airflow requirements as high as 1.6 times the cruise airflow. This is a formidable requirement for conventional, high performance, axisymmetric, translating centerbody mixed compression inlets. An alternate inlet is defined where the second cone of a two cone centerbody collapses to the initial cone angle to provide a large off-design airflow capability, and incorporates modest centerbody translation to minimize spillage drag. Estimates of transonic spillage drag are competitive with those of conventional translating centerbody inlets. The inlet's cruise performance exhibits very low bleed requirements with good recovery and high angle of attack capability.

  2. A twistor sphere of generalized Kahler potentials on hyperkahler manifolds

    Dyckmanns, Malte


    We consider the generalized Kahler structures (g,J_+,J_-) that arise on a hyperkahler manifold (M,g,I,J,K) when we choose J_+ and J_- from the twistor space of M. We find a relation between semichiral and arctic superfields which can be used to determine the generalized Kahler potential for hyperkahler manifolds whose description in projective superspace is fully understood. We use this relation to determine an S^2-family of generalized Kahler potentials for Euclidean space and for the Eguchi-Hanson geometry. Cotangent bundles of Hermitian symmetric spaces constitute a class of hyperkahler manifolds where our method can be applied immediately since the necessary results from projective superspace are already available. As a non-trivial higher-dimensional example, we determine the generalized potential for T*CP^n, which generalizes the Eguchi-Hanson result.

  3. Weyl-Euler-Lagrange Equations of Motion on Flat Manifold

    Zeki Kasap


    Full Text Available This paper deals with Weyl-Euler-Lagrange equations of motion on flat manifold. It is well known that a Riemannian manifold is said to be flat if its curvature is everywhere zero. Furthermore, a flat manifold is one Euclidean space in terms of distances. Weyl introduced a metric with a conformal transformation for unified theory in 1918. Classical mechanics is one of the major subfields of mechanics. Also, one way of solving problems in classical mechanics occurs with the help of the Euler-Lagrange equations. In this study, partial differential equations have been obtained for movement of objects in space and solutions of these equations have been generated by using the symbolic Algebra software. Additionally, the improvements, obtained in this study, will be presented.

  4. Rigidity of complete noncompact bach-flat n-manifolds

    Chu, Yawei; Feng, Pinghua


    Let (Mn,g) be a complete noncompact Bach-flat n-manifold with the positive Yamabe constant and constant scalar curvature. Assume that the L2-norm of the trace-free Riemannian curvature tensor R∘m is finite. In this paper, we prove that (Mn,g) is a constant curvature space if the L-norm of R∘m is sufficiently small. Moreover, we get a gap theorem for (Mn,g) with positive scalar curvature. This can be viewed as a generalization of our earlier results of 4-dimensional Bach-flat manifolds with constant scalar curvature R≥0 [Y.W. Chu, A rigidity theorem for complete noncompact Bach-flat manifolds, J. Geom. Phys. 61 (2011) 516-521]. Furthermore, when n>9, we derive a rigidity result for R<0.

  5. Manifold boundaries give "gray-box" approximations of complex models

    Transtrum, Mark K


    We discuss a method of parameter reduction in complex models known as the Manifold Boundary Approximation Method (MBAM). This approach, based on a geometric interpretation of statistics, maps the model reduction problem to a geometric approximation problem. It operates iteratively, removing one parameter at a time, by approximating a high-dimension, but thin manifold by its boundary. Although the method makes no explicit assumption about the functional form of the model, it does require that the model manifold exhibit a hierarchy of boundaries, i.e., faces, edges, corners, hyper-corners, etc. We empirically show that a variety of model classes have this curious feature, making them amenable to MBAM. These model classes include models composed of elementary functions (e.g., rational functions, exponentials, and partition functions), a variety of dynamical system (e.g., chemical and biochemical kinetics, Linear Time Invariant (LTI) systems, and compartment models), network models (e.g., Bayesian networks, Marko...

  6. Gradient Algorithm on Stiefel Manifold and Application in Feature Extraction

    Zhang Jian-jun


    Full Text Available To improve the computational efficiency of system feature extraction, reduce the occupied memory space, and simplify the program design, a modified gradient descent method on Stiefel manifold is proposed based on the optimization algorithm of geometry frame on the Riemann manifold. Different geodesic calculation formulas are used for different scenarios. A polynomial is also used to lie close to the geodesic equations. JiuZhaoQin-Horner polynomial algorithm and the strategies of line-searching technique and change of the step size of iteration are also adopted. The gradient descent algorithm on Stiefel manifold applied in Principal Component Analysis (PCA is discussed in detail as an example of system feature extraction. Theoretical analysis and simulation experiments show that the new method can achieve superior performance in both the convergence rate and calculation efficiency while ensuring the unitary column orthogonality. In addition, it is easier to implement by software or hardware.

  7. Multiscale singular value manifold for rotating machinery fault diagnosis

    Feng, Yi; Lu, BaoChun; Zhang, Deng Feng [School of Mechanical Engineering, Nanjing University of Science and Technology,Nanjing (United States)


    Time-frequency distribution of vibration signal can be considered as an image that contains more information than signal in time domain. Manifold learning is a novel theory for image recognition that can be also applied to rotating machinery fault pattern recognition based on time-frequency distributions. However, the vibration signal of rotating machinery in fault condition contains cyclical transient impulses with different phrases which are detrimental to image recognition for time-frequency distribution. To eliminate the effects of phase differences and extract the inherent features of time-frequency distributions, a multiscale singular value manifold method is proposed. The obtained low-dimensional multiscale singular value manifold features can reveal the differences of different fault patterns and they are applicable to classification and diagnosis. Experimental verification proves that the performance of the proposed method is superior in rotating machinery fault diagnosis.

  8. Schoen manifold with line bundles as resolved magnetized orbifolds

    Groot Nibbelink, Stefan [Muenchen Univ. (Germany). Arnold Sommerfeld Center for Theoretical Physics; Vaudrevange, Patrick K.S. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)


    We give an alternative description of the Schoen manifold as the blow-up of a Z{sub 2} x Z{sub 2} orbifold in which one Z{sub 2} factor acts as a roto-translation. Since for this orbifold the fixed tori are only identified in pairs but not orbifolded, four-dimensional chirality can never be obtained using standard techniques alone. However, chirality is recovered when its tori become magnetized. To exemplify this, we construct an SU(5) GUT on the Schoen manifold with Abelian gauge fluxes, which becomes an MSSM with three generations after an appropriate Wilson line is associated to its freely acting involution. We reproduce this model as a standard orbifold CFT of the (partially) blown down Schoen manifold with a magnetic flux. Finally, in analogy to a proposal for non-perturbative heterotic models by Aldazabal et al. we suggest modifications to the heterotic orbifold spectrum formulae in the presence of magnetized tori.

  9. Planetary Gearbox Fault Diagnosis Using Envelope Manifold Demodulation

    Weigang Wen


    Full Text Available The important issue in planetary gear fault diagnosis is to extract the dependable fault characteristics from the noisy vibration signal of planetary gearbox. To address this critical problem, an envelope manifold demodulation method is proposed for planetary gear fault detection in the paper. This method combines complex wavelet, manifold learning, and frequency spectrogram to implement planetary gear fault characteristic extraction. The vibration signal of planetary gear is demodulated by wavelet enveloping. The envelope energy is adopted as an indicator to select meshing frequency band. Manifold learning is utilized to reduce the effect of noise within meshing frequency band. The fault characteristic frequency of the planetary gear is shown by spectrogram. The planetary gearbox model and test rig are established and experiments with planet gear faults are conducted for verification. All results of experiment analysis demonstrate its effectiveness and reliability.

  10. Quantum Chaos on Hyperbolic Manifolds A New Approach to Cosmology

    Tomaschitz, R


    We consider classical and quantum motion on multiply connected hyperbolic spaces, which appear as space-like slices in Robertson-Walker cosmologies. The topological structure of these manifolds creates on the one hand bounded chaotic trajectories, and on the other hand quantal bound states whose wave functions can be reconstructed from the chaotic geodesics. We obtain an exact relation between a probabilistic quantum mechanical wave field and the corresponding classical system, which is likewise probabilistic because of the instabilities of the trajectories with respect to the initial conditions. The central part in this reconstruction is played by the fractal limit set of the covering group of the manifold. This limit set determines the bounded chaotic trajectories on the manifold. Its Hausdorff measure and dimension determine the wave function of the quantum mechanical bound state for geodesic motion. We investigate relativistic scalar wave fields in de Sitter cosmologies, coupled to the curvature scalar of...

  11. Why Deep Learning Works: A Manifold Disentanglement Perspective.

    Brahma, Pratik Prabhanjan; Wu, Dapeng; She, Yiyuan


    Deep hierarchical representations of the data have been found out to provide better informative features for several machine learning applications. In addition, multilayer neural networks surprisingly tend to achieve better performance when they are subject to an unsupervised pretraining. The booming of deep learning motivates researchers to identify the factors that contribute to its success. One possible reason identified is the flattening of manifold-shaped data in higher layers of neural networks. However, it is not clear how to measure the flattening of such manifold-shaped data and what amount of flattening a deep neural network can achieve. For the first time, this paper provides quantitative evidence to validate the flattening hypothesis. To achieve this, we propose a few quantities for measuring manifold entanglement under certain assumptions and conduct experiments with both synthetic and real-world data. Our experimental results validate the proposition and lead to new insights on deep learning.

  12. Adaptive sampling for nonlinear dimensionality reduction based on manifold learning

    Franz, Thomas; Zimmermann, Ralf; Goertz, Stefan


    We make use of the non-intrusive dimensionality reduction method Isomap in order to emulate nonlinear parametric flow problems that are governed by the Reynolds-averaged Navier-Stokes equations. Isomap is a manifold learning approach that provides a low-dimensional embedding space...... that is approximately isometric to the manifold that is assumed to be formed by the high-fidelity Navier-Stokes flow solutions under smooth variations of the inflow conditions. The focus of the work at hand is the adaptive construction and refinement of the Isomap emulator: We exploit the non-Euclidean Isomap metric...... to detect and fill up gaps in the sampling in the embedding space. The performance of the proposed manifold filling method will be illustrated by numerical experiments, where we consider nonlinear parameter-dependent steady-state Navier-Stokes flows in the transonic regime....

  13. Behavior of Graph Laplacians on Manifolds with Boundary

    Zhou, Xueyuan


    In manifold learning, algorithms based on graph Laplacians constructed from data have received considerable attention both in practical applications and theoretical analysis. In particular, the convergence of graph Laplacians obtained from sampled data to certain continuous operators has become an active research topic recently. Most of the existing work has been done under the assumption that the data is sampled from a manifold without boundary or that the functions of interests are evaluated at a point away from the boundary. However, the question of boundary behavior is of considerable practical and theoretical interest. In this paper we provide an analysis of the behavior of graph Laplacians at a point near or on the boundary, discuss their convergence rates and their implications and provide some numerical results. It turns out that while points near the boundary occupy only a small part of the total volume of a manifold, the behavior of graph Laplacian there has different scaling properties from its beh...

  14. Valve and Manifold considerations for Efficient Digital Hydraulic Machines

    Roemer, Daniel Beck; Nørgård, Christian; Bech, Michael Møller


    This paper seeks to shed light on the topic of design and sizing of switching valves and connecting manifolds found in large digital hydraulic motors, also known commercially as Digital Displacement Motors. These motors promise very high operation efficiencies with broad operation ranges, which set...... strict requirements to the switching valves and the overall manifold design. To investigate this topic, the largest known digital motor (3.5 megawatt) is studied using models and optimization. Based on the limited information available about this motor, a detailed reconstruction of the motor architecture...... valves when considering also the manifold flow losses. A global optimization is conducted by use of the generalized differential evolution 3 algorithm, where the valve diameters, valve stroke lengths, actuator force capabilities and actuator timing signals are used as design variables. The results...

  15. Nonlinear damped oscillators on Riemannian manifolds: Numerical simulation

    Fiori, Simone


    Nonlinear oscillators are ubiquitous in sciences, being able to model the behavior of complex nonlinear phenomena, as well as in engineering, being able to generate repeating (i.e., periodic) or non-repeating (i.e., chaotic) reference signals. The state of the classical oscillators known from the literature evolves in the space Rn , typically with n = 1 (e.g., the famous van der Pol vacuum-tube model), n = 2 (e.g., the FitzHugh-Nagumo model of spiking neurons) or n = 3 (e.g., the Lorenz simplified model of turbulence). The aim of the current paper is to present a general scheme for the numerical differential-geometry-based integration of a general second-order, nonlinear oscillator model on Riemannian manifolds and to present several instances of such model on manifolds of interest in sciences and engineering, such as the Stiefel manifold and the space of symmetric, positive-definite matrices.

  16. Cone fields and topological sampling in manifolds with bounded curvature

    Turner, Katharine


    Often noisy point clouds are given as an approximation of a particular compact set of interest. A finite point cloud is a compact set. This paper proves a reconstruction theorem which gives a sufficient condition, as a bound on the Hausdorff distance between two compact sets, for when certain offsets of these two sets are homotopic in terms of the absence of {\\mu}-critical points in an annular region. Since an offset of a set deformation retracts to the set itself provided that there are no critical points of the distance function nearby, we can use this theorem to show when the offset of a point cloud is homotopy equivalent to the set it is sampled from. The ambient space can be any Riemannian manifold but we focus on ambient manifolds which have nowhere negative curvature. In the process, we prove stability theorems for {\\mu}-critical points when the ambient space is a manifold.

  17. Pseudo-differential operators on manifolds with singularities

    Schulze, B-W


    The analysis of differential equations in domains and on manifolds with singularities belongs to the main streams of recent developments in applied and pure mathematics. The applications and concrete models from engineering and physics are often classical but the modern structure calculus was only possible since the achievements of pseudo-differential operators. This led to deep connections with index theory, topology and mathematical physics. The present book is devoted to elliptic partial differential equations in the framework of pseudo-differential operators. The first chapter contains the Mellin pseudo-differential calculus on R+ and the functional analysis of weighted Sobolev spaces with discrete and continuous asymptotics. Chapter 2 is devoted to the analogous theory on manifolds with conical singularities, Chapter 3 to manifolds with edges. Employed are pseudo-differential operators along edges with cone-operator-valued symbols.

  18. Total Variation Regularization for Functions with Values in a Manifold

    Lellmann, Jan


    While total variation is among the most popular regularizers for variational problems, its extension to functions with values in a manifold is an open problem. In this paper, we propose the first algorithm to solve such problems which applies to arbitrary Riemannian manifolds. The key idea is to reformulate the variational problem as a multilabel optimization problem with an infinite number of labels. This leads to a hard optimization problem which can be approximately solved using convex relaxation techniques. The framework can be easily adapted to different manifolds including spheres and three-dimensional rotations, and allows to obtain accurate solutions even with a relatively coarse discretization. With numerous examples we demonstrate that the proposed framework can be applied to variational models that incorporate chromaticity values, normal fields, or camera trajectories. © 2013 IEEE.

  19. Usage of Connor Inlets to Eliminate Shrinkage

    D. Fecko


    Full Text Available The demand for castings of high quality and sound work is nowadays very high. The production of sound castings without foundryerrors is the big issue in modern foundries. Foundry simulation software can do a lot to help improve the disposition of castings, gatingsystem and feeder system, and assure good filling and solidification conditions, and also produce sound casting without the need of the oldmethod of "try and error". One can easily change a lot of parameters for filling and solidification, and create the best proposal forproduction. Connor inlets have two functions. One is that it serves as an ingate, through which molten metal passes and comes into themould cavity. The second function is that it serves as a feeder and substitutes the metal contracted during solidification and cooling of the castings. It can also save quite a lot of metal in comparison to classic feeders.

  20. Postoperative 3D spine reconstruction by navigating partitioning manifolds

    Kadoury, Samuel, E-mail: [Department of Computer and Software Engineering, Ecole Polytechnique Montreal, Montréal, Québec H3C 3A7 (Canada); Labelle, Hubert, E-mail:; Parent, Stefan, E-mail: [CHU Sainte-Justine Hospital Research Center, Montréal, Québec H3T 1C5 (Canada)


    Purpose: The postoperative evaluation of scoliosis patients undergoing corrective treatment is an important task to assess the strategy of the spinal surgery. Using accurate 3D geometric models of the patient’s spine is essential to measure longitudinal changes in the patient’s anatomy. On the other hand, reconstructing the spine in 3D from postoperative radiographs is a challenging problem due to the presence of instrumentation (metallic rods and screws) occluding vertebrae on the spine. Methods: This paper describes the reconstruction problem by searching for the optimal model within a manifold space of articulated spines learned from a training dataset of pathological cases who underwent surgery. The manifold structure is implemented based on a multilevel manifold ensemble to structure the data, incorporating connections between nodes within a single manifold, in addition to connections between different multilevel manifolds, representing subregions with similar characteristics. Results: The reconstruction pipeline was evaluated on x-ray datasets from both preoperative patients and patients with spinal surgery. By comparing the method to ground-truth models, a 3D reconstruction accuracy of 2.24 ± 0.90 mm was obtained from 30 postoperative scoliotic patients, while handling patients with highly deformed spines. Conclusions: This paper illustrates how this manifold model can accurately identify similar spine models by navigating in the low-dimensional space, as well as computing nonlinear charts within local neighborhoods of the embedded space during the testing phase. This technique allows postoperative follow-ups of spinal surgery using personalized 3D spine models and assess surgical strategies for spinal deformities.

  1. Detecting Lo cal Manifold Structure for Unsup ervised Feature Selection

    FENG Ding-Cheng; CHEN Feng; XU Wen-Li


    Unsupervised feature selection is fundamental in statistical pattern recognition, and has drawn persistent attention in the past several decades. Recently, much work has shown that feature selection can be formulated as nonlinear dimensionality reduction with discrete constraints. This line of research emphasizes utilizing the manifold learning techniques, where feature selection and learning can be studied based on the manifold assumption in data distribution. Many existing feature selection methods such as Laplacian score, SPEC (spectrum decomposition of graph Laplacian), TR (trace ratio) criterion, MSFS (multi-cluster feature selection) and EVSC (eigenvalue sensitive criterion) apply the basic properties of graph Laplacian, and select the optimal feature subsets which best preserve the manifold structure defined on the graph Laplacian. In this paper, we propose a new feature selection perspective from locally linear embedding (LLE), which is another popular manifold learning method. The main difficulty of using LLE for feature selection is that its optimization involves quadratic programming and eigenvalue decomposition, both of which are continuous procedures and different from discrete feature selection. We prove that the LLE objective can be decomposed with respect to data dimensionalities in the subset selection problem, which also facilitates constructing better coordinates from data using the principal component analysis (PCA) technique. Based on these results, we propose a novel unsupervised feature selection algorithm, called locally linear selection (LLS), to select a feature subset representing the underlying data manifold. The local relationship among samples is computed from the LLE formulation, which is then used to estimate the contribution of each individual feature to the underlying manifold structure. These contributions, represented as LLS scores, are ranked and selected as the candidate solution to feature selection. We further develop a

  2. Manifold learning techniques and model reduction applied to dissipative PDEs

    Sonday, Benjamin E; Gear, C William; Kevrekidis, Ioannis G


    We link nonlinear manifold learning techniques for data analysis/compression with model reduction techniques for evolution equations with time scale separation. In particular, we demonstrate a `"nonlinear extension" of the POD-Galerkin approach to obtaining reduced dynamic models of dissipative evolution equations. The approach is illustrated through a reaction-diffusion PDE, and the performance of different simulators on the full and the reduced models is compared. We also discuss the relation of this nonlinear extension with the so-called "nonlinear Galerkin" methods developed in the context of Approximate Inertial Manifolds.

  3. Geometry and physics of pseudodifferential operators on manifolds

    Esposito, Giampiero; Napolitano, George M.


    A review is made of the basic tools used in mathematics to define a calculus for pseudodifferential operators on Riemannian manifolds endowed with a connection: existence theorem for the function that generalizes the phase; analogue of Taylor's theorem; torsion and curvature terms in the symbolic calculus; the two kinds of derivative acting on smooth sections of the cotangent bundle of the Riemannian manifold; the concept of symbol as an equivalence class. Physical motivations and applications are then outlined, with emphasis on Green functions of quantum field theory and Parker's evaluation of Hawking radiation.

  4. Frobenius manifolds, Integrable Hierarchies and Minimal Liouville Gravity

    Belavin, A A


    We use the connection between the Frobrenius manifold and the Douglas string equation to further investigate Minimal Liouville gravity. We search a solution of the Douglas string equation and simultaneously a proper transformation from the KdV to the Liouville frame which ensure the fulfilment of the conformal and fusion selection rules. We find that the desired solution of the string equation has explicit and simple form in the flat coordinates on the Frobenious manifold in the general case of (p,q) Minimal Liouville gravity.

  5. Stabilizing and destabilizing Heegaard splittings of sufficiently complicated 3-manifolds

    Bachman, David


    Let M_1 and M_2 be compact, orientable 3-manifolds with incompressible boundary, and M the manifold obtained by gluing with a homeomorphism $\\phi:\\bdy M_1 \\to \\bdy M_2$. We analyze the relationship between the sets of low genus Heegaard splittings of M_1, M_2, and M, assuming the map \\phi is "sufficiently complicated." This analysis yields counter-examples to the Stabilization Conjecture, a resolution of the higher genus analogue of a conjecture of Gordon, and a result about the uniqueness of expressions of Heegaard splittings as amalgamations.

  6. A New Infinite Class of Sasaki-Einstein Manifolds

    Gauntlett, J P; Sparks, J F; Waldram, D; Gauntlett, Jerome P.; Martelli, Dario; Sparks, James F.; Waldram, Daniel


    We show that for every positive curvature Kahler-Einstein manifold in dimension 2n there is a countably infinite class of associated Sasaki-Einstein manifolds X_{2n+3} in dimension 2n+3. When n=1 we recover a recently discovered family of supersymmetric AdS_5 x X_5 solutions of type IIB string theory, while when n=2 we obtain new supersymmetric AdS_4 x X_7 solutions of D=11 supergravity. Both are expected to provide new supergravity duals of superconformal field theories.

  7. Valve and Manifold considerations for Efficient Digital Hydraulic Machines

    Roemer, Daniel Beck; Nørgård, Christian; Bech, Michael Møller;


    This paper seeks to shed light on the topic of design and sizing of switching valves and connecting manifolds found in large digital hydraulic motors, also known commercially as Digital Displacement Motors. These motors promise very high operation efficiencies with broad operation ranges, which set...... valves when considering also the manifold flow losses. A global optimization is conducted by use of the generalized differential evolution 3 algorithm, where the valve diameters, valve stroke lengths, actuator force capabilities and actuator timing signals are used as design variables. The results...

  8. Latent common manifold learning with alternating diffusion: analysis and applications

    Talmon, Ronen


    The analysis of data sets arising from multiple sensors has drawn significant research attention over the years. Traditional methods, including kernel-based methods, are typically incapable of capturing nonlinear geometric structures. We introduce a latent common manifold model underlying multiple sensor observations for the purpose of multimodal data fusion. A method based on alternating diffusion is presented and analyzed; we provide theoretical analysis of the method under the latent common manifold model. To exemplify the power of the proposed framework, experimental results in several applications are reported.

  9. Rapid Mixing of Geodesic Walks on Manifolds with Positive Curvature

    Mangoubi, Oren; Smith, Aaron


    We introduce a Markov chain for sampling from the uniform distribution on a Riemannian manifold $\\mathcal{M}$, which we call the $\\textit{geodesic walk}$. We prove that the mixing time of this walk on any manifold with positive sectional curvature $C_{x}(u,v)$ bounded both above and below by $0 < \\mathfrak{m}_{2} \\leq C_{x}(u,v) \\leq \\mathfrak{M}_2 < \\infty$ is $\\mathcal{O}^*\\left(\\frac{\\mathfrak{M}_2}{\\mathfrak{m}_2}\\right)$. In particular, this bound on the mixing time does not depend expli...

  10. Information Geometry and Chaos on Negatively Curved Statistical Manifolds

    Cafaro, Carlo


    A novel information-geometric approach to chaotic dynamics on curved statistical manifolds based on Entropic Dynamics (ED) is suggested. Furthermore, an information-geometric analogue of the Zurek-Paz quantum chaos criterion is proposed. It is shown that the hyperbolicity of a non-maximally symmetric 6N-dimensional statistical manifold M_{s} underlying an ED Gaussian model describing an arbitrary system of 3N non-interacting degrees of freedom leads to linear information-geometric entropy growth and to exponential divergence of the Jacobi vector field intensity, quantum and classical features of chaos respectively.

  11. Scars of Invariant Manifolds in Interacting Few-Body Systems

    Papenbrock, T; Weidenmüller, H A


    We present a novel extension of the concept of scars for the wave functions of classically chaotic few--body systems of identical particles with rotation and permutation symmetry. Generically there exist manifolds in classical phase space which are invariant under the action of a common subgroup of these two symmetries. Such manifolds are associated with highly symmetric configurations and, if sufficiently stable, support quantum resonances. Although not directly associated to individual periodic orbits, the resonances nevertheless cause scars which signify collective motion on the quantum level and which should be experimentally observable.

  12. Distributed mean curvature on a discrete manifold for Regge calculus

    Conboye, Rory; Ray, Shannon


    The integrated mean curvature of a simplicial manifold is well understood in both Regge Calculus and Discrete Differential Geometry. However, a well motivated pointwise definition of curvature requires a careful choice of volume over which to uniformly distribute the local integrated curvature. We show that hybrid cells formed using both the simplicial lattice and its circumcentric dual emerge as a remarkably natural structure for the distribution of this local integrated curvature. These hybrid cells form a complete tessellation of the simplicial manifold, contain a geometric orthonormal basis, and are also shown to give a pointwise mean curvature with a natural interpretation as a fractional rate of change of the normal vector.

  13. String Corrected Spacetimes and SU(N)-Structure Manifolds

    Becker, Katrin; Robbins, Daniel


    Using an effective field theory approach and the language of SU(N)-structures, we study higher derivative corrections to the supersymmetry constraints for compactifications of string or M-theory to Minkowski space. Our analysis is done entirely in the target space and is thus very general, and does not rely on theory-dependent details such as the amount of worldsheet supersymmetry. For manifolds of real dimension n<4 we show that the internal geometry remains flat and uncorrected. For n=4, 6, Kahler manifolds with SU(N)-holonomy can become corrected to SU(N)-structure, while preserving supersymmetry, once corrections are included.

  14. String corrected spacetimes and SU(N-structure manifolds

    Katrin Becker


    Full Text Available Using an effective field theory approach and the language of SU(N-structures, we study higher derivative corrections to the supersymmetry constraints for compactifications of string or M-theory to Minkowski space. Our analysis is done entirely in the target space and is thus very general, and does not rely on theory-dependent details such as the amount of worldsheet supersymmetry. For manifolds of real dimension n<4 we show that internal geometry remains flat and uncorrected. For n=4,6, Kähler manifolds with SU(N-holonomy can become corrected to SU(N-structure, while preserving supersymmetry, once corrections are included.

  15. 46 CFR 45.155 - Inlets and discharge piping: Valves.


    ... 46 Shipping 2 2010-10-01 2010-10-01 false Inlets and discharge piping: Valves. 45.155 Section 45... LINES Conditions of Assignment § 45.155 Inlets and discharge piping: Valves. (a) Except as provided in... visited by the crew. (e) Through-hull piping systems in machinery spaces may have valves with...

  16. Bedform evolution in a tidal inlet referred from wavelet analysis

    Fraccascia, Serena; Winter, Christian; Ernstsen, Verner Brandbyge;


    inlet and evaluate how they changed over consecutive years, when morphology was modified and bedforms migrated. High resolution bathymetric data from the Grådyb tidal inlet channel (Danish Wadden Sea) from seven years from 2002 to 2009 (not in 2004) were analyzed. Continuous wavelet transform of bed...

  17. Morphodynamics of tidal inlets in a tropical monsoon area

    Lam, N.T.; Stive, M.J.F.; Verhagen, H.J.; Wang, Z.B.


    Morphodynamics of a tidal inlet system on a micro-tidal coast in a tropical monsoon influenced region is modelled and discussed. Influences of river flow and wave climate on the inlet morphology are investigated with the aid of process-based state-of-the-art numerical models. Seasonal and episodic b

  18. 14 CFR 25.941 - Inlet, engine, and exhaust compatibility.


    ... 14 Aeronautics and Space 1 2010-01-01 2010-01-01 false Inlet, engine, and exhaust compatibility. 25.941 Section 25.941 Aeronautics and Space FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF..., engine, and exhaust compatibility. For airplanes using variable inlet or exhaust system geometry, or...

  19. Hydroxyl radical reactions with adenine: reactant complexes, transition states, and product complexes.

    Cheng, Qianyi; Gu, Jiande; Compaan, Katherine R; Schaefer, Henry F


    In order to address problems such as aging, cell death, and cancer, it is important to understand the mechanisms behind reactions causing DNA damage. One specific reaction implicated in DNA oxidative damage is hydroxyl free-radical attack on adenine (A) and other nucleic acid bases. The adenine reaction has been studied experimentally, but there are few theoretical results. In the present study, adenine dehydrogenation at various sites, and the potential-energy surfaces for these reactions, are investigated theoretically. Four reactant complexes [A···OH]* have been found, with binding energies relative to A+OH* of 32.8, 11.4, 10.7, and 10.1 kcal mol(-1). These four reactant complexes lead to six transition states, which in turn lie +4.3, -5.4, (-3.7 and +0.8), and (-2.3 and +0.8) kcal mol(-1) below A+OH*, respectively. Thus the lowest lying [A···OH]* complex faces the highest local barrier to formation of the product (A-H)*+H(2)O. Between the transition states and the products lie six product complexes. Adopting the same order as the reactant complexes, the product complexes [(A-H)···H(2)O]* lie at -10.9, -22.4, (-24.2 and -18.7), and (-20.5 and -17.5) kcal mol(-1), respectively, again relative to separated A+OH*. All six A+OH* → (A-H)*+H(2)O pathways are exothermic, by -0.3, -14.7, (-17.4 and -7.8), and (-13.7 and -7.8) kcal mol(-1), respectively. The transition state for dehydrogenation at N(6) lies at the lowest energy (-5.4 kcal mol(-1) relative to A+OH*), and thus reaction is likely to occur at this site. This theoretical prediction dovetails with the observed high reactivity of OH radicals with the NH(2) group of aromatic amines. However, the high barrier (37.1 kcal mol(-1)) for reaction at the C(8) site makes C(8) dehydrogenation unlikely. This last result is consistent with experimental observation of the imidazole ring opening upon OH radical addition to C(8). In addition, TD-DFT computed electronic transitions of the N(6) product around 420 nm

  20. Effect of inlet box on performance of axial flow fans

    Jingyin LI; Hua TIAN; Xiaofang YUAN


    Numerical investigations on 3D flow fields in an axial flow fan with and without an inlet box have been extensively conducted, focusing on the variation of fan performance caused by the internal flow fields and the velocity evenness at the exit of the inlet box. It is interest-ing to find that although the inlet box is well designed in accordance with basic design principles, there is a flow separation region in it. Furthermore, this flow separation and the resulting uneven velocity distribution at the exit lead to some decrease in the efficiency and an increase in the total pressure rise of the fan. This research shows that the inlet box needs further improvement and such a check on the flow fields is of value for the design of inlet boxes.

  1. A Regime Diagram for Autoignition of Homogeneous Reactant Mixtures with Turbulent Velocity and Temperature Fluctuations

    Im, Hong G.


    A theoretical scaling analysis is conducted to propose a diagram to predict weak and strong ignition regimes for a compositionally homogeneous reactant mixture with turbulent velocity and temperature fluctuations. The diagram provides guidance on expected ignition behavior based on the thermo-chemical properties of the mixture and the flow/scalar field conditions. The analysis is an extension of the original Zeldovich’s analysis by combining the turbulent flow and scalar characteristics in terms of the characteristic Damköhler and Reynolds numbers of the system, thereby providing unified and comprehensive understanding of the physical and chemical mechanisms controlling ignition characteristics. Estimated parameters for existing experimental measurements in a rapid compression facility show that the regime diagram predicts the observed ignition characteristics with good fidelity.

  2. Controlling an electron-transfer reaction at a metal surface by manipulating reactant motion and orientation.

    Bartels, Nils; Krüger, Bastian C; Auerbach, Daniel J; Wodtke, Alec M; Schäfer, Tim


    The loss or gain of vibrational energy in collisions of an NO molecule with the surface of a gold single crystal proceeds by electron transfer. With the advent of new optical pumping and orientation methods, we can now control all molecular degrees of freedom important to this electron-transfer-mediated process, providing the most detailed look yet into the inner workings of an electron-transfer reaction and showing how to control its outcome. We find the probability of electron transfer increases with increasing translational and vibrational energy as well as with proper orientation of the reactant. However, as the vibrational energy increases, translational excitation becomes unimportant and proper orientation becomes less critical. One can understand the interplay of all three control parameters from simple model potentials. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  3. Crosslinking-property relationships in PMR polyimide composites. I. [polymerization of monomer reactants

    Pater, R. H.; Whitley, K.; Morgan, C.; Chang, A.


    The effect of the crosslink density of the matrix on physical and mechanical properties of a graphite-fiber-reinforced PMR (for polymerization of monomer reactants) polyimide composites during isothermal aging was investigated in experiments where unidirectional composite specimens of Celion 6000/PMR-P1 were isothermally exposed at 288 C in air for various time periods up to 5000 hrs. It was found that, as the crosslink density increased, the glass transition temperature, density, and elevated-temperature interlaminar shear strength of a composite increased, while the initial moisture absorption and the coefficient of thermal expansion decreased. However, after reaching the highest possible matrix crosslink density, several of the composite properties began to deteriorate rapidly.

  4. Power Reactant Storage Assembly (PRSA) (Space Shuttle). PRSA hydrogen and oxygen DVT tank refurbishment


    The Power Reactant Storage Assembly (PRSA) liquid hydrogen Development Verification Test (H2 DVT) tank assembly (Beech Aircraft Corporation P/N 15548-0116-1, S/N 07399000SHT0001) and liquid oxygen (O2) DVT tank assembly (Beech Aircraft Corporation P/N 15548-0115-1, S/N 07399000SXT0001) were refurbished by Ball Electro-Optics and Cryogenics Division to provide NASA JSC, Propulsion and Power Division, the capability of performing engineering tests. The refurbishments incorporated the latest flight configuration hardware and avionics changes necessary to make the tanks function like flight articles. This final report summarizes these refurbishment activities. Also included are up-to-date records of the pressure time and cycle histories.

  5. Validity of the Michaelis-Menten equation--steady-state or reactant stationary assumption: that is the question.

    Schnell, Santiago


    The Michaelis-Menten equation is generally used to estimate the kinetic parameters, V and K(M), when the steady-state assumption is valid. Following a brief overview of the derivation of the Michaelis-Menten equation for the single-enzyme, single-substrate reaction, a critical review of the criteria for validity of the steady-state assumption is presented. The application of the steady-state assumption makes the implicit assumption that there is an initial transient during which the substrate concentration remains approximately constant, equal to the initial substrate concentration, while the enzyme-substrate complex concentration builds up. This implicit assumption is known as the reactant stationary assumption. This review presents evidence showing that the reactant stationary assumption is distinct from and independent of the steady-state assumption. Contrary to the widely believed notion that the Michaelis-Menten equation can always be applied under the steady-state assumption, the reactant stationary assumption is truly the necessary condition for validity of the Michaelis-Menten equation to estimate kinetic parameters. Therefore, the application of the Michaelis-Menten equation only leads to accurate estimation of kinetic parameters when it is used under experimental conditions meeting the reactant stationary assumption. The criterion for validity of the reactant stationary assumption does not require the restrictive condition of choosing a substrate concentration that is much higher than the enzyme concentration in initial rate experiments. © 2013 FEBS.

  6. Manifold adaptation for constant false alarm rate ship detection in South African oceans

    Schwegmann, CP


    Full Text Available into a threshold manifold. The manifold is adjusted using a Simulated Annealing algorithm to optimally fit to information provided by the ship distribution map which is generated from transponder data. By carefully selecting the input solution...

  7. Besov continuity for pseudo-differential operators on compact homogeneous manifolds

    Cardona, Duván


    In this paper we study the Besov continuity of pseudo-differential operators on compact homogeneous manifolds $M=G/K.$ We use the global quantization of these operators in terms of the representation theory of compact homogeneous manifolds.

  8. Conjugate Points on a Type of K(a)hler Manifolds

    Wei Ming LIU; Fu Sheng DENG


    We study conjugate points on a type of K(a)hler manifolds,which are submanifolds of Grassmannian manifolds.And then we give the applications to the study of the index of geodesics and homotopy groups.

  9. A new construction of Calabi–Yau manifolds: Generalized CICYs

    Lara B. Anderson


    Full Text Available We present a generalization of the complete intersection in products of projective space (CICY construction of Calabi–Yau manifolds. CICY three-folds and four-folds have been studied extensively in the physics literature. Their utility stems from the fact that they can be simply described in terms of a ‘configuration matrix’, a matrix of integers from which many of the details of the geometries can be easily extracted. The generalization we present is to allow negative integers in the configuration matrices which were previously taken to have positive semi-definite entries. This broadening of the complete intersection construction leads to a larger class of Calabi–Yau manifolds than that considered in previous work, which nevertheless enjoys much of the same degree of calculational control. These new Calabi–Yau manifolds are complete intersections in (not necessarily Fano ambient spaces with an effective anticanonical class. We find examples with topology distinct from any that has appeared in the literature to date. The new manifolds thus obtained have many interesting features. For example, they can have smaller Hodge numbers than ordinary CICYs and lead to many examples with elliptic and K3-fibration structures relevant to F-theory and string dualities.

  10. On the Kobayashi-Royden pseudonorm for almost complex manifolds

    Kruglikov, Boris S.


    In this paper we define Kobayashi-Royden pseudonorm for almost complex manifolds. Its basic properties known from the complex analysis are preserved in the nonintegrable case as well. We prove that the pseudodistance induced by this pseudonorm coincides with the Kobayashi pseudodistance defined for the almost complex case earlier. We also consider a geometric application for moduli spaces of pseudoholomorphic curves.

  11. Quantum general relativity and the classification of smooth manifolds

    Pfeiffer, H


    The gauge symmetry of classical general relativity under space-time diffeomorphisms implies that any path integral quantization which can be interpreted as a sum over space-time geometries, gives rise to a formal invariant of smooth manifolds. This is an opportunity to review results on the classification of smooth, piecewise-linear and topological manifolds. It turns out that differential topology distinguishes the space-time dimension d=3+1 from any other lower or higher dimension and relates the sought-after path integral quantization of general relativity in d=3+1 with an open problem in topology, namely to construct non-trivial invariants of smooth manifolds using their piecewise-linear structure. In any dimension d<=5+1, the classification results provide us with triangulations of space-time which are not merely approximations nor introduce any physical cut-off, but which rather capture the full information about smooth manifolds up to diffeomorphism. Conditions on refinements of these triangulations...

  12. Invariants of 3-Manifolds derived from finite dimensional hopf algebras

    Kauffman, L H; Louis H Kauffman; David E Radford


    Abstract: This paper studies invariants of 3-manifolds derived from certain fin ite dimensional Hopf algebras. The invariants are based on right integrals for these algebras. It is shown that the resulting class of invariants is distinct from the class of Witten-Reshetikhin-Turaev invariants.

  13. Conjectures on counting associative 3-folds in $G_2$-manifolds

    Joyce, Dominic


    There is a strong analogy between compact, torsion-free $G_2$-manifolds $(X,\\varphi,*\\varphi)$ and Calabi-Yau 3-folds $(Y,J,g,\\omega)$. We can also generalize $(X,\\varphi,*\\varphi)$ to 'tamed almost $G_2$-manifolds' $(X,\\varphi,\\psi)$, where we compare $\\varphi$ with $\\omega$ and $\\psi$ with $J$. Associative 3-folds in $X$, a special kind of minimal submanifold, are analogous to $J$-holomorphic curves in $Y$. Several areas of Symplectic Geometry -- Gromov-Witten theory, Quantum Cohomology, Lagrangian Floer cohomology, Fukaya categories -- are built using 'counts' of moduli spaces of $J$-holomorphic curves in $Y$, but give an answer depending only on the symplectic manifold $(Y,\\omega)$, not on the (almost) complex structure $J$. We investigate whether it may be possible to define interesting invariants of tamed almost $G_2$-manifolds $(X,\\varphi,\\psi)$ by 'counting' compact associative 3-folds $N\\subset X$, such that the invariants depend only on $\\varphi$, and are independent of the 4-form $\\psi$ used to def...

  14. The Persistence of a Slow Manifold with Bifurcation

    Kristiansen, Kristian Uldall; Palmer, P.; Robert, M.


    his paper considers the persistence of a slow manifold with bifurcation in a slow-fast two degree of freedom Hamiltonian system. In particular, we consider a system with a supercritical pitchfork bifurcation in the fast space which is unfolded by the slow coordinate. The model system is motivated...

  15. Curvature Properties of Lorentzian Manifolds with Large Isometry Groups

    Batat, Wafaa [Ecole Normale Superieure de L' Enseignement Technique d' Oran, Departement de Mathematiques et Informatique (Algeria)], E-mail:; Calvaruso, Giovanni, E-mail:; Leo, Barbara De [University of Salento, Dipartimento di Matematica ' E. De Giorgi' (Italy)], E-mail:


    The curvature of Lorentzian manifolds (M{sup n},g), admitting a group of isometries of dimension at least 1/2n(n - 1) + 1, is completely described. Interesting behaviours are found, in particular as concerns local symmetry, local homogeneity and conformal flatness.

  16. The Koppelman-Leray formula on complex Finsler manifolds

    QIU Chunhui; ZHONG Tongde


    By means of the invariant integral kernel (the Berndtsson kernel), the complex Finsler metric and the non-linear connection associated with the Chern-Finsler connection to research into the integral representation theory on complex Finsler manifolds, theKoppelman and Koppelman-Leray formulas are obtained, and the - -equations are solved.

  17. Coordination of a heterogeneous coastal hydrodynamics application in manifold

    C.L. Blom (Kees); F. Arbab (Farhad); S. Hummel; I.J.P. Elshoff


    textabstractIn this paper we show how the coordination language Manifold can be used to control the interactions of multiple heterogeneous application programs. We use a concrete example from Delft Hydaulics, a consulting and research company which develops models of natural hydraulic systems (e.g.,

  18. AdS 3-manifolds and Higgs bundles

    Alessandrini, Daniele; Li, Qiongling


    In this paper we investigate the relationships between closed AdS 3-manifolds and Higgs bundles. We have a new way to construct AdS structures that allows us to see many of their properties explicitly, for example we can recover the very recent formula by Tholozan for the volumes. We also find...

  19. Electromagnetic Field in Lyra Manifold: A First Order Approach

    Casana, R.; de Melo, C. A. M.; Pimentel, B. M.


    We discuss the coupling of the electromagnetic field with a curved and torsioned Lyra manifold using the Duffin-Kemmer-Petiau theory. We will show how to obtain the equations of motion and energy-momentum and spin density tensors by means of the Schwinger Variational Principle.

  20. Quadrature rules and distribution of points on manifolds

    Brandolini, Luca; Colzani, Leonardo; Gigante, Giacomo; Seri, Raffaello; Travaglini, Giancarlo


    We study the error in quadrature rules on a compact manifold. As in the Koksma-Hlawka inequality, we consider a discrepancy of the sampling points and a generalized variation of the function. In particular, we give sharp quantitative estimates for quadrature rules of functions in Sobolev classes.