Federal Laboratory Consortium — Purpose: The mission of the Geometric Design Laboratory (GDL) is to support the Office of Safety Research and Development in research related to the geometric design...
Polar metals by geometric design
Kim, T. H.; Puggioni, D.; Yuan, Y.; Xie, L.; Zhou, H.; Campbell, N.; Ryan, P. J.; Choi, Y.; Kim, J.-W.; Patzner, J. R.; Ryu, S.; Podkaminer, J. P.; Irwin, J.; Ma, Y.; Fennie, C. J.; Rzchowski, M. S.; Pan, X. Q.; Gopalan, V.; Rondinelli, J. M.; Eom, C. B.
2016-05-01
Gauss’s law dictates that the net electric field inside a conductor in electrostatic equilibrium is zero by effective charge screening; free carriers within a metal eliminate internal dipoles that may arise owing to asymmetric charge distributions. Quantum physics supports this view, demonstrating that delocalized electrons make a static macroscopic polarization, an ill-defined quantity in metals—it is exceedingly unusual to find a polar metal that exhibits long-range ordered dipoles owing to cooperative atomic displacements aligned from dipolar interactions as in insulating phases. Here we describe the quantum mechanical design and experimental realization of room-temperature polar metals in thin-film ANiO3 perovskite nickelates using a strategy based on atomic-scale control of inversion-preserving (centric) displacements. We predict with ab initio calculations that cooperative polar A cation displacements are geometrically stabilized with a non-equilibrium amplitude and tilt pattern of the corner-connected NiO6 octahedra—the structural signatures of perovskites—owing to geometric constraints imposed by the underlying substrate. Heteroepitaxial thin-films grown on LaAlO3 (111) substrates fulfil the design principles. We achieve both a conducting polar monoclinic oxide that is inaccessible in compositionally identical films grown on (001) substrates, and observe a hidden, previously unreported, non-equilibrium structure in thin-film geometries. We expect that the geometric stabilization approach will provide novel avenues for realizing new multifunctional materials with unusual coexisting properties.
Polar Metals by Geometric Design
Energy Technology Data Exchange (ETDEWEB)
Kim, T. H.; Puggioni, D.; Yuan, Y.; Xie, L.; Zhou, H.; Campbell, N.; Ryan, P. J.; Choi, Y.; Kim, J. -W.; Patzner, J. R.; Ryu, S.; Podkaminer, J. P.; Irwin, J.; Ma, Y.; Fennie, C. J.; Rzchowski, M. S.; Pan, X. Q.; Gopalan, V.; Rondinelli, J. M.; Eom, C. B.
2016-05-05
Gauss's law dictates that the net electric field inside a conductor in electrostatic equilibrium is zero by effective charge screening; free carriers within a metal eliminate internal dipoles that may arise owing to asymmetric charge distributions(1). Quantum physics supports this view(2), demonstrating that delocalized electrons make a static macroscopic polarization, an ill-defined quantity in metals(3)-it is exceedingly unusual to find a polar metal that exhibits long-range ordered dipoles owing to cooperative atomic displacements aligned from dipolar interactions as in insulating phases(4). Here we describe the quantum mechanical design and experimental realization of room-temperature polar metals in thin-film ANiO(3) perovskite nickelates using a strategy based on atomic-scale control of inversion-preserving (centric) displacements(5). We predict with ab initio calculations that cooperative polar A cation displacements are geometrically stabilized with a non-equilibrium amplitude and tilt pattern of the corner-connected NiO6 octahedra-the structural signatures of perovskites-owing to geometric constraints imposed by the underlying substrate. Heteroepitaxial thin-films grown on LaAlO3 (111) substrates fulfil the design principles. We achieve both a conducting polar monoclinic oxide that is inaccessible in compositionally identical films grown on (001) substrates, and observe a hidden, previously unreported(6-10), non-equilibrium structure in thin-film geometries. We expect that the geometric stabilization approach will provide novel avenues for realizing new multifunctional materials with unusual coexisting properties.
Transition curves for highway geometric design
Kobryń, Andrzej
2017-01-01
This book provides concise descriptions of the various solutions of transition curves, which can be used in geometric design of roads and highways. It presents mathematical methods and curvature functions for defining transition curves. .
Wooden Geometric Puzzles: Design and Hardness Proofs
Alt, H.; Bodlaender, H.L.; Kreveld, M.J. van; Rote, G.; Tel, G.
2007-01-01
We discuss some new geometric puzzles and the complexity of their extension to arbitrary sizes. For gate puzzles and two-layer puzzles we prove NP-completeness of solving them. Not only the solution of puzzles leads to interesting questions, but also puzzle design gives rise to interesting
Wooden Geometric Puzzles: Design and Hardness Proofs
Alt, H.; Bodlaender, H.L.; Kreveld, M.J. van; Rote, G.; Tel, G.
2008-01-01
We discuss some new geometric puzzles and the complexity of their extension to arbitrary sizes. For gate puzzles and two-layer puzzles we prove NP-completeness of solving them. Not only the solution of puzzles leads to interesting questions, but also puzzle design gives rise to interesting
Wooden Geometric Puzzles: Design and Hardness Proofs
Alt, H.; Bodlaender, H.L.; Kreveld, M.J. van; Rote, G.; Tel, G.
2007-01-01
We discuss some new geometric puzzles and the complexity of their extension to arbitrary sizes. For gate puzzles and two-layer puzzles we prove NP-completeness of solving them. Not only the solution of puzzles leads to interesting questions, but also puzzle design gives rise to interesting theoretic
Wooden Geometric Puzzles: Design and Hardness Proofs
Alt, H.; Bodlaender, H.L.; Kreveld, M.J. van; Rote, G.; Tel, G.
2008-01-01
We discuss some new geometric puzzles and the complexity of their extension to arbitrary sizes. For gate puzzles and two-layer puzzles we prove NP-completeness of solving them. Not only the solution of puzzles leads to interesting questions, but also puzzle design gives rise to interesting theoretic
Salt bridges: geometrically specific, designable interactions.
Donald, Jason E; Kulp, Daniel W; DeGrado, William F
2011-03-01
Salt bridges occur frequently in proteins, providing conformational specificity and contributing to molecular recognition and catalysis. We present a comprehensive analysis of these interactions in protein structures by surveying a large database of protein structures. Salt bridges between Asp or Glu and His, Arg, or Lys display extremely well-defined geometric preferences. Several previously observed preferences are confirmed, and others that were previously unrecognized are discovered. Salt bridges are explored for their preferences for different separations in sequence and in space, geometric preferences within proteins and at protein-protein interfaces, co-operativity in networked salt bridges, inclusion within metal-binding sites, preference for acidic electrons, apparent conformational side chain entropy reduction on formation, and degree of burial. Salt bridges occur far more frequently between residues at close than distant sequence separations, but, at close distances, there remain strong preferences for salt bridges at specific separations. Specific types of complex salt bridges, involving three or more members, are also discovered. As we observe a strong relationship between the propensity to form a salt bridge and the placement of salt-bridging residues in protein sequences, we discuss the role that salt bridges might play in kinetically influencing protein folding and thermodynamically stabilizing the native conformation. We also develop a quantitative method to select appropriate crystal structure resolution and B-factor cutoffs. Detailed knowledge of these geometric and sequence dependences should aid de novo design and prediction algorithms.
Evaluation of Design Methods for Geometric Control
DEFF Research Database (Denmark)
Kymmel, Mogens; Beran, M.; Foldager, L.;
1985-01-01
Geometric control can produce desirable control by decoupling the input disturbances from the selected output variables. The basic principle for this method was originally introduced by Wonham. The mathematical complexity involved, however, makes the method very hard to get accepted by the chemical...... community. The paper evaluates Wonham's original method together with three other methods, i.e. eigenvalue/eigenvector methods by Shah et al, the graph theory by Schizas and Evans and the simplified method by KÃ¼mmel et al. The evaluation considers the basic potential of the methods, the prerequisite...... of the designer, transparency, computer demand, and potential for pole shift....
Creativity and Motivation for Geometric Tasks Designing in Education
Rumanová, Lucia; Smiešková, Edita
2015-01-01
In this paper we focus on creativity needed for geometric tasks designing, visualization of geometric problems and use of ICT. We present some examples of various problems related to tessellations. Altogether 21 students--pre-service teachers participated in our activity within a geometry course at CPU in Nitra, Slovakia. Our attempt was to…
Generalizations of fuzzy linguistic control points in geometric design
Sallehuddin, M. H.; Wahab, A. F.; Gobithaasan, R. U.
2014-07-01
Control points are geometric primitives that play an important role in designing the geometry curve and surface. When these control points are blended with some basis functions, there are several geometric models such as Bezier, B-spline and NURBS(Non-Uniform Rational B-Spline) will be produced. If the control points are defined by the theory of fuzzy sets, then fuzzy geometric models are produced. But the fuzzy geometric models can only solve the problem of uncertainty complex. This paper proposes a new definition of fuzzy control points with linguistic terms. When the fuzzy control points with linguistic terms are blended with basis functions, then a fuzzy linguistic geometric model is produced. This paper ends with some numerical examples illustrating linguistic control attributes of fuzzy geometric models.
Geometric Design of Highways in USA
Directory of Open Access Journals (Sweden)
Hrvoje Baričević
2012-10-01
Full Text Available This paper describes the criteria, standards, and engineeringprocedures used to design principal elements of the highwayalignment, highway cross sections, and adjacent roadside environment.Development of a comprehensive highway design focuseson the establishment of travel lane configuration, alignmentlocation, and all dimensions related to the highway crosssection. A three-dimensional physical location is determinedthrough calculation of a horizontal and vertical alignment ofthe highway centerline, based on a variety of operational considerations.The results of these activities are refe"ed to as thegeometric design and represent all the visible features of a highwayor street. The first and major portion of the paper deals withthe design of motor-vehicle facilities. Specific design elementsare described and discussed with respect to design methodology.
Teaching geometrical principles to design students
Directory of Open Access Journals (Sweden)
Christoph Bartneck
2009-12-01
Full Text Available We propose a new method of teaching the principles of geometry to design students. The students focus on a field of design in which geometry is the design: tessellation. We review different approaches to geometry and the field of tessellation before we discuss the setup of the course. Instead of employing 2D drawing tools, such as Adobe Illustrator, the students define their tessellation in mathematical formulas, using the Mathematica software. This procedure enables them to understand the mathematical principles on which graphical tools, such as Illustrator are built upon. But we do not stop at a digital representation of their tessellation design we continue to cut their tessellations in Perspex. It moves the abstract concepts of math into the real world, so that the students can experience them directly, which provides a tremendous reward to the students.
SIAM Conference on Geometric Design and Computing. Final Technical Report
Energy Technology Data Exchange (ETDEWEB)
None
2002-03-11
The SIAM Conference on Geometric Design and Computing attracted 164 domestic and international researchers, from academia, industry, and government. It provided a stimulating forum in which to learn about the latest developments, to discuss exciting new research directions, and to forge stronger ties between theory and applications. Final Report
Geometric design of crab-like climbing and walking robots
Institute of Scientific and Technical Information of China (English)
LIU An-min; David Howard
2004-01-01
This paper considers the geometric design of crab-like walkers and climbers, without decoupling leg design from overall machine design. Crab-like machines represent an important sub-class of multi-legged robots, being particularly well suited to crossing difficult terrains. Firstly, the kinematic configurations and constraints are described, which determine the machine's kinematic characteristics. The influence of the design parameters on the kinematic workspace is discussed. Finally,a two stage design methodology is presented, comprising kinematic design and design optimisation, the latter being based on the use of design maps rather than numerical optimisation. The performance measures considered during design optimisation include kinematic, static and quasi-static measures.
Geometric design constratins for controlled fragmentation of metallic cylindrical shells
Pike, Allen William
Geometric designs for the controlled fragmentation of cylindrical shells have been successfully modeled by means of CTH hydrocode simulation. Design parameters varied include the shell radius, thickness, and the depth and spacing of interior notches. A large number of shell designs were analyzed and their controlled fragmentation effectiveness categorized. The best overall controlled fragmentation designs exhibit full and complete fragment breakup as prescribed along the system of interior grooves or notches without any of the individual fragments naturally fragmenting throughout their thicknesses. For the combination of the Composition C-4 explosive and the 4340 steel, the best performing designs were shown to commonly possess the following characteristics: (1) they each have notch or groove depths greater than half of the shell thickness, (2) they each have notch or groove spacing within a range that is approximately the same as the shell thickness, and (3) they each have shell thicknesses many times smaller than the shell radius.
Geometric programming prediction of design trends for OMV protective structures
Mog, R. A.; Horn, J. R.
1990-01-01
The global optimization trends of protective honeycomb structural designs for spacecraft subject to hypervelocity meteroid and space debris are presented. This nonlinear problem is first formulated for weight minimization of the orbital maneuvering vehicle (OMV) using a generic monomial predictor. Five problem formulations are considered, each dependent on the selection of independent design variables. Each case is optimized by considering the dual geometric programming problem. The dual variables are solved for in terms of the generic estimated exponents of the monomial predictor. The primal variables are then solved for by conversion. Finally, parametric design trends are developed for ranges of the estimated regression parameters. Results specify nonmonotonic relationships for the optimal first and second sheet mass per unit areas in terms of the estimated exponents.
Design of geometric phase measurement in EAST Tokamak
Lan, T; Liu, J; Jie, Y X; Wang, Y L; Gao, X; Qin, H
2016-01-01
The optimum scheme for geometric phase measurement in EAST Tokamak is proposed in this paper. The theoretical values of geometric phase for the probe beams of EAST Polarimeter-Interferometer (POINT) system are calculated by path integration in parameter space. Meanwhile, the influences of some controllable parameters on geometric phase are evaluated. The feasibility and challenge of distinguishing geometric effect in the POINT signal are also assessed in detail.
Geometric design of the best performing auto-rotating wing
Liu, Yucen; Vincent, Lionel; Kanso, Eva
2016-11-01
Many plants use gravity and aerodynamics to disperse their seeds away from the parent plant. Various seed designs result in different dispersal modes from gliding to auto-rotating. Here, we are interested in understanding the effect of geometric design of auto-rotating seedpods on their aerodynamic performance. As an experimentally tractable surrogate to real seedpods, we investigate auto-rotating paper wings of various shape designs. We compare these designs to a control case consisting of the canonical rectangular wing. Inspired by aerodynamics, we begin by considering the benefit of an elliptical planform, and test the effect of aspect ratio on flight range and descent angle. We find the elliptical planform improves the tumbling rate and the aspect ratio has a positive effect on the flight performance of the wings. We then test two families of more complex shapes: one of tapered planform and one of a planform with sharp tips. We look for an optimal flight performance while constraining either the mass or the maximum length and width of the wing. We find that wings with sharper tips and larger length have higher auto-rotation rates and improved performance. The results imply that both the planform and length of the wing contribute to the wing's flight performance.
Geometric Theory for the Design of Multielement Optical Systems
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
To establish a theoretical basis for providing a better design method of multielement optical systems, we have developed a third-order geometric theory of a plane-symmetric multielement optical system that consists of a planar light source, an arbitrary number of ellipsoidal gratings, and an image plane. Analytic formulas of spot diagrams are derived for the system by analytically following a ray-tracing formalism. With these formulas, coma, spherical aberration, and resultant aberration are discussed. To make the theory practical, we determine the aberration coefficients numerically, rather than analytically, with the aid of ray tracing that takes into account the angular distribution of rays originating from a given light source. A merit function is defined so as to represent closely the variance of the spots formed when an infinite number of rays are traced and to take into account the dimensions of the source and the last optical element. The theory is also applicable to mirror-grating or mirror systems.
Yilmaz, Gül Kaleli; Koparan, Timur
2016-01-01
The aim of this study is to find out how designed Geometry Teaching Lesson affects candidate teachers' Van Hiele Geometric Thinking Levels. For that purpose, 14 weeks long study was performed with 44 candidate teachers who were university students in Turkey. Van Hiele Geometric Thinking Test was applied to candidate teachers before and after…
Fifth SIAM conference on geometric design 97: Final program and abstracts. Final technical report
Energy Technology Data Exchange (ETDEWEB)
NONE
1997-12-31
The meeting was divided into the following sessions: (1) CAD/CAM; (2) Curve/Surface Design; (3) Geometric Algorithms; (4) Multiresolution Methods; (5) Robotics; (6) Solid Modeling; and (7) Visualization. This report contains the abstracts of papers presented at the meeting. Proceding the conference there was a short course entitled ``Wavelets for Geometric Modeling and Computer Graphics``.
Research on HJ-1A/B satellite data automatic geometric precision correction design
Institute of Scientific and Technical Information of China (English)
Xiong Wencheng; Shen Wenming; Wang Qiao; Shi Yuanli; Xiao Rulin; Fu Zhuo
2014-01-01
Developed independently by China,HJ-1A/B satellites have operated well on-orbit for five years and acquired a large number of high-quality observation data. The realization of the observation data geometric precision correction is of great significance for macro and dynamic ecological environment monitoring. The pa-per analyzed the parameter characteristics of HJ-1 satellite and geometric features of HJ-1 satellite level 2 data (systematic geo-corrected data). Based on this,the overall HJ-1 multi-sensor geometric correction flow and charge-coupled device (CCD) automatic geometric precision correction method were designed. Actual operating data showed that the method could achieve good result for automatic geometric precision correction of HJ-1 sat-ellite data,automatic HJ-1 CCD image geometric precision correction accuracy could be achieved within two pixels and automatic matching accuracy between the images of same satellite could be obtained less than one pixel.
A study of mathematical thoughts in the geometrical design of bertam (wild Bornean sago) weaving
Wan Bakar, Wan Norliza; Ahmad Shukri, Fuziatul Norsyiha; Ramli, Masnira
2013-04-01
Kelarai, a design for weaving, which is made up of various motifs can be produced by a variety of natural products. The main focus of the study is on Kelarai Bertam which is selected based on the firm and robust quality of the wood which was often used as the building materials of traditional houses. The objective of the study is to investigate the geometrical design in the weaving art of kelarai bertam, the stimulation of mathematical thoughts in geometrical designs and the evolution of geometrical designs in the weaving art of kelarai bertam. The research method utilized in the study was the triangulation method consisting of observation, interview and analysis. The findings revealed that quadrilateral forms and symmetrical forms such as reflection, translation, rotation and magnification were present in the weaving of kelarai bertam. The design of kelarai has undergone the process of evolution beginning from the Siku Keluang motif and has now expanded to 20 exquisite motifs. The evolution of the design and motifs resulted from the observation made upon the natives' house and wall decorations from Indonesia. In fact, geometrical concept has long been applied in the weaving art but this was not realized by the individual weaver. It is suggested that extensive research can be conducted on the combination of different weaving materials such as wild bertam and bamboo which will produce different geometrical designs such as polygon.
Curves and surfaces for computer-aided geometric design a practical guide
Farin, Gerald
1992-01-01
A leading expert in CAGD, Gerald Farin covers the representation, manipulation, and evaluation of geometric shapes in this the Third Edition of Curves and Surfaces for Computer Aided Geometric Design. The book offers an introduction to the field that emphasizes Bernstein-Bezier methods and presents subjects in an informal, readable style, making this an ideal text for an introductory course at the advanced undergraduate or graduate level.The Third Edition includes a new chapter on Topology, offers new exercises and sections within most chapters, combines the material on Geometric Continuity i
Murugan, Karmani; Choonara, Yahya E; Kumar, Pradeep; du Toit, Lisa C; Pillay, Viness
2017-09-01
This study aimed to highlight a statistic design to precisely engineer homogenous geometric copper nanoparticles (CuNPs) for enhanced intracellular drug delivery as a function of geometrical structure. CuNPs with a dual functionality comprising geometric attributes for enhanced cell uptake and exerting cytotoxic activity on proliferating cells were synthesized as a novel drug delivery system. This paper investigated the defined concentrations of two key surfactants used in the reaction to mutually control and manipulate nano-shape and optimisation of the geometric nanosystems. A statistical experimental design comprising a full factorial model served as a refining factor to achieve homogenous geometric nanoparticles using a one-pot method for the systematic optimisation of the geometric CuNPs. Shapes of the nanoparticles were investigated to determine the result of the surfactant variation as the aim of the study and zeta potential was studied to ensure the stability of the system and establish a nanosystem of low aggregation potential. After optimisation of the nano-shapes, extensive cellular internalisation studies were conducted to elucidate the effect of geometric CuNPs on uptake rates, in addition to the vital toxicity assays to further understand the cellular effect of geometric CuNPs as a drug delivery system. In addition to geometry; volume, surface area, orientation to the cell membrane and colloidal stability is also addressed. The outcomes of the study demonstrated the success of homogenous geometric NP formation, in addition to a stable surface charge. The findings of the study can be utilized for the development of a drug delivery system for promoted cellular internalisation and effective drug delivery. Copyright © 2017 Elsevier B.V. All rights reserved.
Evolution of Geometric Sensitivity Derivatives from Computer Aided Design Models
Jones, William T.; Lazzara, David; Haimes, Robert
2010-01-01
The generation of design parameter sensitivity derivatives is required for gradient-based optimization. Such sensitivity derivatives are elusive at best when working with geometry defined within the solid modeling context of Computer-Aided Design (CAD) systems. Solid modeling CAD systems are often proprietary and always complex, thereby necessitating ad hoc procedures to infer parameter sensitivity. A new perspective is presented that makes direct use of the hierarchical associativity of CAD features to trace their evolution and thereby track design parameter sensitivity. In contrast to ad hoc methods, this method provides a more concise procedure following the model design intent and determining the sensitivity of CAD geometry directly to its respective defining parameters.
Design developing conceptual models blade with geometric combined surface
Juraev, T. H.; Bukhara Technological Institute of Engineering, Bukhara
2013-01-01
A conceptual model of the blade using the methods of geometricmodeling principles of industrial design and CAD technologies. Variants are functional use of the proposed model for various working bodies.
DEFF Research Database (Denmark)
Yoon, Gil Ho; Joung, Young Soo; Kim, Yoon Young
2005-01-01
The topology design optimization of “three-dimensional geometrically-nonlinear” continuum structures is still a difficult problem not only because of its problem size but also the occurrence of unstable continuum finite elements during the design optimization. To overcome this difficulty...
DEFF Research Database (Denmark)
Lindgaard, Esben; Lund, Erik
2012-01-01
This paper presents a novel FEM-based approach for fiber angle optimal design of laminated composite structures exhibiting complicated nonlinear buckling behavior, thus enabling design of lighter and more cost-effective structures. The approach accounts for the geometrically nonlinear behavior...
Geometric constraints for shape and topology optimization in architectural design
Dapogny, Charles; Faure, Alexis; Michailidis, Georgios; Allaire, Grégoire; Couvelas, Agnes; Estevez, Rafael
2017-02-01
This work proposes a shape and topology optimization framework oriented towards conceptual architectural design. A particular emphasis is put on the possibility for the user to interfere on the optimization process by supplying information about his personal taste. More precisely, we formulate three novel constraints on the geometry of shapes; while the first two are mainly related to aesthetics, the third one may also be used to handle several fabrication issues that are of special interest in the device of civil structures. The common mathematical ingredient to all three models is the signed distance function to a domain, and its sensitivity analysis with respect to perturbations of this domain; in the present work, this material is extended to the case where the ambient space is equipped with an anisotropic metric tensor. Numerical examples are discussed in two and three space dimensions.
Mathematical calculation model for geometrical parameters of timber mesh design with orthogonal grid
Directory of Open Access Journals (Sweden)
Loktev Dmitriy Aleksandrovich
Full Text Available Mesh cover design, a multi-element design, which ensures the correct geometrical arrangement of the elements, is a very important task. The purpose of the given article is the development of a mathematical model for selecting the geometric parameters of wooden arches with mesh orthogonal grid with different input data. In this article three variants of design were observed. The main differences between them are in the relative position of longitudinal and transverse components. When performing static calculations of such designs in order to achieve their subsequent correct assembly, the following location conditions were observed: all the items must strictly match with each other without a gap and without overlap. However, these conditions must be met for any ratio of height to the arch span, the number of longitudinal members and the thickness of longitudinal members. Inverse problems also take place. In this case, the geometric calculation is not possible to vary the cross-section elements, and the stress-strain state of the cover is provided by varying the pitch of the transverse arches of the elements, on which the geometric calculation has no influence. All this determines the need for universal mathematical models describing any geometrical parameter of the designs needed for their geometrical calculation. The basic approach for the development of such models is the use of the known trigonometric formulas, giving a complete description of the desired geometry of the arch. Finally three transcendental equations were obtained, the solution algorithm of which using Newton’s method is presented in the MathCAD. The complexity of solving such equations using the proposed algorithm in the MathCAD is reduced to a minimum.
Influence of geometric design characteristics on safety under heterogeneous traffic flow
Directory of Open Access Journals (Sweden)
Praveen Vayalamkuzhi
2016-12-01
Full Text Available This paper focuses on analysing the influence of geometric design characteristics on traffic safety using bi-directional data on a divided roadway operated under heterogeneous traffic conditions in India. The study was carried out on a four lane divided inter-city highway in plain and rolling terrain. Statistical modelling approach by Poisson regression and Negative binomial regression were used to assess the safety performance as occurrence of crashes are random events and to identify the influence of the geometric design variables on the crash frequency. Negative binomial regression model was found to be more suitable to identify the variables contributing to road crashes. The study enabled better understanding of the factors related to road geometrics that influence road crash frequency. The study also established that operating speed has a significant contribution to the total number of crashes. Negative binomial models are found to be appropriate to predict road crashes on divided roadways under heterogeneous traffic conditions.
DEFF Research Database (Denmark)
Endelt, Benny Ørtoft; Volk, Wolfram
2013-01-01
, the reaction speed may be insufficient compared to the production rate in an industrial application. We propose to design an iterative learning control (ILC) algorithm which can control and update the blank-holder force as well as the distribution of the blank-holder force based on limited geometric data from...
Geometric optimal design of MR damper considering damping force, control energy and time constant
Energy Technology Data Exchange (ETDEWEB)
Nguyen, Q H; Choi, S B [Smart Structures and Systems Laboratory, Department of Mechanical Engineering, INHA University, Incheon 402-751 (Korea, Republic of); Kim, K S [Department of Mechanical and Automotive Engineering, Kongju National University, Chonan 330-240 (Korea, Republic of)], E-mail: seungbok@inha.ac.kr
2009-02-01
This paper presents an optimal design of magnetorheological (MR) damper based on finite element analysis. The MR damper is constrained in a specific volume and the optimization problem identifies geometric dimensions of the damper that minimizes an objective function. The objective function is proposed by considering the damping force, dynamic range and the inductive time constant of the damper. After describing the configuration of the MR damper, a quasi-static modelling of the damper is performed based on Bingham model of MR fluid. The initial geometric dimensions of the damper are then determined based on the assumption of constant magnetic flux density throughout the magnetic circuit of the damper. Subsequently, the optimal design variables that minimize the objective function are determined using a golden-section algorithm and a local quadratic fitting technique via commercial finite element method parametric design language. A comparative work on damping force and time constant between the initial and optimal design is undertaken.
Jung-Woon Yoo, John
2016-06-01
Since customer preferences change rapidly, there is a need for design processes with shorter product development cycles. Modularization plays a key role in achieving mass customization, which is crucial in today's competitive global market environments. Standardized interfaces among modularized parts have facilitated computational product design. To incorporate product size and weight constraints during computational design procedures, a mixed integer programming formulation is presented in this article. Product size and weight are two of the most important design parameters, as evidenced by recent smart-phone products. This article focuses on the integration of geometric, weight and interface constraints into the proposed mathematical formulation. The formulation generates the optimal selection of components for a target product, which satisfies geometric, weight and interface constraints. The formulation is verified through a case study and experiments are performed to demonstrate the performance of the formulation.
Textile surface design: a study of the geometrical knowledge in African American Freedom Quilts
Directory of Open Access Journals (Sweden)
Franciele Menegucci
2016-06-01
Full Text Available This paper discusses the presence of materials, technical and technological knowledge originating in the African culture in surface and textile construction work through the analysis of geometric patterns and their compositions derived, present in work with the quilt technique. This relationship is discussed from the perspective of geometry and the textile surface design showing how reflection on the ethnic and cultural diversity can contribute to the affirmation and appreciation of certain crops and their knowledge that, in many instances, are rootless and wrongly attributed the European and euro descendants cultures. This paper seeks to highlight the African origin of some geometric patterns lavishly designed in textile surfaces, often played, taught and disseminated without their proper provenances are granted. This reflection will demonstrate the contributions of African culture and African descent in the textile surface design, legitimizing the systematization of knowledge and African knowledge that can be understood through the study of its artifacts.
Design of macro-filter-lens with simultaneous chromatic and geometric aberration correction.
Prasad, Dilip K; Brown, Michael S
2014-01-01
A macro-filter-lens design that can correct for chromatic and geometric aberrations simultaneously while providing for a long focal length is presented. The filter is easy to fabricate since it involves two spherical surfaces and a planar surface. Chromatic aberration correction is achieved by making all the rays travel the same optical distance inside the filter element (negative meniscus). Geometric aberration is corrected for by the lens element (plano-convex), which makes the output rays parallel to the optic axis. This macro-filter-lens design does not need additional macro lenses and it provides an inexpensive and optically good (aberration compensated) solution for macro imaging of objects not placed close to the camera.
Three-dimensional geometric analysis of the talus for designing talar prosthetics.
Islam, Kamrul; Dobbe, Ashlee; Duke, Kajsa; El-Rich, Marwan; Dhillon, Sukhvinder; Adeeb, Samer; Jomha, Nadr M
2014-04-01
Proper understanding of the complex geometric shape of the talus bone is important for the design of generic talar body prosthetics and restoration of the proper ankle joint function after surgery. To date, all talus implants have been patient-specific with the limitation that complex computer modeling is required to produce a mirrored image from the unaffected opposite side followed by machining a patient-specific prosthesis. To develop an "off-the-shelf" non-custom talar prosthesis, it is important to perform a thorough investigation of the geometric shape of the talus bone. This article addresses the applicability of a scaling approach for investigating the geometric shape and similarity of talus bones. This study used computed tomography scan images of the ankle joints of 27 different subjects to perform the analysis. Results of the deviation analyses showed that the deviation in the articulating surfaces of the talus bones was not excessive in terms of talus size. These results suggest that a proposed range of five implant sizes is possible. Finally, it is concluded that the talus bones of the ankle joints are geometrically similar, and a proposed range of five implant sizes will fit a wide range of subjects. This information may help to develop generic talus implants that might be applicable to patients with a severe talus injury.
Directory of Open Access Journals (Sweden)
Kurt E. Clothier
2010-01-01
Full Text Available This paper presents a geometric approach to solve the unknown joint angles required for the autonomous positioning of a robotic arm. A plethora of complex mathematical processes is reduced using basic trigonometric in the modeling of the robotic arm. This modeling and analysis approach is tested using a five-degree-of-freedom arm with a gripper style end effector mounted to an iRobot Create mobile platform. The geometric method is easily modifiable for similar robotic system architectures and provides the capability of local autonomy to a system which is very difficult to manually control.
Bio-inspired design of geometrically interlocked 3D printed joints
Kumar, S.; Oliva, Noel; Kumar's Lab Team
The morphology of the adhesive-adherend interface significantly affects the mechanical behavior of adhesive joints. As seen in some biocomposites like human skull, or the nacre of some bivalve molluscs' shells, a geometrically interlocking architecture of interfaces creates toughening and strengthening mechanisms enhancing the mechanical properties of the joint. In an attempt to characterize this mechanical interlocking mechanism, this study is focused on computational and experimental investigation of a single-lap joint with a very simple geometrically interlocked interface design in which both adherends have a square waveform configuration of the joining surfaces. This square waveform configuration contains a positive and a negative rectangular teeth per cycle in such a way that the joint is symmetric about the mid-bondlength. Both physical tests performed on 3D printed prototypes of joints and computational results indicate that the joints with square waveform design have higher strength and damage tolerance than those of joints with flat interface. In order to identify an optimal design configuration of this interface, a systematic parametric study is conducted by varying the geometric and material properties of the non-flat interface. This work was supported by Lockheed Martin (Award No: 12NZZ1).
Design of an ultra-thin near-eye display with geometrical waveguide and freeform optics.
Cheng, Dewen; Wang, Yongtian; Xu, Chen; Song, Weitao; Jin, Guofan
2014-08-25
Small thickness and light weight are two important requirements for a see-through near-eye display which are achieved in this paper by using two advanced technologies: geometrical waveguide and freeform optics. A major problem associated with the geometrical waveguide is the stray light which can severely degrade the display quality. The causes and solutions to this problem are thoroughly studied. A mathematical model of the waveguide is established and a non-sequential ray tracing algorithm is developed, which enable us to carefully examine the stray light of the planar waveguide and explore a global searching method to find an optimum design with the least amount of stray light. A projection optics using freeform surfaces on a wedge shaped prism is also designed. The near-eye display integrating the projection optics and the waveguide has a field of view of 28°, an exit pupil diameter of 9.6mm and an exit pupil distance of 20mm. In our final design, the proportion of the stray light energy over the image output energy of the waveguide is reduced to 2%, the modulation transfer function values across the entire field of the eyepiece are above 0.5 at 30 line pairs/mm (lps/mm). A proof-of-concept prototype of the proposed geometrical waveguide near-eye display is developed and demonstrated.
Designing a Composable Geometric Toolkit for Versatility in Applications to Simulation Development
Reed, Gregory S.; Campbell, Thomas
2008-01-01
Conceived and implemented through the development of probabilistic risk assessment simulations for Project Constellation, the Geometric Toolkit allows users to create, analyze, and visualize relationships between geometric shapes in three-space using the MATLAB computing environment. The key output of the toolkit is an analysis of how emanations from one "source" geometry (e.g., a leak in a pipe) will affect another "target" geometry (e.g., another heat-sensitive component). It can import computer-aided design (CAD) depictions of a system to be analyzed, allowing the user to reliably and easily represent components within the design and determine the relationships between them, ultimately supporting more technical or physics-based simulations that use the toolkit. We opted to develop a variety of modular, interconnecting software tools to extend the scope of the toolkit, providing the capability to support a range of applications. This concept of simulation composability allows specially-developed tools to be reused by assembling them in various combinations. As a result, the concepts described here and implemented in this toolkit have a wide range of applications outside the domain of risk assessment. To that end, the Geometric Toolkit has been evaluated for use in other unrelated applications due to the advantages provided by its underlying design.
Geometrical design parameters for journal bearings with flexure pads and compliant liners
DEFF Research Database (Denmark)
Thomsen, Kim; Klit, Peder
2012-01-01
A hydrodynamic journal bearing utilizing flexure pads with a compliant liner is studied and its performance enhanced through a parametric study. The main geometrical dimensions are varied and the affect on pad performance is analyzed. This will put more knowledge into the design and function...... of flexure pads. uidelines are given to the design of the pads and are also covering the polymer liner. It is found that the use of flexure pads is an attractive alternative to pivoted pads. Pivot contact-related failure modes are eliminated and load capacity is not restricted by the force that can...
Design Optimization with Geometric Programming for Core Type Large Power Transformers
Directory of Open Access Journals (Sweden)
Orosz Tamás
2014-10-01
Full Text Available A good transformer design satisfies certain functions and requirements. We can satisfy these requirements by various designs. The aim of the manufacturers is to find the most economic choice within the limitations imposed by the constraint functions, which are the combination of the design parameters resulting in the lowest cost unit. One of the earliest application of the Geometric Programming [GP] is the optimization of power transformers. The GP formalism has two main advantages. First the formalism guarantees that the obtained solution is the global minimum. Second the new solution methods can solve even large-scale GPs extremely efficiently and reliably. The design optimization program seeks a minimum capitalized cost solution by optimally setting the transformer's geometrical and electrical parameters. The transformer's capitalized cost chosen for object function, because it takes into consideration the manufacturing and the operational costs. This paper considers the optimization for three winding, three phase, core-form power transformers. This paper presents the implemented transformer cost optimization model and the optimization results.
Kolhar, Poornima
The areas of drug delivery and tissue engineering have experienced extraordinary growth in recent years with the application of engineering principles and their potential to support and improve the field of medicine. The tremendous progress in nanotechnology and biotechnology has lead to this explosion of research and development in biomedical applications. Biomaterials can now be engineered at a nanoscale and their specific interactions with the biological tissues can be modulated. Various design parameters are being established and researched for design of drug-delivery carriers and scaffolds to be implanted into humans. Nanoparticles made from versatile biomaterial can deliver both small-molecule drugs and various classes of bio-macromolecules, such as proteins and oligonucleotides. Similarly in the field of tissue engineering, current approaches emphasize nanoscale control of cell behavior by mimicking the natural extracellular matrix (ECM) unlike, traditional scaffolds. Drug delivery and tissue engineering are closely connected fields and both of these applications require materials with exceptional physical, chemical, biological, and biomechanical properties to provide superior therapy. In the current study the surface functionalization and the geometric features of the biomaterials has been explored. In particular, a synthetic surface for culture of human embryonic stem cells has been developed, demonstrating the importance of surface functionalization in maintaining the pluripotency of hESCs. In the second study, the geometric features of the drug delivery carriers are investigated and the polymeric nanoneedles mediated cellular permeabilization and direct cytoplasmic delivery is reported. In the third study, the combined effect of surface functionalization and geometric modification of carriers for vascular targeting is enunciated. These studies illustrate how the biomaterials can be designed to achieve various cellular behaviors and control the
Directory of Open Access Journals (Sweden)
D. L. Robinette
2008-01-01
Full Text Available Dimensional analysis has been applied to automotive torque converters to understand the response of performance to changes in torque, size, working fluid, or operating temperature. The objective of this investigation was to develop a suitable dimensional analysis for estimating the effect of exact geometric scaling of a particular torque converter design on the onset of cavitation. Torque converter operating thresholds for cavitation were determined experimentally with a dynamometer test cell at the stall operating condition using nearfield acoustical measurements. Dimensionless quantities based upon either speed or torque at the onset of cavitation and flow properties (e.g., pressures and temperature dependent fluid properties were developed and compared. The proposed dimensionless stator torque quantity was found to be the most appropriate scaling law for extrapolating cavitation thresholds to multiple diameters. A power product model was fit on dimensionless stator torque data to create a model capable of predicting cavitation thresholds. Comparison of the model to test data taken over a range of operating points showed an error of 3.7%. This is the first paper of a two-part paper. In Part II, application of dimensional analysis will be expanded from torque converters with exact geometric similitude to those of more general design.
A geometric approach to regulator and tracker design for an aerospace plane
Van Buren, Mark A.; Mease, Kenneth D.
1991-01-01
The paper presents a nonlinear design approach drawing from singular perturbations, feedback linearization, and variable structure control, that leads to regulators with automatic gain scheduling which exhibit similar dynamic behavior over the entire flight envelope of the aerospace plane. Additionally, design approach provides for a systematic way to counter disturbance effects as well as modeling uncertainties. The unifying feature of the three nonlinear feedback control methodologies is that they all have a geometric interpretation. First, the translational dynamics are decomposed into reduced-order slow and fast dynamics by way of a formal singular perturbation analysis. After feedback linearization the fast dynamics are robustly stabilized via a variable structure control approach. The slow dynamics are stabilized using conventional proportional-integral compensation based on the nominal slow dynamics. A number of sample command and disturbance responses at opposite ends of the flight envelope are presented for a nonlinear aerospace plane model.
Annicchiarico, W
2001-01-01
Structural optimization is an engineering field which deal with the improvement of existing solutions or even more find new solutions that are better than the previous ones under some selected criterion. Shape optimization is a research area in this field and it is involved in developing new methodologies to find better structural design based on the shape as resistant element, as for example solutions with the less stress concentration zones and made with the minimum amount of material. The goal of this doctoral dissertation is to present and discuss a general structural shape optimization methodology able to optimize several structural systems or mechanical devices. The approach presented herein is based on global search optimization tools such as Genetic Algorithms and geometric design elements by means of beta-splines curves and surfaces representation. Finally the great versatility of the developed tool is presented and discussed with an application example.
Design and construction of an Offner spectrometer based on geometrical analysis of ring fields.
Kim, Seo Hyun; Kong, Hong Jin; Lee, Jong Ung; Lee, Jun Ho; Lee, Jai Hoon
2014-08-01
A method to obtain an aberration-corrected Offner spectrometer without ray obstruction is proposed. A new, more efficient spectrometer optics design is suggested in order to increase its spectral resolution. The derivation of a new ring equation to eliminate ray obstruction is based on geometrical analysis of the ring fields for various numerical apertures. The analytical design applying this equation was demonstrated using the optical design software Code V in order to manufacture a spectrometer working in wavelengths of 900-1700 nm. The simulation results show that the new concept offers an analytical initial design taking the least time of calculation. The simulated spectrometer exhibited a modulation transfer function over 80% at Nyquist frequency, root-mean-square spot diameters under 8.6 μm, and a spectral resolution of 3.2 nm. The final design and its realization of a high resolution Offner spectrometer was demonstrated based on the simulation result. The equation and analytical design procedure shown here can be applied to most Offner systems regardless of the wavelength range.
New geometric design consistency model based on operating speed profiles for road safety evaluation.
Camacho-Torregrosa, Francisco J; Pérez-Zuriaga, Ana M; Campoy-Ungría, J Manuel; García-García, Alfredo
2013-12-01
To assist in the on-going effort to reduce road fatalities as much as possible, this paper presents a new methodology to evaluate road safety in both the design and redesign stages of two-lane rural highways. This methodology is based on the analysis of road geometric design consistency, a value which will be a surrogate measure of the safety level of the two-lane rural road segment. The consistency model presented in this paper is based on the consideration of continuous operating speed profiles. The models used for their construction were obtained by using an innovative GPS-data collection method that is based on continuous operating speed profiles recorded from individual drivers. This new methodology allowed the researchers to observe the actual behavior of drivers and to develop more accurate operating speed models than was previously possible with spot-speed data collection, thereby enabling a more accurate approximation to the real phenomenon and thus a better consistency measurement. Operating speed profiles were built for 33 Spanish two-lane rural road segments, and several consistency measurements based on the global and local operating speed were checked. The final consistency model takes into account not only the global dispersion of the operating speed, but also some indexes that consider both local speed decelerations and speeds over posted speeds as well. For the development of the consistency model, the crash frequency for each study site was considered, which allowed estimating the number of crashes on a road segment by means of the calculation of its geometric design consistency. Consequently, the presented consistency evaluation method is a promising innovative tool that can be used as a surrogate measure to estimate the safety of a road segment.
Directory of Open Access Journals (Sweden)
Robert Bork
2014-06-01
Full Text Available This essay explores the proportioning strategies used by Gothic architects. It argues that Gothic design practice involved conventions of procedure, governing the dynamic unfolding of successive geometrical steps. Because this procedure proves difficult to capture in words, and because it produces forms with a qualitatively different kind of architectural order than the more familiar conventions of classical design, which govern the proportions of the final building rather than the logic of the steps used in creating it, Gothic design practice has been widely misunderstood since the Renaissance. Although some authors in the nineteenth and twentieth centuries attempted to sympathetically explain Gothic geometry, much of this work has been dismissed as unreliable, especially in the influential work of Konrad Hecht. This essay seeks to put the study of Gothic proportion onto a new and firmer foundation, by using computer-aided design software to analyze the geometry of carefully measured buildings and original design drawings. Examples under consideration include the parish church towers of Ulm and Freiburg, and the cross sections of the cathedrals of Reims, Prague, and Clermont-Ferrand, and of the Cistercian church at Altenberg. The sequence of images being analysed can be viewed as supplementary material at:http://dx.doi.org/10.5334/ah.bq.s1
DEFF Research Database (Denmark)
Endelt, Benny Ørtoft; Volk, Wolfram
2013-01-01
Feedback control of sheet metal forming operations has been an active research field the last two decades and highly advanced control algorithms have been proposed - controlling both the total blank-holder force and in some cases also the distribution of the blank-holder force. However, there is ......Feedback control of sheet metal forming operations has been an active research field the last two decades and highly advanced control algorithms have been proposed - controlling both the total blank-holder force and in some cases also the distribution of the blank-holder force. However......, the reaction speed may be insufficient compared to the production rate in an industrial application. We propose to design an iterative learning control (ILC) algorithm which can control and update the blank-holder force as well as the distribution of the blank-holder force based on limited geometric data from...
Penta, Francesco; Rossi, Cesare; Savino, Sergio
2016-06-01
This study aims to optimize the geometrical parameters of an under-actuated mechanical finger by conducting a theoretical analysis of these parameters. The finger is actuated by a flexion tendon and an extension tendon. The considered parameters are the tendon guide positions with respect to the hinges. By applying such an optimization, the correct kinematical and dynamical behavior of the closing cycle of the finger can be obtained. The results of this study are useful for avoiding the snapthrough and the single joint hyperflexion, which are the two breakdowns most frequently observed during experimentation on prototypes. Diagrams are established to identify the optimum values for the tendon guides position of a finger with specified dimensions. The findings of this study can serve as guide for future finger design.
Séguinot, Jacques; Chesi, Enrico Guido; Joram, C; Mathot, S; Weilhammer, P; Chamizo-Llatas, M; Correia, J G; Ribeiro da Silva, M; Garibaldi, F; De Leo, R; Nappi, E; Corsi, F; Dragone, A; Schoenahl, F; Zaidi, H
2006-01-01
We present the principle, a possible implementation and performance estimates of a novel geometrical concept for a high resolution positron emission tomograph. The concept, which can for example be implemented in a brain PET device, promisses to lead to an essentially parallax free 3D image reconstruction with excellent spatial resolution and constrast, uniform over the complete field of view. The key components are matrices of long axially oriented scintillator crystals which are read out at both extremities by segmented Hybrid Photon Detectors. We discuss the relevant design considerations for a 3D axial PET camera module, motivate parameter and material choices, and estimate its performance in terms of spatial and energy resolution. We support these estimates by Monte Carlo simulations and in some cases by first experimental results. From the performance of a camera module, we extrapolate to the reconstruction resolution of a 3D axial PET scanner in a semi-analytical way and compare it to an existing state...
DEFF Research Database (Denmark)
Christiansen, Rasmus E.; Lazarov, Boyan S.; Jensen, Jakob S.;
2015-01-01
and limitations are discussed. In addition, a known explicit penalization approach is considered for comparison. For near-uniform spatial variations it is shown that highly robust designs can be obtained using the double filter approach. It is finally demonstrated that taking non-uniform variations into account...
Designing of self-deploying origami structures using geometrically misaligned crease patterns.
Saito, Kazuya; Tsukahara, Akira; Okabe, Yoji
2016-01-01
Usually, origami-based morphing structures are designed on the premise of 'rigid folding', i.e. the facets and fold lines of origami can be replaced with rigid panels and ideal hinges, respectively. From a structural mechanics viewpoint, some rigid-foldable origami models are overconstrained and have negative degrees of freedom (d.f.). In these cases, the singularity in crease patterns guarantees their rigid foldability. This study presents a new method for designing self-deploying origami using the geometrically misaligned creases. In this method, some facets are replaced by 'holes' such that the systems become a 1-d.f. mechanism. These perforated origami models can be folded and unfolded similar to rigid-foldable (without misalignment) models because of their d.f. focusing on the removed facets, the holes will deform according to the motion of the frame of the remaining parts. In the proposed method, these holes are filled with elastic parts and store elastic energy for self-deployment. First, a new extended rigid-folding simulation technique is proposed to estimate the deformation of the holes. Next, the proposed method is applied on arbitrary-size quadrilateral mesh origami. Finally, by using the finite-element method, the authors conduct numerical simulations and confirm the deployment capabilities of the models.
Modeling cotton (Gossypium spp) leaves and canopy using computer aided geometric design (CAGD)
The goal of this research is to develop a geometrically accurate model of cotton crop canopies for exploring changes in canopy microenvironment and physiological function with leaf structure. We develop an accurate representation of the leaves, including changes in three-dimensional folding and orie...
Computational fluid dynamics simulation and geometric design of hydraulic turbine draft tube
Directory of Open Access Journals (Sweden)
JB Sosa
2015-10-01
Full Text Available Any hydraulic reaction turbine is installed with a draft tube that impacts widely the entire turbine performance, on which its functions are as follows: drive the flux in appropriate manner after it releases its energy to the runner; recover the suction head by a suction effect; and improve the dynamic energy in the runner outlet. All these functions are strongly linked to the geometric definition of the draft tube. This article proposes a geometric parametrization and analysis of a Francis turbine draft tube. Based on the parametric definition, geometric changes in the draft tube are proposed and the turbine performance is modeled by computational fluid dynamics; the boundary conditions are set by measurements performed in a hydroelectric power plant. This modeling allows us to see the influence of the draft tube shape on the entire turbine performance. The numerical analysis is based on the steady-state solution of the turbine component flows for different guide vanes opening and multiple modified draft tubes. The computational fluid dynamics predictions are validated using hydroelectric plant measurements. The prediction of the turbine performance is successful and it is linked to the draft tube geometric features; therefore, it is possible to obtain a draft tube parameter value that results in a desired turbine performance.
Directory of Open Access Journals (Sweden)
N. Jafferi
2009-09-01
Full Text Available This paper focuses on the geometrical design of active noise control (ANC in free- field propagation medium. The development and performance assessment uses genetic optimisation techniques to arrange system components so as to satisfy several performance requirements, such as physical extent of cancellation, controller design restriction and system stability. The ANC system design can be effectively addressed if it is considered as multi – objective optimisation problems. The multi-objective genetic algorithms (MOGAs are well suited to the design of an ANC system and the approach used for it is based on a multi - objective method, with which the physical extent of cancellation and relative stability assessment are dealt with simultaneously.
Ma, F. M.; Li, W.; Liu, A. H.; Yu, Z. L.; Ruan, M.; Feng, W.; Chen, H. X.; Chen, Y.
2017-09-01
Superhydrophobic surfaces with high water contact angles and low contact angle hysteresis or sliding angles have received tremendous attention for both academic research and industrial applications in recent years. In general, such surfaces possess rough microtextures, particularly, show micro/nano hierarchical structures like lotus leaves. Now it has been recognized that to achieve the artificial superhydrophobic surfaces, the simple and effective strategy is to mimic such hierarchical structures. However, fabrications of such structures for these artificial surfaces involve generally expensive and complex processes. On the other hand, the relationships between structural parameters of various surface topography and wetting properties have not been fully understood yet. In order to provide guidance for the simple fabrication and particularly, to promote practical applications of superhydrophobic surfaces, the geometrical designs of optimal microtextures or patterns have been proposed. In this work, the recent developments on geometrical effect, optimal design and controlled fabrication of various superhydrophobic structures, such as unitary, anisotropic, dual-scale hierarchical, and some other surface geometries, are reviewed. The effects of surface topography and structural parameters on wetting states (composite and noncomposite) and wetting properties (contact angle, contact angle hysteresis and sliding angle) as well as adhesive forces are discussed in detail. Finally, the research prospects in this field are briefly addressed.
Shen, Yuyi; Yanagimachi, Kurt
2011-01-01
The inclined multiplate (lamella) gravity settler has proven to be an effective cell retention device in industrial perfusion cell culture applications. Investigations on the effects of geometric design and operational variables of the cell settler are crucial to understanding how to best improve the settler performance. Maximizing the harvest/perfusion flow rate while minimizing viable cell loss out of the harvest is the primary challenge for optimization of the settler design. This study demonstrated that computational fluid dynamics (CFD) can be utilized to accurately model and evaluate the settler separation performance for near-monodisperse suspensions and therefore aid in the design optimization of the settler under these baseline conditions. With the preferred geometric features that were identified from CFD modeling results, we proposed design guidelines for the scale-up of these multiplate settler systems. With these guidelines and performance verification using the CFD model, a new large-scale settler was designed and fabricated for a perfusion cell culture process using a minimally aggregating production cell line. Perfusion cell culture runs with this particular cell line were performed with this settler, and the CFD model was able to predict the initial ramp-up performance, proving it to be a valuable scale-up design tool for this production process.
Le-Duc, Thang; Ho-Huu, Vinh; Nguyen-Thoi, Trung; Nguyen-Quoc, Hung
2016-12-01
In recent years, various types of magnetorheological brakes (MRBs) have been proposed and optimized by different optimization algorithms that are integrated in commercial software such as ANSYS and Comsol Multiphysics. However, many of these optimization algorithms often possess some noteworthy shortcomings such as the trap of solutions at local extremes, or the limited number of design variables or the difficulty of dealing with discrete design variables. Thus, to overcome these limitations and develop an efficient computation tool for optimal design of the MRBs, an optimization procedure that combines differential evolution (DE), a gradient-free global optimization method with finite element analysis (FEA) is proposed in this paper. The proposed approach is then applied to the optimal design of MRBs with different configurations including conventional MRBs and MRBs with coils placed on the side housings. Moreover, to approach a real-life design, some necessary design variables of MRBs are considered as discrete variables in the optimization process. The obtained optimal design results are compared with those of available optimal designs in the literature. The results reveal that the proposed method outperforms some traditional approaches.
Geometric Computing Based on Computerized Descriptive Geometric
Institute of Scientific and Technical Information of China (English)
YU Hai-yan; HE Yuan-Jun
2011-01-01
Computer-aided Design （CAD）, video games and other computer graphic related technology evolves substantial processing to geometric elements. A novel geometric computing method is proposed with the integration of descriptive geometry, math and computer algorithm. Firstly, geometric elements in general position are transformed to a special position in new coordinate system. Then a 3D problem is projected to new coordinate planes. Finally, according to 2D/3D correspondence principle in descriptive geometry, the solution is constructed computerized drawing process with ruler and compasses. In order to make this method a regular operation, a two-level pattern is established. Basic Layer is a set algebraic packaged function including about ten Primary Geometric Functions （PGF） and one projection transformation. In Application Layer, a proper coordinate is established and a sequence of PGFs is sought for to get the final results. Examples illustrate the advantages of our method on dimension reduction, regulatory and visual computing and robustness.
Geometric Design Rule Check of VLSI Layouts in Mesh Connected Processors
Directory of Open Access Journals (Sweden)
S. K. Nandy
1994-01-01
Full Text Available Design Rule Checking is a compute-intensive VLSI CAD tool. In this paper we propose a parallel algorithm to perform Design Rule Check (DRC of Layout geometries in a VLSI layout. The algorithm assumes the parallel architecture to be a two-dimensional mesh of processors. The algorithm is based on a linear quadtree representation of the layout. Through a complexity analysis it is shown that it is possible to achieve a linear speedup in DRC with respect to the number of processors.
Energy Technology Data Exchange (ETDEWEB)
Rimza, Sandeep, E-mail: sandeepr@ipr.res.in [Divertor and First Wall Technology Development Division, Institute for Plasma Research (IPR), Bhat – 382428, Gandhinagar, Gujarat (India); Satpathy, Kamalakanta, E-mail: satpathy@ipr.res.in [Divertor and First Wall Technology Development Division, Institute for Plasma Research (IPR), Bhat – 382428, Gandhinagar, Gujarat (India); Khirwadkar, Samir, E-mail: sameer@ipr.res.in [Divertor and First Wall Technology Development Division, Institute for Plasma Research (IPR), Bhat – 382428, Gandhinagar, Gujarat (India); Velusamy, Karupanna, E-mail: kvelu@igcar.gov.in [Mechanics and Hydraulics Division, Indira Gandhi Centre for Atomic Research (IGCAR), Kalpakkam 603102 (India)
2015-11-15
Highlights: • Effect of design variables in enhancing heat removal potential with pumping power assessed. • The optimization objective is to minimize the thimble temperature. • Investigation of optimum design parameters for various Reynolds number. • Practicability of the optimum designs is verified through structural analysis. • Benchmark validation of divertor finger mock-up against in-house experiment and good agreement is achieved. - Abstract: Cooling of fusion reactor divertor by helium is widely accepted due to its chemical and neutronic inertness and superior safety aspect. However, its poor thermo physical characteristics need high pressure to remove large heat flux encountered in fusion power plant (DEMO). In the perspective of DEMO, it is desirable to explore efficient cooling technology for divertor that can handle high heat flux. Toward this, a novel sectorial extended surface (SES) was proposed by the authors Rimza et al. (2014) [2]. The present work focuses on design optimization of divertor finger mock-up with SES to enhance the thermal hydraulic performance. The maximum thimble temperature is considered as the vital design constraint. Various non-dimensional design variables, viz., relative pitch, thickness, jet diameter, the ratio of height of SES to jet diameter and circumferential position of the SES are considered for the present optimization study. The effects of design variables on thermal performance of the divertor are evaluated in the Reynolds number (Re) range of 7.5 × 10{sup 4}–1.2 × 10{sup 5}. The analysis reveals that, the heat transfer performance of divertor finger mock-up with SES is improved for two optimum designs having relative pitch and thickness of 0.30 and 0.56, respectively. Also, it is observed that finger mock-up heat sink with SES performs better, when the ratio of SES height to jet diameter, reduces to 0.75 at the cost of marginally higher pumping power. The effects of jet diameter and circumferential
Geometric and engineering drawing
Morling, K
2010-01-01
The new edition of this successful text describes all the geometric instructions and engineering drawing information that are likely to be needed by anyone preparing or interpreting drawings or designs with plenty of exercises to practice these principles.
Experimental designs developed to address mixtures are ideally suited for many areas of experimental biology including pheromone blend studies because they address the confounding of proportionality and concentration intrinsic to factorial and one-factor-at-a-time designs. Geometric multivariate des...
Geometric design and simulation of tooth profile using elliptical segments as its line of action
Institute of Scientific and Technical Information of China (English)
王建; 罗善明; 苏德瑜; 常雪峰
2015-01-01
A mathematical model of gear tooth profiles using the ellipse curve, whose curvature is convenient to control by changing the mathematical parameters as its line of action, was built based on the meshing theory. The equation of undercutting condition was derived from the model. A special epicycloidal tooth profile was also presented. An example gear drive with variation of the ellipse parameters was taken to illustrate the proposed method. The contact ratio of the gear drive designed by the proposed method was analyzed. A comparison of the property of the gear drive designed with the involute gear drive was also carried out. The results confirm that the proposed gear drive has higher contact ratio in comparison with the involute gear drive.
Geometric optics theory and design of astronomical optical systems using Mathematica
Romano, Antonio
2016-01-01
This text, now in its second edition, presents the mathematical background needed to design many optical combinations that are used in astronomical telescopes and cameras. It uses a novel approach to third-order aberration theory based on Fermat’s principle and the use of particular optical paths (called stigmatic paths) instead of rays, allowing for easier derivation of third-order formulae. Each optical combination analyzed is accompanied by a downloadable Mathematica® notebook that automates its third-order design, eliminating the need for lengthy calculations. The essential aspects of an optical system with an axis of rotational symmetry are introduced first, along with a development of Gaussian optics from Fermat’s principal. A simpler approach to third-order monochromatic aberrations based on both Fermat’s principle and stigmatic paths is then described, followed by a new chapter on fifth-order aberrations and their classification. Several specific optical devices are discussed and analyzed, incl...
Optimization of geometrical design of nested conical Wolter-I X-ray telescope
Institute of Scientific and Technical Information of China (English)
Baozhong Mu; Hongying Liu; Huijun Jin; Xiajun Yang; Fangfang Wang; Wenbin Li; Hong Chen; Zhanshan Wang
2012-01-01
Optical design of nested conical Wolter I X-ray telescope covering energy band from 1 to 30 keV is investigated systematically.Recurrence relation of the nested structure is deduced,and the impact of the initial parameters on the performance is analyzed.Due to the need for hard X-ray astronomical observations in China,the initial structure is presented,for which six groups of W/B4C aperiodic multilayer coatings between the innermost and the outermost shell of the mirror are designed.The effective area,resolution,and field of view are calculated in the simulation.The results show that the effective area can achieve 71 cm2 and the field of view can achieve 13' at 30 keV.The resolution is estimated to be ～10" in half-power diameter.
Geometrical Bioelectrodynamics
Ivancevic, Vladimir G
2008-01-01
This paper proposes rigorous geometrical treatment of bioelectrodynamics, underpinning two fast-growing biomedical research fields: bioelectromagnetism, which deals with the ability of life to produce its own electromagnetism, and bioelectromagnetics, which deals with the effect on life from external electromagnetism. Keywords: Bioelectrodynamics, exterior geometrical machinery, Dirac-Feynman quantum electrodynamics, functional electrical stimulation
Directory of Open Access Journals (Sweden)
Trunev A. P.
2014-05-01
Full Text Available In this article we have investigated the solutions of Maxwell's equations, Navier-Stokes equations and the Schrödinger associated with the solutions of Einstein's equations for empty space. It is shown that in some cases the geometric instability leading to turbulence on the mechanism of alternating viscosity, which offered by N.N. Yanenko. The mechanism of generation of matter from dark energy due to the geometric turbulence in the Big Bang has been discussed
Miller, Sabbie A.; Horvath, Arpad; Monteiro, Paulo J. M.; Ostertag, Claudia P.
2015-11-01
With increased awareness of the emissions of greenhouse gases (GHGs) and the significant contribution from the cement industry, research efforts are being advanced to reduce the impacts associated with concrete production and consumption. A variety of methods have been proposed, one of the most common being the replacement of cement as a binder in concrete with supplementary cementitious materials, such as fly ash (FA), which can have lower environmental effects. The use of FA can change the kinetics of the hydration reactions and, consequently, modify the evolution of the concrete strength over time. Yet the influence of designing structural elements to obtain the required strength at later ages has not been examined in terms of their influence on global warming potential (GWP) of concrete. This research investigates the influence of design age, in addition to mix proportions and geometric aspects, on the GWP associated with making beams, columns, and a concrete building frame. Findings suggest that while the GWP for beams is not highly dependent on concrete mixture strength, the GWP for columns is dependent on strength, thus the influence of required strength at later ages influences GWP of making columns more so than beams. For the concrete frame analyzed, a potential 45% reduction in GWP, depending on mix proportions and design age, was found. Using the findings from this research, the GWP associated with production of concrete in California could be reduced by approximately 1.8 million metric tons of CO2-eq emissions, equivalent to approximately 2% of all industrial GHG emissions in California.
Muniz Oliva, Waldyr
2002-01-01
Geometric Mechanics here means mechanics on a pseudo-riemannian manifold and the main goal is the study of some mechanical models and concepts, with emphasis on the intrinsic and geometric aspects arising in classical problems. The first seven chapters are written in the spirit of Newtonian Mechanics while the last two ones as well as two of the four appendices describe the foundations and some aspects of Special and General Relativity. All the material has a coordinate free presentation but, for the sake of motivation, many examples and exercises are included in order to exhibit the desirable flavor of physical applications.
Chisolm, Eric
2012-01-01
This is an introduction to geometric algebra, an alternative to traditional vector algebra that expands on it in two ways: 1. In addition to scalars and vectors, it defines new objects representing subspaces of any dimension. 2. It defines a product that's strongly motivated by geometry and can be taken between any two objects. For example, the product of two vectors taken in a certain way represents their common plane. This system was invented by William Clifford and is more commonly known as Clifford algebra. It's actually older than the vector algebra that we use today (due to Gibbs) and includes it as a subset. Over the years, various parts of Clifford algebra have been reinvented independently by many people who found they needed it, often not realizing that all those parts belonged in one system. This suggests that Clifford had the right idea, and that geometric algebra, not the reduced version we use today, deserves to be the standard "vector algebra." My goal in these notes is to describe geometric al...
Wang, J.; Ge, Y.; Heuvelink, G.B.M.; Zhou, C.; Brus, D.J.
2012-01-01
The acquirement of ground control points (GCPs) is a basic and important step in the geometric correction of remotely sensed imagery. In particular, the spatial distribution of GCPs may affect the accuracy and quality of image correction. In this paper, both a simulation experiment and actual-image
Burgess, Claudia R.
2014-01-01
Designed for a broad audience, including educators, camp directors, afterschool coordinators, and preservice teachers, this investigation aims to help individuals experience mathematics in unconventional and exciting ways by engaging them in the physical activity of building geometric shapes using ropes. Through this engagement, the author…
Pascu, A. T.; Besnea, D.; Constantin, V.; Spanu, A.; Ciobanu, R.
2016-08-01
The paper presents the usual methods and means for geometrical evaluation and measurement for the anterior pole of the eyeball applied in studies conducted on real patients. The results were centralized, evaluated and presented in a summary in the paper. The purpose of the studies is to determine the range of dimensional values of the anterior pole of the human eyeball for the parameterization of the devices and checking tools when manufacturing the contact lenses.
Directory of Open Access Journals (Sweden)
Marco A. Velasco
2016-10-01
Full Text Available Scaffolds are essential in bone tissue engineering, as they provide support to cells and growth factors necessary to regenerate tissue. In addition, they meet the mechanical function of the bone while it regenerates. Currently, the multiple methods for designing and manufacturing scaffolds are based on regular structures from a unit cell that repeats in a given domain. However, these methods do not resemble the actual structure of the trabecular bone which may work against osseous tissue regeneration. To explore the design of porous structures with similar mechanical properties to native bone, a geometric generation scheme from a reaction-diffusion model and its manufacturing via a material jetting system is proposed. This article presents the methodology used, the geometric characteristics and the modulus of elasticity of the scaffolds designed and manufactured. The method proposed shows its potential to generate structures that allow to control the basic scaffold properties for bone tissue engineering such as the width of the channels and porosity. The mechanical properties of our scaffolds are similar to trabecular tissue present in vertebrae and tibia bones. Tests on the manufactured scaffolds show that it is necessary to consider the orientation of the object relative to the printing system because the channel geometry, mechanical properties and roughness are heavily influenced by the position of the surface analyzed with respect to the printing axis. A possible line for future work may be the establishment of a set of guidelines to consider the effects of manufacturing processes in designing stages.
Mario, Hirz; Gfrerrer, Anton; Lang, Johann
2013-01-01
The automotive industry faces constant pressure to reduce development costs and time while still increasing vehicle quality. To meet this challenge, engineers and researchers in both science and industry are developing effective strategies and flexible tools by enhancing and further integrating powerful, computer-aided design technology. This book provides a valuable overview of the development tools and methods of today and tomorrow. It is targeted not only towards professional project and design engineers, but also to students and to anyone who is interested in state-of-the-art computer-aided development. The book begins with an overview of automotive development processes and the principles of virtual product development. Focusing on computer-aided design, a comprehensive outline of the fundamentals of geometry representation provides a deeper insight into the mathematical techniques used to describe and model geometrical elements. The book then explores the link between the demands of integrated design pr...
Wheeler, Bruce C; Brewer, Gregory J
2010-03-01
Technology has advanced to where it is possible to design and grow-with predefined geometry and surprisingly good fidelity-living networks of neurons in culture dishes. Here we overview the elements of design, emphasizing the lithographic techniques that alter the cell culture surface which in turn influences the attachment and growth of the neural networks. Advanced capability in this area makes it possible to design networks of desired complexity. Other issues addressed include the influence of glial cells and media on activity and the potential for extending the designs into three dimensions. Investigators are advancing the art and science of analyzing and controlling through stimulation the function of the neural networks, including the ability to take advantage of their geometric form in order to influence functional properties.
Design of Wideband MIMO Car-to-Car Channel Models Based on the Geometrical Street Scattering Model
Directory of Open Access Journals (Sweden)
Nurilla Avazov
2012-01-01
Full Text Available We propose a wideband multiple-input multiple-output (MIMO car-to-car (C2C channel model based on the geometrical street scattering model. Starting from the geometrical model, a MIMO reference channel model is derived under the assumption of single-bounce scattering in line-of-sight (LOS and non-LOS (NLOS propagation environments. The proposed channel model assumes an infinite number of scatterers, which are uniformly distributed in two rectangular areas located on both sides of the street. Analytical solutions are presented for the space-time-frequency cross-correlation function (STF-CCF, the two-dimensional (2D space CCF, the time-frequency CCF (TF-CCF, the temporal autocorrelation function (ACF, and the frequency correlation function (FCF. An efficient sum-of-cisoids (SOCs channel simulator is derived from the reference model. It is shown that the temporal ACF and the FCF of the SOC channel simulator fit very well to the corresponding correlation functions of the reference model. To validate the proposed channel model, the mean Doppler shift and the Doppler spread of the reference model have been matched to real-world measurement data. The comparison results demonstrate an excellent agreement between theory and measurements, which confirms the validity of the derived reference model. The proposed geometry-based channel simulator allows us to study the effect of nearby street scatterers on the performance of C2C communication systems.
Development of a Geometric Spatial Visualization Tool
Ganesh, Bibi; Wilhelm, Jennifer; Sherrod, Sonya
2009-01-01
This paper documents the development of the Geometric Spatial Assessment. We detail the development of this instrument which was designed to identify middle school students' strategies and advancement in understanding of four geometric concept domains (geometric spatial visualization, spatial projection, cardinal directions, and periodic patterns)…
Bestvina, Mladen; Vogtmann, Karen
2014-01-01
Geometric group theory refers to the study of discrete groups using tools from topology, geometry, dynamics and analysis. The field is evolving very rapidly and the present volume provides an introduction to and overview of various topics which have played critical roles in this evolution. The book contains lecture notes from courses given at the Park City Math Institute on Geometric Group Theory. The institute consists of a set of intensive short courses offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The courses begin at an introductory level suitable for graduate students and lead up to currently active topics of research. The articles in this volume include introductions to CAT(0) cube complexes and groups, to modern small cancellation theory, to isometry groups of general CAT(0) spaces, and a discussion of nilpotent genus in the context of mapping class groups and CAT(0) gro...
Geometric Computing for Freeform Architecture
Wallner, J.
2011-06-03
Geometric computing has recently found a new field of applications, namely the various geometric problems which lie at the heart of rationalization and construction-aware design processes of freeform architecture. We report on our work in this area, dealing with meshes with planar faces and meshes which allow multilayer constructions (which is related to discrete surfaces and their curvatures), triangles meshes with circle-packing properties (which is related to conformal uniformization), and with the paneling problem. We emphasize the combination of numerical optimization and geometric knowledge.
Lim, Ju Won; Lee, Young Tack; Pandey, Rina; Yoo, Tae-Hee; Sang, Byoung-In; Ju, Byeong-Kwon; Hwang, Do Kyung; Choi, Won Kook
2014-11-03
Silver (Ag) grid transparent electrode is one of the most promising transparent conducting electrodes (TCEs) to replace conventional indium tin oxide (ITO). We systematically investigate an effect of geometric lattice modifications on optical and electrical properties of Ag grid electrode. The reference Ag grid with 5 μm width and 100 μm pitch (duty of 0.05) prepared by conventional photo-lithography and lift-off processes shows the sheet resistance of 13.27 Ω/sq, transmittance of 81.1%, and resultant figure of merit (FOM) of 129.05. Three different modified Ag grid electrodes with stripe added-mesh (SAM), triangle-added mesh (TAM), and diagonal-added mesh (DAM) are suggested to improve optical and electrical properties. Although all three of SAM, TAM, and DAM Ag grid electrodes exhibit the lower transmittance values of about 72 - 77%, they showed much decreased sheet resistance of 6 - 8 Ω/sq. As a result, all of the lattice-modified Ag grid electrodes display significant improvement of FOM and the highest value of 171.14 is obtained from DAM Ag grid, which is comparable to that of conventional ITO electrode (175.46). Also, the feasibility of DAM Ag gird electrode for use in organic solar cell is confirmed by finite difference time domain (FDTD) simulations. Unlike a conventional ITO electrode, DAM Ag grid electrode can induce light scattering and trapping due to the diffuse transmission that compensates for the loss in optical transparency, resulting in comparable light absorption in the photo active layer of poly(3-hexylthiophene) (P3HT): [6,6]-phenyl-C61-butyric acid methyl ester (PC₆₀BM). P3HT:PC₆₀BM based OSCs with the DAM Ag grid electrode were fabricated, which also showed the potential for ITO-free transparent electrode.
展开/折叠式伸展臂几何设计%GEOMETRIC DESIGN OF DEPLOYABLE/RETRACTABLE MAST
Institute of Scientific and Technical Information of China (English)
杨玉龙
2006-01-01
介绍了展开/折叠式结构的设计过程,分3阶段:设计阶段、模型阶段和优化阶段,每一阶段均有相应的控制指标.由此设计出一种三棱柱伸展臂,该伸展臂由三棱柱模块叠加而成,通过电机驱动滑块进行展开/折叠运动.对伸展臂的运动机理进行了分析,最后经过优化阶段,最终确定了杆件的直径和节点形式.实验室模型表明,该伸展臂具有驱动简单,杆件类型少,制造方便的优点.%To simplify the complicated design process of deployable/retractable structures, a new design process is developed. The process is divided into three phases: the concept design phase, the model phase and the optimization phase. In each phase, different parameter targets have to be fulfilled. According to three phases, a deployable/retractable mast composed of four right triangle prism modules in the longitudinal direction is designed. It can be deployed and folded simultaneously by the linear movements of sleeve-joints. The deployable and retractable movement of the mast is analyzed and key joint forms are designed. Then bar diameters and joint forms are modified based on mast structural mechanics characteristics in the optimization phase. Finally a 1:1 scaled model mast is built to verify the design and the optimization. Analytical results show that the model mast has the advantages of simple locking mechanism, fewer types of joints and bars, so it can be easily manufactured.
Pheromone blends composed of one or more components are mixtures. Mixtures present a unique problem for experiment design when response (e.g., insect attraction to a blend) is a function of proportionality of the blend's components. In mixtures, the ingredients must total to a constant value. Prop...
Institute of Scientific and Technical Information of China (English)
马利民; 王金星; 蒋向前; 李柱; 徐振高
2004-01-01
Geometrical Product Specification and verification (GPS) is an ISO standard system coveting standards of size, dimension,geometrical tolerance and surface texture of geometrical product. ISO/TC213 on the GPS has been working towards coordination of the previous standards in tolerance and related metrology in order to publish the next generation of the GPS language. This paper introduces the geometrical product specification model for design, manufacturing and verification based on the improved GPS and its new concepts,i.e., surface models, geometrical features and operations. An application example for the geometrical product specification model is then given.
Geometric constraint solving with geometric transformation
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
This paper proposes two algorithms for solving geometric constraint systems. The first algorithm is for constrained systems without loops and has linear complexity. The second algorithm can solve constraint systems with loops. The latter algorithm is of quadratic complexity and is complete for constraint problems about simple polygons. The key to it is to combine the idea of graph based methods for geometric constraint solving and geometric transformations coming from rule-based methods.
Dewi Syarifah, Ratna; Su'ud, Zaki; Basar, Khairul; Irwanto, Dwi
2017-07-01
Nuclear power has progressive improvement in the operating performance of exiting reactors and ensuring economic competitiveness of nuclear electricity around the world. The GFR use gas coolant and fast neutron spectrum. This research use helium coolant which has low neutron moderation, chemical inert and single phase. Comparative study on various geometrical core design for modular GFR with UN-PuN fuel long life without refuelling has been done. The calculation use SRAC2006 code both PIJ calculation and CITATION calculation. The data libraries use JENDL 4.0. The variation of fuel fraction is 40% until 65%. In this research, we varied the geometry of core reactor to find the optimum geometry design. The variation of the geometry design is balance cylinder; it means that the diameter active core (D) same with height active core (H). Second, pancake cylinder (D>H) and third, tall cylinder (D
Design of the image detection system for general parts geometric parameters%通用零件几何参数图像检测系统设计
Institute of Scientific and Technical Information of China (English)
张建; 温坚; 林菁
2009-01-01
Gave image detection system for general parts geometric parameters,the optical lens,industrial digital camera and micro-computer constitute the basic detection system;designed to test preparation,test system to adjust,image acquisition,etreatment,boundary identification,and system parameters to strike a job detect calibration process;described the detection aspect of the role and application of the key questions;designed detect application software;established a detection system,comparison test for typical parts.Gave the detection system is the best and practical.%为实现通用零件几何参数图像检测,采用光学镜头、工业数字摄像机和微型计算机构成基本检测系统,包括测试准备、测试系统调整、图像获取、预处理、边界确定、参数求取和系统标定等检测工作环节.阐述各检测环节的作用和应用中的关键问题、检测应用软件设计.通过所构建的检测系统,对典型零件进行对比测试表明,给出的通用零件几何参数图像检测系统是实用的.
Directory of Open Access Journals (Sweden)
Cheewapattananuwong Weeradej
2016-01-01
Full Text Available Traffic problems in Bangkok have an influence on road users during peak hours. Especially, the traffic bottleneck on curves under the saturation flow situation must be remedied in order to increase the roadway capacity and speed. However, the appropriate speed for heavy vehicles is taken into consideration during off peak after the increasing lanes. This leads to the Rollover of heavy truck and rear-end collisions which are the main causes of vehicles accidents on curves. In addition, road accidents on curves account for the majority of all accidents in Thailand. According to the road accidents data collected in Thailand, 44 road deaths per 100,000 people, the country ranks second in the world for road accidents. When Thailand’s Code of Geometrical Design is compared with AASHTO (The American Association of State Highway and Transportation Officials, the super elevation length of Thailand’s Code is more than AASHTO. As a result, drivers are not made aware of the appropriate speed and the stooping sight distances (SSD on curves. Therefore, the Design of Traffic Signage under the Perception and Reaction Times (PRT for Thai Drivers will be taken into account.
On Geometric Infinite Divisibility
Sandhya, E.; Pillai, R. N.
2014-01-01
The notion of geometric version of an infinitely divisible law is introduced. Concepts parallel to attraction and partial attraction are developed and studied in the setup of geometric summing of random variables.
Bidimensionality and Geometric Graphs
Fomin, Fedor V; Saurabh, Saket
2011-01-01
In this paper we use several of the key ideas from Bidimensionality to give a new generic approach to design EPTASs and subexponential time parameterized algorithms for problems on classes of graphs which are not minor closed, but instead exhibit a geometric structure. In particular we present EPTASs and subexponential time parameterized algorithms for Feedback Vertex Set, Vertex Cover, Connected Vertex Cover, Diamond Hitting Set, on map graphs and unit disk graphs, and for Cycle Packing and Minimum-Vertex Feedback Edge Set on unit disk graphs. Our results are based on the recent decomposition theorems proved by Fomin et al [SODA 2011], and our algorithms work directly on the input graph. Thus it is not necessary to compute the geometric representations of the input graph. To the best of our knowledge, these results are previously unknown, with the exception of the EPTAS and a subexponential time parameterized algorithm on unit disk graphs for Vertex Cover, which were obtained by Marx [ESA 2005] and Alber and...
Geometric design of part feeders
Berretty, R.-P.M.
2001-01-01
This thesis presents solutions for problems derived from industrial assembly and robotic manipulation. The basic tasks in a factory are manufacturing the parts, and combining them into the desired product. In automating these tasks, we want to use robot manipulators that require little or no h
Geometric Control of Patterned Linear Systems
Hamilton, Sarah C
2012-01-01
This monograph is aiming at researchers of systems control, especially those interested in multiagent systems, distributed and decentralized control, and structured systems. The book assumes no prior background in geometric control theory; however, a first year graduate course in linear control systems is desirable. Since not all control researchers today are exposed to geometric control theory, the book also adopts a tutorial style by way of examples that illustrate the geometric and abstract algebra concepts used in linear geometric control. In addition, the matrix calculations required for the studied control synthesis problems of linear multivariable control are illustrated via a set of running design examples. As such, some of the design examples are of higher dimension than one may typically see in a text; this is so that all the geometric features of the design problem are illuminated.
Geometrization of Trace Formulas
Frenkel, Edward
2010-01-01
Following our joint work arXiv:1003.4578 with Robert Langlands, we make the first steps toward developing geometric methods for analyzing trace formulas in the case of the function field of a curve defined over a finite field. We also suggest a conjectural framework of geometric trace formulas for curves defined over the complex field, which exploits the categorical version of the geometric Langlands correspondence.
Localized Geometric Query Problems
Augustine, John; Maheshwari, Anil; Nandy, Subhas C; Roy, Sasanka; Sarvattomananda, Swami
2011-01-01
A new class of geometric query problems are studied in this paper. We are required to preprocess a set of geometric objects $P$ in the plane, so that for any arbitrary query point $q$, the largest circle that contains $q$ but does not contain any member of $P$, can be reported efficiently. The geometric sets that we consider are point sets and boundaries of simple polygons.
Exploring New Geometric Worlds
Nirode, Wayne
2015-01-01
When students work with a non-Euclidean distance formula, geometric objects such as circles and segment bisectors can look very different from their Euclidean counterparts. Students and even teachers can experience the thrill of creative discovery when investigating these differences among geometric worlds. In this article, the author describes a…
Hierarchical Geometric Constraint Model for Parametric Feature Based Modeling
Institute of Scientific and Technical Information of China (English)
高曙明; 彭群生
1997-01-01
A new geometric constraint model is described,which is hierarchical and suitable for parametric feature based modeling.In this model,different levels of geometric information are repesented to support various stages of a design process.An efficient approach to parametric feature based modeling is also presented,adopting the high level geometric constraint model.The low level geometric model such as B-reps can be derived automatically from the hig level geometric constraint model,enabling designers to perform their task of detailed design.
Geometric Transformations in Engineering Geometry
Directory of Open Access Journals (Sweden)
I. F. Borovikov
2015-01-01
Full Text Available Recently, for business purposes, in view of current trends and world experience in training engineers, research and faculty staff there has been a need to transform traditional courses of descriptive geometry into the course of engineering geometry in which the geometrical transformations have to become its main section. On the basis of critical analysis the paper gives suggestions to improve a presentation technique of this section both in the classroom and in academic literature, extend an application scope of geometrical transformations to solve the position and metric tasks and simulation of surfaces, as well as to design complex engineering configurations, which meet a number of pre-specified conditions.The article offers to make a number of considerable amendments to the terms and definitions used in the existing courses of descriptive geometry. It draws some conclusions and makes the appropriate proposals on feasibility of coordination in teaching the movement transformation in the courses of analytical and descriptive geometry. This will provide interdisciplinary team teaching and allow students to be convinced that a combination of analytical and graphic ways to solve geometric tasks is useful and reasonable.The traditional sections of learning courses need to be added with a theory of projective and bi-rational transformations. In terms of application simplicity and convenience it is enough to consider the central transformations when solving the applied tasks. These transformations contain a beam of sub-invariant (low-invariant straight lines on which the invariant curve induces non-involution and involution projectivities. The expediency of nonlinear transformations application is shown in the article by a specific example of geometric modeling of the interfacing surface "spar-blade".Implementation of these suggestions will contribute to a real transformation of a traditional course of descriptive geometry to the engineering geometry
Geometric and unipotent crystals
Berenstein, Arkady; Kazhdan, David
1999-01-01
In this paper we introduce geometric crystals and unipotent crystals which are algebro-geometric analogues of Kashiwara's crystal bases. Given a reductive group G, let I be the set of vertices of the Dynkin diagram of G and T be the maximal torus of G. The structure of a geometric G-crystal on an algebraic variety X consists of a rational morphism \\gamma:X-->T and a compatible family e_i:G_m\\times X-->X, i\\in I of rational actions of the multiplicative group G_m satisfying certain braid-like ...
Differential geometric structures
Poor, Walter A
2007-01-01
This introductory text defines geometric structure by specifying parallel transport in an appropriate fiber bundle and focusing on simplest cases of linear parallel transport in a vector bundle. 1981 edition.
Bledsoe, Gloria J
1987-01-01
The game of "Guess What" is described as a stimulating vehicle for students to consider the unifying or distinguishing features of geometric figures. Teaching suggestions as well as the gameboard are provided. (MNS)
Geometric Rationalization for Freeform Architecture
Jiang, Caigui
2016-06-20
The emergence of freeform architecture provides interesting geometric challenges with regards to the design and manufacturing of large-scale structures. To design these architectural structures, we have to consider two types of constraints. First, aesthetic constraints are important because the buildings have to be visually impressive. Sec- ond, functional constraints are important for the performance of a building and its e cient construction. This thesis contributes to the area of architectural geometry. Specifically, we are interested in the geometric rationalization of freeform architec- ture with the goal of combining aesthetic and functional constraints and construction requirements. Aesthetic requirements typically come from designers and architects. To obtain visually pleasing structures, they favor smoothness of the building shape, but also smoothness of the visible patterns on the surface. Functional requirements typically come from the engineers involved in the construction process. For exam- ple, covering freeform structures using planar panels is much cheaper than using non-planar ones. Further, constructed buildings have to be stable and should not collapse. In this thesis, we explore the geometric rationalization of freeform archi- tecture using four specific example problems inspired by real life applications. We achieve our results by developing optimization algorithms and a theoretical study of the underlying geometrical structure of the problems. The four example problems are the following: (1) The design of shading and lighting systems which are torsion-free structures with planar beams based on quad meshes. They satisfy the functionality requirements of preventing light from going inside a building as shad- ing systems or reflecting light into a building as lighting systems. (2) The Design of freeform honeycomb structures that are constructed based on hex-dominant meshes with a planar beam mounted along each edge. The beams intersect without
Saturation and geometrical scaling
Praszalowicz, Michal
2016-01-01
We discuss emergence of geometrical scaling as a consequence of the nonlinear evolution equations of QCD, which generate a new dynamical scale, known as the saturation momentum: Qs. In the kinematical region where no other energy scales exist, particle spectra exhibit geometrical scaling (GS), i.e. they depend on the ratio pT=Qs, and the energy dependence enters solely through the energy dependence of the saturation momentum. We confront the hypothesis of GS in different systems with experimental data.
Geometric Modelling by Recursively Cutting Vertices
Institute of Scientific and Technical Information of China (English)
吕伟; 梁友栋; 等
1989-01-01
In this paper,a new method for curve and surface modelling is introduced which generates curves and surfaces by recursively cutting and grinding polygons and polyhedra.It is a generalization of the existing corner-cutting methods.A lot of properties,such as geometric continuity,representation,shape-preserving,and the algorithm are studied which show that such curves and surfaces are suitable for geometric designs in CAD,computer graphics and their application fields.
Geometric systematic prostate biopsy.
Chang, Doyoung; Chong, Xue; Kim, Chunwoo; Jun, Changhan; Petrisor, Doru; Han, Misop; Stoianovici, Dan
2017-04-01
The common sextant prostate biopsy schema lacks a three-dimensional (3D) geometric definition. The study objective was to determine the influence of the geometric distribution of the cores on the detection probability of prostate cancer (PCa). The detection probability of significant (>0.5 cm(3)) and insignificant (geometric distribution of the cores was optimized to maximize the probability of detecting significant cancer for various prostate sizes (20-100cm(3)), number of biopsy cores (6-40 cores) and biopsy core lengths (14-40 mm) for transrectal and transperineal biopsies. The detection of significant cancer can be improved by geometric optimization. With the current sextant biopsy, up to 20% of tumors may be missed at biopsy in a 20 cm(3) prostate due to the schema. Higher number and longer biopsy cores are required to sample with an equal detection probability in larger prostates. Higher number of cores increases both significant and insignificant tumor detection probability, but predominantly increases the detection of insignificant tumors. The study demonstrates mathematically that the geometric biopsy schema plays an important clinical role, and that increasing the number of biopsy cores is not necessarily helpful.
Field guide to geometrical optics
Greivenkamp, John E
2004-01-01
This Field Guide derives from the treatment of geometrical optics that has evolved from both the undergraduate and graduate programs at the Optical Sciences Center at the University of Arizona. The development is both rigorous and complete, and it features a consistent notation and sign convention. This volume covers Gaussian imagery, paraxial optics, first-order optical system design, system examples, illumination, chromatic effects, and an introduction to aberrations. The appendices provide supplemental material on radiometry and photometry, the human eye, and several other topics.
Janssen, S.T.M.C.
1976-01-01
The paper and a shortened version were presented to the OECD symposium on methods for determining geometric road design standards 1976, Helsingoer, denmark, 10-12 may 1976. The paper advocated the recategorisation of existing networks of roads on the basis of a functional physical planning (effici
Janssen, S.T.M.C.
1976-01-01
The paper and a shortened version were presented to the OECD symposium on methods for determining geometric road design standards 1976, Helsingoer, denmark, 10-12 may 1976. The paper advocated the recategorisation of existing networks of roads on the basis of a functional physical planning (effici
Geometric Photonic Spin Hall Effect with Metapolarization
Ling, Xiaohui; Yi, Xunong; Luo, Hailu; Wen, Shuangchun
2014-01-01
We develop a geometric photonic spin Hall effect (PSHE) which manifests as spin-dependent shift in momentum space. It originates from an effective space-variant Pancharatnam-Berry (PB) phase created by artificially engineering the polarization distribution of the incident light. Unlikely the previously reported PSHE involving the light-matter interaction, the resulting spin-dependent splitting in the geometric PSHE is purely geometrically depend upon the polarization distribution of light which can be tailored by assembling its circular polarization basis with suitably magnitude and phase. This metapolarization idea enables us to manipulate the geometric PSHE by suitably tailoring the polarization geometry of light. Our scheme provides great flexibility in the design of various polarization geometry and polarization-dependent application, and can be extrapolated to other physical system, such as electron beam or atom beam, with the similar spin-orbit coupling underlying.
5th Dagstuhl Seminar on Geometric Modelling
Brunnett, Guido; Farin, Gerald; Goldman, Ron
2004-01-01
In 19 articles presented by leading experts in the field of geometric modelling the state-of-the-art on representing, modeling, and analyzing curves, surfaces as well as other 3-dimensional geometry is given. The range of applications include CAD/CAM-systems, computer graphics, scientific visualization, virtual reality, simulation and medical imaging. The content of this book is based on selected lectures given at a workshop held at IBFI Schloss Dagstuhl, Germany. Topics treated are: – curve and surface modelling – non-manifold modelling in CAD – multiresolution analysis of complex geometric models – surface reconstruction – variational design – computational geometry of curves and surfaces – 3D meshing – geometric modelling for scientific visualization – geometric models for biomedical applications
Geometrical charged-particle optics
Rose, Harald H
2009-01-01
This reference monograph covers all theoretical aspects of modern geometrical charged-particle optics. It is intended as a guide for researchers, who are involved in the design of electron optical instruments and beam-guiding systems for charged particles, and as a tutorial for graduate students seeking a comprehensive treatment. Procedures for calculating the properties of systems with arbitrarily curved axes are outlined in detail and methods are discussed for designing and optimizing special components such as aberration correctors, spectrometers, energy filters, monochromators, ion traps, electron mirrors and cathode lenses. Also addressed is the design of novel electron optical components enabling sub-Angstroem spatial resolution and sub-0.1eV energy resolution. Relativistic motion and spin precession of the electron is treated in a concise way by employing a covariant five-dimensional procedure.
PREFACE: Geometrically frustrated magnetism Geometrically frustrated magnetism
Gardner, Jason S.
2011-04-01
Frustrated magnetism is an exciting and diverse field in condensed matter physics that has grown tremendously over the past 20 years. This special issue aims to capture some of that excitement in the field of geometrically frustrated magnets and is inspired by the 2010 Highly Frustrated Magnetism (HFM 2010) meeting in Baltimore, MD, USA. Geometric frustration is a broad phenomenon that results from an intrinsic incompatibility between some fundamental interactions and the underlying lattice geometry based on triangles and tetrahedra. Most studies have centred around the kagomé and pyrochlore based magnets but recent work has looked at other structures including the delafossite, langasites, hyper-kagomé, garnets and Laves phase materials to name a few. Personally, I hope this issue serves as a great reference to scientist both new and old to this field, and that we all continue to have fun in this very frustrated playground. Finally, I want to thank the HFM 2010 organizers and all the sponsors whose contributions were an essential part of the success of the meeting in Baltimore. Geometrically frustrated magnetism contents Spangolite: an s = 1/2 maple leaf lattice antiferromagnet? T Fennell, J O Piatek, R A Stephenson, G J Nilsen and H M Rønnow Two-dimensional magnetism and spin-size effect in the S = 1 triangular antiferromagnet NiGa2S4 Yusuke Nambu and Satoru Nakatsuji Short range ordering in the modified honeycomb lattice compound SrHo2O4 S Ghosh, H D Zhou, L Balicas, S Hill, J S Gardner, Y Qi and C R Wiebe Heavy fermion compounds on the geometrically frustrated Shastry-Sutherland lattice M S Kim and M C Aronson A neutron polarization analysis study of moment correlations in (Dy0.4Y0.6)T2 (T = Mn, Al) J R Stewart, J M Hillier, P Manuel and R Cywinski Elemental analysis and magnetism of hydronium jarosites—model kagome antiferromagnets and topological spin glasses A S Wills and W G Bisson The Herbertsmithite Hamiltonian: μSR measurements on single crystals
Mahavira's Geometrical Problems
DEFF Research Database (Denmark)
Høyrup, Jens
2004-01-01
Analysis of the geometrical chapters Mahavira's 9th-century Ganita-sara-sangraha reveals inspiration from several chronological levels of Near-Eastern and Mediterranean mathematics: (1)that known from Old Babylonian tablets, c. 1800-1600 BCE; (2)a Late Babylonian but pre-Seleucid Stratum, probably...
Pragmatic geometric model evaluation
Pamer, Robert
2015-04-01
Quantification of subsurface model reliability is mathematically and technically demanding as there are many different sources of uncertainty and some of the factors can be assessed merely in a subjective way. For many practical applications in industry or risk assessment (e. g. geothermal drilling) a quantitative estimation of possible geometric variations in depth unit is preferred over relative numbers because of cost calculations for different scenarios. The talk gives an overview of several factors that affect the geometry of structural subsurface models that are based upon typical geological survey organization (GSO) data like geological maps, borehole data and conceptually driven construction of subsurface elements (e. g. fault network). Within the context of the trans-European project "GeoMol" uncertainty analysis has to be very pragmatic also because of different data rights, data policies and modelling software between the project partners. In a case study a two-step evaluation methodology for geometric subsurface model uncertainty is being developed. In a first step several models of the same volume of interest have been calculated by omitting successively more and more input data types (seismic constraints, fault network, outcrop data). The positions of the various horizon surfaces are then compared. The procedure is equivalent to comparing data of various levels of detail and therefore structural complexity. This gives a measure of the structural significance of each data set in space and as a consequence areas of geometric complexity are identified. These areas are usually very data sensitive hence geometric variability in between individual data points in these areas is higher than in areas of low structural complexity. Instead of calculating a multitude of different models by varying some input data or parameters as it is done by Monte-Carlo-simulations, the aim of the second step of the evaluation procedure (which is part of the ongoing work) is to
Geometrical charged-particle optics
Rose, Harald
2012-01-01
This second edition is an extended version of the first edition of Geometrical Charged-Particle Optics. The updated reference monograph is intended as a guide for researchers and graduate students who are seeking a comprehensive treatment of the design of instruments and beam-guiding systems of charged particles and their propagation in electromagnetic fields. Wave aspects are included in this edition for explaining electron holography, the Aharanov-Bohm effect and the resolution of electron microscopes limited by diffraction. Several methods for calculating the electromagnetic field are presented and procedures are outlined for calculating the properties of systems with arbitrarily curved axis. Detailed methods are presented for designing and optimizing special components such as aberration correctors, spectrometers, energy filters monochromators, ion traps, electron mirrors and cathode lenses. In particular, the optics of rotationally symmetric lenses, quadrupoles, and systems composed of these elements are...
Frè, Pietro Giuseppe
2013-01-01
‘Gravity, a Geometrical Course’ presents general relativity (GR) in a systematic and exhaustive way, covering three aspects that are homogenized into a single texture: i) the mathematical, geometrical foundations, exposed in a self consistent contemporary formalism, ii) the main physical, astrophysical and cosmological applications, updated to the issues of contemporary research and observations, with glimpses on supergravity and superstring theory, iii) the historical development of scientific ideas underlying both the birth of general relativity and its subsequent evolution. The book is divided in two volumes. Volume One is dedicated to the development of the theory and basic physical applications. It guides the reader from the foundation of special relativity to Einstein field equations, illustrating some basic applications in astrophysics. A detailed account of the historical and conceptual development of the theory is combined with the presentation of its mathematical foundations. Differe...
Testing algebraic geometric codes
Institute of Scientific and Technical Information of China (English)
CHEN Hao
2009-01-01
Property testing was initially studied from various motivations in 1990's.A code C (∩)GF(r)n is locally testable if there is a randomized algorithm which can distinguish with high possibility the codewords from a vector essentially far from the code by only accessing a very small (typically constant) number of the vector's coordinates.The problem of testing codes was firstly studied by Blum,Luby and Rubinfeld and closely related to probabilistically checkable proofs (PCPs).How to characterize locally testable codes is a complex and challenge problem.The local tests have been studied for Reed-Solomon (RS),Reed-Muller (RM),cyclic,dual of BCH and the trace subcode of algebraicgeometric codes.In this paper we give testers for algebraic geometric codes with linear parameters (as functions of dimensions).We also give a moderate condition under which the family of algebraic geometric codes cannot be locally testable.
Testing algebraic geometric codes
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Property testing was initially studied from various motivations in 1990’s. A code C GF (r)n is locally testable if there is a randomized algorithm which can distinguish with high possibility the codewords from a vector essentially far from the code by only accessing a very small (typically constant) number of the vector’s coordinates. The problem of testing codes was firstly studied by Blum, Luby and Rubinfeld and closely related to probabilistically checkable proofs (PCPs). How to characterize locally testable codes is a complex and challenge problem. The local tests have been studied for Reed-Solomon (RS), Reed-Muller (RM), cyclic, dual of BCH and the trace subcode of algebraicgeometric codes. In this paper we give testers for algebraic geometric codes with linear parameters (as functions of dimensions). We also give a moderate condition under which the family of algebraic geometric codes cannot be locally testable.
Dynamics in geometrical confinement
Kremer, Friedrich
2014-01-01
This book describes the dynamics of low molecular weight and polymeric molecules when they are constrained under conditions of geometrical confinement. It covers geometrical confinement in different dimensionalities: (i) in nanometer thin layers or self supporting films (1-dimensional confinement) (ii) in pores or tubes with nanometric diameters (2-dimensional confinement) (iii) as micelles embedded in matrices (3-dimensional) or as nanodroplets.The dynamics under such conditions have been a much discussed and central topic in the focus of intense worldwide research activities within the last two decades. The present book discusses how the resulting molecular mobility is influenced by the subtle counterbalance between surface effects (typically slowing down molecular dynamics through attractive guest/host interactions) and confinement effects (typically increasing the mobility). It also explains how these influences can be modified and tuned, e.g. through appropriate surface coatings, film thicknesses or pore...
Progressive geometric algorithms
Directory of Open Access Journals (Sweden)
Sander P.A. Alewijnse
2015-01-01
Full Text Available Progressive algorithms are algorithms that, on the way to computing a complete solution to the problem at hand, output intermediate solutions that approximate the complete solution increasingly well. We present a framework for analyzing such algorithms, and develop efficient progressive algorithms for two geometric problems: computing the convex hull of a planar point set, and finding popular places in a set of trajectories.
Geometric Time Delay Interferometry
Vallisneri, Michele
2005-01-01
The space-based gravitational-wave observatory LISA, a NASA-ESA mission to be launched after 2012, will achieve its optimal sensitivity using Time Delay Interferometry (TDI), a LISA-specific technique needed to cancel the otherwise overwhelming laser noise in the inter-spacecraft phase measurements. The TDI observables of the Michelson and Sagnac types have been interpreted physically as the virtual measurements of a synthesized interferometer. In this paper, I present Geometric TDI, a new an...
Geometric unsharpness calculations
Energy Technology Data Exchange (ETDEWEB)
Anderson, D.J. [International Training and Education Group (INTEG), Oakville, Ontario (Canada)
2008-07-15
The majority of radiographers' geometric unsharpness calculations are normally performed with a mathematical formula. However, a majority of codes and standards refer to the use of a nomograph for this calculation. Upon first review, the use of a nomograph appears more complicated but with a few minutes of study and practice it can be just as effective. A review of this article should provide enlightenment. (author)
Geometric Stochastic Resonance
Ghosh, Pulak Kumar; Savel'ev, Sergey E; Nori, Franco
2015-01-01
A Brownian particle moving across a porous membrane subject to an oscillating force exhibits stochastic resonance with properties which strongly depend on the geometry of the confining cavities on the two sides of the membrane. Such a manifestation of stochastic resonance requires neither energetic nor entropic barriers, and can thus be regarded as a purely geometric effect. The magnitude of this effect is sensitive to the geometry of both the cavities and the pores, thus leading to distinctive optimal synchronization conditions.
Geometrically Consistent Mesh Modification
Bonito, A.
2010-01-01
A new paradigm of adaptivity is to execute refinement, coarsening, and smoothing of meshes on manifolds with incomplete information about their geometry and yet preserve position and curvature accuracy. We refer to this collectively as geometrically consistent (GC) mesh modification. We discuss the concept of discrete GC, show the failure of naive approaches, and propose and analyze a simple algorithm that is GC and accuracy preserving. © 2010 Society for Industrial and Applied Mathematics.
Geometric properties of eigenfunctions
Energy Technology Data Exchange (ETDEWEB)
Jakobson, D; Nadirashvili, N [McGill University, Montreal, Quebec (Canada); Toth, John [University of Chicago, Chicago, Illinois (United States)
2001-12-31
We give an overview of some new and old results on geometric properties of eigenfunctions of Laplacians on Riemannian manifolds. We discuss properties of nodal sets and critical points, the number of nodal domains, and asymptotic properties of eigenfunctions in the high-energy limit (such as weak * limits, the rate of growth of L{sup p} norms, and relationships between positive and negative parts of eigenfunctions)
Geometric theory of information
2014-01-01
This book brings together geometric tools and their applications for Information analysis. It collects current and many uses of in the interdisciplinary fields of Information Geometry Manifolds in Advanced Signal, Image & Video Processing, Complex Data Modeling and Analysis, Information Ranking and Retrieval, Coding, Cognitive Systems, Optimal Control, Statistics on Manifolds, Machine Learning, Speech/sound recognition, and natural language treatment which are also substantially relevant for the industry.
Perspective: Geometrically frustrated assemblies
Grason, Gregory M.
2016-09-01
This perspective will overview an emerging paradigm for self-organized soft materials, geometrically frustrated assemblies, where interactions between self-assembling elements (e.g., particles, macromolecules, proteins) favor local packing motifs that are incompatible with uniform global order in the assembly. This classification applies to a broad range of material assemblies including self-twisting protein filament bundles, amyloid fibers, chiral smectics and membranes, particle-coated droplets, curved protein shells, and phase-separated lipid vesicles. In assemblies, geometric frustration leads to a host of anomalous structural and thermodynamic properties, including heterogeneous and internally stressed equilibrium structures, self-limiting assembly, and topological defects in the equilibrium assembly structures. The purpose of this perspective is to (1) highlight the unifying principles and consequences of geometric frustration in soft matter assemblies; (2) classify the known distinct modes of frustration and review corresponding experimental examples; and (3) describe outstanding questions not yet addressed about the unique properties and behaviors of this broad class of systems.
Lloyd, Seth
2012-01-01
This letter analyzes the limits that quantum mechanics imposes on the accuracy to which spacetime geometry can be measured. By applying the fundamental physical bounds to measurement accuracy to ensembles of clocks and signals moving in curved spacetime -- e.g., the global positioning system -- I derive a covariant version of the quantum geometric limit: the total number of ticks of clocks and clicks of detectors that can be contained in a four volume of spacetime of radius r and temporal extent t is less than or equal to rt/\\pi x_P t_P, where x_P, t_P are the Planck length and time. The quantum geometric limit bounds the number of events or `ops' that can take place in a four-volume of spacetime: each event is associated with a Planck-scale area. Conversely, I show that if each quantum event is associated with such an area, then Einstein's equations must hold. The quantum geometric limit is consistent with and complementary to the holographic bound which limits the number of bits that can exist within a spat...
Geometric diffusion of quantum trajectories.
Yang, Fan; Liu, Ren-Bao
2015-07-16
A quantum object can acquire a geometric phase (such as Berry phases and Aharonov-Bohm phases) when evolving along a path in a parameter space with non-trivial gauge structures. Inherent to quantum evolutions of wavepackets, quantum diffusion occurs along quantum trajectories. Here we show that quantum diffusion can also be geometric as characterized by the imaginary part of a geometric phase. The geometric quantum diffusion results from interference between different instantaneous eigenstate pathways which have different geometric phases during the adiabatic evolution. As a specific example, we study the quantum trajectories of optically excited electron-hole pairs in time-reversal symmetric insulators, driven by an elliptically polarized terahertz field. The imaginary geometric phase manifests itself as elliptical polarization in the terahertz sideband generation. The geometric quantum diffusion adds a new dimension to geometric phases and may have applications in many fields of physics, e.g., transport in topological insulators and novel electro-optical effects.
Algebraic geometric codes with applications
Institute of Scientific and Technical Information of China (English)
CHEN Hao
2007-01-01
The theory of linear error-correcting codes from algebraic geomet-ric curves (algebraic geometric (AG) codes or geometric Goppa codes) has been well-developed since the work of Goppa and Tsfasman, Vladut, and Zink in 1981-1982. In this paper we introduce to readers some recent progress in algebraic geometric codes and their applications in quantum error-correcting codes, secure multi-party computation and the construction of good binary codes.
Robust Geometric Control of a Distillation Column
DEFF Research Database (Denmark)
Kymmel, Mogens; Andersen, Henrik Weisberg
1987-01-01
A frequency domain method, which makes it possible to adjust multivariable controllers with respect to both nominal performance and robustness, is presented. The basic idea in the approach is that the designer assigns objectives such as steady-state tracking, maximum resonance peaks, bandwidth, m...... is used to examine and improve geometric control of a binary distillation column....
Geometric Number Systems and Spinors
Sobczyk, Garret
2015-01-01
The real number system is geometrically extended to include three new anticommuting square roots of plus one, each such root representing the direction of a unit vector along the orthonormal coordinate axes of Euclidean 3-space. The resulting geometric (Clifford) algebra provides a geometric basis for the famous Pauli matrices which, in turn, proves the consistency of the rules of geometric algebra. The flexibility of the concept of geometric numbers opens the door to new understanding of the nature of space-time, and of Pauli and Dirac spinors as points on the Riemann sphere, including Lorentz boosts.
Ambrosetti, Antonio; Malchiodi, Andrea
2009-01-01
This volume contains lecture notes on some topics in geometric analysis, a growing mathematical subject which uses analytical techniques, mostly of partial differential equations, to treat problems in differential geometry and mathematical physics. The presentation of the material should be rather accessible to non-experts in the field, since the presentation is didactic in nature. The reader will be provided with a survey containing some of the most exciting topics in the field, with a series of techniques used to treat such problems.
Bose, Prosenjit; Morin, Pat; Smid, Michiel
2012-01-01
Highly connected and yet sparse graphs (such as expanders or graphs of high treewidth) are fundamental, widely applicable and extensively studied combinatorial objects. We initiate the study of such highly connected graphs that are, in addition, geometric spanners. We define a property of spanners called robustness. Informally, when one removes a few vertices from a robust spanner, this harms only a small number of other vertices. We show that robust spanners must have a superlinear number of edges, even in one dimension. On the positive side, we give constructions, for any dimension, of robust spanners with a near-linear number of edges.
Corrochano, Eduardo Bayro
2010-01-01
This book presents contributions from a global selection of experts in the field. This useful text offers new insights and solutions for the development of theorems, algorithms and advanced methods for real-time applications across a range of disciplines. Written in an accessible style, the discussion of all applications is enhanced by the inclusion of numerous examples, figures and experimental analysis. Features: provides a thorough discussion of several tasks for image processing, pattern recognition, computer vision, robotics and computer graphics using the geometric algebra framework; int
Shapere, Alfred D
1989-01-01
During the last few years, considerable interest has been focused on the phase that waves accumulate when the equations governing the waves vary slowly. The recent flurry of activity was set off by a paper by Michael Berry, where it was found that the adiabatic evolution of energy eigenfunctions in quantum mechanics contains a phase of geometric origin (now known as 'Berry's phase') in addition to the usual dynamical phase derived from Schrödinger's equation. This observation, though basically elementary, seems to be quite profound. Phases with similar mathematical origins have been identified
Phenomenological modeling of Geometric Metasurfaces
Ye, Weimin; Xiang, Yuanjiang; Fan, Dianyuan; Zhang, Shuang
2015-01-01
Metasurfaces, with their superior capability in manipulating the optical wavefront at the subwavelength scale and low manufacturing complexity, have shown great potential for planar photonics and novel optical devices. However, vector field simulation of metasurfaces is so far limited to periodic-structured metasurfaces containing a small number of meta-atoms in the unit cell by using full-wave numerical methods. Here, we propose a general phenomenological method to analytically model metasurfaces made up of arbitrarily distributed meta-atoms based on the assumption that the meta-atoms possess localized resonances with Lorentz-Drude forms, whose exact form can be retrieved from the full wave simulation of a single element. Applied to phase modulated geometric metasurfaces, our analytical results show good agreement with full-wave numerical simulations. The proposed theory provides an efficient method to model and design optical devices based on metasurfaces.
Manwani, Naresh
2010-01-01
In this paper we present a new algorithm for learning oblique decision trees. Most of the current decision tree algorithms rely on impurity measures to assess the goodness of hyperplanes at each node while learning a decision tree in a top-down fashion. These impurity measures do not properly capture the geometric structures in the data. Motivated by this, our algorithm uses a strategy to assess the hyperplanes in such a way that the geometric structure in the data is taken into account. At each node of the decision tree, we find the clustering hyperplanes for both the classes and use their angle bisectors as the split rule at that node. We show through empirical studies that this idea leads to small decision trees and better performance. We also present some analysis to show that the angle bisectors of clustering hyperplanes that we use as the split rules at each node, are solutions of an interesting optimization problem and hence argue that this is a principled method of learning a decision tree.
Geometrically nonlinear creeping mathematic models of shells with variable thickness
Directory of Open Access Journals (Sweden)
V.M. Zhgoutov
2012-08-01
Full Text Available Calculations of strength, stability and vibration of shell structures play an important role in the design of modern devices machines and structures. However, the behavior of thin-walled structures of variable thickness during which geometric nonlinearity, lateral shifts, viscoelasticity (creep of the material, the variability of the profile take place and thermal deformation starts up is not studied enough.In this paper the mathematical deformation models of variable thickness shells (smoothly variable and ribbed shells, experiencing either mechanical load or permanent temperature field and taking into account the geometrical nonlinearity, creeping and transverse shear, were developed. The refined geometrical proportions for geometrically nonlinear and steadiness problems are given.
Developing a Network of and for Geometric Reasoning
Mamolo, Ami; Ruttenberg-Rozen, Robyn; Whiteley, Walter
2015-01-01
In this article, we develop a theoretical model for restructuring mathematical tasks, usually considered advanced, with a network of spatial visual representations designed to support geometric reasoning for learners of disparate ages, stages, strengths, and preparation. Through our geometric reworking of the well-known "open box…
Forward error correction based on algebraic-geometric theory
A Alzubi, Jafar; M Chen, Thomas
2014-01-01
This book covers the design, construction, and implementation of algebraic-geometric codes from Hermitian curves. Matlab simulations of algebraic-geometric codes and Reed-Solomon codes compare their bit error rate using different modulation schemes over additive white Gaussian noise channel model. Simulation results of Algebraic-geometric codes bit error rate performance using quadrature amplitude modulation (16QAM and 64QAM) are presented for the first time and shown to outperform Reed-Solomon codes at various code rates and channel models. The book proposes algebraic-geometric block turbo codes. It also presents simulation results that show an improved bit error rate performance at the cost of high system complexity due to using algebraic-geometric codes and Chase-Pyndiah’s algorithm simultaneously. The book proposes algebraic-geometric irregular block turbo codes (AG-IBTC) to reduce system complexity. Simulation results for AG-IBTCs are presented for the first time.
Geometric Complexity Theory: Introduction
Sohoni, Ketan D Mulmuley Milind
2007-01-01
These are lectures notes for the introductory graduate courses on geometric complexity theory (GCT) in the computer science department, the university of Chicago. Part I consists of the lecture notes for the course given by the first author in the spring quarter, 2007. It gives introduction to the basic structure of GCT. Part II consists of the lecture notes for the course given by the second author in the spring quarter, 2003. It gives introduction to invariant theory with a view towards GCT. No background in algebraic geometry or representation theory is assumed. These lecture notes in conjunction with the article \\cite{GCTflip1}, which describes in detail the basic plan of GCT based on the principle called the flip, should provide a high level picture of GCT assuming familiarity with only basic notions of algebra, such as groups, rings, fields etc.
The Geometric Transition Revisited
Gwyn, Rhiannon
2007-01-01
Our intention in this article is to review known facts and to summarise recent advances in the understanding of geometric transitions and the underlying open/closed duality in string theory. We aim to present a pedagogical discussion of the gauge theory underlying the Klebanov--Strassler model and review the Gopakumar--Vafa conjecture based on topological string theory. These models are also compared in the T-dual brane constructions. We then summarise a series of papers verifying both models on the supergravity level. An appendix provides extensive background material about conifold geometries. We pay special attention to their complex structures and re-evaluate the supersymmetry conditions on the background flux in constructions with fractional D3-branes on the singular (Klebanov--Strassler) and resolved (Pando Zayas--Tseytlin) conifolds. We agree with earlier results that only the singular solution allows a supersymmetric flux, but point out the importance of using the correct complex structure to reach th...
Kahle, Matthew
2009-01-01
We study the expected topological properties of Cech and Vietoris-Rips complexes built on randomly sampled points in R^d. These are, in some cases, analogues of known results for connectivity and component counts for random geometric graphs. However, an important difference in this setting is that homology is not monotone in the underlying parameter. In the sparse range, we compute the expectation and variance of the Betti numbers, and establish Central Limit Theorems and concentration of measure. In the dense range, we introduce Morse theoretic arguments to bound the expectation of the Betti numbers, which is the main technical contribution of this article. These results provide a detailed probabilistic picture to compare with the topological statistics of point cloud data.
Geometrical Destabilization of Inflation
Renaux-Petel, Sébastien; Turzyński, Krzysztof
2016-09-01
We show the existence of a general mechanism by which heavy scalar fields can be destabilized during inflation, relying on the fact that the curvature of the field space manifold can dominate the stabilizing force from the potential and destabilize inflationary trajectories. We describe a simple and rather universal setup in which higher-order operators suppressed by a large energy scale trigger this instability. This phenomenon can prematurely end inflation, thereby leading to important observational consequences and sometimes excluding models that would otherwise perfectly fit the data. More generally, it modifies the interpretation of cosmological constraints in terms of fundamental physics. We also explain how the geometrical destabilization can lead to powerful selection criteria on the field space curvature of inflationary models.
Institute of Scientific and Technical Information of China (English)
梁松; 李海波; 张义民
2014-01-01
以渐开线齿廓几何模型为基础，结合开源程序和类库，在Windows平台上开发了齿轮辅助几何设计程序。简要介绍了国内外学者针对齿轮几何模型的建立和基于g nuplo t的数据可视化模块设计的研究概况。针对计算模块的程序实现，推导并给出全齿廓的曲线参数方程。用C编写计算模块，在g nuplo t的基础上编写数据可视化模块。两模块以纯文本方式传递数据，通过管道传递指令。以Windows API的方式建立窗口程序过程，并为程序设计了图形用户界面。用CxImage库替代picture控件，解决png格式设计结果图片的显示问题。这里将计算机程序设计技术融入传统机械设计理论，并借鉴众多开源软件和函数库，开发的辅助机械设计软件提升了机械设计效率和水平。%Based on the geometric model of involute tooth profile ,the geometric design software for gears was developed on the platform of Windows .The software was written in C program-ming language ,including open source programs and libraries such as gnuplot and CxImage .Many geometric modeling approaches for gears were proposed .Gnuplot had been regarded as the mod-ule of graphical output in many application software ,in which the proposed approaches were used .For the implementation of the calculation module ,the curve parameter equations for tooth profile were proposed .The module of computing kernel was written in C language .Gnuplot was the kernel of data visualization module . Data was transmitted by plain text and commands through pipes .The process of windows was established on the the method of Windows Applica-tion Programming Interface (API) .Graphical User Interface (GUI) had been used in the soft-ware .The display problem of png format pictures was solved by using CxImage library in stand of picture control .Modern computer program design technique is involved in traditional mechani-cal design theory .Drawing on the
几何非线性新梁柱单元及结构程序设计%A geometric nonlinear new beam-column element and structure program design
Institute of Scientific and Technical Information of China (English)
张俊峰; 王利娟; 郝际平; 李天
2011-01-01
基于更新拉格朗日构形的增量虚位移原理,在其势能项中引入了全部6个应力分量,采用可计人单元剪切变形影响的三次多项式插值函数,详细推导了考虑剪切变形及翘曲的空间梁一柱单元几何非线性切线刚度矩阵.根据面向对象的程序设计思想,将整个有限元域划分为8个基本类,在单元基类的基础上派生了新的单元类,采用C++语言编制了面向对象的空间钢结构分析程序.几何非线性算例分析结果表明,本文提出的理论分析方法和计算程序是正确的和高效的.%According to the increment virtual displacement principle based on the updated Lagrange configuration,the potential energy associated with all six stress components was taken into account. The cubic interpolation function which can be used to consider the shear deformation effects has been applied to derive the geometrical nonlinear stiffness matrix of the space beam-column element considering the shear deformation and warping effects. Based on the object-oriented design conception, the finite element analysis domain is divided into eight classes. A new class is derived from the base element class. Using C+ + language,the spatial steel frame advanced analysis program is complied. Numerical examples including both geometric and material nonlinearities are used to demonstrate the accuracy and efficiency of the proposed analytical method and computer program.
Knowledge-based geometric modeling in construction
DEFF Research Database (Denmark)
Bonev, Martin; Hvam, Lars
2012-01-01
a considerably high amount of their recourses is required for designing and specifying the majority of their product assortment. As design decisions are hereby based on knowledge and experience about behaviour and applicability of construction techniques and materials for a predefined design situation, smart...... tools need to be developed, to support these activities. In order to achieve a higher degree of design automation, this study proposes a framework for using configuration systems within the CAD environment together with suitable geometric modeling techniques on the example of a Danish manufacturer...
Discrete geometric structures for architecture
Pottmann, Helmut
2010-06-13
The emergence of freeform structures in contemporary architecture raises numerous challenging research problems, most of which are related to the actual fabrication and are a rich source of research topics in geometry and geometric computing. The talk will provide an overview of recent progress in this field, with a particular focus on discrete geometric structures. Most of these result from practical requirements on segmenting a freeform shape into planar panels and on the physical realization of supporting beams and nodes. A study of quadrilateral meshes with planar faces reveals beautiful relations to discrete differential geometry. In particular, we discuss meshes which discretize the network of principal curvature lines. Conical meshes are among these meshes; they possess conical offset meshes at a constant face/face distance, which in turn leads to a supporting beam layout with so-called torsion free nodes. This work can be generalized to a variety of multilayer structures and laid the ground for an adapted curvature theory for these meshes. There are also efforts on segmenting surfaces into planar hexagonal panels. Though these are less constrained than planar quadrilateral panels, this problem is still waiting for an elegant solution. Inspired by freeform designs in architecture which involve circles and spheres, we present a new kind of triangle mesh whose faces\\' in-circles form a packing, i.e., the in-circles of two triangles with a common edge have the same contact point on that edge. These "circle packing (CP) meshes" exhibit an aesthetic balance of shape and size of their faces. They are closely tied to sphere packings on surfaces and to various remarkable structures and patterns which are of interest in art, architecture, and design. CP meshes constitute a new link between architectural freeform design and computational conformal geometry. Recently, certain timber structures motivated us to study discrete patterns of geodesics on surfaces. This
Harmonic and geometric analysis
Citti, Giovanna; Pérez, Carlos; Sarti, Alessandro; Zhong, Xiao
2015-01-01
This book presents an expanded version of four series of lectures delivered by the authors at the CRM. Harmonic analysis, understood in a broad sense, has a very wide interplay with partial differential equations and in particular with the theory of quasiconformal mappings and its applications. Some areas in which real analysis has been extremely influential are PDE's and geometric analysis. Their foundations and subsequent developments made extensive use of the Calderón–Zygmund theory, especially the Lp inequalities for Calderón–Zygmund operators (Beurling transform and Riesz transform, among others) and the theory of Muckenhoupt weights. The first chapter is an application of harmonic analysis and the Heisenberg group to understanding human vision, while the second and third chapters cover some of the main topics on linear and multilinear harmonic analysis. The last serves as a comprehensive introduction to a deep result from De Giorgi, Moser and Nash on the regularity of elliptic partial differen...
Geometrical approach to fluid models
Kuvshinov, B. N.; Schep, T. J.
1997-01-01
Differential geometry based upon the Cartan calculus of differential forms is applied to investigate invariant properties of equations that describe the motion of continuous media. The main feature of this approach is that physical quantities are treated as geometrical objects. The geometrical
In Defence of Geometrical Algebra
Blasjo, V.N.E.
2016-01-01
The geometrical algebra hypothesis was once the received interpretation of Greek mathematics. In recent decades, however, it has become anathema to many. I give a critical review of all arguments against it and offer a consistent rebuttal case against the modern consensus. Consequently, I find that the geometrical algebra interpretation should be reinstated as a viable historical hypothesis.
Homological Type of Geometric Transitions
Rossi, Michele
2010-01-01
The present paper gives an account and quantifies the change in topology induced by small and type II geometric transitions, by introducing the notion of the \\emph{homological type} of a geometric transition. The obtained results agree with, and go further than, most results and estimates, given to date by several authors, both in mathematical and physical literature.
Geometrical approach to fluid models
Kuvshinov, B. N.; Schep, T. J.
1997-01-01
Differential geometry based upon the Cartan calculus of differential forms is applied to investigate invariant properties of equations that describe the motion of continuous media. The main feature of this approach is that physical quantities are treated as geometrical objects. The geometrical notio
New computation methods for geometrical optics
Lin, Psang Dain
2014-01-01
This book employs homogeneous coordinate notation to compute the first- and second-order derivative matrices of various optical quantities. It will be one of the important mathematical tools for automatic optical design. The traditional geometrical optics is based on raytracing only. It is very difficult, if possible, to compute the first- and second-order derivatives of a ray and optical path length with respect to system variables, since they are recursive functions. Consequently, current commercial software packages use a finite difference approximation methodology to estimate these derivatives for use in optical design and analysis. Furthermore, previous publications of geometrical optics use vector notation, which is comparatively awkward for computations for non-axially symmetrical systems.
Transmuted Complementary Weibull Geometric Distribution
Directory of Open Access Journals (Sweden)
Ahmed Z. A fify
2014-12-01
Full Text Available This paper provides a new generalization of the complementary Weibull geometric distribution that introduced by Tojeiro et al. (2014, using the quadratic rank transmutation map studied by Shaw and Buckley (2007. The new distribution is referred to as transmuted complementary Weibull geometric distribution (TCWGD. The TCWG distribution includes as special cases the complementary Weibull geometric distribution (CWGD, complementary exponential geometric distribution(CEGD,Weibull distribution (WD and exponential distribution (ED. Various structural properties of the new distribution including moments, quantiles, moment generating function and RØnyi entropy of the subject distribution are derived. We proposed the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. A real data set are used to compare the exibility of the transmuted version versus the complementary Weibull geometric distribution.
Geometric Mechanics of Periodic Pleated Origami
Wei, Zhiyan; Dudte, Levi; Liang, Haiyi; Mahadevan, L
2012-01-01
Origami is the archetype of a structural material with unusual mechanical properties that arise almost exclusively from the geometry of its constituent folds and forms the basis for mechanical metamaterials with an extreme deformation response. Here we consider a simple periodically folded structure Miura-ori, which is composed of identical unit cells of mountain and valley folds with four-coordinated ridges, de?fined completely by 2 angles and 2 lengths. We use the geometrical properties of a Miura-ori plate to characterize its elastic response to planar and non-planar piece- wise isometric deformations and calculate the two-dimensional stretching and bending response of a Miura-ori sheet, and show that the in-plane and out-of-plane Poisson's ratios are equal in magnitude, but opposite in sign. Our geometric approach also allows us to solve the inverse design problem of determining the geometric parameters that achieve the optimal geometric and mechanical response of such structures.
Institute of Scientific and Technical Information of China (English)
李楠; 韩颖
2014-01-01
To deal with the weak signal strength in the measurement of capacitive proximity sensors, the effects of geometric parameter design were investigated,and the sensor measurement performance was greatly improved by the geometric parameter optimization. The comprehensive evaluation standards of sensor performance were presented, including penetration depth, signal strength and noise tolerance,measurement sensitivity and dynamic range. For round capacitive proximity sensors,the effects of the surface area on sensor performance were analyzed. Four different structures including rectangular,round,interdigital and spiral-shaped sensors were designed. In the same conditions,the electric field distributions of the sensors with four structures were simulated and the measured fringe capacitance was compared. The results indicate that the geometric parameters have remarkable influence on the measured signal strength and measurement sensitivity;comparing with rectangular and round sensors,the measurement sensitivity of interdigital and spiral-shaped sesnros was increased by 66 . 8% and 33 . 5%.%针对相邻电容传感器存在的测量信号微弱的问题，研究了相邻电容传感器的几何参数设计对传感器性能的具体影响，并通过几何参数的优化大幅度提高传感器测量性能．提出包括穿透深度、信号强度与噪声抑制、测量灵敏度与动态测量范围的相邻电容传感器性能综合评价细则．针对环形相邻电容传感器进行了极板几何面积变化对传感器性能影响的研究分析；设计了矩形、环形、交叉指形和螺旋盘形4种结构的相邻电容传感器，在等参数同测量环境下，对各相邻电容传感器分别进行电场仿真和边缘电容测量值比较，确定传感器几何形状对传感器性能的具体影响．实验结果表明，相邻电容传感器几何参数对传感器测量信号强度与测量灵敏度影响明显，复杂交叉指形与螺旋盘形的
Geometrical method of decoupling
Baumgarten, C.
2012-12-01
The computation of tunes and matched beam distributions are essential steps in the analysis of circular accelerators. If certain symmetries—like midplane symmetry—are present, then it is possible to treat the betatron motion in the horizontal, the vertical plane, and (under certain circumstances) the longitudinal motion separately using the well-known Courant-Snyder theory, or to apply transformations that have been described previously as, for instance, the method of Teng and Edwards. In a preceding paper, it has been shown that this method requires a modification for the treatment of isochronous cyclotrons with non-negligible space charge forces. Unfortunately, the modification was numerically not as stable as desired and it was still unclear, if the extension would work for all conceivable cases. Hence, a systematic derivation of a more general treatment seemed advisable. In a second paper, the author suggested the use of real Dirac matrices as basic tools for coupled linear optics and gave a straightforward recipe to decouple positive definite Hamiltonians with imaginary eigenvalues. In this article this method is generalized and simplified in order to formulate a straightforward method to decouple Hamiltonian matrices with eigenvalues on the real and the imaginary axis. The decoupling of symplectic matrices which are exponentials of such Hamiltonian matrices can be deduced from this in a few steps. It is shown that this algebraic decoupling is closely related to a geometric “decoupling” by the orthogonalization of the vectors E→, B→, and P→, which were introduced with the so-called “electromechanical equivalence.” A mathematical analysis of the problem can be traced down to the task of finding a structure-preserving block diagonalization of symplectic or Hamiltonian matrices. Structure preservation means in this context that the (sequence of) transformations must be symplectic and hence canonical. When used iteratively, the decoupling
Institute of Scientific and Technical Information of China (English)
毛志平
2012-01-01
Under the guidance of modem restoration theories, a Warring States bronze pot inlaid with red copper in birds, animals and geometric designs were restored. With the processes of scientific analysis and research, restoration planning, cleaning, reconstructing and decoration technology, this paper ana- lyzes the basic requirements and steps of modern restoration. It discusses the best way to reconstruct a special decorated bronze pot, and then puts forward a proposal of preservation after the bronze pot was restored.%在现代修复理念的指导下,对一件战国镶红铜鸟兽几何纹青铜壶进行保护修复,通过分析检测与研究、制定修复方案、保护修复处理、装饰工艺等步骤,介绍了现代青铜文物保护修复的基本要求和流程,探讨了此件特殊工艺青铜器的修复工艺,对其精美纹饰和装饰工艺进行赏析,同时提出了保护修复后的保存建议.
The Effects of Computer-assisted and Distance Learning of Geometric Modeling
Directory of Open Access Journals (Sweden)
Omer Faruk Sozcu
2013-01-01
Full Text Available The effects of computer-assisted and distance learning of geometric modeling and computer aided geometric design are studied. It was shown that computer algebra systems and dynamic geometric environments can be considered as excellent tools for teaching mathematical concepts of mentioned areas, and distance education technologies would be indispensable for consolidation of successfully passed topics
Geometrical method of decoupling
Directory of Open Access Journals (Sweden)
C. Baumgarten
2012-12-01
Full Text Available The computation of tunes and matched beam distributions are essential steps in the analysis of circular accelerators. If certain symmetries—like midplane symmetry—are present, then it is possible to treat the betatron motion in the horizontal, the vertical plane, and (under certain circumstances the longitudinal motion separately using the well-known Courant-Snyder theory, or to apply transformations that have been described previously as, for instance, the method of Teng and Edwards. In a preceding paper, it has been shown that this method requires a modification for the treatment of isochronous cyclotrons with non-negligible space charge forces. Unfortunately, the modification was numerically not as stable as desired and it was still unclear, if the extension would work for all conceivable cases. Hence, a systematic derivation of a more general treatment seemed advisable. In a second paper, the author suggested the use of real Dirac matrices as basic tools for coupled linear optics and gave a straightforward recipe to decouple positive definite Hamiltonians with imaginary eigenvalues. In this article this method is generalized and simplified in order to formulate a straightforward method to decouple Hamiltonian matrices with eigenvalues on the real and the imaginary axis. The decoupling of symplectic matrices which are exponentials of such Hamiltonian matrices can be deduced from this in a few steps. It is shown that this algebraic decoupling is closely related to a geometric “decoupling” by the orthogonalization of the vectors E[over →], B[over →], and P[over →], which were introduced with the so-called “electromechanical equivalence.” A mathematical analysis of the problem can be traced down to the task of finding a structure-preserving block diagonalization of symplectic or Hamiltonian matrices. Structure preservation means in this context that the (sequence of transformations must be symplectic and hence canonical. When
Geometric inequalities for black holes
Energy Technology Data Exchange (ETDEWEB)
Dain, Sergio [Universidad Nacional de Cordoba (Argentina)
2013-07-01
Full text: A geometric inequality in General Relativity relates quantities that have both a physical interpretation and a geometrical definition. It is well known that the parameters that characterize the Kerr-Newman black hole satisfy several important geometric inequalities. Remarkably enough, some of these inequalities also hold for dynamical black holes. This kind of inequalities, which are valid in the dynamical and strong field regime, play an important role in the characterization of the gravitational collapse. They are closed related with the cosmic censorship conjecture. In this talk I will review recent results in this subject. (author)
Institute of Scientific and Technical Information of China (English)
谢波; 陈波涛
2012-01-01
采用平底端刀五轴端铣加工模具曲面时，由于存在干涉和编程困难等问题，而大大影响其应用。对此，基于平底端刀端铣加工模具曲面的特点，将平底端刀五轴端铣加工模具曲面时的平底端刀和被加工曲面看作是一对互为共轭的空间啮合包络曲面，并用微分几何Frenet标架来描述数控加工的刀具轨迹，通过计算得到刀具轨迹的刀位点，从而设计平底端刀五轴端铣加工模具曲面的几何模型。%The interference and program trouble has contributed unsatisfactory effects when applying a five-axis flat-end tool to machine mold surface. Taking the feature into consideration, this design takes the fiat-end tool and machined surface as a pair of mutually conjugate space contact tooth envelope surface, and uses the Frenet frame of differential geometry to describe the NC machining tool path, thus getting tool path and calculating the cutter location point. As a result, the geometric model in five-axis CNC end milling mold surface with fiat-end tools is designed.
Mobile Watermarking against Geometrical Distortions
Directory of Open Access Journals (Sweden)
Jing Zhang
2015-08-01
Full Text Available Mobile watermarking robust to geometrical distortions is still a great challenge. In mobile watermarking, efficient computation is necessary because mobile devices have very limited resources due to power consumption. In this paper, we propose a low-complexity geometrically resilient watermarking approach based on the optimal tradeoff circular harmonic function (OTCHF correlation filter and the minimum average correlation energy Mellin radial harmonic (MACE-MRH correlation filter. By the rotation, translation and scale tolerance properties of the two kinds of filter, the proposed watermark detector can be robust to geometrical attacks. The embedded watermark is weighted by a perceptual mask which matches very well with the properties of the human visual system. Before correlation, a whitening process is utilized to improve watermark detection reliability. Experimental results demonstrate that the proposed watermarking approach is computationally efficient and robust to geometrical distortions.
Geometric structure of gauge theories
Energy Technology Data Exchange (ETDEWEB)
Mangiarotti, L.; Modugno, M.
1985-06-01
In the framework of the adjoint forms over the jet spaces of connections and using a canonical jet shift differential, we give a geometrical interpretation of the Yang--Mills equations both in a direct and Lagrangian formulation.
Geometric phases in graphitic cones
Energy Technology Data Exchange (ETDEWEB)
Furtado, Claudio [Departamento de Fisica, CCEN, Universidade Federal da Paraiba, Cidade Universitaria, 58051-970 Joao Pessoa, PB (Brazil)], E-mail: furtado@fisica.ufpb.br; Moraes, Fernando [Departamento de Fisica, CCEN, Universidade Federal da Paraiba, Cidade Universitaria, 58051-970 Joao Pessoa, PB (Brazil); Carvalho, A.M. de M [Departamento de Fisica, Universidade Estadual de Feira de Santana, BR116-Norte, Km 3, 44031-460 Feira de Santana, BA (Brazil)
2008-08-04
In this Letter we use a geometric approach to study geometric phases in graphitic cones. The spinor that describes the low energy states near the Fermi energy acquires a phase when transported around the apex of the cone, as found by a holonomy transformation. This topological result can be viewed as an analogue of the Aharonov-Bohm effect. The topological analysis is extended to a system with n cones, whose resulting configuration is described by an effective defect00.
Determining Geometric Accuracy in Turning
Institute of Scientific and Technical Information of China (English)
Kwong; Chi; Kit; A; Geddam
2002-01-01
Mechanical components machined to high levels of ac cu racy are vital to achieve various functional requirements in engineering product s. In particular, the geometric accuracy of turned components play an important role in determining the form, fit and function of mechanical assembly requiremen ts. The geometric accuracy requirements of turned components are usually specifi ed in terms of roundness, straightness, cylindricity and concentricity. In pract ice, the accuracy specifications achievable are infl...
The Geometric Gravitational Internal Problem
González-Martin, G R
2000-01-01
In a geometric unified theory there is an energy momentum equation, apart from the field equations and equations of motion. The general relativity Einstein equation with cosmological constant follows from this energy momentum equation for empty space. For non empty space we obtain a generalized Einstein equation, relating the Einstein tensor to a geometric stress energy tensor. The matching exterior solution is in agreement with the standard relativity tests. Furthermore, there is a Newtonian limit where we obtain Poisson's equation.
Geometric symmetries in light nuclei
Bijker, Roelof
2016-01-01
The algebraic cluster model is is applied to study cluster states in the nuclei 12C and 16O. The observed level sequences can be understood in terms of the underlying discrete symmetry that characterizes the geometrical configuration of the alpha-particles, i.e. an equilateral triangle for 12C, and a regular tetrahedron for 16O. The structure of rotational bands provides a fingerprint of the underlying geometrical configuration of alpha-particles.
Geometric inequalities methods of proving
Sedrakyan, Hayk
2017-01-01
This unique collection of new and classical problems provides full coverage of geometric inequalities. Many of the 1,000 exercises are presented with detailed author-prepared-solutions, developing creativity and an arsenal of new approaches for solving mathematical problems. This book can serve teachers, high-school students, and mathematical competitors. It may also be used as supplemental reading, providing readers with new and classical methods for proving geometric inequalities. .
A practical guide to geometric regulation for distributed parameter systems
Aulisa, Eugenio
2015-01-01
A Practical Guide to Geometric Regulation for Distributed Parameter Systems provides an introduction to geometric control design methodologies for asymptotic tracking and disturbance rejection of infinite-dimensional systems. The book also introduces several new control algorithms inspired by geometric invariance and asymptotic attraction for a wide range of dynamical control systems. The first part of the book is devoted to regulation of linear systems, beginning with the mathematical setup, general theory, and solution strategy for regulation problems with bounded input and output operators.
Geometrical product specifications. Datums and coordinate systems
Glukhov, V. I.; Ivleva, I. A.; Zlatkina, O. Y.
2017-06-01
The work is devoted to the relevant topic such as the technical products quality improvement due to the geometrical specifications accuracy. The research purpose is to ensure the quality indicators on the basis of the systematic approach to the values normalization and geometrical specifications accuracy in the workpiece coordinate systems in the process of design. To achieve the goal two tasks are completed such as the datum features classification according to the number of linear and angular freedom degrees constraints, called the datums informativeness, and the rectangular coordinate systems identification, materialized by workpiece datums sets. The datum features informativeness characterizes the datums functional purpose to limit product workpiece linear and angular degrees of freedom. The datum features informativeness numerically coincides with the kinematic pairs classes and couplings in mechanics. The datum features informativeness identifies the coordinate system without the location redundancy. Each coordinate plane of a rectangular coordinate system has different informativeness 3 + 2 + 1. Each coordinate axis also has different informativeness 4+2+Θ (zero). It is possible to establish the associated workpiece position with three linear and three angular coordinates relative to two axes with the informativeness 4 and 2. is higher, the more informativeness of the coordinate axis or a coordinate plane is, the higher is the linear and angular coordinates accuracy, the coordinate being plotted along the coordinate axis or plane. The systematic approach to the geometrical products specifications positioning in coordinate systems is the scientific basis for a natural transition to the functional dimensions of features position - coordinating dimensions and the size of the features form - feature dimensions of two measures: linear and angular ones. The products technical quality improving is possible due to the coordinate systems introduction materialized by
Antenna with Dielectric Having Geometric Patterns
Dudley, Kenneth L. (Inventor); Elliott, Holly A. (Inventor); Cravey, Robin L. (Inventor); Connell, John W. (Inventor); Ghose, Sayata (Inventor); Watson, Kent A. (Inventor); Smith, Jr., Joseph G. (Inventor)
2013-01-01
An antenna includes a ground plane, a dielectric disposed on the ground plane, and an electrically-conductive radiator disposed on the dielectric. The dielectric includes at least one layer of a first dielectric material and a second dielectric material that collectively define a dielectric geometric pattern, which may comprise a fractal geometry. The radiator defines a radiator geometric pattern, and the dielectric geometric pattern is geometrically identical, or substantially geometrically identical, to the radiator geometric pattern.
Facades structure detection by geometric moment
Jiang, Diqiong; Chen, Hui; Song, Rui; Meng, Lei
2017-06-01
This paper proposes a novel method for extracting facades structure from real-world pictures by using local geometric moment. Compared with existing methods, the proposed method has advantages of easy-to-implement, low computational cost, and robustness to noises, such as uneven illumination, shadow, and shade from other objects. Besides, our method is faster and has a lower space complexity, making it feasible for mobile devices and the situation where real-time data processing is required. Specifically, a facades structure modal is first proposed to support the use of our special noise reduction method, which is based on a self-adapt local threshold with Gaussian weighted average for image binarization processing and the feature of the facades structure. Next, we divide the picture of the building into many individual areas, each of which represents a door or a window in the picture. Subsequently we calculate the geometric moment and centroid for each individual area, for identifying those collinear ones based on the feature vectors, each of which is thereafter replaced with a line. Finally, we comprehensively analyze all the geometric moment and centroid to find out the facades structure of the building. We compare our result with other methods and especially report the result from the pictures taken in bad environmental conditions. Our system is designed for two application, i.e, the reconstruction of facades based on higher resolution ground-based on imagery, and the positional system based on recognize the urban building.
Wegman, F.C.M. & Slop, M.
1996-01-01
This paper deals with the result of a study carried out for the European Commission by the SWOV Institute for Road Safety Research, in co-operation with a number of other European institutes, and which was reported in 1994. The title of the study is "Safety Effects of Road Design Standards." The aim
Wegman, F.C.M. & Slop, M.
1996-01-01
This paper deals with the result of a study carried out for the European Commission by the SWOV Institute for Road Safety Research, in co-operation with a number of other European institutes, and which was reported in 1994. The title of the study is "Safety Effects of Road Design Standards." The aim
Geometric procedures for civil engineers
Tonias, Elias C
2016-01-01
This book provides a multitude of geometric constructions usually encountered in civil engineering and surveying practice. A detailed geometric solution is provided to each construction as well as a step-by-step set of programming instructions for incorporation into a computing system. The volume is comprised of 12 chapters and appendices that may be grouped in three major parts: the first is intended for those who love geometry for its own sake and its evolution through the ages, in general, and, more specifically, with the introduction of the computer. The second section addresses geometric features used in the book and provides support procedures used by the constructions presented. The remaining chapters and the appendices contain the various constructions. The volume is ideal for engineering practitioners in civil and construction engineering and allied areas.
Geometric scalar theory of gravity
Energy Technology Data Exchange (ETDEWEB)
Novello, M.; Bittencourt, E.; Goulart, E.; Salim, J.M.; Toniato, J.D. [Instituto de Cosmologia Relatividade Astrofisica ICRA - CBPF Rua Dr. Xavier Sigaud 150 - 22290-180 Rio de Janeiro - Brazil (Brazil); Moschella, U., E-mail: novello@cbpf.br, E-mail: eduhsb@cbpf.br, E-mail: Ugo.Moschella@uninsubria.it, E-mail: egoulart@cbpf.br, E-mail: jsalim@cbpf.br, E-mail: toniato@cbpf.br [Università degli Studi dell' Insubria - Dipartamento di Fisica e Matematica Via Valleggio 11 - 22100 Como - Italy (Italy)
2013-06-01
We present a geometric scalar theory of gravity. Our proposal will be described using the ''background field method'' introduced by Gupta, Feynman, Deser and others as a field theory formulation of general relativity. We analyze previous criticisms against scalar gravity and show how the present proposal avoids these difficulties. This concerns not only the theoretical complaints but also those related to observations. In particular, we show that the widespread belief of the conjecture that the source of scalar gravity must be the trace of the energy-momentum tensor — which is one of the main difficulties to couple gravity with electromagnetic phenomenon in previous models — does not apply to our geometric scalar theory. From the very beginning this is not a special relativistic scalar gravity. The adjective ''geometric'' pinpoints its similarity with general relativity: this is a metric theory of gravity. Some consequences of this new scalar theory are explored.
Geometric identities in stereological particle analysis
DEFF Research Database (Denmark)
Kötzer, S.; Jensen, Eva Bjørn Vedel; Baddeley, A.
We review recent findings about geometric identities in integral geometry and geometric tomography, and their statistical application to stereological particle analysis. Open questions are discussed.......We review recent findings about geometric identities in integral geometry and geometric tomography, and their statistical application to stereological particle analysis. Open questions are discussed....
Geometric orbit datum and orbit covers
Institute of Scientific and Technical Information of China (English)
梁科; 侯自新
2001-01-01
Vogan conjectured that the parabolic induction of orbit data is independent of the choice of the parabolic subgroup. In this paper we first give the parabolic induction of orbit covers, whose relationship with geometric orbit datum is also induced. Hence we show a geometric interpretation of orbit data and finally prove the conjugation for geometric orbit datum using geometric method.
Geometric formula for prism deflection
Indian Academy of Sciences (India)
Apoorva G Wagh; Veer Chand Rakhecha
2004-08-01
While studying neutron deflections produced by a magnetic prism, we have stumbled upon a simple `geometric' formula. For a prism of refractive index close to unity, the deflection simply equals the product of the refractive power − 1 and the base-to-height ratio of the prism, regardless of the apex angle. The base and height of the prism are measured respectively along and perpendicular to the direction of beam propagation within the prism. The geometric formula greatly simplifies the optimisation of prism parameters to suit any specific experiment.
A Geometric Formulation of Supersymmetry
Freedman, Daniel Z; Van Proeyen, Antoine
2016-01-01
The scalar fields of supersymmetric models are coordinates of a geometric space. We propose a formulation of supersymmetry that is covariant with respect to reparametrizations of this target space. Employing chiral multiplets as an example, we introduce modified supersymmetry variations and redefined auxiliary fields that transform covariantly under reparametrizations. The resulting action and transformation laws are manifestly covariant and highlight the geometric structure of the supersymmetric theory. The covariant methods are developed first for general theories (not necessarily supersymmetric) whose scalar fields are coordinates of a Riemannian target space.
Height and Tilt Geometric Texture
DEFF Research Database (Denmark)
Andersen, Vedrana; Desbrun, Mathieu; Bærentzen, Jakob Andreas
2009-01-01
We propose a new intrinsic representation of geometric texture over triangle meshes. Our approach extends the conventional height field texture representation by incorporating displacements in the tangential plane in the form of a normal tilt. This texture representation offers a good practical...... compromise between functionality and simplicity: it can efficiently handle and process geometric texture too complex to be represented as a height field, without having recourse to full blown mesh editing algorithms. The height-and-tilt representation proposed here is fully intrinsic to the mesh, making...
Geometric integration for particle accelerators
Energy Technology Data Exchange (ETDEWEB)
Forest, Etienne [High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba, Ibaraki 305-0801 (Japan)
2006-05-12
This paper is a very personal view of the field of geometric integration in accelerator physics-a field where often work of the highest quality is buried in lost technical notes or even not published; one has only to think of Simon van der Meer Nobel prize work on stochastic cooling-unpublished in any refereed journal. So I reconstructed the relevant history of geometrical integration in accelerator physics as much as I could by talking to collaborators and using my own understanding of the field. The reader should not be too surprised if this account is somewhere between history, science and perhaps even fiction.
Geometric pumping in autophoretic channels
Michelin, Sebastien; De Canio, Gabriele; Lobato-Dauzier, Nicolas; Lauga, Eric
2015-01-01
Many microfluidic devices use macroscopic pressure differentials to overcome viscous friction and generate flows in microchannels. In this work, we investigate how the chemical and geometric properties of the channel walls can drive a net flow by exploiting the autophoretic slip flows induced along active walls by local concentration gradients of a solute species. We show that chemical patterning of the wall is not required to generate and control a net flux within the channel, rather channel geometry alone is sufficient. Using numerical simulations, we determine how geometric characteristics of the wall influence channel flow rate, and confirm our results analytically in the asymptotic limit of lubrication theory.
Asymptotic geometric analysis, part I
Artstein-Avidan, Shiri
2015-01-01
The authors present the theory of asymptotic geometric analysis, a field which lies on the border between geometry and functional analysis. In this field, isometric problems that are typical for geometry in low dimensions are substituted by an "isomorphic" point of view, and an asymptotic approach (as dimension tends to infinity) is introduced. Geometry and analysis meet here in a non-trivial way. Basic examples of geometric inequalities in isomorphic form which are encountered in the book are the "isomorphic isoperimetric inequalities" which led to the discovery of the "concentration phenomen
An introduction to geometrical physics
Aldrovandi, R
1995-01-01
This book stresses the unifying power of the geometrical framework in bringing together concepts from the different areas of physics. Common underpinnings of optics, elasticity, gravitation, relativistic fields, particle mechanics and other subjects are underlined. It attempts to extricate the notion of space currently in the physical literature from the metric connotation.The book's goal is to present mathematical ideas associated with geometrical physics in a rather introductory language. Included are many examples from elementary physics and also, for those wishing to reach a higher level o
Geometric properties of optimal photonic crystals
DEFF Research Database (Denmark)
Sigmund, Ole; Hougaard, Kristian G.
2008-01-01
Photonic crystals can be designed to control and confine light. Since the introduction of the concept by Yablonovitch and John two decades ago, there has been a quest for the optimal structure, i.e., the periodic arrangement of dielectric and air that maximizes the photonic band gap. Based...... on numerical optimization studies, we have discovered some surprisingly simple geometric properties of optimal planar band gap structures. We conjecture that optimal structures for gaps between bands n and n+1 correspond to n elliptic rods with centers defined by the generators of an optimal centroidal Voronoi...
Institute of Scientific and Technical Information of China (English)
安宏雷; 李杰; 王剑; 王建文; 马宏绪
2013-01-01
Traditional quaternion-based sliding mode observer for angular velocity estimating has to introduce the process of mandatory rescaling which affects the tracking performance of the observer algorithm.In this work,a sliding mode observer design framework is proposed, based on the Lie group method of numerical integration on manifolds for angular velocity estimation of quadrotor attitude.The algorithm constructs sliding mode feedback in the space of equivalent Lie algebra of homogeneous manifolds on the basis of equivariant mapping ideological.It avoids the complexity of constructing sliding mode feedback in homogeneous space directly,and eliminates the process of mandatory rescaling which is required by the traditional methods in each integration step.The simulation results show that the algorithm of geometric sliding mode observer is effective.%对四旋翼无人机的角速度进行估计时，传统的基于单位四元数的滑模观测器需要引入强制比例重调，因而影响了跟踪精度。提出一种基于数值积分的李群方法的滑模观测器设计框架。该算法基于等变映射思想，在齐性流形空间的等价李代数空间中设计滑模反馈，从而避免了直接在流形空间中设计反馈的复杂性，并消除了传统方法在每个积分步骤中强制加入的比例重调，提高了观测器的跟踪性能。仿真结果表明，几何滑模观测器算法可以有效地对四旋翼无人机的角速度进行估计。
In Defence of Geometrical Algebra
Blasjo, V.N.E.
2016-01-01
The geometrical algebra hypothesis was once the received interpretation of Greek mathematics. In recent decades, however, it has become anathema to many. I give a critical review of all arguments against it and offer a consistent rebuttal case against the modern consensus. Consequently, I find that
Metastable vacua and geometric deformations
Amariti, A; Girardello, L; Mariotti, A
2008-01-01
We study the geometric interpretation of metastable vacua for systems of D3 branes at non isolated toric deformable singularities. Using the L^{aba} examples, we investigate the relations between the field theoretic susy breaking and restoration and the complex deformations of the CY singularities.
DEFF Research Database (Denmark)
Jensen, Find Mølholt; Puri, Amit S.; Dear, John P.
2011-01-01
This article is the first part of a three-article series and it deals with full-scale tests of a load-carrying box girder. The two other articles present more details on smaller sub-component levels as well as cap specimens (article 2) and shear webs (article 3). This article also links to the two...... may also have a significant impact on present wind turbine blades. In this article, a 34 m long load-carrying box girder has been tested in static flap-wise bending, and it has been demonstrated that, for this design, the Brazier effect is a critical phenomenon of great relevance for the ultimate...
Geometric hashing and object recognition
Stiller, Peter F.; Huber, Birkett
1999-09-01
We discuss a new geometric hashing method for searching large databases of 2D images (or 3D objects) to match a query built from geometric information presented by a single 3D object (or single 2D image). The goal is to rapidly determine a small subset of the images that potentially contain a view of the given object (or a small set of objects that potentially match the item in the image). Since this must be accomplished independent of the pose of the object, the objects and images, which are characterized by configurations of geometric features such as points, lines and/or conics, must be treated using a viewpoint invariant formulation. We are therefore forced to characterize these configurations in terms of their 3D and 2D geometric invariants. The crucial relationship between the 3D geometry and its 'residual' in 2D is expressible as a correspondence (in the sense of algebraic geometry). Computing a set of generating equations for the ideal of this correspondence gives a complete characterization of the view of independent relationships between an object and all of its possible images. Once a set of generators is in hand, it can be used to devise efficient recognition algorithms and to give an efficient geometric hashing scheme. This requires exploiting the form and symmetry of the equations. The result is a multidimensional access scheme whose efficiency we examine. Several potential directions for improving this scheme are also discussed. Finally, in a brief appendix, we discuss an alternative approach to invariants for generalized perspective that replaces the standard invariants by a subvariety of a Grassmannian. The advantage of this is that one can circumvent many annoying general position assumptions and arrive at invariant equations (in the Plucker coordinates) that are more numerically robust in applications.
Geometric modeling and analysis of large latticed surfaces
Nayfeh, A. H.; Hefzy, M. S.
1980-01-01
The application of geometrical schemes, similar to geodesic domes, to large spherical antenna reflectors was investigated. The shape and size of flat segmented latticed surfaces which approximate general shells of revolution, and in particular spherical and paraboloidal reflective surfaces, were determined. The extensive mathematical and computational geometric analyses of the reflector resulted in the development of a general purpose computer program capable of generating the complete design parameters of the dish. The program also includes a graphical self contained subroutine for graphic display of the required design.
Geometrical Phases in Quantum Mechanics
Christian, Joy Julius
In quantum mechanics, the path-dependent geometrical phase associated with a physical system, over and above the familiar dynamical phase, was initially discovered in the context of adiabatically changing environments. Subsequently, Aharonov and Anandan liberated this phase from the original formulation of Berry, which used Hamiltonians, dependent on curves in a classical parameter space, to represent the cyclic variations of the environments. Their purely quantum mechanical treatment, independent of Hamiltonians, instead used the non-trivial topological structure of the projective space of one-dimensional subspaces of an appropriate Hilbert space. The geometrical phase, in their treatment, results from a parallel transport of the time-dependent pure quantum states along a curve in this space, which is endowed with an abelian connection. Unlike Berry, they were able to achieve this without resort to an adiabatic approximation or to a time-independent eigenvalue equation. Prima facie, these two approaches are conceptually quite different. After a review of both approaches, an exposition bridging this apparent conceptual gap is given; by rigorously analyzing a model composite system, it is shown that, in an appropriate correspondence limit, the Berry phase can be recovered as a special case from the Aharonov-Anandan phase. Moreover, the model composite system is used to show that Berry's correction to the traditional Born-Oppenheimer energy spectra indeed brings the spectra closer to the exact results. Then, an experimental arrangement to measure geometrical phases associated with cyclic and non-cyclic variations of quantum states of an entangled composite system is proposed, utilizing the fundamental ideas of the recently opened field of two-particle interferometry. This arrangement not only resolves the controversy regarding the true nature of the phases associated with photon states, but also unequivocally predicts experimentally accessible geometrical phases in a
Guiding light via geometric phases
Slussarenko, Sergei; Jisha, Chandroth P; Piccirillo, Bruno; Santamato, Enrico; Assanto, Gaetano; Marrucci, Lorenzo
2015-01-01
Known methods for transverse confinement and guidance of light can be grouped into a few basic mechanisms, the most common being metallic reflection, total internal reflection and photonic-bandgap (or Bragg) reflection. All of them essentially rely on changes of the refractive index, that is on scalar properties of light. Recently, processes based on "geometric Berry phases", such as manipulation of polarization states or deflection of spinning-light rays, have attracted considerable interest in the contexts of singular optics and structured light. Here, we disclose a new approach to light waveguiding, using geometric Berry phases and exploiting polarization states and their handling. This can be realized in structured three-dimensional anisotropic media, in which the optic axis lies orthogonal to the propagation direction and is modulated along it and across the transverse plane, so that the refractive index remains constant but a phase distortion can be imposed on a beam. In addition to a complete theoretic...
A Geometrical Method of Decoupling
Baumgarten, Christian
2012-01-01
In a preceeding paper the real Dirac matrices have been introduced to coupled linear optics and a recipe to decouple positive definite Hamiltonians has been given. In this article a geometrical method is presented which allows to decouple regular {\\it and} irregular systems with the same straightforward method and to compute the eigenvalues and eigenvectors of Hamiltonian matrices with both, real and imaginary eigenvalues. It is shown that the algebraic decoupling is closely related to a geometric "decoupling" by the orthogonalization of the vectors $\\vec E$, $\\vec B$ and $\\vec p$, that were introduced with the so-called "electromechanical equivalence" (EMEQ). When used iteratively, the decoupling algorithm can also be applied to n-dimensional non-dissipative systems.
Mechanical and geometric advantages in compliant mechanism optimization
Institute of Scientific and Technical Information of China (English)
Michael Yu WANG
2009-01-01
This paper presents a focused examination of the mechanical and geometric advantages in compliant mechanisms and their ramifications in the design formula-tions of compliant mechanisms posed as a topology optimization problem. With a linear elastic structuralanalysis, we quantify mechanical (and geometric) advan-tage in terms of the stiffness elements of the mechanism's structure. We then analyze the common formulations of compliant mechanism optimization and the role of the external springs added in the formulations. It is shown that the common formulations using mechanical (or geometric) advantage would directly emulate at best a rigid-body linkage to the true optimum design. As a result, the topology optimization generates point flexures in the resulting optimal mechanisms. A case study is investigated to demonstrate the resulting trends in the current formula-tions.
Geometrical Aspects of Venus Transit
Bertuola, Alberto C; Magalhães, N S; Filho, Victo S
2016-01-01
We obtained two astronomical values, the Earth-Venus distance and Venus diameter, by means of a geometrical treatment of photos taken of Venus transit in June of 2012. Here we presented the static and translational modelsthat were elaborated taking into account the Earth and Venus orbital movements. An additional correction was also added by considering the Earth rotation movement. The results obtained were compared with the values of reference from literature, showing very good concordance.
Geometric Hyperplanes: Desargues Encodes Doily
Saniga, Metod
2011-01-01
It is shown that the structure of the generalized quadrangle of order two is fully encoded in the properties of the Desargues configuration. A point of the quadrangle is represented by a geometric hyperplane of the Desargues configuration and its line by a set of three hyperplanes such that one of them is the complement of the symmetric difference of the remaining two and they all share a pair of non-collinear points.
Geometrical interpretation of optical absorption
Energy Technology Data Exchange (ETDEWEB)
Monzon, J. J.; Barriuso, A. G.; Sanchez-Soto, L. L. [Departamento de Optica, Facultad de Fisica, Universidad Complutense, E-28040 Madrid (Spain); Montesinos-Amilibia, J. M. [Departamento de Geometria y Topologia, Facultad de Matematicas, Universidad Complutense, E-28040 Madrid (Spain)
2011-08-15
We reinterpret the transfer matrix for an absorbing system in very simple geometrical terms. In appropriate variables, the system appears as performing a Lorentz transformation in a (1 + 3)-dimensional space. Using homogeneous coordinates, we map that action on the unit sphere, which is at the realm of the Klein model of hyperbolic geometry. The effects of absorption appear then as a loxodromic transformation, that is, a rhumb line crossing all the meridians at the same angle.
Some geometrical iteration methods for nonlinear equations
Institute of Scientific and Technical Information of China (English)
LU Xing-jiang; QIAN Chun
2008-01-01
This paper describes geometrical essentials of some iteration methods (e.g. Newton iteration,secant line method,etc.) for solving nonlinear equations and advances some geomet-rical methods of iteration that are flexible and efficient.
Geometric modeling of subcellular structures, organelles, and multiprotein complexes
Feng, Xin; Xia, Kelin; Tong, Yiying; Wei, Guo-Wei
2013-01-01
SUMMARY Recently, the structure, function, stability, and dynamics of subcellular structures, organelles, and multi-protein complexes have emerged as a leading interest in structural biology. Geometric modeling not only provides visualizations of shapes for large biomolecular complexes but also fills the gap between structural information and theoretical modeling, and enables the understanding of function, stability, and dynamics. This paper introduces a suite of computational tools for volumetric data processing, information extraction, surface mesh rendering, geometric measurement, and curvature estimation of biomolecular complexes. Particular emphasis is given to the modeling of cryo-electron microscopy data. Lagrangian-triangle meshes are employed for the surface presentation. On the basis of this representation, algorithms are developed for surface area and surface-enclosed volume calculation, and curvature estimation. Methods for volumetric meshing have also been presented. Because the technological development in computer science and mathematics has led to multiple choices at each stage of the geometric modeling, we discuss the rationales in the design and selection of various algorithms. Analytical models are designed to test the computational accuracy and convergence of proposed algorithms. Finally, we select a set of six cryo-electron microscopy data representing typical subcellular complexes to demonstrate the efficacy of the proposed algorithms in handling biomolecular surfaces and explore their capability of geometric characterization of binding targets. This paper offers a comprehensive protocol for the geometric modeling of subcellular structures, organelles, and multiprotein complexes. PMID:23212797
Adiabatic geometric phases in hydrogenlike atoms
Sjöqvist, Erik; Yi, X. X.; Åberg, J.
2005-01-01
We examine the effect of spin-orbit coupling on geometric phases in hydrogenlike atoms exposed to a slowly varying magnetic field. The marginal geometric phases associated with the orbital angular momentum and the intrinsic spin fulfill a sum rule that explicitly relates them to the corresponding geometric phase of the whole system. The marginal geometric phases in the Zeeman and Paschen-Back limit are analyzed. We point out the existence of nodal points in the marginal phases that may be det...
GEOMETRIC AND RADIOMETRIC EVALUATION OF RASAT IMAGES
Directory of Open Access Journals (Sweden)
A. Cam
2016-06-01
Full Text Available RASAT, the second remote sensing satellite of Turkey, was designed and assembled, and also is being operated by TÜBİTAK Uzay (Space Technologies Research Institute (Ankara. RASAT images in various levels are available free-of-charge via Gezgin portal for Turkish citizens. In this paper, the images in panchromatic (7.5 m GSD and RGB (15 m GSD bands in various levels were investigated with respect to its geometric and radiometric characteristics. The first geometric analysis is the estimation of the effective GSD as less than 1 pixel for radiometrically processed level (L1R of both panchromatic and RGB images. Secondly, 2D georeferencing accuracy is estimated by various non-physical transformation models (similarity, 2D affine, polynomial, affine projection, projective, DLT and GCP based RFM reaching sub-pixel accuracy using minimum 39 and maximum 52 GCPs. The radiometric characteristics are also investigated for 8 bits, estimating SNR between 21.8-42.2, and noise 0.0-3.5 for panchromatic and MS images for L1R when the sea is masked to obtain the results for land areas. The analysis show that RASAT images satisfies requirements for various applications. The research is carried out in Zonguldak test site which is mountainous and partly covered by dense forest and urban areas.
Solving Topological and Geometrical Constraints in Bridge Feature Model
Institute of Scientific and Technical Information of China (English)
PENG Weibing; SONG Liangliang; PAN Guoshuai
2008-01-01
The capacity that computer can solve more complex design problem was gradually increased.Bridge designs need a breakthrough in the current development limitations, and then become more intelli-gent and integrated. This paper proposes a new parametric and feature-based computer aided design (CAD) models which can represent families of bridge objects, includes knowledge representation, three-dimensional geometric topology relationships. The realization of a family member is found by solving first the geometdc constraints, and then the topological constraints. From the geometric solution, constraint equations are constructed. Topology solution is developed by feature dependencies graph between bridge objects. Finally, feature parameters are proposed to drive bridge design with feature parameters. Results from our implementation show that the method can help to facilitate bridge design.
Exact Solutions for Einstein's Hyperbolic Geometric Flow
Institute of Scientific and Technical Information of China (English)
HE Chun-Lei
2008-01-01
In this paper we investigate the Einstein's hyperbolic geometric flow and obtain some interesting exact solutions for this kind of flow. Many interesting properties of these exact solutions have also been analyzed and we believe that these properties of Einstein's hyperbolic geometric flow are very helpful to understanding the Einstein equations and the hyperbolic geometric flow.
Generalized geometrically convex functions and inequalities.
Noor, Muhammad Aslam; Noor, Khalida Inayat; Safdar, Farhat
2017-01-01
In this paper, we introduce and study a new class of generalized functions, called generalized geometrically convex functions. We establish several basic inequalities related to generalized geometrically convex functions. We also derive several new inequalities of the Hermite-Hadamard type for generalized geometrically convex functions. Several special cases are discussed, which can be deduced from our main results.
Three dimensional geometric modeling of processing-tomatoes
Characterizing tomato geometries with different shapes and sizes would facilitate the design of tomato processing equipments and promote computer-based engineering simulations. This research sought to develop a three-dimensional geometric model that can describe the morphological attributes of proce...
Absolute instruments and perfect imaging in geometrical optics
Tyc, Tomas; Sarbort, Martin; Bering, Klaus
2011-01-01
We investigate imaging by spherically symmetric absolute instruments that provide perfect imaging in the sense of geometrical optics. We derive a number of properties of such devices, present a general method for designing them and use this method to propose several new absolute instruments, in particular a lens providing a stigmatic image of an optically homogeneous region and having a moderate refractive index range.
Geometric Modeling and Reasoning of Human-Centered Freeform Products
Wang, Charlie C L
2013-01-01
The recent trend in user-customized product design requires the shape of products to be automatically adjusted according to the human body’s shape, so that people will feel more comfortable when wearing these products. Geometric approaches can be used to design the freeform shape of products worn by people, which can greatly improve the efficiency of design processes in various industries involving customized products (e.g., garment design, toy design, jewel design, shoe design, and design of medical devices, etc.). These products are usually composed of very complex geometric shapes (represented by free-form surfaces), and are not driven by a parameter table but a digital human model with free-form shapes or part of human bodies (e.g., wrist, foot, and head models). Geometric Modeling and Reasoning of Human-Centered Freeform Products introduces the algorithms of human body reconstruction, freeform product modeling, constraining and reconstructing freeform products, and shape optimization for improving...
Institute of Scientific and Technical Information of China (English)
李丹; 戎蒙恬; 殳国华
2011-01-01
探讨了几何规划在基于短沟道模型的互补金属氧化物半导体(CMOS)电路中的应用.首先采用Level 1模型得到电路的初始规划,然后将所得元件值代入Hspice仿真程序,再从仿真输出的列表文件中取出各CMOS管的静态电压电流变量和等效小信号模型参数.将它们代入以修正因子为规划变量的几何规划算法,在前一次工作点附近搜索本次的最优设计.修正后的电路再次进行Hspice仿真.几何规划和仿真反复交替进行,直到最优化的目标值稳定.模拟集成电路的仿真实例表明,算法对短沟道模型电路是有效的.%A method of applying geometric programming to complementary metal oxide semiconductor (CMOS) based on short-channel models is described. An original solution based on Level 1 model via geometric programming is obtained first. Then simulate the original circuit by Hspice and acquire important parameters of all CMOS transistors from the output list file. These parameters are used in adjusting software to search the adjusting factors and achieve a new solution near the previous one. Simulating and geometric programming iteratively until the objective of optimization keeps stable. A simulation example proves the algorithm is effective in short-channel techniques.
A history of geometrical methods
Coolidge, Julian Lowell
2013-01-01
Full and authoritative, this history of the techniques for dealing with geometric questions begins with synthetic geometry and its origins in Babylonian and Egyptian mathematics; reviews the contributions of China, Japan, India, and Greece; and discusses the non-Euclidean geometries. Subsequent sections cover algebraic geometry, starting with the precursors and advancing to the great awakening with Descartes; and differential geometry, from the early work of Huygens and Newton to projective and absolute differential geometry. The author's emphasis on proofs and notations, his comparisons betwe
Science, Art and Geometrical Imagination
Luminet, J -P
2009-01-01
From the geocentric, closed world model of Antiquity to the wraparound universe models of relativistic cosmology, the parallel history of space representations in science and art illustrates the fundamental role of geometric imagination in innovative findings. Through the analysis of works of various artists and scientists like Plato, Durer, Kepler, Escher, Grisey or the present author, it is shown how the process of creation in science and in the arts rests on aesthetical principles such as symmetry, regular polyhedra, laws of harmonic proportion, tessellations, group theory, etc., as well as beauty, conciseness and emotional approach of the world.
Science, art and geometrical imagination
Luminet, Jean-Pierre
2011-06-01
From the geocentric, closed world model of Antiquity to the wraparound universe models of relativistic cosmology, the parallel history of space representations in science and art illustrates the fundamental rôle of geometric imagination in innovative findings. Through the analysis of works of various artists and scientists like Plato, Dürer, Kepler, Escher, Grisey or the author, it is shown how the process of creation in science and in the arts rests on aesthetical principles such as symmetry, regular polyhedra, laws of harmonic proportion, tessellations, group theory, etc., as well as on beauty, conciseness and an emotional approach of the world.
Hubbard model with geometrical frustration
Energy Technology Data Exchange (ETDEWEB)
Lee, Hunpyo
2009-10-15
At first we present the details of the dual fermion (DF), the cluster extension of dynamical mean field theory (CDMFT) and continuous-time quantum Monte Carlo (CT QMC) methods. Using a panoply of these methods we explore the Hubbard model on the triangular and hyperkagome lattice. We find a first-order transition and continuous transition on the triangular and hyper-kagome lattice, respectively. Moreover, we find the reentrant behavior due to competition between the magnetic correlation and itinerancy of electrons by source of geometrical frustration on both lattices. (orig.)
Buildings, spiders, and geometric Satake
Fontaine, Bruce; Kuperberg, Greg
2011-01-01
Let G be a simple algebraic group. Labelled trivalent graphs called webs can be used to product invariants in tensor products of minuscule representations. For each web, we construct a configuration space of points in the affine Grassmannian. Via the geometric Satake correspondence, we relate these configuration spaces to the invariant vectors coming from webs. In the case G = SL(3), non-elliptic webs yield a basis for the invariant spaces. The non-elliptic condition, which is equivalent to the condition that the dual diskoid of the web is CAT(0), is explained by the fact that affine buildings are CAT(0).
Geometric Topology and Shape Theory
Segal, Jack
1987-01-01
The aim of this international conference the third of its type was to survey recent developments in Geometric Topology and Shape Theory with an emphasis on their interaction. The volume contains original research papers and carefully selected survey of currently active areas. The main topics and themes represented by the papers of this volume include decomposition theory, cell-like mappings and CE-equivalent compacta, covering dimension versus cohomological dimension, ANR's and LCn-compacta, homology manifolds, embeddings of continua into manifolds, complement theorems in shape theory, approximate fibrations and shape fibrations, fibered shape, exact homologies and strong shape theory.
Geometric Heat Engines Featuring Power that Grows with Efficiency.
Raz, O; Subaşı, Y; Pugatch, R
2016-04-22
Thermodynamics places a limit on the efficiency of heat engines, but not on their output power or on how the power and efficiency change with the engine's cycle time. In this Letter, we develop a geometrical description of the power and efficiency as a function of the cycle time, applicable to an important class of heat engine models. This geometrical description is used to design engine protocols that attain both the maximal power and maximal efficiency at the fast driving limit. Furthermore, using this method, we also prove that no protocol can exactly attain the Carnot efficiency at nonzero power.
Geometric Heat Engines Featuring Power that Grows with Efficiency
Raz, O.; Subaşı, Y.; Pugatch, R.
2016-04-01
Thermodynamics places a limit on the efficiency of heat engines, but not on their output power or on how the power and efficiency change with the engine's cycle time. In this Letter, we develop a geometrical description of the power and efficiency as a function of the cycle time, applicable to an important class of heat engine models. This geometrical description is used to design engine protocols that attain both the maximal power and maximal efficiency at the fast driving limit. Furthermore, using this method, we also prove that no protocol can exactly attain the Carnot efficiency at nonzero power.
Numerical and experimental investigation of geometric parameters in projection welding
DEFF Research Database (Denmark)
Kristensen, Lars; Zhang, Wenqi; Bay, Niels
2000-01-01
Resistance projection welding is widely used for joining of workpieces with almost any geometric combination. This makes standardization of projection welding impossible. In order to facilitate industrial applications of projection welding, systematic investigations are carried out on the geometric...... parameters by numerical modeling and experimental studies. SORPAS, an FEM program for numerical modeling of resistance welding, is developed as a tool to help in the phase of product design and process optimization in both spot and projection welding. A systematic experimental investigation of projection...... welding a disc to a ring with a triangular ring projection has been carried out to study the influence of the geometric parameters in various metal combinations. In these studies, SORPAS has been used as a supporting tool to understand the relationship of the parameters and the phenomena occurring...
Study on geometric correction of airborne multiangular imagery
Institute of Scientific and Technical Information of China (English)
LIU; Qiang; (刘强); LIU; Qinhuo; (柳钦火); XIAO; Qing; (肖青); TIAN; Guoliang; (田国良)
2002-01-01
An automatic image matching algorithm, and its application to geometric correction of airborne multiangular remote sensed imagery, are presented in this paper. The image-matching algorithm is designed to find correct match for images containing localized geometric distortion and spectral variation. Mathematical tools such as wavelet decomposition, B-spline, and multi-variant correlation estimator are integrated in the frame of pyramidal matching. The simulated experiment and our practice in correcting airborne multiangular images show that the matching algorithm is robust to the few random abnormal points and can achieve subpixel match accuracy in most area of the image. After geometric correction and registration, multiangular observations for each ground pixel are extracted and sun/view geometry is also simultaneously derived.
A Mathematical Unification of Geometric Crossovers Defined on Phenotype Space
Yoon, Yourim; Moraglio, Alberto; Moon, Byung-Ro
2009-01-01
Geometric crossover is a representation-independent definition of crossover based on the distance of the search space interpreted as a metric space. It generalizes the traditional crossover for binary strings and other important recombination operators for the most frequently used representations. Using a distance tailored to the problem at hand, the abstract definition of crossover can be used to design new problem specific crossovers that embed problem knowledge in the search. This paper is motivated by the fact that genotype-phenotype mapping can be theoretically interpreted using the concept of quotient space in mathematics. In this paper, we study a metric transformation, the quotient metric space, that gives rise to the notion of quotient geometric crossover. This turns out to be a very versatile notion. We give many example applications of the quotient geometric crossover.
GEOMETRIC TURBULENCE IN GENERAL RELATIVITY
Directory of Open Access Journals (Sweden)
Trunev A. P.
2015-03-01
Full Text Available The article presents the simulation results of the metric of elementary particles, atoms, stars and galaxies in the general theory of relativity and Yang-Mills theory. We have shown metrics and field equations describing the transition to turbulence. The problems of a unified field theory with the turbulent fluctuations of the metric are considered. A transition from the Einstein equations to the diffusion equation and the Schrödinger equation in quantum mechanics is shown. Ther are examples of metrics in which the field equations are reduced to a single equation, it changes type depending on the equation of state. These examples can be seen as a transition to the geometric turbulence. It is shown that the field equations in general relativity can be reduced to a hyperbolic, elliptic or parabolic type. The equation of parabolic type describing the perturbations of the gravitational field on the scale of stars, galaxies and clusters of galaxies, which is a generalization of the theory of gravitation Newton-Poisson in case of Riemannian geometry, taking into account the curvature of space-time has been derived. It was found that the geometric turbulence leads to an exchange between regions of different scale. Under turbulent exchange material formed of two types of clusters, having positive and negative energy density that corresponds to the classical and quantum particle motion respectively. These results allow us to answer the question about the origin of the quantum theory
Geometric decompositions of collective motion
Mischiati, Matteo; Krishnaprasad, P. S.
2017-04-01
Collective motion in nature is a captivating phenomenon. Revealing the underlying mechanisms, which are of biological and theoretical interest, will require empirical data, modelling and analysis techniques. Here, we contribute a geometric viewpoint, yielding a novel method of analysing movement. Snapshots of collective motion are portrayed as tangent vectors on configuration space, with length determined by the total kinetic energy. Using the geometry of fibre bundles and connections, this portrait is split into orthogonal components each tangential to a lower dimensional manifold derived from configuration space. The resulting decomposition, when interleaved with classical shape space construction, is categorized into a family of kinematic modes-including rigid translations, rigid rotations, inertia tensor transformations, expansions and compressions. Snapshots of empirical data from natural collectives can be allocated to these modes and weighted by fractions of total kinetic energy. Such quantitative measures can provide insight into the variation of the driving goals of a collective, as illustrated by applying these methods to a publicly available dataset of pigeon flocking. The geometric framework may also be profitably employed in the control of artificial systems of interacting agents such as robots.
Image coding with geometric wavelets.
Alani, Dror; Averbuch, Amir; Dekel, Shai
2007-01-01
This paper describes a new and efficient method for low bit-rate image coding which is based on recent development in the theory of multivariate nonlinear piecewise polynomial approximation. It combines a binary space partition scheme with geometric wavelet (GW) tree approximation so as to efficiently capture curve singularities and provide a sparse representation of the image. The GW method successfully competes with state-of-the-art wavelet methods such as the EZW, SPIHT, and EBCOT algorithms. We report a gain of about 0.4 dB over the SPIHT and EBCOT algorithms at the bit-rate 0.0625 bits-per-pixels (bpp). It also outperforms other recent methods that are based on "sparse geometric representation." For example, we report a gain of 0.27 dB over the Bandelets algorithm at 0.1 bpp. Although the algorithm is computationally intensive, its time complexity can be significantely reduced by collecting a "global" GW n-term approximation to the image from a collection of GW trees, each constructed separately over tiles of the image.
Measurement error in geometric morphometrics.
Fruciano, Carmelo
2016-06-01
Geometric morphometrics-a set of methods for the statistical analysis of shape once saluted as a revolutionary advancement in the analysis of morphology -is now mature and routinely used in ecology and evolution. However, a factor often disregarded in empirical studies is the presence and the extent of measurement error. This is potentially a very serious issue because random measurement error can inflate the amount of variance and, since many statistical analyses are based on the amount of "explained" relative to "residual" variance, can result in loss of statistical power. On the other hand, systematic bias can affect statistical analyses by biasing the results (i.e. variation due to bias is incorporated in the analysis and treated as biologically-meaningful variation). Here, I briefly review common sources of error in geometric morphometrics. I then review the most commonly used methods to measure and account for both random and non-random measurement error, providing a worked example using a real dataset.
NPP VIIRS Geometric Performance Status
Lin, Guoqing; Wolfe, Robert E.; Nishihama, Masahiro
2011-01-01
Visible Infrared Imager Radiometer Suite (VIIRS) instrument on-board the National Polar-orbiting Operational Environmental Satellite System (NPOESS) Preparatory Project (NPP) satellite is scheduled for launch in October, 2011. It is to provide satellite measured radiance/reflectance data for both weather and climate applications. Along with radiometric calibration, geometric characterization and calibration of Sensor Data Records (SDRs) are crucial to the VIIRS Environmental Data Record (EDR) algorithms and products which are used in numerical weather prediction (NWP). The instrument geometric performance includes: 1) sensor (detector) spatial response, parameterized by the dynamic field of view (DFOV) in the scan direction and instantaneous FOV (IFOV) in the track direction, modulation transfer function (MTF) for the 17 moderate resolution bands (M-bands), and horizontal spatial resolution (HSR) for the five imagery bands (I-bands); 2) matrices of band-to-band co-registration (BBR) from the corresponding detectors in all band pairs; and 3) pointing knowledge and stability characteristics that includes scan plane tilt, scan rate and scan start position variations, and thermally induced variations in pointing with respect to orbital position. They have been calibrated and characterized through ground testing under ambient and thermal vacuum conditions, numerical modeling and analysis. This paper summarizes the results, which are in general compliance with specifications, along with anomaly investigations, and describes paths forward for characterizing on-orbit BBR and spatial response, and for improving instrument on-orbit performance in pointing and geolocation.
Landsat 8 thermal infrared sensor geometric characterization and calibration
Storey, James C.; Choate, Michael J.; Moe, Donald
2014-01-01
The Landsat 8 spacecraft was launched on 11 February 2013 carrying two imaging payloads: the Operational Land Imager (OLI) and the Thermal Infrared Sensor (TIRS). The TIRS instrument employs a refractive telescope design that is opaque to visible wavelengths making prelaunch geometric characterization challenging. TIRS geometric calibration thus relied heavily on on-orbit measurements. Since the two Landsat 8 payloads are complementary and generate combined Level 1 data products, the TIRS geometric performance requirements emphasize the co-alignment of the OLI and TIRS instrument fields of view and the registration of the OLI reflective bands to the TIRS long-wave infrared emissive bands. The TIRS on-orbit calibration procedures include measuring the TIRS-to-OLI alignment, refining the alignment of the three TIRS sensor chips, and ensuring the alignment of the two TIRS spectral bands. The two key TIRS performance metrics are the OLI reflective to TIRS emissive band registration accuracy, and the registration accuracy between the TIRS thermal bands. The on-orbit calibration campaign conducted during the commissioning period provided an accurate TIRS geometric model that enabled TIRS Level 1 data to meet all geometric accuracy requirements. Seasonal variations in TIRS-to-OLI alignment have led to several small calibration parameter adjustments since commissioning.
An Application of the Rasch Measurement Theory to an Assessment of Geometric Thinking Levels
Stols, Gerrit; Long, Caroline; Dunne, Tim
2015-01-01
The purpose of this study is to apply the Rasch model to investigate both the Van Hiele theory for geometric development and an associated test. In terms of the test, the objective is to investigate the functioning of a classic 25-item instrument designed to identify levels of geometric proficiency. The dataset of responses by 244 students (106…
Miranda, Alexandre F; Sampaio, Francisco J B
2014-06-01
A surgical approach with plaque incision and graft (PIG) to correct Peyronie's disease is the best method for complex, large deviations. However, the geometric and mechanical consequences of this intervention are poorly understood. The aim of this study was to analyze the geometric and mechanical consequences of PIG on penile straighten surgery. A tridimensional penile simile model with a curvature of 85° was created to test all of the most common PIG techniques. PIG with double-Y, H-shape, and Egydio techniques were used to rectify the curved penile model. The results that differed from a rectified cylinder shape were highlighted. All of the analyzed techniques created a geometric distortion that could be linked to poor surgical results. We suggest a new technique to resolve these abnormalities. Current techniques designed to correct penile deviation using PIG present geometric and mechanical imperfections with potential consequences to the postoperative success rate. The new technique proposed in this report could be a possible solution to solve the geometric distortion caused by PIG. © 2014 International Society for Sexual Medicine.
On chromatic and geometrical calibration
DEFF Research Database (Denmark)
Folm-Hansen, Jørgen
1999-01-01
of non-uniformity of the illumination of the image plane. Only the image deforming aberrations and the non-uniformity of illumination are included in the calibration models. The topics of the pinhole camera model and the extension to the Direct Linear Transform (DLT) are described. It is shown how......The main subject of the present thesis is different methods for the geometrical and chromatic calibration of cameras in various environments. For the monochromatic issues of the calibration we present the acquisition of monochrome images, the classic monochrome aberrations and the various sources...... the DLT can be extended with non-linear models of the common lens aberrations/errors some of them caused by manufacturing defects like decentering and thin prism distortion. The relation between a warping and the non-linear defects are shown. The issue of making a good resampling of an image by using...
LUNGEOMETRY- GEOMETRICAL INVESTIGATION OF LUNGE
Directory of Open Access Journals (Sweden)
R.Vinodh Rajkumar
2015-02-01
Full Text Available Physiotherapists must learn the biomechanics of lunge in detail to clearly understand its significance in human life and implement effective training measures to overcome the limiting factors of proper lunge of their clientele. To understand the biomechanical value of every movement, interesting experimental learning methods must be employed to kindle the Physiotherapists to actively take part in research activities from the under-graduate level onwards. Lungeometry is a novel, simple and inexpensive experimental investigation of lunge, applying basic geometrical methods taking near normal lower limb length dimensions and rationale approaches into consideration. Lungeometry can give a foundation to learn other forms of lunges like forward lunge, weighted lunges, lateral lunges. This model of learning biomechanics of movements using fundamental geometry techniques is expected to strongly connect with any futuristic Physiotherapy curricular structure.
Geometric interpretation of phyllotaxis transition
Okabe, Takuya
2012-01-01
The original problem of phyllotaxis was focused on the regular arrangements of leaves on mature stems represented by common fractions such as 1/2, 1/3, 2/5, 3/8, 5/13, etc. The phyllotaxis fraction is not fixed for each plant but it may undergo stepwise transitions during ontogeny, despite contrasting observation that the arrangement of leaf primordia at shoot apical meristems changes continuously. No explanation has been given so far for the mechanism of the phyllotaxis transition, excepting suggestion resorting to genetic programs operating at some specific stages. Here it is pointed out that varying length of the leaf trace acts as an important factor to control the transition by analyzing Larson's diagram of the procambial system of young cottonwood plants. The transition is interpreted as a necessary consequence of geometric constraints that the leaf traces cannot be fitted into a fractional pattern unless their length is shorter than the denominator times the internode.
Elastic scattering in geometrical model
Plebaniak, Zbigniew; Wibig, Tadeusz
2016-10-01
The experimental data on proton-proton elastic and inelastic scattering emerging from the measurements at the Large Hadron Collider, calls for an efficient model to fit the data. We have examined the optical, geometrical picture and we have found the simplest, linear dependence of this model parameters on the logarithm of the interaction energy with the significant change of the respective slopes at one point corresponding to the energy of about 300 GeV. The logarithmic dependence observed at high energies allows one to extrapolate the proton-proton elastic, total (and inelastic) cross sections to ultra high energies seen in cosmic rays events which makes a solid justification of the extrapolation to very high energy domain of cosmic rays and could help us to interpret the data from an astrophysical and a high energy physics point of view.
Microlocal Analysis of the Geometric Separation Problem
Donoho, David L
2010-01-01
Image data are often composed of two or more geometrically distinct constituents; in galaxy catalogs, for instance, one sees a mixture of pointlike structures (galaxy superclusters) and curvelike structures (filaments). It would be ideal to process a single image and extract two geometrically `pure' images, each one containing features from only one of the two geometric constituents. This seems to be a seriously underdetermined problem, but recent empirical work achieved highly persuasive separations. We present a theoretical analysis showing that accurate geometric separation of point and curve singularities can be achieved by minimizing the $\\ell_1$ norm of the representing coefficients in two geometrically complementary frames: wavelets and curvelets. Driving our analysis is a specific property of the ideal (but unachievable) representation where each content type is expanded in the frame best adapted to it. This ideal representation has the property that important coefficients are clustered geometrically ...
Geometric solitons of Hamiltonian flows on manifolds
Energy Technology Data Exchange (ETDEWEB)
Song, Chong, E-mail: songchong@xmu.edu.cn [School of Mathematical Sciences, Xiamen University, Xiamen 361005 (China); Sun, Xiaowei, E-mail: sunxw@cufe.edu.cn [School of Applied Mathematics, Central University of Finance and Economics, Beijing 100081 (China); Wang, Youde, E-mail: wyd@math.ac.cn [Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190 (China)
2013-12-15
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.
Manipulation of the geometric and electronic parameters of metal nanocatalysts
Laskar, Moitree
Metal nanoparticles find wide use in the field of catalysis owing to their high surface to volume ratio. The catalytic activity depends on the interaction between the molecular substrate and catalyst surface. This substrate-catalyst interaction can be regulated by manipulating the geometric and electronic parameters of these nanoparticles. The shape and size of the nanoparticles dictate the geometric parameters whereas their composition controls the electronics of these catalysts. Manipulation of these parameters can be used to tune catalytic activities; hence, a better understanding of their regulation will help in designing efficient catalysts. The synthesis and characterization of a series of monometallic Pd and core shell Au Pd nanoparticles with varying shapes and sizes will be discussed in this presentation. These nanocrystals were used to catalyze two model reactions: selective hydrogenation of 2-hexyne and oxidation of formic acid. Comparison of their catalytic activities by varying one parameter at a time (either size or shape) helps to identify the effect of geometric parameters on catalysis. Additionally, comparison of particles with varying composition but same geometric features provides insight into how the electronics underlying the catalysis can be manipulated through nanostructure architecture. We find that a balance in binding interaction between the substrate and catalyst surface is necessary to design an efficient catalyst and can be achieved with shape-controlled core shell nanocrystals.
Geometric Photonic Spin Hall Effect with Metapolarization
2014-01-01
We develop a geometric photonic spin Hall effect (PSHE) which manifests as spin-dependent shift in momentum space. It originates from an effective space-variant Pancharatnam-Berry (PB) phase created by artificially engineering the polarization distribution of the incident light. Unlikely the previously reported PSHE involving the light-matter interaction, the resulting spin-dependent splitting in the geometric PSHE is purely geometrically depend upon the polarization distribution of light whi...
A Geometric Approach to Noncommutative Principal Bundles
Wagner, Stefan
2011-01-01
From a geometrical point of view it is, so far, not sufficiently well understood what should be a "noncommutative principal bundle". Still, there is a well-developed abstract algebraic approach using the theory of Hopf algebras. An important handicap of this approach is the ignorance of topological and geometrical aspects. The aim of this thesis is to develop a geometrically oriented approach to the noncommutative geometry of principal bundles based on dynamical systems and the representation theory of the corresponding transformation group.
Guide to Geometric Algebra in Practice
Dorst, Leo
2011-01-01
This highly practical "Guide to Geometric Algebra in Practice" reviews algebraic techniques for geometrical problems in computer science and engineering, and the relationships between them. The topics covered range from powerful new theoretical developments, to successful applications, and the development of new software and hardware tools. This title: provides hands-on review exercises throughout the book, together with helpful chapter summaries; presents a concise introductory tutorial to conformal geometric algebra (CGA) in the appendices; examines the application of CGA for the d
Free-form geometric modeling by integrating parametric and implicit PDEs.
Du, Haixia; Qin, Hong
2007-01-01
Parametric PDE techniques, which use partial differential equations (PDEs) defined over a 2D or 3D parametric domain to model graphical objects and processes, can unify geometric attributes and functional constraints of the models. PDEs can also model implicit shapes defined by level sets of scalar intensity fields. In this paper, we present an approach that integrates parametric and implicit trivariate PDEs to define geometric solid models containing both geometric information and intensity distribution subject to flexible boundary conditions. The integrated formulation of second-order or fourth-order elliptic PDEs permits designers to manipulate PDE objects of complex geometry and/or arbitrary topology through direct sculpting and free-form modeling. We developed a PDE-based geometric modeling system for shape design and manipulation of PDE objects. The integration of implicit PDEs with parametric geometry offers more general and arbitrary shape blending and free-form modeling for objects with intensity attributes than pure geometric models.
Islamic geometric patterns their historical development and traditional methods of construction
Bonner, Jay
2017-01-01
The main focus of this unique book is an in-depth examination of the polygonal technique; the primary method used by master artists of the past in creating Islamic geometric patterns. The author details the design methodology responsible for this all-but-lost art form and presents evidence for its use from the historical record, both of which are vital contributions to the understanding of this ornamental tradition. Additionally, the author examines the historical development of Islamic geometric patterns, the significance of geometric design within the broader context of Islamic ornament as a whole, the formative role that geometry plays throughout the Islamic ornamental arts (including calligraphy, the floral idiom, dome decoration, geometric patterns, and more), and the underexamined question of pattern classification. Featuring over 600 beautiful color images, Islamic Geometric Patterns: Their Historical Development and Traditional Methods of Construction is a valuable addition to the literature of Islam...
Report on Workshop on Geometric Scattering
DEFF Research Database (Denmark)
As part of the activities of MaPhySto a workshop on geometric scattering was organized at University of Aarhus, November 5-7, 1998. The workshop was narrowly focused on geometric scattering, and in particular the use of geometric scattering in understanding the structure of the scattering operator...... for the quantum mechanical many-body problem. A number of other questions were also discussed in detail, including the resonances and various geometric questions. This report includes the program of the workshop, a collection of previews, abstracts, and reports on the lectures, with extensive references....
Higher-Dimensional Geometric $\\sigma$-Models
Vasilic, M
1999-01-01
Geometric $\\sigma$-models have been defined as purely geometric theories of scalar fields coupled to gravity. By construction, these theories possess arbitrarily chosen vacuum solutions. Using this fact, one can build a Kaluza--Klein geometric $\\sigma$-model by specifying the vacuum metric of the form $M^4\\times B^d$. The obtained higher dimensional theory has vanishing cosmological constant but fails to give massless gauge fields after the dimensional reduction. In this paper, a modified geometric $\\sigma$-model is suggested, which solves the above problem.
Adiabatic geometric phases in hydrogenlike atoms
Sjöqvist, Erik; Yi, X. X.; Åberg, Johan
2005-11-01
We examine the effect of spin-orbit coupling on geometric phases in hydrogenlike atoms exposed to a slowly varying magnetic field. The marginal geometric phases associated with the orbital angular momentum and the intrinsic spin fulfill a sum rule that explicitly relates them to the corresponding geometric phase of the whole system. The marginal geometric phases in the Zeeman and Paschen-Back limits are analyzed. We point out the existence of nodal points in the marginal phases that may be detected by topological means.
Adiabatic geometric phases in hydrogenlike atoms
Sjöqvist, E; Sj\\"{o}qvist, Erik
2005-01-01
We examine the effect of spin-orbit coupling on geometric phases in hydrogenlike atoms exposed to a slowly varying magnetic field. The marginal geometric phases associated with the orbital angular momentum and the intrinsic spin fulfill a sum rule that explicitly relates them to the corresponding geometric phase of the whole system. The marginal geometric phases in the Zeeman and Paschen-Back limit are analyzed. We point out the existence of nodal points in the marginal phases that may be detected by topological means.
Observer-based FDI for Gain Fault Detection in Ship Propulsion Benchmark:a Geometric Approach
Lootsma, T.F.; Izadi-Zamanabadi, Roozbeh; Nijmeijer, H.
2001-01-01
A geometric approach for input-affine nonlinear systems is briefly described and then applied to a ship propulsion benchmark. The obtained results are used to design a diagnostic nonlinear observer for successful FDI of the diesel engine gain fault
Geometric reasoning about assembly tools
Energy Technology Data Exchange (ETDEWEB)
Wilson, R.H.
1997-01-01
Planning for assembly requires reasoning about various tools used by humans, robots, or other automation to manipulate, attach, and test parts and subassemblies. This paper presents a general framework to represent and reason about geometric accessibility issues for a wide variety of such assembly tools. Central to the framework is a use volume encoding a minimum space that must be free in an assembly state to apply a given tool, and placement constraints on where that volume must be placed relative to the parts on which the tool acts. Determining whether a tool can be applied in a given assembly state is then reduced to an instance of the FINDPLACE problem. In addition, the author presents more efficient methods to integrate the framework into assembly planning. For tools that are applied either before or after their target parts are mated, one method pre-processes a single tool application for all possible states of assembly of a product in polynomial time, reducing all later state-tool queries to evaluations of a simple expression. For tools applied after their target parts are mated, a complementary method guarantees polynomial-time assembly planning. The author presents a wide variety of tools that can be described adequately using the approach, and surveys tool catalogs to determine coverage of standard tools. Finally, the author describes an implementation of the approach in an assembly planning system and experiments with a library of over one hundred manual and robotic tools and several complex assemblies.
Simulating geometrically complex blast scenarios
Directory of Open Access Journals (Sweden)
Ian G. Cullis
2016-04-01
Full Text Available The effects of blast waves generated by energetic and non-energetic sources are of continuing interest to the ballistics research community. Modern conflicts are increasingly characterised by asymmetric urban warfare, with improvised explosive devices (IEDs often playing a dominant role on the one hand and an armed forces requirement for minimal collateral effects from their weapons on the other. These problems are characterised by disparate length- and time-scales and may also be governed by complex physics. There is thus an increasing need to be able to rapidly assess and accurately predict the effects of energetic blast in topologically complex scenarios. To this end, this paper presents a new QinetiQ-developed advanced computational package called EAGLE-Blast, which is capable of accurately resolving the generation, propagation and interaction of blast waves around geometrically complex shapes such as vehicles and buildings. After a brief description of the numerical methodology, various blast scenario simulations are described and the results compared with experimental data to demonstrate the validation of the scheme and its ability to describe these complex scenarios accurately and efficiently. The paper concludes with a brief discussion on the use of the code in supporting the development of algorithms for fast running engineering models.
Generalized Geometric Quantum Speed Limits
Pires, Diego Paiva; Cianciaruso, Marco; Céleri, Lucas C.; Adesso, Gerardo; Soares-Pinto, Diogo O.
2016-04-01
The attempt to gain a theoretical understanding of the concept of time in quantum mechanics has triggered significant progress towards the search for faster and more efficient quantum technologies. One of such advances consists in the interpretation of the time-energy uncertainty relations as lower bounds for the minimal evolution time between two distinguishable states of a quantum system, also known as quantum speed limits. We investigate how the nonuniqueness of a bona fide measure of distinguishability defined on the quantum-state space affects the quantum speed limits and can be exploited in order to derive improved bounds. Specifically, we establish an infinite family of quantum speed limits valid for unitary and nonunitary evolutions, based on an elegant information geometric formalism. Our work unifies and generalizes existing results on quantum speed limits and provides instances of novel bounds that are tighter than any established one based on the conventional quantum Fisher information. We illustrate our findings with relevant examples, demonstrating the importance of choosing different information metrics for open system dynamics, as well as clarifying the roles of classical populations versus quantum coherences, in the determination and saturation of the speed limits. Our results can find applications in the optimization and control of quantum technologies such as quantum computation and metrology, and might provide new insights in fundamental investigations of quantum thermodynamics.
Simulating geometrically complex blast scenarios
Institute of Scientific and Technical Information of China (English)
Ian G. CULLIS; Nikos NIKIFORAKIS; Peter FRANKL; Philip BLAKELY; Paul BENNETT; Paul GREENWOOD
2016-01-01
The effects of blast waves generated by energetic and non-energetic sources are of continuing interest to the ballistics research community. Modern conflicts are increasingly characterised by asymmetric urban warfare, with improvised explosive devices (IEDs) often playing a dominant role on the one hand and an armed forces requirement for minimal collateral effects from their weapons on the other. These problems are characterised by disparate length-and time-scales and may also be governed by complex physics. There is thus an increasing need to be able to rapidly assess and accurately predict the effects of energetic blast in topologically complex scenarios. To this end, this paper presents a new QinetiQ-developed advanced computational package called EAGLE-Blast, which is capable of accurately resolving the generation, propagation and interaction of blast waves around geometrically complex shapes such as vehicles and buildings. After a brief description of the numerical methodology, various blast scenario simulations are described and the results compared with experimental data to demonstrate the validation of the scheme and its ability to describe these complex scenarios accurately and efficiently. The paper concludes with a brief discussion on the use of the code in supporting the development of algorithms for fast running engineering models.
Geometric Reasoning for Automated Planning
Clement, Bradley J.; Knight, Russell L.; Broderick, Daniel
2012-01-01
An important aspect of mission planning for NASA s operation of the International Space Station is the allocation and management of space for supplies and equipment. The Stowage, Configuration Analysis, and Operations Planning teams collaborate to perform the bulk of that planning. A Geometric Reasoning Engine is developed in a way that can be shared by the teams to optimize item placement in the context of crew planning. The ISS crew spends (at the time of this writing) a third or more of their time moving supplies and equipment around. Better logistical support and optimized packing could make a significant impact on operational efficiency of the ISS. Currently, computational geometry and motion planning do not focus specifically on the optimized orientation and placement of 3D objects based on multiple distance and containment preferences and constraints. The software performs reasoning about the manipulation of 3D solid models in order to maximize an objective function based on distance. It optimizes for 3D orientation and placement. Spatial placement optimization is a general problem and can be applied to object packing or asset relocation.
Generalized Geometric Quantum Speed Limits
Directory of Open Access Journals (Sweden)
Diego Paiva Pires
2016-06-01
Full Text Available The attempt to gain a theoretical understanding of the concept of time in quantum mechanics has triggered significant progress towards the search for faster and more efficient quantum technologies. One of such advances consists in the interpretation of the time-energy uncertainty relations as lower bounds for the minimal evolution time between two distinguishable states of a quantum system, also known as quantum speed limits. We investigate how the nonuniqueness of a bona fide measure of distinguishability defined on the quantum-state space affects the quantum speed limits and can be exploited in order to derive improved bounds. Specifically, we establish an infinite family of quantum speed limits valid for unitary and nonunitary evolutions, based on an elegant information geometric formalism. Our work unifies and generalizes existing results on quantum speed limits and provides instances of novel bounds that are tighter than any established one based on the conventional quantum Fisher information. We illustrate our findings with relevant examples, demonstrating the importance of choosing different information metrics for open system dynamics, as well as clarifying the roles of classical populations versus quantum coherences, in the determination and saturation of the speed limits. Our results can find applications in the optimization and control of quantum technologies such as quantum computation and metrology, and might provide new insights in fundamental investigations of quantum thermodynamics.
Geometrical aspects of quantum spaces
Energy Technology Data Exchange (ETDEWEB)
Ho, P.M. [Lawrence Berkeley Lab., CA (United States). Theoretical Physics Group
1996-05-11
Various geometrical aspects of quantum spaces are presented showing the possibility of building physics on quantum spaces. In the first chapter the authors give the motivations for studying noncommutative geometry and also review the definition of a Hopf algebra and some general features of the differential geometry on quantum groups and quantum planes. In Chapter 2 and Chapter 3 the noncommutative version of differential calculus, integration and complex structure are established for the quantum sphere S{sub 1}{sup 2} and the quantum complex projective space CP{sub q}(N), on which there are quantum group symmetries that are represented nonlinearly, and are respected by all the aforementioned structures. The braiding of S{sub q}{sup 2} and CP{sub q}(N) is also described. In Chapter 4 the quantum projective geometry over the quantum projective space CP{sub q}(N) is developed. Collinearity conditions, coplanarity conditions, intersections and anharmonic ratios is described. In Chapter 5 an algebraic formulation of Reimannian geometry on quantum spaces is presented where Riemannian metric, distance, Laplacian, connection, and curvature have their quantum counterparts. This attempt is also extended to complex manifolds. Examples include the quantum sphere, the complex quantum projective space and the two-sheeted space. The quantum group of general coordinate transformations on some quantum spaces is also given.
Geometrical splitting and reduction of Feynman diagrams
Davydychev, Andrei I.
2016-10-01
A geometrical approach to the calculation of N-point Feynman diagrams is reviewed. It is shown that the geometrical splitting yields useful connections between Feynman integrals with different momenta and masses. It is demonstrated how these results can be used to reduce the number of variables in the occurring functions.
Parabolas: Connection between Algebraic and Geometrical Representations
Shriki, Atara
2011-01-01
A parabola is an interesting curve. What makes it interesting at the secondary school level is the fact that this curve is presented in both its contexts: algebraic and geometric. Being one of Apollonius' conic sections, the parabola is basically a geometric entity. It is, however, typically known for its algebraic characteristics, in particular…
Some technical issues in geometric modeling
Energy Technology Data Exchange (ETDEWEB)
Peterson, D.P.
1983-01-01
The full impact of CAD/CAM will not be felt until geometric modeling systems support dimensioning and tolerancing, have sophisticated user interfaces, and are capable of routinely handling many representation conversions. The attainment of these capabilities requires a joint effort among users, implementors, and theoreticians of geometric modeling.
Geometric Growing Patterns: What's the Rule?
Hourigan, Mairéad; Leavy, Aisling
2015-01-01
While within a geometric repeating pattern, there is an identifiable core which is made up of objects that repeat in a predictable manner, a geometric growing pattern (also called visual or pictorial growing patterns in other curricula) "is a pattern that is made from a sequence of figures [or objects] that change from one term to the next in…
Sudan-decoding generalized geometric Goppa codes
DEFF Research Database (Denmark)
Heydtmann, Agnes Eileen
2003-01-01
Generalized geometric Goppa codes are vector spaces of n-tuples with entries from different extension fields of a ground field. They are derived from evaluating functions similar to conventional geometric Goppa codes, but allowing evaluation in places of arbitrary degree. A decoding scheme...
A Framework for Analyzing Geometric Pattern Tasks
Friel, Susan N.; Markworth, Kimberly A.
2009-01-01
Teachers can use geometric patterns to promote students' understanding of functional relationships. In this article, the authors first look at a problem-solving process that supports the use of figural reasoning to explore and interpret geometric pattern tasks and generalize function rules. Second, the authors discuss a framework for…
On geometric Langlands theory and stacks
Poirier, Cécile Florence Christine
2008-01-01
R.Langlands conjectured the existence of a bridge between two parts of number theory. This correspondence, called 'Langlands conjecture' was proved by L. Lafforgue who obtained a Fields medal for his work. G. Laumon gave a geometric translation of a part of the theorem, called 'geometric Langlands c
Geometrical optics and the diffraction phenomenon
Energy Technology Data Exchange (ETDEWEB)
Timofeev, Aleksandr V [Russian Research Centre ' Kurchatov Institute' , Moscow (Russian Federation)
2005-06-30
This note outlines the principles of the geometrical optics of inhomogeneous waves whose description necessitates the use of complex values of the wave vector. Generalizing geometrical optics to inhomogeneous waves permits including in its scope the analysis of the diffraction phenomenon. (methodological notes)
Variance optimal stopping for geometric Levy processes
DEFF Research Database (Denmark)
Gad, Kamille Sofie Tågholt; Pedersen, Jesper Lund
2015-01-01
The main result of this paper is the solution to the optimal stopping problem of maximizing the variance of a geometric Lévy process. We call this problem the variance problem. We show that, for some geometric Lévy processes, we achieve higher variances by allowing randomized stopping. Furthermore...
Geometrical description of denormalized thermodynamic manifold
Institute of Scientific and Technical Information of China (English)
Wu Li-Ping; Sun Hua-Fei; Cao Li-Mei
2009-01-01
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.
The geometric semantics of algebraic quantum mechanics.
Cruz Morales, John Alexander; Zilber, Boris
2015-08-06
In this paper, we will present an ongoing project that aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We argue that this approach provides a geometric semantics for such a formalism by means of establishing a (non-commutative) duality between certain algebraic and geometric objects.
Geometric phases in discrete dynamical systems
Energy Technology Data Exchange (ETDEWEB)
Cartwright, Julyan H.E., E-mail: julyan.cartwright@csic.es [Instituto Andaluz de Ciencias de la Tierra, CSIC–Universidad de Granada, E-18100 Armilla, Granada (Spain); Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071 Granada (Spain); Piro, Nicolas, E-mail: nicolas.piro@epfl.ch [École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne (Switzerland); Piro, Oreste, E-mail: piro@imedea.uib-csic.es [Departamento de Física, Universitat de les Illes Balears, E-07122 Palma de Mallorca (Spain); Tuval, Idan, E-mail: ituval@imedea.uib-csic.es [Mediterranean Institute for Advanced Studies, CSIC–Universitat de les Illes Balears, E-07190 Mallorca (Spain)
2016-10-14
In order to study the behaviour of discrete dynamical systems under adiabatic cyclic variations of their parameters, we consider discrete versions of adiabatically-rotated rotators. Parallelling the studies in continuous systems, we generalize the concept of geometric phase to discrete dynamics and investigate its presence in these rotators. For the rotated sine circle map, we demonstrate an analytical relationship between the geometric phase and the rotation number of the system. For the discrete version of the rotated rotator considered by Berry, the rotated standard map, we further explore this connection as well as the role of the geometric phase at the onset of chaos. Further into the chaotic regime, we show that the geometric phase is also related to the diffusive behaviour of the dynamical variables and the Lyapunov exponent. - Highlights: • We extend the concept of geometric phase to maps. • For the rotated sine circle map, we demonstrate an analytical relationship between the geometric phase and the rotation number. • For the rotated standard map, we explore the role of the geometric phase at the onset of chaos. • We show that the geometric phase is related to the diffusive behaviour of the dynamical variables and the Lyapunov exponent.
Geometric integrators for stochastic rigid body dynamics
Tretyakov, Mikhail
2016-01-05
Geometric integrators play an important role in simulating dynamical systems on long time intervals with high accuracy. We will illustrate geometric integration ideas within the stochastic context, mostly on examples of stochastic thermostats for rigid body dynamics. The talk will be mainly based on joint recent work with Rusland Davidchak and Tom Ouldridge.
Minimum length scale in topology optimization by geometric constraints
DEFF Research Database (Denmark)
Zhou, Mingdong; Lazarov, Boyan Stefanov; Wang, Fengwen
2015-01-01
A density-based topology optimization approach is proposed to design structures with strict minimum length scale. The idea is based on using a filtering-threshold topology optimization scheme and computationally cheap geometric constraints. The constraints are defined over the underlying structural...... geometry represented by the filtered and physical fields. Satisfying the constraints leads to a design that possesses user-specified minimum length scale. Conventional topology optimization problems can be augmented with the proposed constraints to achieve minimum length scale on the final design....... No additional finite element analysis is required for the constrained optimization. Several benchmark examples are presented to show the effectiveness of this approach....
Rule-based transformations for geometric modelling
Directory of Open Access Journals (Sweden)
Thomas Bellet
2011-02-01
Full Text Available The context of this paper is the use of formal methods for topology-based geometric modelling. Topology-based geometric modelling deals with objects of various dimensions and shapes. Usually, objects are defined by a graph-based topological data structure and by an embedding that associates each topological element (vertex, edge, face, etc. with relevant data as their geometric shape (position, curve, surface, etc. or application dedicated data (e.g. molecule concentration level in a biological context. We propose to define topology-based geometric objects as labelled graphs. The arc labelling defines the topological structure of the object whose topological consistency is then ensured by labelling constraints. Nodes have as many labels as there are different data kinds in the embedding. Labelling constraints ensure then that the embedding is consistent with the topological structure. Thus, topology-based geometric objects constitute a particular subclass of a category of labelled graphs in which nodes have multiple labels.
Rule-based transformations for geometric modelling
Bellet, Thomas; Gall, Pascale Le; 10.4204/EPTCS.48.5
2011-01-01
The context of this paper is the use of formal methods for topology-based geometric modelling. Topology-based geometric modelling deals with objects of various dimensions and shapes. Usually, objects are defined by a graph-based topological data structure and by an embedding that associates each topological element (vertex, edge, face, etc.) with relevant data as their geometric shape (position, curve, surface, etc.) or application dedicated data (e.g. molecule concentration level in a biological context). We propose to define topology-based geometric objects as labelled graphs. The arc labelling defines the topological structure of the object whose topological consistency is then ensured by labelling constraints. Nodes have as many labels as there are different data kinds in the embedding. Labelling constraints ensure then that the embedding is consistent with the topological structure. Thus, topology-based geometric objects constitute a particular subclass of a category of labelled graphs in which nodes hav...
Wegman, F.C.M. Dijkstra, A. Schermers, G. & Vliet, P. van
2005-01-01
Human errors play a vital role in road crashes. This paper deals with the prevention of human errors by proper road planning, road design and improving existing roads within the framework of the Dutch 'Sustainable Safety' vision. This vision focuses on three design principles for road networks and f
Coordination and geometric optimization via distributed dynamical systems
Cortes, Jorge; Bullo, Francesco
2003-01-01
This paper discusses dynamical systems for disk-covering and sphere-packing problems. We present facility location functions from geometric optimization and characterize their differentiable properties. We design and analyze a collection of distributed control laws that are related to nonsmooth gradient systems. The resulting dynamical systems promise to be of use in coordination problems for networked robots; in this setting the distributed control laws correspond to local interactions betwe...
A Mathematical Unification of Geometric Crossovers Defined on Phenotype Space
Yoon, Yourim; Kim, Yong-Hyuk; Moraglio, Alberto; Moon, Byung-Ro
2009-01-01
Geometric crossover is a representation-independent definition of crossover based on the distance of the search space interpreted as a metric space. It generalizes the traditional crossover for binary strings and other important recombination operators for the most frequently used representations. Using a distance tailored to the problem at hand, the abstract definition of crossover can be used to design new problem specific crossovers that embed problem knowledge in the search. This paper is...
Mobility in geometrically confined membranes.
Domanov, Yegor A; Aimon, Sophie; Toombes, Gilman E S; Renner, Marianne; Quemeneur, François; Triller, Antoine; Turner, Matthew S; Bassereau, Patricia
2011-08-02
Lipid and protein lateral mobility is essential for biological function. Our theoretical understanding of this mobility can be traced to the seminal work of Saffman and Delbrück, who predicted a logarithmic dependence of the protein diffusion coefficient (i) on the inverse of the size of the protein and (ii) on the "membrane size" for membranes of finite size [Saffman P, Delbrück M (1975) Proc Natl Acad Sci USA 72:3111-3113]. Although the experimental proof of the first prediction is a matter of debate, the second has not previously been thought to be experimentally accessible. Here, we construct just such a geometrically confined membrane by forming lipid bilayer nanotubes of controlled radii connected to giant liposomes. We followed the diffusion of individual molecules in the tubular membrane using single particle tracking of quantum dots coupled to lipids or voltage-gated potassium channels KvAP, while changing the membrane tube radius from approximately 250 to 10 nm. We found that both lipid and protein diffusion was slower in tubular membranes with smaller radii. The protein diffusion coefficient decreased as much as 5-fold compared to diffusion on the effectively flat membrane of the giant liposomes. Both lipid and protein diffusion data are consistent with the predictions of a hydrodynamic theory that extends the work of Saffman and Delbrück to cylindrical geometries. This study therefore provides strong experimental support for the ubiquitous Saffman-Delbrück theory and elucidates the role of membrane geometry and size in regulating lateral diffusion.
Geometric characterization of polymeric macrofibers
Directory of Open Access Journals (Sweden)
A. R. E. Cáceres
Full Text Available ABSTRACTThe geometric characteristics of synthetic macrofibers are important because they affect the behavior of fiber-reinforced concrete (FRC. Because there is a lack of specific, relevant publications in Brazil, the European standard EN14889-2:2006 was adopted as a reference to perform the characterization. Thus, an experimental plan was developed to assess the adequacy of testing procedures for the qualification of synthetic macrofibers for use in FRC. Two types of macrofibers were evaluated. The length measurement was performed using two methods: the caliper method, which is a manual measurement, and the digital image analysis method using the ImageJ software for image processing. These aforementioned methods were used to determine the diameter together with the density method, which is an indirect method that uses the developed length obtained by one of the previous methods. The statistical analyses revealed that the length results are similar regardless of the method used. However, the macrofibers must be pre-stretched to maximize the accuracy of caliper measurements. The caliper method for diameter determination has the disadvantage of underestimating the macrofiber cross-section because of the pressure applied by the load claws. In contrast, the digital image analysis method obtains the projected diameter in a single plane, which overestimate the diameter because the macrofibers are oriented with the pressure of the scanner cover. Thus, these techniques may result in false projections of the diameters that will depend on the level of torsion in the macrofibers. It was concluded that both the caliper method using previously stretched macrofibers and the digital imaging method can be used to measure length. The density method presented the best results for the diameter determination because these results were not affected by the method chosen to determine the length.
On geometric factors for neutral particle analyzers.
Stagner, L; Heidbrink, W W
2014-11-01
Neutral particle analyzers (NPA) detect neutralized energetic particles that escape from plasmas. Geometric factors relate the counting rate of the detectors to the intensity of the particle source. Accurate geometric factors enable quick simulation of geometric effects without the need to resort to slower Monte Carlo methods. Previously derived expressions [G. R. Thomas and D. M. Willis, "Analytical derivation of the geometric factor of a particle detector having circular or rectangular geometry," J. Phys. E: Sci. Instrum. 5(3), 260 (1972); J. D. Sullivan, "Geometric factor and directional response of single and multi-element particle telescopes," Nucl. Instrum. Methods 95(1), 5-11 (1971)] for the geometric factor implicitly assume that the particle source is very far away from the detector (far-field); this excludes applications close to the detector (near-field). The far-field assumption does not hold in most fusion applications of NPA detectors. We derive, from probability theory, a generalized framework for deriving geometric factors that are valid for both near and far-field applications as well as for non-isotropic sources and nonlinear particle trajectories.
Conceptual aspects of geometric quantum computation
Sjöqvist, Erik; Azimi Mousolou, Vahid; Canali, Carlo M.
2016-10-01
Geometric quantum computation is the idea that geometric phases can be used to implement quantum gates, i.e., the basic elements of the Boolean network that forms a quantum computer. Although originally thought to be limited to adiabatic evolution, controlled by slowly changing parameters, this form of quantum computation can as well be realized at high speed by using nonadiabatic schemes. Recent advances in quantum gate technology have allowed for experimental demonstrations of different types of geometric gates in adiabatic and nonadiabatic evolution. Here, we address some conceptual issues that arise in the realizations of geometric gates. We examine the appearance of dynamical phases in quantum evolution and point out that not all dynamical phases need to be compensated for in geometric quantum computation. We delineate the relation between Abelian and non-Abelian geometric gates and find an explicit physical example where the two types of gates coincide. We identify differences and similarities between adiabatic and nonadiabatic realizations of quantum computation based on non-Abelian geometric phases.
Efficient Geometric Sound Propagation Using Visibility Culling
Chandak, Anish
2011-07-01
Simulating propagation of sound can improve the sense of realism in interactive applications such as video games and can lead to better designs in engineering applications such as architectural acoustics. In this thesis, we present geometric sound propagation techniques which are faster than prior methods and map well to upcoming parallel multi-core CPUs. We model specular reflections by using the image-source method and model finite-edge diffraction by using the well-known Biot-Tolstoy-Medwin (BTM) model. We accelerate the computation of specular reflections by applying novel visibility algorithms, FastV and AD-Frustum, which compute visibility from a point. We accelerate finite-edge diffraction modeling by applying a novel visibility algorithm which computes visibility from a region. Our visibility algorithms are based on frustum tracing and exploit recent advances in fast ray-hierarchy intersections, data-parallel computations, and scalable, multi-core algorithms. The AD-Frustum algorithm adapts its computation to the scene complexity and allows small errors in computing specular reflection paths for higher computational efficiency. FastV and our visibility algorithm from a region are general, object-space, conservative visibility algorithms that together significantly reduce the number of image sources compared to other techniques while preserving the same accuracy. Our geometric propagation algorithms are an order of magnitude faster than prior approaches for modeling specular reflections and two to ten times faster for modeling finite-edge diffraction. Our algorithms are interactive, scale almost linearly on multi-core CPUs, and can handle large, complex, and dynamic scenes. We also compare the accuracy of our sound propagation algorithms with other methods. Once sound propagation is performed, it is desirable to listen to the propagated sound in interactive and engineering applications. We can generate smooth, artifact-free output audio signals by applying
The Geometric Field at a Josephson Junction
Atanasov, Victor
2016-01-01
A geometric potential from the kinetic term of a constrained to a curved hyper-plane of space-time quantum superconducting condensate is derived. An energy conservation relation involving the geometric field at every material point in the superconductor is demonstrated. At a Josephson junction the energy conservation relation implies the possibility to transform electric energy into geometric field energy, that is curvature of space-time. Experimental procedures to verify that the Josephson junction can act as a voltage-to-curvature converter are discussed.
A physics perspective on geometric Langlands duality
Schlesinger, Karl-Georg
2009-01-01
We review the approach to the geometric Langlands program for algebraic curves via S-duality of an N=4 supersymmetric four dimensional gauge theory, initiated by Kapustin and Witten in 2006. We sketch some of the central further developments. Placing this four dimensional gauge theory into a six dimensional framework, as advocated by Witten, holds the promise to lead to a formulation which makes geometric Langlands duality a manifest symmetry (like coavariance in differential geometry). Furthermore, it leads to an approach toward geometric Langlands duality for algebraic surfaces, reproducing and extending the recent results of Braverman and Finkelberg.
A Geometric Characterization of Arithmetic Varieties
Indian Academy of Sciences (India)
Kapil Hari Paranjape
2002-08-01
A result of Belyi can be stated as follows. Every curve defined over a number field can be expressed as a cover of the projective line with branch locus contained in a rigid divisor. We define the notion of geometrically rigid divisors in surfaces and then show that every surface defined over a number field can be expressed as a cover of the projective plane with branch locus contained in a geometrically rigid divisor in the plane. The main result is the characterization of arithmetically defined divisors in the plane as geometrically rigid divisors in the plane.
Geometric-Phase Polarization Fan-out Grating Fabricated with Deep-UV Interference Lithography
Wan, Chenhao; Lombardo, David; Sarangan, Andrew; Zhan, Qiwen
2017-06-01
We report the design, fabrication and testing of a highly efficient polarization fan-out grating for coherent beam combining working at 1550 nm. The grating design exploits the geometric-phase effect. Deep-UV interference lithography is used to fabricate the designed grating. Such a polarization fan-out grating demonstrates several advantages that are ideal for laser beam combining.
Exotic geometric structures on Kodaira surfaces
McKay, Benjamin
2012-01-01
On all compact complex surfaces (modulo finite unramified coverings), we classify all of the locally homogeneous geometric structures which are locally isomorphic to the exotic homogeneous surfaces of Lie.
Hidden geometric correlations in real multiplex networks
Kleineberg, Kaj-Kolja; Boguñá, Marián; Ángeles Serrano, M.; Papadopoulos, Fragkiskos
2016-11-01
Real networks often form interacting parts of larger and more complex systems. Examples can be found in different domains, ranging from the Internet to structural and functional brain networks. Here, we show that these multiplex systems are not random combinations of single network layers. Instead, they are organized in specific ways dictated by hidden geometric correlations between the layers. We find that these correlations are significant in different real multiplexes, and form a key framework for answering many important questions. Specifically, we show that these geometric correlations facilitate the definition and detection of multidimensional communities, which are sets of nodes that are simultaneously similar in multiple layers. They also enable accurate trans-layer link prediction, meaning that connections in one layer can be predicted by observing the hidden geometric space of another layer. And they allow efficient targeted navigation in the multilayer system using only local knowledge, outperforming navigation in the single layers only if the geometric correlations are sufficiently strong.
Study on the Grey Polynomial Geometric Programming
Institute of Scientific and Technical Information of China (English)
LUODang
2005-01-01
In the model of geometric programming, values of parameters cannot be gotten owing to data fluctuation and incompletion. But reasonable bounds of these parameters can be attained. This is to say, parameters of this model can be regarded as interval grey numbers. When the model contains grey numbers, it is hard for common programming method to solve them. By combining the common programming model with the grey system theory,and using some analysis strategies, a model of grey polynomial geometric programming, a model of 8 positioned geometric programming and their quasi-optimum solution or optimum solution are put forward. At the same time, we also developed an algorithm for the problem.This approach brings a new way for the application research of geometric programming. An example at the end of this paper shows the rationality and feasibility of the algorithm.
A geometric approach to acyclic orientations
Ehrenborg, Richard
2009-01-01
The set of acyclic orientations of a connected graph with a given sink has a natural poset structure. We give a geometric proof of a result of Jim Propp: this poset is the disjoint union of distributive lattices.
Concepts and Figures in Geometric Reasoning.
Fischbein, Efraim; Nachlieli, Talli
1998-01-01
Opens with the theoretical construct of figural concepts. Argues that geometrical figures are characterized by both conceptual and sensorial properties. Investigates the effects of interaction between conceptual and figural components. Contains 19 references. (DDR)
Geometric continuum mechanics and induced beam theories
R Eugster, Simon
2015-01-01
This research monograph discusses novel approaches to geometric continuum mechanics and introduces beams as constraint continuous bodies. In the coordinate free and metric independent geometric formulation of continuum mechanics as well as for beam theories, the principle of virtual work serves as the fundamental principle of mechanics. Based on the perception of analytical mechanics that forces of a mechanical system are defined as dual quantities to the kinematical description, the virtual work approach is a systematic way to treat arbitrary mechanical systems. Whereas this methodology is very convenient to formulate induced beam theories, it is essential in geometric continuum mechanics when the assumptions on the physical space are relaxed and the space is modeled as a smooth manifold. The book addresses researcher and graduate students in engineering and mathematics interested in recent developments of a geometric formulation of continuum mechanics and a hierarchical development of induced beam theories.
Directory of Open Access Journals (Sweden)
Ilham Rizkianto
2013-07-01
Full Text Available Previous studies have provided that when learning shapes for the first time, young children tend to use the prototype as the reference point for comparisons, but often fail when doing so since they do not yet think about the defining attributes or the geometric properties of the shapes. Most of the time, elementary students learn geometric properties of shapes only as empty verbal statements to be memorized, without any chance to experience the contepts meaningfully. In the light of it, a sequence of instructional activities along with computer manipulative was designed to support Indonesian third graders in constructing geometric properties of square, rectangle, and triangle. The aim of the present study is to develop a loval instructional theory to support third graders in constructing geometric properties of rectangle, square, and triangle. Thirty seven students of one third grade classes in SD Pupuk Sriwijaya Palembang, along with their class teacher, were involved in the study. Our findings suggest that the combination of computer and non-computer activities suppots third graders in constructing geometric properties of square, rectangle, and triangle in that it provides opportunities to the students to experience and to develop the concepts meaningfully while using their real experiences as the bases to attain a higher geometric thinking level.Key concepts: Geometric properties, rectangle, square, triangle, design research, realistic mathematics education DOI: http://dx.doi.org/10.22342/jme.4.2.414.160-171
Smart mug to measure hand's geometrical mechanical impedance.
Hondori, Hossein Mousavi; Tech, Ang Wei
2011-01-01
A novel device, which looks like a mug, has been proposed for measuring the impedance of human hand. The device is designed to have convenient size and light weight similar to an ordinary coffee mug. It contains a 2-axis inertia sensor to monitor vibration and a small motor to carry an eccentric mass (m=100 gr, r=2 cm, rpm=600). The centrifugal force due to the rotating mass applies a dynamic force to the hand that holds the mug. Correlation of the acceleration signals with the perturbing force gives the geometrical mechanical impedance. Experimental results on a healthy subject shows that impedance is posture dependant while it changes with the direction of the applied perturbing force. For nine postures the geometrical impedance is obtained all of which have elliptical shapes. The method can be used for assessment of spasticity and monitoring stability in patients with stroke or similar problems.
Geometric accuracy of wax bade models manufactured in silicon moulds
Directory of Open Access Journals (Sweden)
G. Budzik
2010-01-01
Full Text Available The article presents the test results of the geometric accuracy of wax blade models manufactured in silicon moulds in the Rapid Tooling process, with the application of the Vacuum Casting technology. In batch production casting waxes are designed for the manufacture of models and components of model sets through injection into a metal die. The objective of the tests was to determine the possibility of using traditional wax for the production of casting models in the rapid prototyping process. Blade models made of five types of casting wax were measured. The definition of the geometric accuracy of wax blade models makes it possible to introduce individual modifications aimed at improving their shape in order to increase the dimensional accuracy of blade models manufactured in the rapid prototyping process.
Geometric Seismic Attributes of Boca de Jaruco Oil Field
Directory of Open Access Journals (Sweden)
Yamicela Tamayo López
2013-06-01
Full Text Available This paper focuses in determining the Geometric Seismic Attributes in the central block of Mouth ofJaruco oil field to decrease the uncertainty in the structural design. The three dimensions seismic datacollected and depth migration processing results were used and was defined that the surface isassociated to the main reserve. A Geometric Attributes maps elaboration (Azimuth, Dip, Curvature andRoughness work flow was developed; and was able to determine structural elements, where traditionalseismic data were not always able to demonstrate a confinable image of the geological structure. Thisstructure includes three structures between 1122 and 1200 m in depth. The Azimuth Attribute differentiatesthe southern flank from the northern flank; and defined accurately the top of the structure. The DipAttribute indicates values of layers inclination between 5 and 30º, the structure top with lowers valuesand the flanks with higher values, mainly to the south. Curvature and Roughness attributes reveal theareas of faults or channels.
Shuttle entry guidance revisited using nonlinear geometric methods
Mease, Kenneth D.; Kremer, Jean-Paul
1994-11-01
The entry guidance law for the space shuttle orbiter is revisited using nonlinear geometric methods. The shuttle guidance concept is to track a reference drag trajectory that has been designed to lead a specified range and velocity. It is shown that the approach taken in the original derivation of the shuttle entry guidance has much in common with the more recently developed feedback linearization method of differential geometric control. Using the feedback linearization method, however, an alternative, potentially superior, guidance law was formulated. Comparing the two guidance laws based performance domains in state space, taking into account the nonlinear dynamics, the alternative guidance law achieves the desired performance over larger domains in state space; the stability domain of the laws are similar. With larger operating domain for the shuttle or some other entry vehicle, the alternative guidance law should be considered.
Geometric database maintenance using CCTV cameras and overlay graphics
Oxenberg, Sheldon C.; Landell, B. Patrick; Kan, Edwin
1988-01-01
An interactive graphics system using closed circuit television (CCTV) cameras for remote verification and maintenance of a geometric world model database has been demonstrated in GE's telerobotics testbed. The database provides geometric models and locations of objects viewed by CCTV cameras and manipulated by telerobots. To update the database, an operator uses the interactive graphics system to superimpose a wireframe line drawing of an object with known dimensions on a live video scene containing that object. The methodology used is multipoint positioning to easily superimpose a wireframe graphic on the CCTV image of an object in the work scene. An enhanced version of GE's interactive graphics system will provide the object designation function for the operator control station of the Jet Propulsion Laboratory's telerobot demonstration system.
Geometric and Meshing Properties of Conjugate Curves for Gear Transmission
Directory of Open Access Journals (Sweden)
Dong Liang
2014-01-01
Full Text Available Conjugate curves have been put forward previously by authors for gear transmission. Compared with traditional conjugate surfaces, the conjugate curves have more flexibility and diversity in aspects of gear design and generation. To further extend its application in power transmission, the geometric and meshing properties of conjugate curves are discussed in this paper. Firstly, general principle descriptions of conjugate curves for arbitrary axial position are introduced. Secondly, geometric analysis of conjugate curves is carried out based on differential geometry including tangent and normal in arbitrary contact direction, characteristic point, and curvature relationships. Then, meshing properties of conjugate curves are further revealed. According to a given plane or spatial curve, the uniqueness of conjugated curve under different contact angle conditions is discussed. Meshing commonality of conjugate curves is also demonstrated in terms of a class of spiral curves contacting in the given direction for various gear axes. Finally, a conclusive summary of this study is given.
Mechanisms of geometrical seismic attenuation
Directory of Open Access Journals (Sweden)
Igor B. Morozov
2011-07-01
Full Text Available In several recent reports, we have explained the frequency dependence of the apparent seismic quality-factor (Q observed in many studies according to the effects of geometrical attenuation, which was defined as the zero-frequency limit of the temporal attenuation coefficient. In particular, geometrical attenuation was found to be positive for most waves traveling within the lithosphere. Here, we present three theoretical models that illustrate the origin of this geometrical attenuation, and we investigate the causes of its preferential positive values. In addition, we discuss the physical basis and limitations of both the conventional and new attenuation models. For waves in media with slowly varying properties, geometrical attenuation is caused by variations in the wavefront curvature, which can be both positive (for defocusing and negative (for focusing. In media with velocity/density contrasts, incoherent reflectivity leads to geometrical-attenuation coefficients which are proportional to the mean squared reflectivity and are always positive. For «coherent» reflectivity, the geometrical attenuation is approximately zero, and the attenuation process can be described according to the concept of «scattering Q». However, the true meaning of this parameter is in describing the mean reflectivity within the medium, and not that of the traditional resonator quality factor known in mechanics. The general conclusion from these models is that non-zero and often positive levels of geometrical attenuation are common in realistic, heterogeneous media, both observationally and theoretically. When transformed into the conventional Q-factor form, this positive geometrical attenuation leads to Q values that quickly increase with frequency. These predictions show that the positive frequency-dependent Q observed in many datasets might represent artifacts of the transformations of the attenuation coefficients into Q.
A Toolbox for Geometric Grain Boundary Characterization
Glowinski, Krzysztof; Morawiec, Adam
Properties of polycrystalline materials are affected by grain boundary networks. The most basic aspect of boundary analysis is boundary geometry. This paper describes a package of computer programs for geometric boundary characterization based on macroscopic boundary parameters. The program allows for determination whether a boundary can be classified as near-tilt, -twist, -symmetric et cetera. Since calculations on experimental, i.e., error affected data are assumed, the program also provides distances to the nearest geometrically characteristic boundaries. The software has a number of other functions helpful in grain boundary analysis. One of them is the determination of planes of all characteristic boundaries for a given misorientation. The resulting diagrams of geometrically characteristic boundaries can be linked to experimentally determined grain boundary distributions. In computations, all symmetrically equivalent representations of boundaries are taken into account. Cubic and hexagonal holohedral crystal symmetries are allowed.
2012-01-01
Este libro, Problemas de Geometría, junto con otros dos, Problemas de Matemáticas y Problemas de Geometría Analítica y Diferencial, están dedicados a la presentación y resolución de problemas que se planteaban hace unas décadas, en la preparación para ingreso en las carreras de ingeniería técnica superior. Incluye 744 problemas que se presentan en dos grandes grupos: • Geometría del plano, con 523 problemas referentes a lugares geométricos, rectas, ángulos, triángulos y su construcción, cuadr...
Spherical projections and liftings in geometric tomography
DEFF Research Database (Denmark)
Goodey, Paul; Kiderlen, Markus; Weil, Wolfgang
2011-01-01
We consider a variety of integral transforms arising in Geometric Tomography. It will be shown that these can be put into a common framework using spherical projection and lifting operators. These operators will be applied to support functions and surface area measures of convex bodies and to rad......We consider a variety of integral transforms arising in Geometric Tomography. It will be shown that these can be put into a common framework using spherical projection and lifting operators. These operators will be applied to support functions and surface area measures of convex bodies...... and to radial functions of star bodies. We then investigate averages of lifted projections and show that they correspond to self-adjoint intertwining operators. We obtain formulas for the eigenvalues of these operators and use them to ascertain circumstances under which tomographic measurements determine...... the original bodies. This approach via mean lifted projections leads us to some unexpected relationships between seemingly disparate geometric constructions....
An Underlying Geometrical Manifold for Hamiltonian Mechanics
Horwitz, L P; Levitan, J; Lewkowicz, M
2015-01-01
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...
Duality orbits of non-geometric fluxes
Energy Technology Data Exchange (ETDEWEB)
Dibitetto, G.; Roest, D. [Centre for Theoretical Physics, University of Groningen, Nijenborgh 4, 9747 AG Groningen (Netherlands); Fernandez-Melgarejo, J.J. [Grupo de Fisica Teorica y Cosmologia, Dept. de Fisica, University of Murcia, Campus de Espinardo, 30100-Murcia (Spain); Marques, D. [Institut de Physique Theorique, CEA/ Saclay, 91191 Gif-sur-Yvette Cedex (France)
2012-11-15
Compactifications in duality covariant constructions such as generalised geometry and double field theory have proven to be suitable frameworks to reproduce gauged supergravities containing non-geometric fluxes. However, it is a priori unclear whether these approaches only provide a reformulation of old results, or also contain new physics. To address this question, we classify the T- and U-duality orbits of gaugings of (half-)maximal supergravities in dimensions seven and higher. It turns out that all orbits have a geometric supergravity origin in the maximal case, while there are non-geometric orbits in the half-maximal case. We show how the latter are obtained from compactifications of double field theory. (Copyright copyright 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
The Geometric Phase of Stock Trading.
Altafini, Claudio
2016-01-01
Geometric phases describe how in a continuous-time dynamical system the displacement of a variable (called phase variable) can be related to other variables (shape variables) undergoing a cyclic motion, according to an area rule. The aim of this paper is to show that geometric phases can exist also for discrete-time systems, and even when the cycles in shape space have zero area. A context in which this principle can be applied is stock trading. A zero-area cycle in shape space represents the type of trading operations normally carried out by high-frequency traders (entering and exiting a position on a fast time-scale), while the phase variable represents the cash balance of a trader. Under the assumption that trading impacts stock prices, even zero-area cyclic trading operations can induce geometric phases, i.e., profits or losses, without affecting the stock quote.
Geometrical families of mechanically stable granular packings
Gao, Guo-Jie; Blawzdziewicz, Jerzy; O'Hern, Corey S.
2009-12-01
We enumerate and classify nearly all of the possible mechanically stable (MS) packings of bidipserse mixtures of frictionless disks in small sheared systems. We find that MS packings form continuous geometrical families, where each family is defined by its particular network of particle contacts. We also monitor the dynamics of MS packings along geometrical families by applying quasistatic simple shear strain at zero pressure. For small numbers of particles (N16 , we observe an increase in the period and random splittings of the trajectories caused by bifurcations in configuration space. We argue that the ratio of the splitting and contraction rates in large systems will determine the distribution of MS-packing geometrical families visited in steady state. This work is part of our long-term research program to develop a master-equation formalism to describe macroscopic slowly driven granular systems in terms of collections of small subsystems.
MM Algorithms for Geometric and Signomial Programming.
Lange, Kenneth; Zhou, Hua
2014-02-01
This paper derives new algorithms for signomial programming, a generalization of geometric programming. The algorithms are based on a generic principle for optimization called the MM algorithm. In this setting, one can apply the geometric-arithmetic mean inequality and a supporting hyperplane inequality to create a surrogate function with parameters separated. Thus, unconstrained signomial programming reduces to a sequence of one-dimensional minimization problems. Simple examples demonstrate that the MM algorithm derived can converge to a boundary point or to one point of a continuum of minimum points. Conditions under which the minimum point is unique or occurs in the interior of parameter space are proved for geometric programming. Convergence to an interior point occurs at a linear rate. Finally, the MM framework easily accommodates equality and inequality constraints of signomial type. For the most important special case, constrained quadratic programming, the MM algorithm involves very simple updates.
Singularity Analysis of Geometric Constraint Systems
Institute of Scientific and Technical Information of China (English)
彭小波; 陈立平; 周凡利; 周济
2002-01-01
Singularity analysis is an important subject of the geometric constraint sat-isfaction problem. In this paper, three kinds of singularities are described and corresponding identification methods are presented for both under-constrained systems and over-constrained systems. Another special but common singularity for under-constrained geometric systems, pseudo-singularity, is analyzed. Pseudo-singularity is caused by a variety of constraint match ing of under-constrained systems and can be removed by improving constraint distribution. To avoid pseudo-singularity and decide redundant constraints adaptively, a differentiation algo rithm is proposed in the paper. Its correctness and efficiency have been validated through its practical applications in a 2D/3D geometric constraint solver CBA.
Geometric optimization and sums of algebraic functions
Vigneron, Antoine E.
2014-01-01
We present a new optimization technique that yields the first FPTAS for several geometric problems. These problems reduce to optimizing a sum of nonnegative, constant description complexity algebraic functions. We first give an FPTAS for optimizing such a sum of algebraic functions, and then we apply it to several geometric optimization problems. We obtain the first FPTAS for two fundamental geometric shape-matching problems in fixed dimension: maximizing the volume of overlap of two polyhedra under rigid motions and minimizing their symmetric difference. We obtain the first FPTAS for other problems in fixed dimension, such as computing an optimal ray in a weighted subdivision, finding the largest axially symmetric subset of a polyhedron, and computing minimum-area hulls.
Understanding geometric algebra for electromagnetic theory
Arthur, John W
2011-01-01
"This book aims to disseminate geometric algebra as a straightforward mathematical tool set for working with and understanding classical electromagnetic theory. It's target readership is anyone who has some knowledge of electromagnetic theory, predominantly ordinary scientists and engineers who use it in the course of their work, or postgraduate students and senior undergraduates who are seeking to broaden their knowledge and increase their understanding of the subject. It is assumed that the reader is not a mathematical specialist and is neither familiar with geometric algebra or its application to electromagnetic theory. The modern approach, geometric algebra, is the mathematical tool set we should all have started out with and once the reader has a grasp of the subject, he or she cannot fail to realize that traditional vector analysis is really awkward and even misleading by comparison"--Provided by publisher.
The effect of photometric and geometric context on photometric and geometric lightness effects.
Lee, Thomas Y; Brainard, David H
2014-01-24
We measured the lightness of probe tabs embedded at different orientations in various contextual images presented on a computer-controlled stereo display. Two background context planes met along a horizontal roof-like ridge. Each plane was a graphic rendering of a set of achromatic surfaces with the simulated illumination for each plane controlled independently. Photometric context was varied by changing the difference in simulated illumination intensity between the two background planes. Geometric context was varied by changing the angle between them. We parsed the data into separate photometric effects and geometric effects. For fixed geometry, varying photometric context led to linear changes in both the photometric and geometric effects. Varying geometric context did not produce a statistically reliable change in either the photometric or geometric effects.
Bayro-Corrochano, Eduardo; Vazquez-Santacruz, Eduardo; Moya-Sanchez, Eduardo; Castillo-Munis, Efrain
2016-10-01
This paper presents the design of radial basis function geometric bioinspired networks and their applications. Until now, the design of neural networks has been inspired by the biological models of neural networks but mostly using vector calculus and linear algebra. However, these designs have never shown the role of geometric computing. The question is how biological neural networks handle complex geometric representations involving Lie group operations like rotations. Even though the actual artificial neural networks are biologically inspired, they are just models which cannot reproduce a plausible biological process. Until now researchers have not shown how, using these models, one can incorporate them into the processing of geometric computing. Here, for the first time in the artificial neural networks domain, we address this issue by designing a kind of geometric RBF using the geometric algebra framework. As a result, using our artificial networks, we show how geometric computing can be carried out by the artificial neural networks. Such geometric neural networks have a great potential in robot vision. This is the most important aspect of this contribution to propose artificial geometric neural networks for challenging tasks in perception and action. In our experimental analysis, we show the applicability of our geometric designs, and present interesting experiments using 2-D data of real images and 3-D screw axis data. In general, our models should be used to process different types of inputs, such as visual cues, touch (texture, elasticity, temperature), taste, and sound. One important task of a perception-action system is to fuse a variety of cues coming from the environment and relate them via a sensor-motor manifold with motor modules to carry out diverse reasoned actions.
Primary School Teacher Candidates' Geometric Habits of Mind
Köse, Nilu¨fer Y.; Tanisli, Dilek
2014-01-01
Geometric habits of mind are productive ways of thinking that support learning and using geometric concepts. Identifying primary school teacher candidates' geometric habits of mind is important as they affect the development of their future students' geometric thinking. Therefore, this study attempts to determine primary school teachers' geometric…
Model-based vision using geometric hashing
Akerman, Alexander, III; Patton, Ronald
1991-04-01
The Geometric Hashing technique developed by the NYU Courant Institute has been applied to various automatic target recognition applications. In particular, I-MATH has extended the hashing algorithm to perform automatic target recognition ofsynthetic aperture radar (SAR) imagery. For this application, the hashing is performed upon the geometric locations of dominant scatterers. In addition to being a robust model-based matching algorithm -- invariant under translation, scale, and 3D rotations of the target -- hashing is of particular utility because it can still perform effective matching when the target is partially obscured. Moreover, hashing is very amenable to a SIMD parallel processing architecture, and thus potentially realtime implementable.
The geometric phase in quantum physics
Energy Technology Data Exchange (ETDEWEB)
Bohm, A.
1993-03-01
After an explanatory introduction, a quantum system in a classical time-dependent environment is discussed; an example is a magnetic moment in a classical magnetic field. At first, the general abelian case is discussed in the adiabatic approximation. Then the geometric phase for nonadiabatic change of the environment (Anandan--Aharonov phase) is introduced, and after that general cyclic (nonadiabatic) evolution is discussed. The mathematics of fiber bundles is introduced, and some of its results are used to describe the relation between the adiabatic Berry phase and the geometric phase for general cyclic evolution of a pure state. The discussion is restricted to the abelian, U(1) phase.
Geometric measure theory a beginner's guide
Morgan, Frank
2008-01-01
Geometric measure theory provides the framework to understand the structure of a crystal, a soap bubble cluster, or a universe. Measure Theory: A Beginner's Guide is essential to any student who wants to learn geometric measure theory, and will appeal to researchers and mathematicians working in the field. Morgan emphasizes geometry over proofs and technicalities providing a fast and efficient insight into many aspects of the subject.New to the 4th edition:* Abundant illustrations, examples, exercises, and solutions.* The latest results on soap bubble clusters, including
Satellite Video Stabilization with Geometric Distortion
Directory of Open Access Journals (Sweden)
WANG Xia
2016-02-01
Full Text Available There is an exterior orientation difference in each satellite video frame, and the corresponding points have different image locations in adjacent frames images which has geometric distortion. So the projection model, affine model and other classical image stabilization registration model cannot accurately describe the relationship between adjacent frames. This paper proposes a new satellite video image stabilization method with geometric distortion to solve the problem, based on the simulated satellite video, we verify the feasibility and accuracy of proposed satellite video stabilization method.
Adiabatic geometric phases and response functions
Jain, S R; Jain, Sudhir R.; Pati, Arun K.
1998-01-01
Treating a many-body Fermi system in terms of a single particle in a deforming mean field. We relate adiabatic geometric phase to susceptibility for the noncyclic case, and to its derivative for the cyclic case. Employing the semiclassical expression of susceptibility, the expression for geometric phase for chaotic quantum system immediately follows. Exploiting the well-known association of the absorptive part of susceptibility with dissipation, our relations may provide a quantum mechanical origin of the damping of collective excitations in Fermi systems.
Classical Light Beams and Geometric Phases
Mukunda, N; Simon, R
2013-01-01
We present a study of geometric phases in classical wave and polarisation optics using the basic mathematical framework of quantum mechanics. Important physical situations taken from scalar wave optics, pure polarisation optics, and the behaviour of polarisation in the eikonal or ray limit of Maxwell's equations in a transparent medium are considered. The case of a beam of light whose propagation direction and polarisation state are both subject to change is dealt with, attention being paid to the validity of Maxwell's equations at all stages. Global topological aspects of the space of all propagation directions are discussed using elementary group theoretical ideas, and the effects on geometric phases are elucidated.
Workshop on Topology and Geometric Group Theory
Fowler, James; Lafont, Jean-Francois; Leary, Ian
2016-01-01
This book presents articles at the interface of two active areas of research: classical topology and the relatively new field of geometric group theory. It includes two long survey articles, one on proofs of the Farrell–Jones conjectures, and the other on ends of spaces and groups. In 2010–2011, Ohio State University (OSU) hosted a special year in topology and geometric group theory. Over the course of the year, there were seminars, workshops, short weekend conferences, and a major conference out of which this book resulted. Four other research articles complement these surveys, making this book ideal for graduate students and established mathematicians interested in entering this area of research.
A lexicographic shellability characterization of geometric lattices
Davidson, Ruth
2011-01-01
Geometric lattices are characterized as those finite, atomic lattices such that every atom ordering induces a lexicographic shelling given by an edge labeling known as a minimal labeling. This new characterization fits into a similar paradigm as McNamara's characterization of supersolvable lattices as those lattices admitting a different type of lexicographic shelling, namely one in which each maximal chain is labeled with a permutation of {1,...,n}. Geometric lattices arise as the intersection lattices of central hyperplane arrangements and more generally as the lattices of flats for matroids.
Geometric, control and numeric aspects of nonholonomic systems
Cortés Monforte, Jorge
2002-01-01
Nonholonomic systems are a widespread topic in several scientific and commercial domains, including robotics, locomotion and space exploration. This work sheds new light on this interdisciplinary character through the investigation of a variety of aspects coming from several disciplines. The main aim is to illustrate the idea that a better understanding of the geometric structures of mechanical systems unveils new and unknown aspects to them, and helps both analysis and design to solve standing problems and identify new challenges. In this way, separate areas of research such as Classical Mechanics, Differential Geometry, Numerical Analysis or Control Theory are brought together in this study of nonholonomic systems.
An integrated introduction to computer graphics and geometric modeling
Goldman, Ronald
2009-01-01
… this book may be the first book on geometric modelling that also covers computer graphics. In addition, it may be the first book on computer graphics that integrates a thorough introduction to 'freedom' curves and surfaces and to the mathematical foundations for computer graphics. … the book is well suited for an undergraduate course. … The entire book is very well presented and obviously written by a distinguished and creative researcher and educator. It certainly is a textbook I would recommend. …-Computer-Aided Design, 42, 2010… Many books concentrate on computer programming and soon beco
Sousa, Diogo; Gamboa, Pedro; Melo, David
2016-12-01
Many studies concerning morphing aircraft concepts in which enhanced performance and increased energy efficiency are two of the main goals have been recently conducted. Some of those concepts deal with wing span changes. In line with those, in a variable-span wing of the telescopic type, the cross-sections of the sliding panels, whether be two, three or more, must be made geometrically compatible among them. This requirement serves two purposes: to minimize the aerofoils' geometric discontinuity which negatively affects wing drag and lift; and to provide a simple structural support between any two sliding panels. This paper describes the methodology employed to develop geometrically compatible aerofoils obtained from a constant geometric offset applied to a given initial aerofoil. This methodology is used to create inward offset aerofoils and outward offset aerofoils. The geometric and aerodynamic characteristics of the resulting offset aerofoils are compared with those of the original aerofoils. From the analysis of six different original aerofoils, strong trends in the geometric changes and in the aerodynamic characteristics of the resulting inward and outward offset aerofoils are observed. Ultimately, this study can help a telescopic wing designer decide whether an inward or an outward offset aerofoil is more appropriate for the specific design at hand.
Geometric calibration of high-resolution remote sensing sensors
Institute of Scientific and Technical Information of China (English)
LIANG Hong-you; GU Xing-fa; TAO Yu; QIAO Chao-fei
2007-01-01
This paper introduces the applications of high-resolution remote sensing imagery and the necessity of geometric calibration for remote sensing sensors considering assurance of the geometric accuracy of remote sensing imagery. Then the paper analyzes the general methodology of geometric calibration. Taking the DMC sensor geometric calibration as an example, the paper discusses the whole calibration procedure. Finally, it gave some concluding remarks on geometric calibration of high-resolution remote sensing sensors.
Optimization of DC-DC Converters via Geometric Programming
Directory of Open Access Journals (Sweden)
U. Ribes-Mallada
2011-01-01
Full Text Available The paper presents a new methodology for optimizing the design of DC-DC converters. The magnitudes that we take into account are efficiency, ripples, bandwidth, and RHP zero placement. We apply a geometric programming approach, because the variables are positives and the constraints can be expressed in a posynomial form. This approach has all the advantages of convex optimization. We apply the proposed methodology to a boost converter. The paper also describes the optimum designs of a buck converter and a synchronous buck converter, and the method can be easily extended to other converters. The last example allows us to compare the efficiency and bandwidth between these optimal-designed topologies.
Geometrical Aberration Suppression for Large Aperture Sub-THz Lenses
Rachon, M.; Liebert, K.; Siemion, A.; Bomba, J.; Sobczyk, A.; Knap, W.; Coquillat, D.; Suszek, J.; Sypek, M.
2017-03-01
Advanced THz setups require high performance optical elements with large numerical apertures and small focal lengths. This is due to the high absorption of humid air and relatively low efficiency of commercially available detectors. Here, we propose a new type of double-sided sub-THz diffractive optical element with suppressed geometrical aberration for narrowband applications (0.3 THz). One side of the element is designed as thin structure in non-paraxial approach which is the exact method, but only for ideally flat elements. The second side will compensate phase distribution differences between ideal thin structure and real volume one. The computer-aided optimization algorithm is performed to design an additional phase distribution of correcting layer assuming volume designing of the first side of the element. The experimental evaluation of the proposed diffractive component created by 3D printing technique shows almost two times larger performance in comparison with uncorrected basic diffractive lens.
Geometrical Aberration Suppression for Large Aperture Sub-THz Lenses
Rachon, M.; Liebert, K.; Siemion, A.; Bomba, J.; Sobczyk, A.; Knap, W.; Coquillat, D.; Suszek, J.; Sypek, M.
2016-11-01
Advanced THz setups require high performance optical elements with large numerical apertures and small focal lengths. This is due to the high absorption of humid air and relatively low efficiency of commercially available detectors. Here, we propose a new type of double-sided sub-THz diffractive optical element with suppressed geometrical aberration for narrowband applications (0.3 THz). One side of the element is designed as thin structure in non-paraxial approach which is the exact method, but only for ideally flat elements. The second side will compensate phase distribution differences between ideal thin structure and real volume one. The computer-aided optimization algorithm is performed to design an additional phase distribution of correcting layer assuming volume designing of the first side of the element. The experimental evaluation of the proposed diffractive component created by 3D printing technique shows almost two times larger performance in comparison with uncorrected basic diffractive lens.
APPROACHES TO GEOMETRIC DATA ANALYSIS ON BIG AREA ADDITIVELY MANUFACTURED (BAAM) PARTS
Energy Technology Data Exchange (ETDEWEB)
Dreifus, Gregory D [ORNL; Ally, Nadya R [ORNL; Post, Brian K [ORNL; Jin, Yuan [ORNL
2016-01-01
The promise of additive manufacturing is that a user can design and print complex geometries that are very difficult, if not impossible, to machine. The capabilities of 3D printing are restricted by a number of factors, including properties of the build material, time constraints, and geometric design restrictions. In this paper, a thorough accounting and study of the geometric restrictions that exist in the current iteration of additive manufacturing (AM) fused deposition modeling (FDM) technologies are discussed. Offline and online methodologies for collecting data sets for qualitative analysis of large scale AM, in particular Oak Ridge National Laboratory s (ORNL) big area additive manufacturing (BAAM) system, are summarized. In doing so, a survey of tools for designers and software developers is provided. In particular, strategies in which geometric data can be used as training sets for smarter AM technologies in the future are explained as well.
Geometric foundation of spin and isospin
Hannibal, L
1996-01-01
Various theories of spinning particles are interpreted as realizing elements of an underlying geometric theory. Classical particles are described by trajectories on the Poincare group. Upon quantization an eleven-dimensional Kaluza-Klein type theory is obtained which incorporates spin and isospin in a local SL(2,C) x U(1) x SU(2) theory with broken U(1)x SU(2) part.
Reinforcing Geometric Properties with Shapedoku Puzzles
Wanko, Jeffrey J.; Nickell, Jennifer V.
2013-01-01
Shapedoku is a new type of puzzle that combines logic and spatial reasoning with understanding of basic geometric concepts such as slope, parallelism, perpendicularity, and properties of shapes. Shapedoku can be solved by individuals and, as demonstrated here, can form the basis of a review for geometry students as they create their own. In this…
An underlying geometrical manifold for Hamiltonian mechanics
Horwitz, L. P.; Yahalom, A.; Levitan, J.; Lewkowicz, M.
2017-02-01
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.
Using geometric algebra to study optical aberrations
Energy Technology Data Exchange (ETDEWEB)
Hanlon, J.; Ziock, H.
1997-05-01
This paper uses Geometric Algebra (GA) to study vector aberrations in optical systems with square and round pupils. GA is a new way to produce the classical optical aberration spot diagrams on the Gaussian image plane and surfaces near the Gaussian image plane. Spot diagrams of the third, fifth and seventh order aberrations for square and round pupils are developed to illustrate the theory.
Geometric singular perturbation theory in biological practice
Hek, G.
2010-01-01
Geometric singular perturbation theory is a useful tool in the analysis of problems with a clear separation in time scales. It uses invariant manifolds in phase space in order to understand the global structure of the phase space or to construct orbits with desired properties. This paper explains an
Saturation and geometrical scaling in small systems
Praszalowicz, Michal
2016-01-01
Saturation and geometrical scaling (GS) of gluon distributions are a consequence of the non-linear evolution equations of QCD. We argue that in pp GS holds for the inelastic cross-section rather than for the multiplicity distributions. We also discuss possible fluctuations of the proton saturation scale in pA collisions at the LHC.
Geometric Interpretations of Some Psychophysical Results.
Levine, Michael V.
A theory of psychophysics is discussed that enlarges the classical theory in three general ways: (1) the multidimensional nature of perception is made explicit; (2) the transformations of the theory are interpreted geometrically; and (3) attributes are distinguished from sensations and only partially ordered. It is shown that, with the enlarged…
Geometric Algorithms for Part Orienting and Probing
Panahi, F.
2015-01-01
In this thesis, detailed solutions are presented to several problems dealing with geometric shape and orientation of an object in the field of robotics and automation. We first have considered a general model for shape variations that allows variation along the entire boundary of an object, both in
On Arithmetic-Geometric-Mean Polynomials
Griffiths, Martin; MacHale, Des
2017-01-01
We study here an aspect of an infinite set "P" of multivariate polynomials, the elements of which are associated with the arithmetic-geometric-mean inequality. In particular, we show in this article that there exist infinite subsets of probability "P" for which every element may be expressed as a finite sum of squares of real…
Geometric properties of optimal photonic crystals
DEFF Research Database (Denmark)
Sigmund, Ole; Hougaard, Kristian G.
2008-01-01
on numerical optimization studies, we have discovered some surprisingly simple geometric properties of optimal planar band gap structures. We conjecture that optimal structures for gaps between bands n and n+1 correspond to n elliptic rods with centers defined by the generators of an optimal centroidal Voronoi...
Geometric Mean--What Does It Mean?
Kalder, Robin S.
2012-01-01
The National Council of Teachers of Mathematics and numerous mathematics educators promote the combination of conceptual understanding and procedural learning in the successful instruction of mathematics. Despite this, when geometric mean is taught in a typical American geometry class, it is taught as a process only despite the many connections…
Geometric Total Variation for Texture Deformation
DEFF Research Database (Denmark)
Bespalov, Dmitriy; Dahl, Anders Lindbjerg; Shokoufandeh, Ali
2010-01-01
of features in texture images leads to significant improvements in localization of these features, when textures undergo geometrical transformations. Accurate localization of features in the presense of unkown deformations is a crucial property for texture characterization methods, and we intend to expoit...
Geometric Abstract Art and Public Health Data
Centers for Disease Control (CDC) Podcasts
2016-10-18
Dr. Salaam Semaan, a CDC behavioral scientist, discusses the similarities between geometric abstract art and public health data analysis. Created: 10/18/2016 by National Center for Emerging and Zoonotic Infectious Diseases (NCEZID). Date Released: 10/18/2016.
Modern Geometric Algebra: A (Very Incomplete!) Survey
Suzuki, Jeff
2009-01-01
Geometric algebra is based on two simple ideas. First, the area of a rectangle is equal to the product of the lengths of its sides. Second, if a figure is broken apart into several pieces, the sum of the areas of the pieces equals the area of the original figure. Remarkably, these two ideas provide an elegant way to introduce, connect, and…
Robust topology optimization accounting for geometric imperfections
DEFF Research Database (Denmark)
Schevenels, M.; Jansen, M.; Lombaert, Geert
2013-01-01
performance. As a consequence, the actual structure may be far from optimal. In this paper, a robust approach to topology optimization is presented, taking into account two types of geometric imperfections: variations of (1) the crosssections and (2) the locations of structural elements. The first type...... of imperfections) and a vertical load carrying system (for the second type). © 2013 Taylor & Francis Group, London....
A Geometric Approach to Fair Division
Barbanel, Julius
2010-01-01
We wish to divide a cake among some collection of people (who may have very different notions of the comparative value of pieces of cake) in a way that is both "fair" and "efficient." We explore the meaning of these terms, introduce two geometric tools to aid our analysis, and present a proof (due to Dietrich Weller) that establishes the existence…
Geometric Reductivity--A Quotient Space Approach
Sastry, Pramathanath
2010-01-01
We give another proof that a reductive algebraic group is geometrically reductive. We show that a quotient of the semi-stable locus (by a linear action of a reductive algebraic group on a projective scheme) exists, and from this Haboush's Theorem (Mumford's Conjecture) follows.
Geometric and Texture Inpainting by Gibbs Sampling
DEFF Research Database (Denmark)
Gustafsson, David Karl John; Pedersen, Kim Steenstrup; Nielsen, Mads
2007-01-01
This paper discuss a method suitable for inpainting both large scale geometric structures and more stochastic texture components. Image inpainting concerns the problem of reconstructing the intensity contents inside regions of missing data. Common techniques for solving this problem are methods...
How Do Young Children Learn Geometric Concepts.
Ohe, Pia
Twenty children (ages 5 and 6) from each of seven cultural groups (Caucasian, Black, Jewish, Puerto Rican, Chinese, Korean-American and native Korean) were given a copying task of 21 geometric shapes to test the cultural invariancy of Piaget's topological-projective-Euclidean concept acquisition sequence. All subjects were either middle or lower…
Geometrical Factors in the Perception of Sacredness.
Costa, Marco; Bonetti, Leonardo
2016-06-28
Geometrical and environmental factors in the perception of sacredness, dominance, and attractiveness were assessed by 137 participants in five tests. In the first test, a two-alternative forced-choice paradigm was used to test the perception of sacredness, dominance, and attractiveness in geometrical figures differing in shape, verticality, size, and symmetry. Verticality, symmetry, and convexity were found to be important factors in the perception of sacredness. In the second test, participants had to mark the point inside geometrical surfaces that was perceived as most sacred, dominant, and attractive. The top and the center areas were associated with sacredness, dominance, and attractiveness. In the third test, peaks and elevated regions in landscapes were evaluated as more sacred, dominant, and attractive than valley regions. In the fourth test, three figures sharing the same area but differing in horizontal and vertical orientation were evaluated on eight scales. The vertical figure was evaluated as more sacred, dominant, and attractive than the horizontal figure. The fifth test demonstrated the significant role of space seclusion and inaccessibility in the perception of sacredness. Geometrical factors in the perception of sacredness, dominance, and attractiveness were largely overlapping.
Geometric inequalities in sub-Riemannian groups
Montefalcone, Francescopaolo
2012-01-01
Let G be a sub-Riemannian k-step Carnot group of homogeneous dimension Q. In this paper, we shall prove several geometric inequalities concerning smooth hypersurfaces (i.e. codimension one submanifolds) immersed in G, endowed with the H-perimeter measure.
Deformable image registration with geometric changes
Institute of Scientific and Technical Information of China (English)
Yu LIU; Bo ZHU
2015-01-01
Geometric changes present a number of difficulties in deformable image registration. In this paper, we propose a global deformation framework to model geometric changes whilst promoting a smooth transformation between source and target images. To achieve this, we have developed an innovative model which significantly reduces the side effects of geometric changes in image registration, and thus improves the registration accuracy. Our key contribution is the introduction of a sparsity-inducing norm, which is typically L1 norm regularization targeting regions where geometric changes occur. This preserves the smoothness of global transformation by eliminating local transformation under different conditions. Numerical solutions are discussed and analyzed to guarantee the stability and fast convergence of our algorithm. To demonstrate the effectiveness and utility of this method, we evaluate it on both synthetic data and real data from traumatic brain injury (TBI). We show that the transformation estimated from our model is able to reconstruct the target image with lower instances of error than a standard elastic registration model.
Toeplitz Quantization and Asymptotic Expansions: Geometric Construction
Directory of Open Access Journals (Sweden)
Miroslav Englis
2009-02-01
Full Text Available For a real symmetric domain G_R/K_R, with complexification G_C/K_C, we introduce the concept of ''star-restriction'' (a real analogue of the ''star-products'' for quantization of Kähler manifolds and give a geometric construction of the G_R-invariant differential operators yielding its asymptotic expansion.
A Geometric Approach to Fair Division
Barbanel, Julius
2010-01-01
We wish to divide a cake among some collection of people (who may have very different notions of the comparative value of pieces of cake) in a way that is both "fair" and "efficient." We explore the meaning of these terms, introduce two geometric tools to aid our analysis, and present a proof (due to Dietrich Weller) that establishes the existence…
Geometric constructions for repulsive gravity and quantization
Energy Technology Data Exchange (ETDEWEB)
Hohmann, Manuel
2010-11-15
In this thesis we present two geometric theories designed to extend general relativity. It can be seen as one of the aims of such theories to model the observed accelerating expansion of the universe as a gravitational phenomenon, or to provide a mathematical structure for the formulation of quantum field theories on curved spacetimes and quantum gravity. This thesis splits into two parts: In the first part we consider multimetric gravity theories containing N>1 standard model copies which interact only gravitationally and repel each other in the Newtonian limit. The dynamics of each of the standard model copies is governed by its own metric tensor. We show that the antisymmetric case, in which the mutual repulsion between the different matter sectors is of equal strength compared to the attractive gravitational force within each sector, is prohibited by a no-go theorem for N=2. We further show that this theorem does not hold for N>2 by explicitly constructing an antisymmetric multimetric repulsive gravity theory. We then examine several properties of this theory. Most notably, we derive a simple cosmological model and show that the accelerating expansion of the late universe can indeed be explained by the mutual repulsion between the different matter sectors. We further present a simple model for structure formation and show that our model leads to the formation of filament-like structures and voids. Finally, we show that multimetric repulsive gravity is compatible with high-precision solar system data using the parametrized post-Newtonian formalism. In the second part of the thesis 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 differentiable manifold structure of classical spacetime. In this picture we demonstrate that classical spacetime emerges as a finite
DEFF Research Database (Denmark)
Volf, Mette
This publication is unique in its demystification and operationalization of the complex and elusive nature of the design process. The publication portrays the designer’s daily work and the creative process, which the designer is a part of. Apart from displaying the designer’s work methods...... and design parameters, the publication shows examples from renowned Danish design firms. Through these examples the reader gets an insight into the designer’s reality....
Can EPR non-locality be geometrical?
Energy Technology Data Exchange (ETDEWEB)
Ne`eman, Y. [Tel-Aviv Univ. (Israel). Raymond and Beverly Sackler Faculty of Exact Sciences]|[Univ. of Texas, Austin, TX (United States). Center for Particle Physics; Botero, A. [Texas Univ., Austin, TX (United States)
1995-10-01
The presence in Quantum Mechanics of non-local correlations is one of the two fundamentally non-intuitive features of that theory. The non-local correlations themselves fall into two classes: EPR and Geometrical. The non-local characteristics of the geometrical type are well-understood and are not suspected of possibly generating acausal features, such as faster-than-light propagation of information. This has especially become true since the emergence of a geometrical treatment for the relevant gauge theories, i.e. Fiber Bundle geometry, in which the quantum non-localities are seen to correspond to pure homotopy considerations. This aspect is reviewed in section 2. Contrary-wise, from its very conception, the EPR situation was felt to be paradoxical. It has been suggested that the non-local features of EPR might also derive from geometrical considerations, like all other non-local characteristics of QM. In[7], one of the authors was able to point out several plausibility arguments for this thesis, emphasizing in particular similarities between the non-local correlations provided by any gauge field theory and those required by the preservation of the quantum numbers of the original EPR state-vector, throughout its spatially-extended mode. The derivation was, however, somewhat incomplete, especially because of the apparent difference between, on the one hand, the closed spatial loops arising in the analysis of the geometrical non-localities, from Aharonov-Bohm and Berry phases to magnetic monopoles and instantons, and on the other hand, in the EPR case, the open line drawn by the positions of the two moving decay products of the disintegrating particle. In what follows, the authors endeavor to remove this obstacle and show that as in all other QM non-localities, EPR is somehow related to closed loops, almost involving homotopy considerations. They develop this view in section 3.
Mask synthesis and verification based on geometric model for surface micro-machined MEMS
Institute of Scientific and Technical Information of China (English)
LI Jian-hua; LIU Yu-sheng; GAO Shu-ming
2005-01-01
Traditional MEMS (microelectromechanical system) design methodology is not a structured method and has become an obstacle for MEMS creative design. In this paper, a novel method of mask synthesis and verification for surface micro-machined MEMS is proposed, which is based on the geometric model of a MEMS device. The emphasis is focused on synthesizing the masks at the basis of the layer model generated from the geometric model of the MEMS device. The method is comprised of several steps: the correction of the layer model, the generation of initial masks and final masks including multi-layer etch masks, and mask simulation. Finally some test results are given.
Inertial particle focusing in microchannels with gradually changing geometrical structures
Fan, Liang-Liang; Yan, Qing; Guo, Jing; Zhao, Hong; Zhao, Liang; Zhe, Jiang
2017-01-01
The influence of gradually changing geometrical structures on the inertial focusing of particles is systematically investigated by numerical simulations and experiments in this paper. The Saffman lift force, often ignored in the straight microchannel, becomes strong in microchannels with gradually changing geometrical structures, affecting the lateral migration of particles in the microchannels. In comparison with microchannels that have straight and gradually constricting structures, microchannels with gradually expanding structures focus all the particles in a much narrower bandwidth due to the combined effect of the Saffman lift force and the inertial lift force at the appropriate flow rates. Additionally, the influence of the different arrangements of gradually expanding structures on the inertial focusing of particles was also studied. Results suggest that to achieve the single-stream inertial focusing of particles, gradually expanding structures should be designed on one side or symmetrically on two sides of the microchannel. This study is of importance for the better design of the microchannels utilized for the efficient separation and manipulation of particle-related applications, such as microflow cytometry.
Mechanism of geometric nonlinearity in a nonprismatic and heterogeneous microbeam resonator
Asadi, Keivan; Li, Junfeng; Peshin, Snehan; Yeom, Junghoon; Cho, Hanna
2017-09-01
Implementation of geometric nonlinearity in microelectromechanical systems (MEMS) resonators offers a flexible and efficient design to overcome the limitations of linear MEMS by utilizing beneficial nonlinear characteristics not attainable in a linear setting. Integration of nonlinear coupling elements into an otherwise purely linear microcantilever is one promising way to intentionally realize geometric nonlinearity. Here, we demonstrate that a nonlinear, heterogeneous microresonator system, consisting of a silicon microcantilever with a polymer attachment exhibits strong nonlinear hardening behavior not only in the first flexural mode but also in the higher modes (i.e., second and third flexural modes). In this design, we deliberately implement a drastic and reversed change in the axial vs bending stiffness between the Si and polymer components by varying the geometric and material properties. By doing so, the resonant oscillations induce the large axial stretching within the polymer component, which effectively introduces the geometric stiffness and damping nonlinearity. The efficacy of the design and the mechanism of geometric nonlinearity are corroborated through a comprehensive experimental, analytical, and numerical (finite element) analysis on the nonlinear dynamics of the proposed system.
View-dependent geometric calibration for offset flat-panel cone beam computed tomography systems
Nguyen, Van-Giang
2016-04-01
Geometric parameters that define the geometry of imaging systems are crucial for image reconstruction and image quality in x-ray computed tomography (CT). The problem of determining geometric parameters for an offset flat-panel cone beam CT (CBCT) system, a recently introduced modality with a large field of view, with the assumption of an unstable mechanism and geometric parameters that vary in each view, is considered. To accurately and rapidly find the geometric parameters for each projection view, we use the projection matrix method and design a dedicated phantom that is partially visible in all projection views. The phantom consists of balls distributed symmetrically in a cylinder to ensure the inclusion of the phantom in all views, and a large portion of the phantom is covered in the projection image. To efficiently use calibrated geometric information in the reconstruction process and get rid of approximation errors, instead of decomposing the projection matrix into actual geometric parameters that are manually corrected before being used in reconstruction, as in conventional methods, we directly use the projection matrix and its pseudo-inverse in projection and backprojection operations of reconstruction algorithms. The experiments illustrate the efficacy of the proposed method with a real offset flat-panel CBCT system in dental imaging.
Multi-Mode GF-3 Satellite Image Geometric Accuracy Verification Using the RPC Model.
Wang, Taoyang; Zhang, Guo; Yu, Lei; Zhao, Ruishan; Deng, Mingjun; Xu, Kai
2017-09-01
The GaoFen-3 (GF-3) satellite is the first C-band multi-polarization synthetic aperture radar (SAR) imaging satellite with a resolution up to 1 m in China. It is also the only SAR satellite of the High-Resolution Earth Observation System designed for civilian use. There are 12 different imaging models to meet the needs of different industry users. However, to use SAR satellite images for related applications, they must possess high geometric accuracy. In order to verify the geometric accuracy achieved by the different modes of GF-3 images, we analyze the SAR geometric error source and perform geometric correction tests based on the RPC model with and without ground control points (GCPs) for five imaging modes. These include the spotlight (SL), ultra-fine strip (UFS), Fine Strip I (FSI), Full polarized Strip I (QPSI), and standard strip (SS) modes. Experimental results show that the check point residuals are large and consistent without GCPs, but the root mean square error of the independent checkpoints for the case of four corner control points is better than 1.5 pixels, achieving a similar level of geometric positioning accuracy to that of international satellites. We conclude that the GF-3 satellite can be used for high-accuracy geometric processing and related industry applications.
Geometric control theory for quantum back-action evasion
Energy Technology Data Exchange (ETDEWEB)
Yokotera, Yu; Yamamoto, Naoki [Keio University, Department of Applied Physics and Physico-Informatics, Yokohama (Japan)
2016-12-15
Engineering a sensor system for detecting an extremely tiny signal such as the gravitational-wave force is a very important subject in quantum physics. A major obstacle to this goal is that, in a simple detection setup, the measurement noise is lower bounded by the so-called standard quantum limit (SQL), which is originated from the intrinsic mechanical back-action noise. Hence, the sensor system has to be carefully engineered so that it evades the back-action noise and eventually beats the SQL. In this paper, based on the well-developed geometric control theory for classical disturbance decoupling problem, we provide a general method for designing an auxiliary (coherent feedback or direct interaction) controller for the sensor system to achieve the above-mentioned goal. This general theory is applied to a typical opto-mechanical sensor system. Also, we demonstrate a controller design for a practical situation where several experimental imperfections are present. (orig.)
Scale effect and geometric shapes of grains
Institute of Scientific and Technical Information of China (English)
GUO Hui; GUO Xing-ming
2007-01-01
The rule-of-mixture approach has become one of the widely spread ways to investigate the mechanical properties of nano-materials and nano-structures, and it is very important for the simulation results to exactly compute phase volume fractions. The nanocrystalline (NC) materials are treated as three-phase composites consisting of grain core phase, grain boundary (GB) phase and triple junction phase, and a two-dimensional three-phase mixture regular polygon model is established to investigate the scale effect of mechanical properties of NC materials due to the geometrical polyhedron characteristics of crystal grain. For different multi-sided geometrical shapes of grains, the corresponding regular polygon model is adopted to obtain more precise phase volume fractions and exactly predict the mechanical properties of NC materials.
Scale-invariant geometric random graphs
Xie, Zheng
2015-01-01
We introduce and analyze a class of growing geometric random graphs that are invariant under rescaling of space and time. Directed connections between nodes are drawn according to an influence zone that depends on node position in space and time, capturing the heterogeneity and increased specialization found in growing networks. Through calculations and numerical simulations we explore the consequences of scale-invariance for geometric graphs generated this way. Our analysis reveals a dichotomy between scale-free and Poisson distributions of in- and out-degree, the existence of a random number of hub nodes, high clustering, and unusual percolation behaviour. Moreover, we show how these properties provide a good fit to those of empirically observed web graphs.
Langlands Program, Trace Formulas, and their Geometrization
Frenkel, Edward
2012-01-01
The Langlands Program relates Galois representations and automorphic representations of reductive algebraic groups. The trace formula is a powerful tool in the study of this connection and the Langlands Functoriality Conjecture. After giving an introduction to the Langlands Program and its geometric version, which applies to curves over finite fields and over the complex field, I give a survey of my recent joint work with Robert Langlands and Ngo Bao Chau (arXiv:1003.4578 and arXiv:1004.5323) on a new approach to proving the Functoriality Conjecture using the trace formulas, and on the geometrization of the trace formulas. In particular, I discuss the connection of the latter to the categorification of the Langlands correspondence.
Geometrical dynamics of Born-Infeld objects
Energy Technology Data Exchange (ETDEWEB)
Cordero, Ruben [Departamento de Fisica, Escuela Superior de Fisica y Matematicas del I.P.N., Unidad Adolfo Lopez Mateos, Edificio 9, 07738 Mexico, D.F. (Mexico); Molgado, Alberto [Facultad de Ciencias, Universidad de Colima, Bernal DIaz del Castillo 340, Col. Villas San Sebastian, Colima (Mexico); Rojas, Efrain [Facultad de Fisica e Inteligencia Artificial, Universidad Veracruzana, 91000 Xalapa, Veracruz (Mexico)
2007-03-21
We present a geometrically inspired study of the dynamics of Dp-branes. We focus on the usual non-polynomial Dirac-Born-Infeld action for the worldvolume swept out by the brane in its evolution in general background spacetimes. We emphasize the form of the resulting equations of motion which are quite simple and resemble Newton's second law, complemented with a conservation law for a worldvolume bicurrent. We take a closer look at the classical Hamiltonian analysis which is supported by the ADM framework of general relativity. The constraints and their algebra are identified as well as the geometrical role they play in phase space. In order to illustrate our results, we review the dynamics of a D1-brane immersed in a AdS{sub 3} x S{sup 3} background spacetime. We exhibit the mechanical properties of Born-Infeld objects paving the way to a consistent quantum formulation.
Advanced Geometric Modeler with Hybrid Representation
Institute of Scientific and Technical Information of China (English)
杨长贵; 陈玉健; 等
1996-01-01
An advanced geometric modeler GEMS4.0 has been developed,in which feature representation is used at the highest level abstraction of a product model.Boundary representation is used at the bottom level,while CSG model is adopted at the median level.A BRep data structure capable of modeling non-manifold is adopted.UNRBS representation is used for all curved surfaces,Quadric surfaces have dual representations consisting of their geometric data such as radius,center point,and center axis.Boundary representation of free form surfaces is easily built by sweeping and skinning method with NURBS geometry.Set operations on curved solids with boundary representation are performed by an evaluation process consisting of four steps.A file exchange facility is provided for the conversion between product data described by STEP and product information generated by GEMS4.0.
GEOMETRICALLY INVARIANT WATERMARKING BASED ON RADON TRANSFORMATION
Institute of Scientific and Technical Information of China (English)
Cai Lian; Du Sidan; Gao Duntang
2005-01-01
The weakness of classical watermarking methods is the vulnerability to geometrical distortions that widely occur during normal use of the media. In this letter, a new imagewatermarking method is presented to resist Rotation, Scale and Translation (RST) attacks. The watermark is embedded into a domain obtained by taking Radon transform of a circular area selected from the original image, and then extracting Two-Dimensional (2-D) Fourier magnitude of the Radon transformed image. Furthermore, to prevent the watermarked image from degrading due to inverse Radon transform, watermark signal is inversely Radon transformed individually.Experimental results demonstrate that the proposed scheme is able to withstand a variety of attacks including common geometric attacks.
A Video Watermarking Against Geometrical Distortions
Institute of Scientific and Technical Information of China (English)
NIUXiamu; SCHMUCKERMartin; BUSCHChristoph; SUNShenghe
2003-01-01
A video watermarking with robustness against frame's geometrical distortions (rotation, aspect ratio, scaling, translation shearing, and bending) is proposed. The watermark information is embedded into pixels along the temporal axis within a Watermark minimum segment (WMS). Since the geometrical distortions operations for every frame along the time axis in a video sequence are the same at a very short interval, the watermark information can be detected from watermarked frames in each WMS subjected to the distortions. Furthermore, adaptive embedding method is proposed for gaining a good quality of the watermarked video. Experimental results show that the proposed technique is robust against common attacks such as rotation, aspect ratio, scaling, translation shearing, and bending of frames, MPEG-2 lossy compression, and color-space conversion.
The bouncing ball through a geometrical series
Flores, Sergio; Alfaro, Luis L.; Chavez, Juan E.; Bastarrachea, Aztlan; Hurtado, Jazmin
2008-10-01
The mathematical representation of the physical situation related to a bouncing ball on the floor is an important understanding difficulty for most of the students during the introductory mechanics and mathematics courses. The research group named Physics and mathematics in context from the University of Ciudad Juarez is concerned about the versatility in the change from a mathematical representation to the own physical context of any problem under a traditional instruction. In this case, the main idea is the association of the physical properties of the bouncing ball situation to the nearest mathematical model based on a geometrical series. The proposal of the cognitive development is based on a geometrical series that shows the time the ball takes to stop. In addition, we show the behavior of the ratio of the consecutive heights during the motion.
Mixed State Geometric Phase from Thomas Rotations
Lévai, Peter
2003-01-01
It is shown that Uhlmann's parallel transport of purifications along a path of mixed states represented by $2\\times 2$ density matrices is just the path ordered product of Thomas rotations. These rotations are invariant under hyperbolic translations inside the Bloch sphere that can be regarded as the Poincar\\'e ball model of hyperbolic geometry. A general expression for the mixed state geometric phase for an {\\it arbitrary} geodesic triangle in terms of the Bures fidelities is derived. The formula gives back the solid angle result well-known from studies of the pure state geometric phase. It is also shown that this mixed state anholonomy can be reinterpreted as the pure state non-Abelian anholonomy of entangled states living in a suitable restriction of the quaternionic Hopf bundle. In this picture Uhlmann's parallel transport is just Pancharatnam transport of quaternionic spinors.
Manfredini, Maria; Morbidelli, Daniele; Polidoro, Sergio; Uguzzoni, Francesco
2015-01-01
The analysis of PDEs is a prominent discipline in mathematics research, both in terms of its theoretical aspects and its relevance in applications. In recent years, the geometric properties of linear and nonlinear second order PDEs of elliptic and parabolic type have been extensively studied by many outstanding researchers. This book collects contributions from a selected group of leading experts who took part in the INdAM meeting "Geometric methods in PDEs", on the occasion of the 70th birthday of Ermanno Lanconelli. They describe a number of new achievements and/or the state of the art in their discipline of research, providing readers an overview of recent progress and future research trends in PDEs. In particular, the volume collects significant results for sub-elliptic equations, potential theory and diffusion equations, with an emphasis on comparing different methodologies and on their implications for theory and applications. .
Superatoms: Electronic and Geometric Effects on Reactivity.
Reber, Arthur C; Khanna, Shiv N
2017-02-21
The relative role of electronic and geometric effects on the stability of clusters has been a contentious topic for quite some time, with the focus on electronic structure generally gaining the upper hand. In this Account, we hope to demonstrate that both electronic shell filling and geometric shell filling are necessary concepts for an intuitive understanding of the reactivity of metal clusters. This work will focus on the reactivity of aluminum based clusters, although these concepts may be applied to clusters of different metals and ligand protected clusters. First we highlight the importance of electronic shell closure in the stability of metallic clusters. Quantum confinement in small compact metal clusters results in the bunching of quantum states that are reminiscent of the electronic shells in atoms. Clusters with closed electronic shells and large HOMO-LUMO (highest occupied molecular orbital-lowest unoccupied molecular orbital) gaps have enhanced stability and reduced reactivity with O2 due to the need for the cluster to accommodate the spin of molecular oxygen during activation of the molecule. To intuitively understand the reactivity of clusters with protic species such as water and methanol, geometric effects are needed. Clusters with unsymmetrical structures and defects usually result in uneven charge distribution over the surface of the cluster, forming active sites. To reduce reactivity, these sites must be quenched. These concepts can also be applied to ligand protected clusters. Clusters with ligands that are balanced across the cluster are less reactive, while clusters with unbalanced ligands can result in induced active sites. Adatoms on the surface of a cluster that are bound to a ligand result in an activated adatom that reacts readily with protic species, offering a mechanism by which the defects will be etched off returning the cluster to a closed geometric shell. The goal of this Account is to argue that both geometric and electronic shell
Geometric Computations on Indecisive and Uncertain Points
Jorgensen, Allan; Phillips, Jeff M
2012-01-01
We study computing geometric problems on uncertain points. An uncertain point is a point that does not have a fixed location, but rather is described by a probability distribution. When these probability distributions are restricted to a finite number of locations, the points are called indecisive points. In particular, we focus on geometric shape-fitting problems and on building compact distributions to describe how the solutions to these problems vary with respect to the uncertainty in the points. Our main results are: (1) a simple and efficient randomized approximation algorithm for calculating the distribution of any statistic on uncertain data sets; (2) a polynomial, deterministic and exact algorithm for computing the distribution of answers for any LP-type problem on an indecisive point set; and (3) the development of shape inclusion probability (SIP) functions which captures the ambient distribution of shapes fit to uncertain or indecisive point sets and are admissible to the two algorithmic constructi...
Geometrical multiresolution adaptive transforms theory and applications
Lisowska, Agnieszka
2014-01-01
Modern image processing techniques are based on multiresolution geometrical methods of image representation. These methods are efficient in sparse approximation of digital images. There is a wide family of functions called simply ‘X-lets’, and these methods can be divided into two groups: the adaptive and the nonadaptive. This book is devoted to the adaptive methods of image approximation, especially to multismoothlets. Besides multismoothlets, several other new ideas are also covered. Current literature considers the black and white images with smooth horizon function as the model for sparse approximation but here, the class of blurred multihorizon is introduced, which is then used in the approximation of images with multiedges. Additionally, the semi-anisotropic model of multiedge representation, the introduction of the shift invariant multismoothlet transform and sliding multismoothlets are also covered. Geometrical Multiresolution Adaptive Transforms should be accessible to both mathematicians and com...
Spectral statistics of random geometric graphs
Dettmann, Carl P; Knight, Georgie
2016-01-01
We study the spectrum of random geometric graphs using random matrix theory. We look at short range correlations in the level spacings via the nearest neighbour and next nearest neighbour spacing distribution and long range correlations via the spectral rigidity $\\Delta_3$ statistic. These correlations in the level spacings give information about localisation of eigenvectors, level of community structure and the level of randomness within the networks. We find that the spectral statistics of random geometric graphs fits the universality of random matrix theory. In particular, the short range correlations are very close to those found in the Gaussian orthogonal ensemble of random matrix theory. For long range correlations we find deviations from Gaussian orthogonal ensemble statistics towards Poisson. We compare with previous results for Erd\\H{o}s-R\\'{e}nyi, Barab{\\'a}si-Albert and Watts-Strogatz random graphs where similar random matrix theory universality has been found.
Gilman, Robert H; Miasnikov, Alexei
2007-01-01
Each relational structure X has an associated Gaifman graph, which endows X with the properties of a graph. Suppose that X is infinite, connected and of bounded degree. A first-order sentence in the language of X is almost surely true (resp. a.s. false) for finite substructures of X if for every element x in X, the fraction of substructures of the ball of radius n around x which satisfy the sentence approaches 1 (resp. 0) as n approaches infinity. Suppose further that, for every finite substructure, X has a disjoint isomorphic substructure. Then every sentence is a.s. true or a.s. false for finite substructures of X. This is one form of the geometric zero-one law. We formulate it also in a form that does not mention the ambient infinite structure. In addition, we investigate various questions related to the geometric zero-one law.
Geometric reconstruction methods for electron tomography
Alpers, Andreas; König, Stefan; Pennington, Robert S; Boothroyd, Chris B; Houben, Lothar; Dunin-Borkowski, Rafal E; Batenburg, Kees Joost
2012-01-01
Electron tomography is becoming an increasingly important tool in materials science for studying three-dimensional morphologies and chemical compositions of nanostructures. The image quality obtained by many current algorithms is seriously affected by the problems of missing wedge artefacts and nonlinear projection intensities due to diffraction effects. The former refers to the fact that data cannot be acquired over the full $180^\\circ$ tilt range; the latter implies that for some orientations, crystalline structures can show strong contrast changes. To overcome these problems we introduce four algorithms from the mathematical fields of geometric and discrete tomography. The algorithms incorporate geometric prior knowledge (mainly convexity and homogeneity), which also in principle considerably reduces the number of tilt angles required. Results are discussed for the reconstruction of an InAs nanowire.
Theoretical discussions on the geometrical phase analysis
Energy Technology Data Exchange (ETDEWEB)
Rouviere, J.L. [CEA-Grenoble, Departement de Recherche Fondamentale sur la Matiere Condensee, SP2M, 17 rue des Martyrs, 38054 Grenoble Cedex 9 (France)]. E-mail: rouvierej@cea.fr; Sarigiannidou, E. [CEA-Grenoble, Departement de Recherche Fondamentale sur la Matiere Condensee, SP2M, 17 rue des Martyrs, 38054 Grenoble Cedex 9 (France)
2005-12-15
The Geometrical phase analysis, which is a very efficient method to measure deformation from High resolution transmission electron microscopy images, is studied from a theoretical point of view. We point out that the basic property of this method is its ability to measure local reciprocal lattice parameters with a high level of accuracy. We attempt to provide some insights into (a) different formula used in the geometrical phase analysis such as the well-known relation between phase and displacement: P{sub g}(r)=-2{pi}g.u(r), (b) the two different definitions of strain, each of which corresponding to a different lattice reference and (c) the meaning of a continuous displacement in a dot-like high resolution image. The case of one-dimensional analysis is also presented. Finally, we show that the method is able to give the position of the dot that is nearest to a given pixel in the image.
Geometrical geodesy techniques in Goddard earth models
Lerch, F. J.
1974-01-01
The method for combining geometrical data with satellite dynamical and gravimetry data for the solution of geopotential and station location parameters is discussed. Geometrical tracking data (simultaneous events) from the global network of BC-4 stations are currently being processed in a solution that will greatly enhance of geodetic world system of stations. Previously the stations in Goddard earth models have been derived only from dynamical tracking data. A linear regression model is formulated from combining the data, based upon the statistical technique of weighted least squares. Reduced normal equations, independent of satellite and instrumental parameters, are derived for the solution of the geodetic parameters. Exterior standards for the evaluation of the solution and for the scale of the earth's figure are discussed.
Geometric Correction for Braille Document Images
Directory of Open Access Journals (Sweden)
Padmavathi.S
2016-04-01
Full Text Available Braille system has been used by the visually impair ed people for reading.The shortage of Braille books has caused a need for conversion of Braille t o text. This paper addresses the geometric correction of a Braille document images. Due to the standard measurement of the Braille cells, identification of Braille characters could be achie ved by simple cell overlapping procedure. The standard measurement varies in a scaled document an d fitting of the cells become difficult if the document is tilted. This paper proposes a line fitt ing algorithm for identifying the tilt (skew angle. The horizontal and vertical scale factor is identified based on the ratio of distance between characters to the distance between dots. Th ese are used in geometric transformation matrix for correction. Rotation correction is done prior to scale correction. This process aids in increased accuracy. The results for various Braille documents are tabulated.
Geometrical vs wave optics under gravitational waves
Angélil, Raymond
2015-01-01
We present some new derivations of the effect of a plane gravitational wave on a light ray. A simple interpretation of the results is that a gravitational wave causes a phase modulation of electromagnetic waves. We arrive at this picture from two contrasting directions, namely null geodesics and Maxwell's equations, or, geometric and wave optics. Under geometric optics, we express the geodesic equations in Hamiltonian form and solve perturbatively for the effect of gravitational waves. We find that the well-known time-delay formula for light generalizes trivially to massive particles. We also recover, by way of a Hamilton-Jacobi equation, the phase modulation obtained under wave optics. Turning then to wave optics, rather than solving Maxwell's equations directly for the fields, as in most previous approaches, we derive a perturbed wave equation (perturbed by the gravitational wave) for the electromagnetic four-potential. From this wave equation it follows that the four-potential and the electric and magnetic...
Color fringe projection profilometry using geometric constraints
Cheng, Teng; Du, Qingyu; Jiang, Yaxi
2017-09-01
A recently proposed phase unwrapping method using geometric constraints performs well without requiring additional camera, more patterns or global search. The major limitation of this technique is the confined measurement depth range (MDR) within 2π in phase domain. To enlarge the MDR, this paper proposes using color fringes for three-dimensional (3D) shape measurement. Each six fringe periods encoded with six different colors are treated as one group. The local order within one group can be identified with reference to the color distribution. Then the phase wrapped period-by-period is converted into the phase wrapped group-by-group. The geometric constraints of the fringe projection system are used to determine the group order. Such that the MDR is extended from 2π to 12π by six times. Experiment results demonstrate the success of the proposed method to measure two isolated objects with large MDR.
Finsler geometric extension of Einstein gravity
Pfeifer, Christian
2011-01-01
We construct gravitational dynamics for Finsler spacetimes in terms of an action integral on the unit tangent bundle. These spacetimes are generalizations of Lorentzian metric manifolds which satisfy necessary causality properties. A coupling procedure for matter fields to Finsler gravity completes our new theory that consistently becomes equivalent to Einstein gravity in the limit of metric geometry. We provide a precise geometric definition of observers and their measurements, and show that the transformations by means of which different observers communicate form a groupoid that generalizes the usual Lorentz group. Moreover, we discuss the implementation of Finsler spacetime symmetries. We use our results to analyze a particular spacetime model that leads to Finsler geometric refinements of the linearized Schwarzschild solution.
Finsler geometric extension of Einstein gravity
Pfeifer, Christian; Wohlfarth, Mattias N. R.
2012-03-01
We construct gravitational dynamics for Finsler spacetimes in terms of an action integral on the unit tangent bundle. These spacetimes are generalizations of Lorentzian metric manifolds which satisfy necessary causality properties. A coupling procedure for matter fields to Finsler gravity completes our new theory that consistently becomes equivalent to Einstein gravity in the limit of metric geometry. We provide a precise geometric definition of observers and their measurements and show that the transformations, by means of which different observers communicate, form a groupoid that generalizes the usual Lorentz group. Moreover, we discuss the implementation of Finsler spacetime symmetries. We use our results to analyze a particular spacetime model that leads to Finsler geometric refinements of the linearized Schwarzschild solution.
Geometric dynamical observables in rare gas crystals
Energy Technology Data Exchange (ETDEWEB)
Casetti, L. [Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa (Italy); Macchi, A. [Istituto Nazionale di Fisica della Materia (INFM), Unita di Firenze, Largo Enrico Fermi 2, 50125 Firenze (Italy)
1997-03-01
We present a detailed description of how a differential geometric approach to Hamiltonian dynamics can be used for determining the existence of a crossover between different dynamical regimes in a realistic system, a model of a rare gas solid. Such a geometric approach allows us to locate the energy threshold between weakly and strongly chaotic regimes, and to estimate the largest Lyapunov exponent. We show how standard methods of classical statistical mechanics, i.e., Monte Carlo simulations, can be used for our computational purposes. Finally we consider a Lennard-Jones crystal modeling solid xenon. The value of the energy threshold turns out to be in excellent agreement with the numerical estimate based on the crossover between slow and fast relaxation to equilibrium obtained in a previous work by molecular dynamics simulations. {copyright} {ital 1997} {ital The American Physical Society}
Geometric dynamical observables in rare gas crystals
Casetti, L; Casetti, Lapo; Macchi, Alessandro
1996-01-01
We present a detailed description of how a differential geometric approach to Hamiltonian dynamics can be used for determining the existence of a crossover between different dynamical regimes in a realistic system, a model of a rare gas solid. Such a geometric approach allows to locate the energy threshold between weakly and strongly chaotic regimes, and to estimate the largest Lyapunov exponent. We show how standard mehods of classical statistical mechanics, i.e. Monte Carlo simulations, can be used for our computational purposes. Finally we consider a Lennard Jones crystal modeling solid Xenon. The value of the energy threshold turns out to be in excellent agreement with the numerical estimate based on the crossover between slow and fast relaxation to equilibrium obtained in a previous work by molecular dynamics simulations.
Topological minimally entangled states via geometric measure
Buerschaper, Oliver; García-Saez, Artur; Orús, Román; Wei, Tzu-Chieh
2014-11-01
Here we show how the Minimally Entangled States (MES) of a 2d system with topological order can be identified using the geometric measure of entanglement. We show this by minimizing this measure for the doubled semion, doubled Fibonacci and toric code models on a torus with non-trivial topological partitions. Our calculations are done either quasi-exactly for small system sizes, or using the tensor network approach in Orús et al (arXiv:1406.0585) for large sizes. As a byproduct of our methods, we see that the minimisation of the geometric entanglement can also determine the number of Abelian quasiparticle excitations in a given model. The results in this paper provide a very efficient and accurate way of extracting the full topological information of a 2d quantum lattice model from the multipartite entanglement structure of its ground states.
Geometric description of images as topographic maps
Caselles, Vicent
2010-01-01
This volume discusses the basic geometric contents of an image and presents a tree data structure to handle those contents efficiently. The nodes of the tree are derived from connected components of level sets of the intensity, while the edges represent inclusion information. Grain filters, morphological operators simplifying these geometric contents, are analyzed and several applications to image comparison and registration, and to edge and corner detection, are presented. The mathematically inclined reader may be most interested in Chapters 2 to 6, which generalize the topological Morse description to continuous or semicontinuous functions, while mathematical morphologists may more closely consider grain filters in Chapter 3. Computer scientists will find algorithmic considerations in Chapters 6 and 7, the full justification of which may be found in Chapters 2 and 4 respectively. Lastly, all readers can learn more about the motivation for this work in the image processing applications presented in Chapter 8...
Bootstrap Percolation on Random Geometric Graphs
Bradonjić, Milan
2012-01-01
Bootstrap percolation has been used effectively to model phenomena as diverse as emergence of magnetism in materials, spread of infection, diffusion of software viruses in computer networks, adoption of new technologies, and emergence of collective action and cultural fads in human societies. It is defined on an (arbitrary) network of interacting agents whose state is determined by the state of their neighbors according to a threshold rule. In a typical setting, bootstrap percolation starts by random and independent "activation" of nodes with a fixed probability $p$, followed by a deterministic process for additional activations based on the density of active nodes in each neighborhood ($\\th$ activated nodes). Here, we study bootstrap percolation on random geometric graphs in the regime when the latter are (almost surely) connected. Random geometric graphs provide an appropriate model in settings where the neighborhood structure of each node is determined by geographical distance, as in wireless {\\it ad hoc} ...
Pose measurement method based on geometrical constraints
Institute of Scientific and Technical Information of China (English)
Zimiao Zhang; Changku Sun; Pengfei Sun; Peng Wang
2011-01-01
@@ The pose estimation method based on geometric constraints is studied.The coordinates of the five feature points in the camera coordinate system are calculated to obtain the pose of an object on the basis of the geometric constraints formed by the connective lines of the feature points and the coordinates of the feature points on the CCD image plane; during the solution process,the scaling and orthography projection model is used to approximate the perspective projection model.%The pose estimation method based on geometric constraints is studied. The coordinates of the five feature points in the camera coordinate system are calculated to obtain the pose of an object on the basis of the geometric constraints formed by the connective lines of the feature points and the coordinates of the feature points on the CCD image plane; during the solution process, the scaling and orthography projection model is used to approximate the perspective projection model. The initial values of the coordinates of the five feature points in the camera coordinate system are obtained to ensure the accuracy and convergence rate of the non-linear algorithm. In accordance with the perspective projection characteristics of the circular feature landmarks, we propose an approach that enables the iterative acquisition of accurate target poses through the correction of the perspective projection coordinates of the circular feature landmark centers. Experimental results show that the translation positioning accuracy reaches ±0.05 mm in the measurement range of 0-40 mm, and the rotation positioning accuracy reaches ±0.06° in the measurement range of 4°-60°.
Protein Folding: A New Geometric Analysis
Simmons, Walter A.; Joel L. Weiner
2008-01-01
A geometric analysis of protein folding, which complements many of the models in the literature, is presented. We examine the process from unfolded strand to the point where the strand becomes self-interacting. A central question is how it is possible that so many initial configurations proceed to fold to a unique final configuration. We put energy and dynamical considerations temporarily aside and focus upon the geometry alone. We parameterize the structure of an idealized protein using the ...
A new geometric approach to Sturmian words
Matomäki, Kaisa
2012-01-01
We introduce a new geometric approach to Sturmian words by means of a mapping that associates certain lines in the n x n -grid and sets of finite Sturmian words of length n. Using this mapping, we give new proofs of the formulas enumerating the finite Sturmian words and the palindromic finite Sturmian words of a given length. We also give a new proof for the well-known result that a factor of a Sturmian word has precisely two return words.
Geometrical characterization of micro end milling tools
DEFF Research Database (Denmark)
Borsetto, Francesca; Bariani, Paolo; Bissacco, Giuliano
2005-01-01
Performance of the milling process is directly affected by the accuracy of tool geometry. Development of methods suitable for dimensional characterization of such tools, with low measurement uncertainties is therefore of relevance. The present article focuses on the geometrical characterization o...... of a flat micro end milling tool with a nominal mill diameter of 200 microns. An experimental investigation was carried out involving two different non-contact systems...
Geometrical characterization of micro end milling tools
DEFF Research Database (Denmark)
Borsetto, Francesca; Bariani, Paolo; Bissacco, Giuliano;
2005-01-01
Performance of the milling process is directly affected by the accuracy of tool geometry. Development of methods suitable for dimensional characterization of such tools, with low measurement uncertainties is therefore of relevance. The present article focuses on the geometrical characterization...... of a flat micro end milling tool with a nominal mill diameter of 200 microns. An experimental investigation was carried out involving two different non-contact systems...
Geometric Measure Theory and Minimal Surfaces
Bombieri, Enrico
2011-01-01
W.K. ALLARD: On the first variation of area and generalized mean curvature.- F.J. ALMGREN Jr.: Geometric measure theory and elliptic variational problems.- E. GIUSTI: Minimal surfaces with obstacles.- J. GUCKENHEIMER: Singularities in soap-bubble-like and soap-film-like surfaces.- D. KINDERLEHRER: The analyticity of the coincidence set in variational inequalities.- M. MIRANDA: Boundaries of Caciopoli sets in the calculus of variations.- L. PICCININI: De Giorgi's measure and thin obstacles.
Noncommutative Geometric Gauge Theory from Superconnections
Lee, Chang-Yeong
1996-01-01
Noncommutative geometric gauge theory is reconstructed based on the superconnection concept. The bosonic action of the Connes-Lott model including the symmetry breaking Higgs sector is obtained by using a new generalized derivative, which consists of the usual 1-form exterior derivative plus an extra element called the matrix derivative, for the curvatures. We first derive the matrix derivative based on superconnections and then show how the matrix derivative can give rise to spontaneous symm...
Chirality: a relational geometric-physical property.
Gerlach, Hans
2013-11-01
The definition of the term chirality by Lord Kelvin in 1893 and 1904 is analyzed by taking crystallography at that time into account. This shows clearly that chirality is a relational geometric-physical property, i.e., two relations between isometric objects are possible: homochiral or heterochiral. In scientific articles the relational term chirality is often mistaken for the two valued measure for the individual (absolute) sense of chirality, an arbitrary attributive term.
Geometric stochastic resonance in a double cavity
Ghosh, Pulak K; Marchesoni, Fabio; Savel'ev, Sergey E; Nori, Franco; 10.1103/PhysRevE.84.011109
2012-01-01
Geometric stochastic resonance of particles diffusing across a porous membrane subject to oscillating forces is characterized as a synchronization process. Noninteracting particle currents through a symmetric membrane pore are driven either perpendicular or parallel to the membrane, whereas harmonic-mixing spectral current components are generated by the combined action of perpendicular and parallel drives. In view of potential applications to the transport of colloids and biological molecules through narrow pores, we also consider the role of particle repulsion as a controlling factor.
A geometrical approach to structural change modeling
Stijepic, Denis
2013-01-01
We propose a model for studying the dynamics of economic structures. The model is based on qualitative information regarding structural dynamics, in particular, (a) the information on the geometrical properties of trajectories (and their domains) which are studied in structural change theory and (b) the empirical information from stylized facts of structural change. We show that structural change is path-dependent in this model and use this fact to restrict the number of future structural cha...
Geometric problems in molecular biology and robotics.
Parsons, D; Canny, J
1994-01-01
Some of the geometric problems of interest to molecular biologists have macroscopic analogues in the field of robotics. Two examples of such analogies are those between protein docking and model-based perception, and between ring closure and inverse kinematics. Molecular dynamics simulation, too, has much in common with the study of robot dynamics. In this paper we give a brief survey of recent work on these and related problems.
Geometric treatment of the gravitomagnetic clock effect
Tartaglia, A
2000-01-01
We have developed a general geometric treatment of the GCE valid for any stationary axisymmetric metric. The method is based on the remark that the world lines of objects rotating along spacely circular trajectories are in any case, for those kind of metrics, helices drawn on the flat bidimensional surface of a cylinder. Applying the obtained formulas to the special cases of the Kerr and weak field metric for a spinning body, known results for time delays and synchrony defects are recovered.
Implicitization of surfaces via geometric tropicalization
Cueto, Maria Angelica
2011-01-01
In this paper we describe tropical methods for implicitization of surfaces. We construct the corresponding tropical surfaces via the theory of geometric tropicalization due to Hacking, Keel and Tevelev, which we enrich with a formula for computing tropical multiplicities of regular points in any dimension. We extend previous results for tropical implicitization of generic surfaces due to Sturmfels, Tevelev and Yu and provide methods for the non-generic case.
The Minimal Geometric Deformation Approach Extended
Casadio, Roberto; da Rocha, Roldao
2015-01-01
The minimal geometric deformation approach was introduced in order to study the exterior space-time around spherically symmetric self-gravitating systems, like stars or similar astrophysical objects as well, in the Randall-Sundrum brane-world framework. A consistent extension of this approach is developed here, which contains modifications of both the time component and the radial component of a spherically symmetric metric. A modified Schwarzschild geometry is obtained as an example of its simplest application.
Geometrical model of multidimensional orbital motion
Energy Technology Data Exchange (ETDEWEB)
Jacak, D [Institute of Mathematics and Computer Science, Wroclaw University of Technology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw (Poland)], E-mail: dorota.jacak@pwr.wroc.pl
2008-05-15
We consider a geometrical n-dimensional model of orbital-type rotation, for n{>=}4. The vectors generating this process are defined and the Fibonacci sequence is found in representation of their lengths. Within the dimension analysis of Planck units, we consider an example of the multidimensional whirl and define a sequence of formal fields. Special attention is paid to the three subsequent elements of this sequence, called here magnetic, electric and energy fields, which allow for some physical interpretations.
Geometrical effective action and Wilsonian flows
Pawlowski, J M
2003-01-01
A gauge invariant flow equation is derived by applying a Wilsonian momentum cut-off to gauge invariant field variables. The construction makes use of the geometrical effective action for gauge theories in the Vilkovisky-DeWitt framework. The approach leads to modified Nielsen identities that pose non-trivial constraints on consistent truncations. We also evaluate the relation of the present approach to gauge fixed formulations as well as discussing possible applications.
Geometric measure theory a beginner's guide
Morgan, Frank
1995-01-01
Geometric measure theory is the mathematical framework for the study of crystal growth, clusters of soap bubbles, and similar structures involving minimization of energy. Morgan emphasizes geometry over proofs and technicalities, and includes a bibliography and abundant illustrations and examples. This Second Edition features a new chapter on soap bubbles as well as updated sections addressing volume constraints, surfaces in manifolds, free boundaries, and Besicovitch constant results. The text will introduce newcomers to the field and appeal to mathematicians working in the field.
Integrating geometric activity images in ANN classification
De Genst, William; Gautama, Sidharta; Bellens, Rik; Canters, Frank
2005-10-01
In this paper we demonstrate how the interaction between innovative methods in the field of computer vision and methods for multi-spectral image classification can help in extracting detailed land-cover / land-use information from Very High Resolution (VHR) satellite imagery. We introduce the novel concept of "geometric activity images", which we define as images encoding the strength of the relationship between a pixel and surrounding features detected through dedicated computer vision methods. These geometric activity images are used as alternatives to more traditional texture images that better describe the geometry of man-made structures and that can be included as additional information in a non-parametric supervised classification framework. We present a number of findings resulting from the integration of geometric activity images and multi-spectral bands in an artificial neural network classification. The geometric activity images we use result from the use of a ridge detector for straight line detection, calculated for different window sizes and for all multi-spectral bands and band-ratio images in a VHR scene. A selection of the most relevant bands to use for classification is carried out using band selection based on a genetic algorithm. Sensitivity analysis is used to assess the importance of each input variable. An application of the proposed methods to part of a Quickbird image taken over the suburban fringe of the city of Ghent (Belgium) shows that we are able to identify roads with much higher accuracy than when using more traditional multi-spectral image classification techniques.
Geometrical Methods for Power Network Analysis
Bellucci, Stefano; Gupta, Neeraj
2013-01-01
This book is a short introduction to power system planning and operation using advanced geometrical methods. The approach is based on well-known insights and techniques developed in theoretical physics in the context of Riemannian manifolds. The proof of principle and robustness of this approach is examined in the context of the IEEE 5 bus system. This work addresses applied mathematicians, theoretical physicists and power engineers interested in novel mathematical approaches to power network theory.
Geometric Effects on the Amplification of First Mode Instability Waves
Kirk, Lindsay C.; Candler, Graham V.
2013-01-01
The effects of geometric changes on the amplification of first mode instability waves in an external supersonic boundary layer were investigated using numerical techniques. Boundary layer stability was analyzed at Mach 6 conditions similar to freestream conditions obtained in quiet ground test facilities so that results obtained in this study may be applied to future test article design to measure first mode instability waves. The DAKOTA optimization software package was used to optimize an axisymmetric geometry to maximize the amplification of the waves at first mode frequencies as computed by the 2D STABL hypersonic boundary layer stability analysis tool. First, geometric parameters such as nose radius, cone half angle, vehicle length, and surface curvature were examined separately to determine the individual effects on the first mode amplification. Finally, all geometric parameters were allowed to vary to produce a shape optimized to maximize the amplification of first mode instability waves while minimizing the amplification of second mode instability waves. Since first mode waves are known to be most unstable in the form of oblique wave, the geometries were optimized using a broad range of wave frequencies as well as a wide range of oblique wave angles to determine the geometry that most amplifies the first mode waves. Since first mode waves are seen most often in flows with low Mach numbers at the edge of the boundary layer, the edge Mach number for each geometry was recorded to determine any relationship between edge Mach number and the stability of first mode waves. Results indicate that an axisymmetric cone with a sharp nose and a slight flare at the aft end under the Mach 6 freestream conditions used here will lower the Mach number at the edge of the boundary layer to less than 4, and the corresponding stability analysis showed maximum first mode N factors of 3.
Edit propagation using geometric relationship functions
Guerrero, Paul
2014-03-01
We propose a method for propagating edit operations in 2D vector graphics, based on geometric relationship functions. These functions quantify the geometric relationship of a point to a polygon, such as the distance to the boundary or the direction to the closest corner vertex. The level sets of the relationship functions describe points with the same relationship to a polygon. For a given query point, we first determine a set of relationships to local features, construct all level sets for these relationships, and accumulate them. The maxima of the resulting distribution are points with similar geometric relationships. We show extensions to handle mirror symmetries, and discuss the use of relationship functions as local coordinate systems. Our method can be applied, for example, to interactive floorplan editing, and it is especially useful for large layouts, where individual edits would be cumbersome. We demonstrate populating 2D layouts with tens to hundreds of objects by propagating relatively few edit operations. © 2014 ACM 0730-0301/2014/03- ART15 $15.00.
Stabilization of LCD devices via geometric alteration.
Jeon, Il; Yoon, MinSung; Lee, Je-Hoon
2013-02-20
Glass bending in LCD displays is an inherent problem that has challenged many engineers. As a solution to this problem, we propose a methodology that can tackle the root of the phenomenon in terms of linear elastic beam theory. Using this hypothesis, we devised a background theory and a solution. In this paper, we present a glass panel to which geometrical changes, such as furrow, groove, and curb have been applied. These geometrical changes are applied to the nonactive area of the glass panel. To confirm the validity of our approach, we conducted simulation tests as well as hands-on experiments to observe the thermo-mechanical behavior of the device under various conditions. The simulation results using the Ansys simulator show that the proposed technique can reduce the deformation level of panel bending by 40%. In the experiment using a bare cell with polarizer films attached and with performing the high temperature reliability test, the deformation level of panel bending is reduced by half compared to the reference glass panel without any geometric alteration.
Geometric absorption of electromagnetic angular momentum
Konz, C.; Benford, Gregory
2003-10-01
Circularly polarized electromagnetic fields carry both energy and angular momentum. We investigate the conditions under which a circularly polarized wave field transfers angular momentum to a perfectly conducting macroscopic object, using exact electromagnetic wave theory in a steady-state calculation. We find that axisymmetric perfect conductors cannot absorb or radiate angular momentum when illuminated. However, any asymmetry allows absorption. A rigorous, steady-state solution of the boundary value problem for the reflection from a perfectly conducting infinite wedge shows that waves convey angular momentum at the edges of asymmetries. Conductors can also radiate angular momentum, so their geometric absorption coefficient for angular momentum can be negative. Such absorption or radiation depends solely on the specific geometry of the conductor. The geometric absorption coefficient can be as high as 0.8, and the coefficient for radiation can be -0.4, larger than typical material absorption coefficients. We apply the results to recent experiments which spun roof-shaped aluminum sheets with polarized microwave beams. Applications of geometric, instead of material, absorption can be quite varied. Though experiments testing these ideas will be simpler at microwavelengths, the ideas work for optical ones as well.
Geometry and topology of geometric limits I
Ohshika, Ken'ichi
2010-01-01
In this paper, we are concerned with hyperbolic 3-manifolds $\\hyperbolic^3/G$ such that $G$ are geometric limits of Kleinian surface groups isomorphic to $\\pi_1(S)$ for a finite-type hyperbolic surface $S$. In the first of the three main theorems, we shall show that such a hyperbolic 3-manifold is uniformly bi-Lipschitz homeomorphic to a model manifold which has a structure called brick decomposition and is embedded in $S \\times (0,1)$. Conversely, any such manifold admitting a brick decomposition with reasonable conditions is bi-Lipschitz homeomorphic to a hyperbolic manifold corresponding to some geometric limit of quasi-Fuchsian groups. Finally, it will be shown that we can define end invariants for hyperbolic 3-manifolds appearing as geometric limits of Kleinian surface groups, and that the homeomorphism type and the end invariants determine the isometric type of a manifold, which is analogous to the ending lamination theorem for the case of finitely generated Kleinian groups.
Geometric Deep Learning: Going beyond Euclidean data
Bronstein, Michael M.; Bruna, Joan; LeCun, Yann; Szlam, Arthur; Vandergheynst, Pierre
2017-07-01
Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions), and are natural targets for machine learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of these structures are built into networks used to model them. Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds. The purpose of this paper is to overview different examples of geometric deep learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field.
Time as a geometric property of space
Chappell, James; Hartnett, John; Iannella, Nicolangelo; Iqbal, Azhar; Abbott, Derek
2016-11-01
The proper description of time remains a key unsolved problem in science. Newton conceived of time as absolute and universal which `flows equably without relation to anything external'. In the nineteenth century, the four-dimensional algebraic structure of the quaternions developed by Hamilton, inspired him to suggest that they could provide a unified representation of space and time. With the publishing of Einstein's theory of special relativity these ideas then lead to the generally accepted Minkowski spacetime formulation in 1908. Minkowski, though, rejected the formalism of quaternions suggested by Hamilton and adopted rather an approach using four-vectors. The Minkowski framework is indeed found to provide a versatile formalism for describing the relationship between space and time in accordance with Einstein's relativistic principles, but nevertheless fails to provide more fundamental insights into the nature of time itself. In order to answer this question we begin by exploring the geometric properties of three-dimensional space that we model using Clifford geometric algebra, which is found to contain sufficient complexity to provide a natural description of spacetime. This description using Clifford algebra is found to provide a natural alternative to the Minkowski formulation as well as providing new insights into the nature of time. Our main result is that time is the scalar component of a Clifford space and can be viewed as an intrinsic geometric property of three-dimensional space without the need for the specific addition of a fourth dimension.
Time as a geometric property of space
Directory of Open Access Journals (Sweden)
James Michael Chappell
2016-11-01
Full Text Available The proper description of time remains a key unsolved problem in science. Newton conceived of time as absolute and universal which it `flows equably without relation to anything external'}. In the nineteenth century, the four-dimensional algebraic structure of the quaternions developed by Hamilton, inspired him to suggest that they could provide a unified representation of space and time. With the publishing of Einstein's theory of special relativity these ideas then lead to the generally accepted Minkowski spacetime formulation in 1908. Minkowski, though, rejected the formalism of quaternions suggested by Hamilton and adopted rather an approach using four-vectors. The Minkowski framework is indeed found to provide a versatile formalism for describing the relationship between space and time in accordance with Einstein's relativistic principles, but nevertheless fails to provide more fundamental insights into the nature of time itself. In order to answer this question we begin by exploring the geometric properties of three-dimensional space that we model using Clifford geometric algebra, which is found to contain sufficient complexity to provide a natural description of spacetime. This description using Clifford algebra is found to provide a natural alternative to the Minkowski formulation as well as providing new insights into the nature of time. Our main result is that time is the scalar component of a Clifford space and can be viewed as an intrinsic geometric property of three-dimensional space without the need for the specific addition of a fourth dimension.
Geometric Approach to Lie Symmetry of Discrete Time Toda Equation
Institute of Scientific and Technical Information of China (English)
JIA Xiao-Yu; WANG Na
2009-01-01
By using the extended Harrison and Estabrook geometric approach,we investigate the Lie symmetry of discrete time Toda equation from the geometric point of view.Its one-dimensional continuous symmetry group is presented.
Geometrical approach to the evaluation of multileg Feynman diagrams
Energy Technology Data Exchange (ETDEWEB)
Davydychev, A.I. [Department of Physics, University of Mainz, Mainz (Germany); Delbourgo, R. [Physics Department, University of Tasmania, Hobart, Tasmania (Australia)
1998-10-01
A connection between one-loop N-point Feynman diagrams and certain geometrical quantities in non-Euclidean geometry is discussed. A geometrical way to calculate the corresponding Feynman integrals is considered. (author)
Geometric Approaches to Quadratic Equations from Other Times and Places.
Allaire, Patricia R.; Bradley, Robert E.
2001-01-01
Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)
Geometrical and computer modeling of mechanical engineering surfaces products intersection line
Panchuk, K. L.; Kaygorodtseva, N. V.; Kaygorodtseva, T. N.; Yurkov, V. Yu
2017-06-01
In the design and manufacture of engineering products geometrical problem is known by shaping the surface of the product. An important element of general solution of this problem is to define the lines of surfaces intersection, forming the shape of designed product. Existing possibilities of modern CAD systems do not allow achieving fullness of the result in this direction. For example, control points and change point of visibility is difficult to identify in the product drawings. In addition, there are no possibilities of detecting imaginary points which are necessary for a complete analysis of intersection surfaces, and mapping these points in the drawing. The aim of the study is to develop a geometric algorithm of constructive determining the intersection line and is devoid of these shortcomings. The objectives of the study are testing the obtained algorithm by experimental verification with geometric modeling solutions to specific problems by tools CAD. This study adopted the method, which is based on quotient of geometric sets, which are regarded as intersecting surfaces in space E3 . One area of practical use of surface engineering products geometric algorithm - shaping is based on their intersection line.
Geometrical and Monte Carlo projectors in 3D PET reconstruction
Aguiar, Pablo; Rafecas López, Magdalena; Ortuno, Juan Enrique; Kontaxakis, George; Santos, Andrés; Pavía, Javier; Ros, Domènec
2010-01-01
Purpose: In the present work, the authors compare geometrical and Monte Carlo projectors in detail. The geometrical projectors considered were the conventional geometrical Siddon ray-tracer (S-RT) and the orthogonal distance-based ray-tracer (OD-RT), based on computing the orthogonal distance from the center of image voxel to the line-of-response. A comparison of these geometrical projectors was performed using different point spread function (PSF) models. The Monte Carlo-based method under c...
Learning with touchscreen devices: game strategies to improve geometric thinking
Soldano, Carlotta; Arzarello, Ferdinando
2016-03-01
The aim of this paper is to reflect on the importance of the students' game-strategic thinking during the development of mathematical activities. In particular, we hypothesise that this type of thinking helps students in the construction of logical links between concepts during the "argumentation phase" of the proving process. The theoretical background of our study lies in the works of J. Hintikka, a Finnish logician, who developed a new type of logic, based on game theory, called the logic of inquiry. In order to experiment with this new approach to the teaching and learning of mathematics, we have prepared five game-activities based on geometric theorems in which two players play against each other in a multi-touch dynamic geometric environment (DGE). In this paper, we present the design of the first game-activity and the relationship between it and the logic of inquiry. Then, adopting the theoretical framework of the instrumental genesis by Vérillon and Rabardel (EJPE 10: 77-101, 1995), we will present and analyse significant actions and dialogues developed by students while they are solving the game. We focus on the presence of a particular way of playing the game introduced by the students, the "reflected game", and highlight its functions for the development of the task.
Scale Problems in Geometric-Kinematic Modelling of Geological Objects
Siehl, Agemar; Thomsen, Andreas
To reveal, to render and to handle complex geological objects and their history of structural development, appropriate geometric models have to be designed. Geological maps, sections, sketches of strain and stress patterns are such well-known analogous two-dimensional models. Normally, the set of observations and measurements supporting them is small in relation to the complexity of the real objects they derive from. Therefore, modelling needs guidance by additional expert knowledge to bridge empty spaces which are not supported by data. Generating digital models of geological objects has some substantial advantages compared to conventional methods, especially if they are supported by an efficient database management system. Consistent 3D models of some complexity can be created, and experiments with time-dependent geological geometries may help to restore coherent sequences of paleogeological states. In order to cope with the problems arising from the combined usage of 3D-geometry models of different scale and resolution within an information system on subsurface geology, geometrical objects need to be annotated with information on the context, within which the geometry model has been established and within which it is valid, and methods supporting storage and retrieval as well as manipulation of geometry at different scales must also take into account and handle such context information to achieve meaningful results. An example is given of a detailed structural study of an open pit lignite mine in the Lower Rhine Basin.
Geometric algebra and information geometry for quantum computational software
Cafaro, Carlo
2017-03-01
The art of quantum algorithm design is highly nontrivial. Grover's search algorithm constitutes a masterpiece of quantum computational software. In this article, we use methods of geometric algebra (GA) and information geometry (IG) to enhance the algebraic efficiency and the geometrical significance of the digital and analog representations of Grover's algorithm, respectively. Specifically, GA is used to describe the Grover iterate and the discretized iterative procedure that exploits quantum interference to amplify the probability amplitude of the target-state before measuring the query register. The transition from digital to analog descriptions occurs via Stone's theorem which relates the (unitary) Grover iterate to a suitable (Hermitian) Hamiltonian that controls Schrodinger's quantum mechanical evolution of a quantum state towards the target state. Once the discrete-to-continuos transition is completed, IG is used to interpret Grover's iterative procedure as a geodesic path on the manifold of the parametric density operators of pure quantum states constructed from the continuous approximation of the parametric quantum output state in Grover's algorithm. Finally, we discuss the dissipationless nature of quantum computing, recover the quadratic speedup relation, and identify the superfluity of the Walsh-Hadamard operation from an IG perspective with emphasis on statistical mechanical considerations.
Weighted Geometric Dilution of Precision Calculations with Matrix Multiplication
Directory of Open Access Journals (Sweden)
Chien-Sheng Chen
2015-01-01
Full Text Available To enhance the performance of location estimation in wireless positioning systems, the geometric dilution of precision (GDOP is widely used as a criterion for selecting measurement units. Since GDOP represents the geometric effect on the relationship between measurement error and positioning determination error, the smallest GDOP of the measurement unit subset is usually chosen for positioning. The conventional GDOP calculation using matrix inversion method requires many operations. Because more and more measurement units can be chosen nowadays, an efficient calculation should be designed to decrease the complexity. Since the performance of each measurement unit is different, the weighted GDOP (WGDOP, instead of GDOP, is used to select the measurement units to improve the accuracy of location. To calculate WGDOP effectively and efficiently, the closed-form solution for WGDOP calculation is proposed when more than four measurements are available. In this paper, an efficient WGDOP calculation method applying matrix multiplication that is easy for hardware implementation is proposed. In addition, the proposed method can be used when more than exactly four measurements are available. Even when using all-in-view method for positioning, the proposed method still can reduce the computational overhead. The proposed WGDOP methods with less computation are compatible with global positioning system (GPS, wireless sensor networks (WSN and cellular communication systems.
Geometric plane shapes for computer-generated holographic engraving codes
Augier, Ángel G.; Rabal, Héctor; Sánchez, Raúl B.
2017-04-01
We report a new theoretical and experimental study on hologravures, as holographic computer-generated laser-engravings. A geometric theory of images based on the general principles of light ray behaviour is shown. The models used are also applicable for similar engravings obtained by any non-laser method, and the solutions allow for the analysis of particular situations, not only in the case of light reflection mode, but also in transmission mode geometry. This approach is a novel perspective allowing the three-dimensional (3D) design of engraved images for specific ends. We prove theoretically that plane curves of very general geometric shapes can be used to encode image information onto a two-dimensional (2D) engraving, showing notable influence on the behaviour of reconstructed images that appears as an exciting investigation topic, extending its applications. Several cases of code using particular curvilinear shapes are experimentally studied. The computer-generated objects are coded by using the chosen curve type, and engraved by a laser on a plane surface of suitable material. All images are recovered optically by adequate illumination. The pseudoscopic or orthoscopic character of these images is considered, and an appropriate interpretation is presented.
A Geometric Algebra Co-Processor for Color Edge Detection
Directory of Open Access Journals (Sweden)
Biswajit Mishra
2015-01-01
Full Text Available This paper describes advancement in color edge detection, using a dedicated Geometric Algebra (GA co-processor implemented on an Application Specific Integrated Circuit (ASIC. GA provides a rich set of geometric operations, giving the advantage that many signal and image processing operations become straightforward and the algorithms intuitive to design. The use of GA allows images to be represented with the three R, G, B color channels defined as a single entity, rather than separate quantities. A novel custom ASIC is proposed and fabricated that directly targets GA operations and results in significant performance improvement for color edge detection. Use of the hardware described in this paper also shows that the convolution operation with the rotor masks within GA belongs to a class of linear vector filters and can be applied to image or speech signals. The contribution of the proposed approach has been demonstrated by implementing three different types of edge detection schemes on the proposed hardware. The overall performance gains using the proposed GA Co-Processor over existing software approaches are more than 3.2× faster than GAIGEN and more than 2800× faster than GABLE. The performance of the fabricated GA co-processor is approximately an order of magnitude faster than previously published results for hardware implementations.
Geometric Optimization of Hydraulic Rotation Device for Neutron Transmutation Doping
Energy Technology Data Exchange (ETDEWEB)
Park, Yongsoo; Kang, Hanok; Park, Kijung; Kim, Seong Hoon; Park, Cheol [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2014-05-15
The Korea Atomic Energy Research Institute (KAERI) is developing a Hydraulic Rotation Device (HRD) for NTD facilities (NTDHRD) as a part of the Kijang Research Reactor (KJRR) project. This concept has many advantages when compared to the motor driven method, which is currently used in the HANARO research reactor located at KAERI. The OPAL research reactor located at ANSTO has already applied this method. To achieve a constant rotation speed, which is substantial for uniform doping, with a minimal amount of fluid flow, certain geometric requirements should be satisfied. This paper describes the approach we used while determining the number of impulse jet nozzles used to rotate the NTDHRD at a set number of blades as well as the angle of the nozzles of the NTDHRD. The approach that our group has used to geometrically optimize the design of a NTDHRD was described. The adaptation of this approach allows one to predict the required amount of inlet fluid flow and to determine the number of nozzles based on the rule that it should avoid being a divisor of the number of blades, and provides a reference while determining the tile angle of the nozzles. A CFD analysis will be performed as a future study.
Geometric magnetic and discriminator sensor for smart pigs
Energy Technology Data Exchange (ETDEWEB)
Vinicius, C. [Pipeway, Lima (Peru); Silva, J.A.P. [Pipeway, Rio de Janeiro (Brazil); Von der Weid, J.P. [Pontifica Univ. Catolica, Rio de Janeiro (Brazil); Oliveira, C.H.F.; Camerini, C.S. [Petrobras, Rio de Janeiro (Brazil)
2004-07-01
A novel sensor head developed for high resolution magnetic flux leakage (MFL) pigs was evaluated. Designed by a Brazilian research team, the geometric magnetic discriminator (GMD) sensor makes high resolution magnetic pipeline readings using 3 different technologies: (1) MFL; (2) geometric readings and (3) a DMC discriminator. The evaluation tests were conducted to verify that the addition of the discriminator was not compromised by the MFL sensors, as well as to determine if the MFL sensors were capable of sizing and discriminating a dent with metal loss. The GMD sensor was tested in a linear test rig at a laboratory. Defects were fabricated on steel plates. Results showed that the MFL sensors showed the same signature both with and without the DMC sensor attachment. However, the DMC sensor signaled external defects when placed inside the MFL module. It observed that the signal originated from the perpendicular components of the field lines. The MFL sensors also emitted signals that were approximately 15 Gauss in amplitude. Flux leakage was observed in dent corners. However, the dent was identified and characterized with the addition of a geometry sensor. For combined dents with external and internal metals, the GMD was capable of characterizing the dent using the geometry sensor, while the metal loss defect was characterized using the MFL sensor. Inside and outside discrimination was characterized by the discriminator. It was concluded that the introduction of a DMC discriminator sensor had little impact on the MFL sensors. 10 refs., 1 tab., 11 figs.
A Geometric Approach to the Six Trigonometric Ratios.
Bonsangue, Martin V.
1993-01-01
Geometric interpretations and derivations of the six trigonometric relationships are demonstrated. Selected for discussion are limiting values, geometric verification of trigonometric identities, a one-dimensional illustration of the Pythagorean relationships, and the geometric derivation of infinite-series relationships. (DE)
Geometric Error Analysis in Applied Calculus Problem Solving
Usman, Ahmed Ibrahim
2017-01-01
The paper investigates geometric errors students made as they tried to use their basic geometric knowledge in the solution of the Applied Calculus Optimization Problem (ACOP). Inaccuracies related to the drawing of geometric diagrams (visualization skills) and those associated with the application of basic differentiation concepts into ACOP…
Identifying and Fostering Higher Levels of Geometric Thinking
Škrbec, Maja; Cadež, Tatjana Hodnik
2015-01-01
Pierre M. Van Hiele created five levels of geometric thinking. We decided to identify the level of geometric thinking in the students in Slovenia, aged 9 to 11 years. The majority of students (60.7%) are at the transition between the zero (visual) level and the first (descriptive) level of geometric thinking. Nearly a third (31.7%) of students is…
Some Asymptotic Inference in Multinomial Nonlinear Models (a Geometric Approach)
Institute of Scientific and Technical Information of China (English)
WEIBOCHENG
1996-01-01
A geometric framework is proposed for multinomlat nonlinear modelsbased on a modified vemlon of the geometric structure presented by Bates & Watts[4]. We use this geometric framework to study some asymptotic inference in terms ofcurvtures for multlnomial nonlinear models. Our previous results [15] for ordlnary nonlinear regression models are extended to multlnomlal nonlinear models.
Non-adiabatic geometrical quantum gates in semiconductor quantum dots
Solinas, P; Zanghì, N; Rossi, F; Solinas, Paolo; Zanardi, Paolo; Zanghì, Nino; Rossi, Fausto
2003-01-01
In this paper we study the implementation of non-adiabatic geometrical quantum gates with in semiconductor quantum dots. Different quantum information enconding/manipulation schemes exploiting excitonic degrees of freedom are discussed. By means of the Aharanov-Anandan geometrical phase one can avoid the limitations of adiabatic schemes relying on adiabatic Berry phase; fast geometrical quantum gates can be in principle implemented
Institute of Scientific and Technical Information of China (English)
姜世平; 马亚光; 李洁
2009-01-01
以潜油单螺杆泵采油系统中的并联行星齿轮减速器为研究对象,结合等圆截面杆的弹性扭转几何大变形位移公式,通过Matlab软件计算,建立了并联行星齿轮减速器中并联太阳轮轴扭转变形的数学模型,应用各段并联太阳轮轴扭转变形协调原理和等功率传递原理,设计了并联行星齿轮减速器.该减速器在传递额定功率的情况下可以大幅度减小径向尺寸.%Taking the parallel planetary gear reducer in the submersible single screw pump oil-extraction system as the target of research, combining with the displacement formula of elastic tor-sional geometric large deformation of equalized circular sectioned rod and through the calculation of Matlab software the mathematical model of torsional deformation of parallel sun gear shaft in the paral-lel planetary gear reducer was established. Using the coordination principle and the uniform power transmission principle of torsional deformations in each section of parallel sun gear shaft, the parallel planetary gear reducer was designed. The radial dimensions of this reducer could be minimized to a large range under the condition of transmitting rated power.
Institute of Scientific and Technical Information of China (English)
张龙; 林珠灿; 张睿卓; 郭素华
2015-01-01
ABSTRACT:OBJECTIVE To study the optimal proportion of the compatibility of Sedum aizoon L .and Semen Ziziphus Spinosa on hypnotic effect .METHODS According to the increase-decrease baseline geometric proportion design method , different proportion compatibility of Sedum aizoon L .and Semen Ziziphus Spinosa were optimized through observing the pentobarbital-induced sleep in mice.RESULTS Compared with the control group,prescrip-tions 3,4 could extent the sleep time significantly and increased the sleep rate (P<0.01),and the prescriptions 3 was best.CONCLUSION Prescriptions 3 is the best proportion of the compatibility of Sedum aizoon L .and Semen Ziziphus Spinosa.on hypnotic effects.%目的：优选养心草与酸枣仁配伍安神作用的最佳配比。方法采用基线等比增减法拟定养心草与酸枣仁不同比例配伍，观察其对小鼠协同戊巴比妥钠睡眠实验的影响。结果与空白组相比，处方3，4能显著延长小鼠的睡眠时间和增加小鼠入睡率（P＜0．01），且以处方3药效最佳。结论处方3为养心草配伍酸枣仁安神作用的最佳比例。
Van Dijk, N.P.
2012-01-01
This thesis aims at understanding and improving topology optimization techniques focusing on density-based level-set methods and geometrical nonlinearities. Central in this work are the numerical modeling of the mechanical response of a design and the consistency of the optimization process itself.
Gol Tabaghi, Shiva; Sinclair, Nathalie
2013-01-01
This article analyses students' thinking as they interacted with a dynamic geometric sketch designed to explore eigenvectors and eigenvalues. We draw on the theory of instrumental genesis and, in particular, attend to the different dragging modalities used by the students throughout their explorations. Given the kinaesthetic and dynamic…
A perturbation method for the A-χ geometric eddy-current formulation
Specogna, R.; Dular, P.; Trevisan, F.
2010-11-01
A perturbation method for the A-χ geometric formulation to solve eddy-current problems is introduced. The proposed formulation is applied to the feasibility design of a non-destructive evaluation device suitable to detect “long” longitudinal flaws in hot steel bars.
Gol Tabaghi, Shiva; Sinclair, Nathalie
2013-01-01
This article analyses students' thinking as they interacted with a dynamic geometric sketch designed to explore eigenvectors and eigenvalues. We draw on the theory of instrumental genesis and, in particular, attend to the different dragging modalities used by the students throughout their explorations. Given the kinaesthetic and dynamic…
Arici, Sevil; Aslan-Tutak, Fatma
2015-01-01
This research study examined the effect of origami-based geometry instruction on spatial visualization, geometry achievement, and geometric reasoning of tenth-grade students in Turkey. The sample ("n" = 184) was chosen from a tenth-grade population of a public high school in Turkey. It was a quasi-experimental pretest/posttest design. A…
Cheung, J; Veldhuizen, AG; Halberts, JPK; Sluiter, WJ; Van Horn, [No Value
2006-01-01
Study Design. The natural history of patients with idiopathic scoliosis was analyzed radiographically and electromyographically in a prospective longitudinal study. Objectives. To identify changes in geometric variables and the sequence in which these changes occur during curve progression in the na
Arici, Sevil; Aslan-Tutak, Fatma
2015-01-01
This research study examined the effect of origami-based geometry instruction on spatial visualization, geometry achievement, and geometric reasoning of tenth-grade students in Turkey. The sample ("n" = 184) was chosen from a tenth-grade population of a public high school in Turkey. It was a quasi-experimental pretest/posttest design. A…
DEFF Research Database (Denmark)
Mahmood, Faisal; Gehl, Julie
2011-01-01
and genes to intracranial tumors in humans, and demonstrate a method to optimize the design (i.e. geometry) of the electrode device prototype to improve both clinical performance and geometrical tolerance (robustness). We have employed a semiempirical objective function based on constraints similar to those...
Akayuure, Peter; Asiedu-Addo, S. K.; Alebna, Victor
2016-01-01
Whereas origami is said to have pedagogical benefits in geometry education, research is inclusive about its effect on spatial ability and geometric knowledge among preservice teachers. The study investigated the effect of origami instruction on these aspects using pretest posttest quasi-experiment design. The experimental group consisted of 52…
DEFF Research Database (Denmark)
Jensen, Ole B.; Pettiway, Keon
2017-01-01
by designers, planners, etc. (staging from above) and mobile subjects (staging from below). A research agenda for studying situated practices of mobility and mobilities design is outlined in three directions: foci of studies, methods and approaches, and epistemologies and frames of thinking. Jensen begins...... with a brief description of how movement is studied within social sciences after the “mobilities turn” versus the idea of physical movement in transport geography and engineering. He then explains how “mobilities design” was derived from connections between traffic and architecture. Jensen concludes......In this chapter, Ole B. Jensen takes a situational approach to mobilities to examine how ordinary life activities are structured by technology and design. Using “staging mobilities” as a theoretical approach, Jensen considers mobilities as overlapping, actions, interactions and decisions...
DEFF Research Database (Denmark)
Volf, Mette
Design - proces & metode iBog® er enestående i sit fokus på afmystificering og operationalisering af designprocessens flygtige og komplekse karakter. Udgivelsen går bag om designerens daglige arbejde og giver et indblik i den kreative skabelsesproces, som designeren er en del af. Udover et bredt...... indblik i designerens arbejdsmetoder og designparametre giver Design - proces & metode en række eksempler fra anerkendte designvirksomheder, der gør det muligt at komme helt tæt på designerens virkelighed....
Optimization of biotechnological systems through geometric programming
Directory of Open Access Journals (Sweden)
Torres Nestor V
2007-09-01
Full Text Available Abstract Background In the past, tasks of model based yield optimization in metabolic engineering were either approached with stoichiometric models or with structured nonlinear models such as S-systems or linear-logarithmic representations. These models stand out among most others, because they allow the optimization task to be converted into a linear program, for which efficient solution methods are widely available. For pathway models not in one of these formats, an Indirect Optimization Method (IOM was developed where the original model is sequentially represented as an S-system model, optimized in this format with linear programming methods, reinterpreted in the initial model form, and further optimized as necessary. Results A new method is proposed for this task. We show here that the model format of a Generalized Mass Action (GMA system may be optimized very efficiently with techniques of geometric programming. We briefly review the basics of GMA systems and of geometric programming, demonstrate how the latter may be applied to the former, and illustrate the combined method with a didactic problem and two examples based on models of real systems. The first is a relatively small yet representative model of the anaerobic fermentation pathway in S. cerevisiae, while the second describes the dynamics of the tryptophan operon in E. coli. Both models have previously been used for benchmarking purposes, thus facilitating comparisons with the proposed new method. In these comparisons, the geometric programming method was found to be equal or better than the earlier methods in terms of successful identification of optima and efficiency. Conclusion GMA systems are of importance, because they contain stoichiometric, mass action and S-systems as special cases, along with many other models. Furthermore, it was previously shown that algebraic equivalence transformations of variables are sufficient to convert virtually any types of dynamical models into
Geometric transition in Non-perturbative Topological string
Sugimoto, Yuji
2016-01-01
We study a geometric transition in non-perturbative topological string. We consider two cases. One is the geometric transition from the closed topological string on the local $\\mathcal{B}_{3}$ to the closed topological string on the resolved conifold. The other is the geometric transition from the closed topological string on the local $\\mathcal{B}_{3}$ to the open topological string on the resolved conifold with a toric A-brane. We find that, in both cases, the geometric transition can be applied for the non-perturbative topological string. We also find the corrections of the value of K\\"ahler parameters at which the geometric transition occurs.
Some Geometrical Aspects of M-Theory
de Azcárraga, José A.; Izquierdo, José M.
2008-06-01
Some geometrical aspects of super-p-brane theory, M-theory, and their connection with supergravity, are reviewed. In particular, the different fractions of preserved supersymmetries are discussed both from the algebraic and the supergravity solutions point of view. We also review the `preon conjecture' according to which states preserving a 31/32 fraction of supersymmetries would be the building blocks of M-theory, and on the failed attempts made so far to find these states in terms of supergravity solutions.
Aerospace plane guidance using geometric control theory
Van Buren, Mark A.; Mease, Kenneth D.
1990-01-01
A reduced-order method employing decomposition, based on time-scale separation, of the 4-D state space in a 2-D slow manifold and a family of 2-D fast manifolds is shown to provide an excellent approximation to the full-order minimum-fuel ascent trajectory. Near-optimal guidance is obtained by tracking the reduced-order trajectory. The tracking problem is solved as regulation problems on the family of fast manifolds, using the exact linearization methodology from nonlinear geometric control theory. The validity of the overall guidance approach is indicated by simulation.
The Geometric Nature of the Fundamental Lemma
Nadler, David
2010-01-01
The Fundamental Lemma is a somewhat obscure combinatorial identity introduced by Robert P. Langlands as an ingredient in the theory of automorphic representations. After many years of deep contributions by mathematicians working in representation theory, number theory, algebraic geometry, and algebraic topology, a proof of the Fundamental Lemma was recently completed by Ngo Bau Chau, for which he was awarded a Fields Medal. Our aim here is to touch on some of the beautiful ideas contributing to the Fundamental Lemma and its proof. We highlight the geometric nature of the problem which allows one to attack a question in p-adic analysis with the tools of algebraic geometry.
Robust topology optimization accounting for geometric imperfections
DEFF Research Database (Denmark)
Schevenels, M.; Jansen, M.; Lombaert, Geert
2013-01-01
performance. As a consequence, the actual structure may be far from optimal. In this paper, a robust approach to topology optimization is presented, taking into account two types of geometric imperfections: variations of (1) the crosssections and (2) the locations of structural elements. The first type...... is modeled by means of a scalar non-Gaussian random field, which is represented as a translation process. The underlying Gaussian field is simulated by means of the EOLE method. The second type of imperfections is modeled as a Gaussian vector-valued random field, which is simulated directly by means...
A geometrical introduction to screw theory
Minguzzi, E
2012-01-01
Since the addition of applied forces must take into account the line of action, applied forces do not belong to a vector space. Screw theory removes this geometrical limitation and solves other mechanical problems by unifying, in a single concept, the translational and rotational degrees of freedom. Although venerable this theory is little known. By introducing some innovations, I show how screw theory can help us to rapidly develop several standard and less standard results in classical mechanics. The connection with the Lie algebra of the group of rigid maps is clarified.
Minimal representations, geometric quantization, and unitarity.
Brylinski, R; Kostant, B
1994-06-21
In the framework of geometric quantization we explicitly construct, in a uniform fashion, a unitary minimal representation pio of every simply-connected real Lie group Go such that the maximal compact subgroup of Go has finite center and Go admits some minimal representation. We obtain algebraic and analytic results about pio. We give several results on the algebraic and symplectic geometry of the minimal nilpotent orbits and then "quantize" these results to obtain the corresponding representations. We assume (Lie Go)C is simple.
Non-geometric branes are DFT monopoles
Bakhmatov, Ilya; Musaev, Edvard T
2016-01-01
The double field theory monopole solution by Berman and Rudolph is shown to reproduce non-geometric backgrounds with non-vanishing Q- and R-flux upon an appropriate choice of physical and dual coordinates. The obtained backgrounds depend non-trivially on dual coordinates and have only trivial monodromies. Upon smearing the solutions along the dual coordinates one reproduces the known $5^2_2$ solution for the Q-brane and co-dimension 1 solution for the R-brane. The T-duality invariant magnetic charge is explicitly calculated for all these backgrounds and is found to be equal to the magnetic charge of (unsmeared) NS5-brane.
The Electromagnetic Duality Formulation of Geometric Phases
Zhang, Yuchao; Li, Kang
2015-06-01
This paper focuses on the electromagnetic(EM) duality formulation of geometric phases of Aharonov-Bohm(A-B) effect and Aharonov-Casher(A-C) effect. Through the two four-vector potential formulation of electromagnetic theory, we construct a EM duality formulation for both A-B effect and A-C effect. The He-McKellar-Wilkens(HMW) effect is included as a EM duality counterpart of the A-C effect, and also the EM duality counterpart of the A-B effect is also predicted.
Geometric and numerical foundations of movements
Mansard, Nicolas; Lasserre, Jean-Bernard
2017-01-01
This book aims at gathering roboticists, control theorists, neuroscientists, and mathematicians, in order to promote a multidisciplinary research on movement analysis. It follows the workshop “ Geometric and Numerical Foundations of Movements ” held at LAAS-CNRS in Toulouse in November 2015[1]. Its objective is to lay the foundations for a mutual understanding that is essential for synergetic development in motion research. In particular, the book promotes applications to robotics --and control in general-- of new optimization techniques based on recent results from real algebraic geometry.
Geometric Models of the Relativistic Harmonic Oscillator
Cotaescu, I I
1997-01-01
A family of relativistic geometric models is defined as a generalization of the actual anti-de Sitter (1+1) model of the relativistic harmonic oscillator. It is shown that all these models lead to the usual harmonic oscillator in the non-relativistic limit, even though their relativistic behavior is quite different. Among quantum models we find a set of models with countable energy spectra, and another one having only a finite number of energy levels and in addition a continuous spectrum.
Geometric Formulation of Gauge Theory of Gravity
Institute of Scientific and Technical Information of China (English)
WUNing; ZHANGDa-Hua; RUANTu-Nan
2003-01-01
DitTerential geometric formulation of quantum gauge theory of gravity is studied in this paper. The quantum gauge theory of gravity is formulated completely in the framework of traditional quantum field theory. In order to study the relationship between quantum gauge theory of gravity and traditional quantum gravity which is formulated in curved space, it is important to set up the geometry picture of quantum gauge theory of gravity. The correspondence between quantum gauge theory of gravity and differential geometry is discussed and the geometry picture of quantum gauge theory of gravity is studied.
Geometric Formulation of Gauge Theory of Gravity
Institute of Scientific and Technical Information of China (English)
WU Ning; ZHANG Da-Hua; RUAN Tu-Nan
2003-01-01
Differential geometric formulation of quantum gauge theory of gravity is studied in this paper. The quantumgauge theory of gravity is formulated completely in the framework of traditional quantum field theory. In order to studythe relationship between quantum gauge theory of gravity and traditional quantum gravity which is formulated in curvedspace, it is important to set up the geometry picture of quantum gauge theory of gravity. The correspondence betweenquantum gauge theory of gravity and differential geometry is discussed and the geometry picture of quantum gaugetheory of gravity is studied.
Conformal invariants topics in geometric function theory
Ahlfors, Lars V
2010-01-01
Most conformal invariants can be described in terms of extremal properties. Conformal invariants and extremal problems are therefore intimately linked and form together the central theme of this classic book which is primarily intended for students with approximately a year's background in complex variable theory. The book emphasizes the geometric approach as well as classical and semi-classical results which Lars Ahlfors felt every student of complex analysis should know before embarking on independent research. At the time of the book's original appearance, much of this material had never ap
More On Gauge Theory And Geometric Langlands
Witten, Edward
2015-01-01
The geometric Langlands correspondence was described some years ago in terms of $S$-duality of $\\N=4$ super Yang-Mills theory. Some additional matters relevant to this story are described here. The main goal is to explain directly why an $A$-brane of a certain simple kind can be an eigenbrane for the action of 't Hooft operators. To set the stage, we review some facts about Higgs bundles and the Hitchin fibration. We consider only the simplest examples, in which many technical questions can be avoided.
1995-01-01
El método de las coordenadas, además de tener un conjunto de aplicaciones de amplio espectro -cronología, geógrafa, topógrafa, ﬁsica, geometría....- y de permitir la trascripción algebraica de determinados problemas geométricos, se fundamenta en ideas que son clave a la hora de comprender la eficacia de las matemáticas como herramienta de las ciencias. La tesis que aquí se sostiene es que esas ideas claves no se transparentan restringiendo la utilización del método de las coordenadas al est...
Geometric calibration of ERS satellite SAR images
DEFF Research Database (Denmark)
Mohr, Johan Jacob; Madsen, Søren Nørvang
2001-01-01
Geometric calibration of the European Remote Sensing (ERS) Satellite synthetic aperture radar (SAR) slant range images is important in relation to mapping areas without ground reference points and also in relation to automated processing. The relevant SAR system parameters are discussed...... on a seven-year ERS-1 and a four-year ERS-2 time series, the long term stability is found to be sufficient to allow a single calibration covering the entire mission period. A descending and an ascending orbit tandem pair of the ESA calibration site on Flevoland, suitable for calibration of ERS SAR processors...
A geometric interpretation of integrable motions
Clementi, C; Clementi, Cecilia; Pettini, Marco
2001-01-01
Integrability, one of the classic issues in galactic dynamics and in general in celestial mechanics, is here revisited in a Riemannian geometric framework, where newtonian motions are seen as geodesics of suitable ``mechanical'' manifolds. The existence of constants of motion that entail integrability is associated with the existence of Killing tensor fields on the mechanical manifolds. Such tensor fields correspond to hidden symmetries of non-Noetherian kind. Explicit expressions for Killing tensor fields are given for the N=2 Toda model, and for a modified Henon-Heiles model, recovering the already known analytic expressions of the second conserved quantity besides energy for each model respectively.
Geometric Algebra Model of Distributed Representations
Patyk, Agnieszka
2010-01-01
Formalism based on GA is an alternative to distributed representation models developed so far --- Smolensky's tensor product, Holographic Reduced Representations (HRR) and Binary Spatter Code (BSC). Convolutions are replaced by geometric products, interpretable in terms of geometry which seems to be the most natural language for visualization of higher concepts. This paper recalls the main ideas behind the GA model and investigates recognition test results using both inner product and a clipped version of matrix representation. The influence of accidental blade equality on recognition is also studied. Finally, the efficiency of the GA model is compared to that of previously developed models.
Geometric measure theory and real analysis
2014-01-01
In 2013, a school on Geometric Measure Theory and Real Analysis, organized by G. Alberti, C. De Lellis and myself, took place at the Centro De Giorgi in Pisa, with lectures by V. Bogachev, R. Monti, E. Spadaro and D. Vittone. The book collects the notes of the courses. The courses provide a deep and up to date insight on challenging mathematical problems and their recent developments: infinite-dimensional analysis, minimal surfaces and isoperimetric problems in the Heisenberg group, regularity of sub-Riemannian geodesics and the regularity theory of minimal currents in any dimension and codimension.
ERC Workshop on Geometric Partial Differential Equations
Novaga, Matteo; Valdinoci, Enrico
2013-01-01
This book is the outcome of a conference held at the Centro De Giorgi of the Scuola Normale of Pisa in September 2012. The aim of the conference was to discuss recent results on nonlinear partial differential equations, and more specifically geometric evolutions and reaction-diffusion equations. Particular attention was paid to self-similar solutions, such as solitons and travelling waves, asymptotic behaviour, formation of singularities and qualitative properties of solutions. These problems arise in many models from Physics, Biology, Image Processing and Applied Mathematics in general, and have attracted a lot of attention in recent years.
Multiscale Geometric Analysis: Theory, Applications, and Opportunities
2007-11-02
eiωΦν(x,t) ( a0ν(x, t) + a1ν(x, t) ω + a2ν(x, t) ω2 + . . . ) • Plug into wave equation – Eikonal equations ∂tΦν + λν(x,∇xΦ) = 0. λν(x, k) are the...space ẋ(t) = ∇kλν(x, k), x(0) = x0,k̇(t) = −∇xλν(x, k), k(0) = k0. • Eikonal equations from geometric optics ∂tΦν + λν(x,∇xΦ) = 0. Φ is constant
Geometric massive higher spins and current exchanges
Francia, Dario
2008-01-01
Generalised Fierz-Pauli mass terms allow to describe massive higher-spin fields on flat background by means of simple quadratic deformations of the corresponding geometric, massless Lagrangians. In this framework there is no need for auxiliary fields. We briefly review the construction in the bosonic case and study the interaction of these massive fields with external sources, computing the corresponding propagators. In the same fashion as for the massive graviton, but differently from theories where auxiliary fields are present, the structure of the current exchange is completely determined by the form of the mass term itself.
The minimal geometric deformation approach extended
Casadio, R.; Ovalle, J.; da Rocha, Roldão
2015-11-01
The minimal geometric deformation approach was introduced in order to study the exterior spacetime around spherically symmetric self-gravitating systems, such as stars or similar astrophysical objects, in the Randall-Sundrum brane-world framework. A consistent extension of this approach is developed here, which contains modifications of both the time component and the radial component of a spherically symmetric metric. A modified Schwarzschild geometry is obtained as an example of its simplest application, and a new solution that is potentially useful to describe stars in the brane-world is also presented.
Parabolic non-diffracting beams: geometrical approach
Sosa-Sánchez, Citlalli Teresa; Silva-Ortigoza, Gilberto; Alejandro Juárez-Reyes, Salvador; de Jesús Cabrera-Rosas, Omar; Espíndola-Ramos, Ernesto; Julián-Macías, Israel; Ortega-Vidals, Paula
2017-08-01
The aim of this work is to present a geometrical characterization of parabolic non-diffracting beams. To this end, we compute the corresponding angular spectrum of the separable non-diffracting parabolic beams in order to determine the one-parameter family of solutions of the eikonal equation associated with this type of beam. Using this information, we compute the corresponding wavefronts and caustic, and find that qualitatively the caustic corresponds to the maximum of the intensity pattern and the wavefronts are deformations of conical surfaces.
Toroidal Precession as a Geometric Phase
Energy Technology Data Exchange (ETDEWEB)
J.W. Burby and H. Qin
2012-09-26
Toroidal precession is commonly understood as the orbit-averaged toroidal drift of guiding centers in axisymmetric and quasisymmetric configurations. We give a new, more natural description of precession as a geometric phase effect. In particular, we show that the precession angle arises as the holonomy of a guiding center's poloidal trajectory relative to a principal connection. The fact that this description is physically appropriate is borne out with new, manifestly coordinate-independent expressions for the precession angle that apply to all types of orbits in tokamaks and quasisymmetric stellarators alike. We then describe how these expressions may be fruitfully employed in numerical calculations of precession.
Non-Riemannian geometrical optics in QED
Garcia de Andrade, L C
2003-01-01
A non-minimal photon-torsion axial coupling in the quantum electrodynamics (QED) framework is considered. The geometrical optics in Riemannian-Cartan spacetime is considering and a plane wave expansion of the electromagnetic vector potential is considered leading to a set of the equations for the ray congruence. Since we are interested mainly on the torsion effects in this first report we just consider the Riemann-flat case composed of the Minkowskian spacetime with torsion. It is also shown that in torsionic de Sitter background the vacuum polarisation does alter the propagation of individual photons, an effect which is absent in Riemannian spaces.
Computational morphology a computational geometric approach to the analysis of form
Toussaint, GT
1988-01-01
Computational Geometry is a new discipline of computer science that deals with the design and analysis of algorithms for solving geometric problems. There are many areas of study in different disciplines which, while being of a geometric nature, have as their main component the extraction of a description of the shape or form of the input data. This notion is more imprecise and subjective than pure geometry. Such fields include cluster analysis in statistics, computer vision and pattern recognition, and the measurement of form and form-change in such areas as stereology and developmental biolo
Buchanan, Richard; Cross, Nigel; Durling, David; Nelson, Harold; Owen, Charles; Valtonen, Anna; Boling, Elizabeth; Gibbons, Andrew; Visscher-Voerman, Irene
2013-01-01
Scholars representing the field of design were asked to identify what they considered to be the most exciting and imaginative work currently being done in their field, as well as how that work might change our understanding. The scholars included Richard Buchanan, Nigel Cross, David Durling, Harold Nelson, Charles Owen, and Anna Valtonen. Scholars…
Buchanan, Richard; Cross, Nigel; Durling, David; Nelson, Harold; Owen, Charles; Valtonen, Anna; Boling, Elizabeth; Gibbons, Andrew; Visscher-Voerman, Irene
2013-01-01
Scholars representing the field of design were asked to identify what they considered to be the most exciting and imaginative work currently being done in their field, as well as how that work might change our understanding. The scholars included Richard Buchanan, Nigel Cross, David Durling, Harold Nelson, Charles Owen, and Anna Valtonen. Scholars…