Blow-Ups in Generalized Complex Geometry
van der Leer Duran, J.L.
2016-01-01
Generalized complex geometry is a theory that unifies complex geometry and symplectic geometry into one single framework. It was introduced by Hitchin and Gualtieri around 2002. In this thesis we address the following question: given a generalized complex manifold together with a submanifold, does
Geometric Transitions, Topological Strings, and Generalized Complex Geometry
Energy Technology Data Exchange (ETDEWEB)
Chuang, Wu-yen; /SLAC /Stanford U., Phys. Dept.
2007-06-29
Mirror symmetry is one of the most beautiful symmetries in string theory. It helps us very effectively gain insights into non-perturbative worldsheet instanton effects. It was also shown that the study of mirror symmetry for Calabi-Yau flux compactification leads us to the territory of ''Non-Kaehlerity''. In this thesis we demonstrate how to construct a new class of symplectic non-Kaehler and complex non-Kaehler string theory vacua via generalized geometric transitions. The class admits a mirror pairing by construction. From a variety of sources, including super-gravity analysis and KK reduction on SU(3) structure manifolds, we conclude that string theory connects Calabi-Yau spaces to both complex non-Kaehler and symplectic non-Kaehler manifolds and the resulting manifolds lie in generalized complex geometry. We go on to study the topological twisted models on a class of generalized complex geometry, bi-Hermitian geometry, which is the most general target space for (2, 2) world-sheet theory with non-trivial H flux turned on. We show that the usual Kaehler A and B models are generalized in a natural way. Since the gauged supergravity is the low energy effective theory for the compactifications on generalized geometries, we study the fate of flux-induced isometry gauging in N = 2 IIA and heterotic strings under non-perturbative instanton effects. Interestingly, we find we have protection mechanisms preventing the corrections to the hyper moduli spaces. Besides generalized geometries, we also discuss the possibility of new NS-NS fluxes in a new doubled formalism.
Zheng, Fangyang
2002-01-01
The theory of complex manifolds overlaps with several branches of mathematics, including differential geometry, algebraic geometry, several complex variables, global analysis, topology, algebraic number theory, and mathematical physics. Complex manifolds provide a rich class of geometric objects, for example the (common) zero locus of any generic set of complex polynomials is always a complex manifold. Yet complex manifolds behave differently than generic smooth manifolds; they are more coherent and fragile. The rich yet restrictive character of complex manifolds makes them a special and interesting object of study. This book is a self-contained graduate textbook that discusses the differential geometric aspects of complex manifolds. The first part contains standard materials from general topology, differentiable manifolds, and basic Riemannian geometry. The second part discusses complex manifolds and analytic varieties, sheaves and holomorphic vector bundles, and gives a brief account of the surface classifi...
Silva, Alessandro
1993-01-01
The papers in this wide-ranging collection report on the results of investigations from a number of linked disciplines, including complex algebraic geometry, complex analytic geometry of manifolds and spaces, and complex differential geometry.
General Geometry and Geometry of Electromagnetism
Shahverdiyev, Shervgi S.
2002-01-01
It is shown that Electromagnetism creates geometry different from Riemannian geometry. General geometry including Riemannian geometry as a special case is constructed. It is proven that the most simplest special case of General Geometry is geometry underlying Electromagnetism. Action for electromagnetic field and Maxwell equations are derived from curvature function of geometry underlying Electromagnetism. And it is shown that equation of motion for a particle interacting with electromagnetic...
Complex and symplectic geometry
Medori, Costantino; Tomassini, Adriano
2017-01-01
This book arises from the INdAM Meeting "Complex and Symplectic Geometry", which was held in Cortona in June 2016. Several leading specialists, including young researchers, in the field of complex and symplectic geometry, present the state of the art of their research on topics such as the cohomology of complex manifolds; analytic techniques in Kähler and non-Kähler geometry; almost-complex and symplectic structures; special structures on complex manifolds; and deformations of complex objects. The work is intended for researchers in these areas.
String theory flux vacua on twisted tori and generalized complex geometry
International Nuclear Information System (INIS)
Andriot, David
2010-01-01
This thesis is devoted to the study of flux vacua of string theory, with the ten-dimensional space-time split into a four-dimensional maximally symmetric space-time, and a six-dimensional internal manifold M, taken to be a solv-manifold (twisted torus). Such vacua are of particular interest when trying to relate string theory to supersymmetric (SUSY) extensions of the standard model of particles, or to cosmological models. For SUSY solutions of type II supergravities, allowing for fluxes on M helps to solve the moduli problem. Then, a broader class of manifolds than just the Calabi-Yau can be considered for M, and a general characterization is given in terms of Generalized Complex Geometry: M has to be a Generalized Calabi-Yau (GCY). A subclass of solv-manifolds have been proven to be GCY, so we look for solutions with such M. To do so, we use an algorithmic resolution method. Then we focus on specific new solutions: those admitting an intermediate SU(2) structure. A transformation named the twist is then discussed. It relates solutions on torus to solutions on solv-manifolds. Working out constraints on the twist to generate solutions, we can relate known solutions, and find a new one. We also use the twist to relate flux vacua of heterotic string. Finally we consider ten-dimensional de Sitter solutions. Looking for such solutions is difficult, because of several problems among which the breaking of SUSY. We propose an Ansatz for SUSY breaking sources which helps to overcome these difficulties. We give an explicit solution on a solv-manifold, and discuss partially its four-dimensional stability. (author)
Kollár, János
1997-01-01
This volume contains the lectures presented at the third Regional Geometry Institute at Park City in 1993. The lectures provide an introduction to the subject, complex algebraic geometry, making the book suitable as a text for second- and third-year graduate students. The book deals with topics in algebraic geometry where one can reach the level of current research while starting with the basics. Topics covered include the theory of surfaces from the viewpoint of recent higher-dimensional developments, providing an excellent introduction to more advanced topics such as the minimal model program. Also included is an introduction to Hodge theory and intersection homology based on the simple topological ideas of Lefschetz and an overview of the recent interactions between algebraic geometry and theoretical physics, which involve mirror symmetry and string theory.
Flux compactifications and generalized geometries
International Nuclear Information System (INIS)
Grana, Mariana
2006-01-01
Following the lectures given at CERN Winter School 2006, we present a pedagogical overview of flux compactifications and generalized geometries, concentrating on closed string fluxes in type II theories. We start by reviewing the supersymmetric flux configurations with maximally symmetric four-dimensional spaces. We then discuss the no-go theorems (and their evasion) for compactifications with fluxes. We analyse the resulting four-dimensional effective theories for Calabi-Yau and Calabi-Yau orientifold compactifications, concentrating on the flux-induced superpotentials. We discuss the generic mechanism of moduli stabilization and illustrate with two examples: the conifold in IIB and a T 6 /(Z 3 x Z 3 ) torus in IIA. We finish by studying the effective action and flux vacua for generalized geometries in the context of generalized complex geometry
Complex Numbers and Plane Geometry
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 13; Issue 1. Complex Numbers and Plane Geometry. Anant R Shastri. General Article Volume 13 Issue 1 January 2008 pp 35-53. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/013/01/0035-0053. Keywords.
DEFF Research Database (Denmark)
Tamke, Martin; Ramsgaard Thomsen, Mette; Riiber Nielsen, Jacob
2009-01-01
The versatility of wood constructions and traditional wood joints for the production of non standard elements was in focus of a design based research. Herein we established a seamless process from digital design to fabrication. A first research phase centered on the development of a robust...... parametric model and a generic design language a later explored the possibilities to construct complex shaped geometries with self registering joints on modern wood crafting machines. The research was carried out as collaboration with industrial partners....
DEFF Research Database (Denmark)
Tamke, Martin; Ramsgaard Thomsen, Mette; Riiber Nielsen, Jacob
2009-01-01
The versatility of wood constructions and traditional wood joints for the production of non standard elements was in focus of a design based research. Herein we established a seamless process from digital design to fabrication. A first research phase centered on the development of a robust parame...... parametric model and a generic design language a later explored the possibilities to construct complex shaped geometries with self registering joints on modern wood crafting machines. The research was carried out as collaboration with industrial partners....
Complex Kerr geometry and nonstationary Kerr solutions
International Nuclear Information System (INIS)
Burinskii, Alexander
2003-01-01
In the frame of the Kerr-Schild approach, we consider the complex structure of Kerr geometry which is determined by a complex world line of a complex source. The real Kerr geometry is represented as a real slice of this complex structure. The Kerr geometry is generalized to the nonstationary case when the current geometry is determined by a retarded time and is defined by a retarded-time construction via a given complex world line of source. A general exact solution corresponding to arbitrary motion of a spinning source is obtained. The acceleration of the source is accompanied by a lightlike radiation along the principal null congruence. It generalizes to the rotating case, the known Kinnersley class of 'photon rocket' solutions
General Relativity: Geometry Meets Physics
Thomsen, Dietrick E.
1975-01-01
Observing the relationship of general relativity and the geometry of space-time, the author questions whether the rest of physics has geometrical explanations. As a partial answer he discusses current research on subatomic particles employing geometric transformations, and cites the existence of geometrical definitions of physical quantities such…
GEOMETRY AND COMPLEXITY IN ARCHITECTURE
Directory of Open Access Journals (Sweden)
RUSU Maria Ana
2015-06-01
Full Text Available As Constantin Brancuși (1876-1956 said „Simplicity is complexity itself“, simplicity and regularity through the use of basic geometric forms has always played a central role in architectural design, during the 20th century. A diachronic perspective, shows as the use of geometry and mathematics to describe built form provided a common basis for communication between the processes of design, fabrication and stability. Classic ways of representing geometry, based on descriptive methods, favor precise language of bidimensionality easy to represent in a rectangular coordinate system. In recent years, the importance of geometry has been re-emphasized by significant advances in the digital age, where computers are increasingly used in design, fabrication and construction to explore the art of the possible. Contemporary architecture transcend the limitations of Euclidean geometry and create new forms that are emerging through the convergence of complex systems, computational design and robotic fabrication devices, but which can also achieve higher levels of performance. Freeform architectural shapes and structures play an increasingly important role in 21st century architectural design. Through a series of examples, the paper relates to contemporary architectural explorations of complex, curvilinear surfaces in the digital age and discusses how it has required rethinking the mode in which we traditionally operate as architects. The analysis creates the possibility of comparisons between original and current design.
Hyperbolic Metamaterials with Complex Geometry
DEFF Research Database (Denmark)
Lavrinenko, Andrei; Andryieuski, Andrei; Zhukovsky, Sergei
2016-01-01
We investigate new geometries of hyperbolic metamaterialssuch as highly corrugated structures, nanoparticle monolayer assemblies, super-structured or vertically arranged multilayersand nanopillars. All structures retain basic propertiesof hyperbolic metamaterials, but have functionality improved...
Elementary differential geometry from a generalized standpoint
International Nuclear Information System (INIS)
Weinberg, S.
1986-01-01
The authors describe the essential ingredients of differential geometry-vielbeins, connections, curvatures and isometries-on a level somewhat more general than is commonly found in the literature of physics and mathematics. Most often, one finds differential geometry discussed in terms either of a metric (especially in the older textbooks), or equivalently in terms of a vielbein together with a principle of invariance under independent rotations or Lorentz transformations at each point, as well as invariance under general coordinate transformations. They adopt the same general framework, but keep an open mind as to whether the local invariance group is a rotation or Lorentz group or something quite different. Differential geometry based on a metric or on local rotational or Lorentz invariance is called Riemannian geometry; the more general quasi-Riemannian geometry described here is known in the mathematical literature as the theory of G-structures
Geometry of generalized coherent states
International Nuclear Information System (INIS)
Bacry, H.; Centre National de la Recherche Scientifique, 13 - Marseille; Grossmann, A.; Zak, J.
1975-09-01
Various attempts have been made to generalize the concept of coherent states (c.s.). One of them, due to Perelomov, seems to be very promising but no restrictive enough. The Perelomov c.s. are briefly reviewed. One shows how his definition gives rise to Radcliffe's c.s. Relationship between the usual and Radcliffe's c.s. can be investigated either from group contraction point of view (Arecchi et al.) or from a physical point of view (with the aid of the Poincare sphere of elliptic polarizations of electromagnetic plane waves). The question of finding complete subsets of c.s. is revisited and an attempt is made to restrict the Perelomov definition [fr
Chemotactic droplet swimmers in complex geometries
Jin, Chenyu; Hokmabad, Babak V.; Baldwin, Kyle A.; Maass, Corinna C.
2018-02-01
Chemotaxis1 and auto-chemotaxis are key mechanisms in the dynamics of micro-organisms, e.g. in the acquisition of nutrients and in the communication between individuals, influencing the collective behaviour. However, chemical signalling and the natural environment of biological swimmers are generally complex, making them hard to access analytically. We present a well-controlled, tunable artificial model to study chemotaxis and autochemotaxis in complex geometries, using microfluidic assays of self-propelling oil droplets in an aqueous surfactant solution (Herminghaus et al 2014 Soft Matter 10 7008–22 Krüger et al 2016 Phys. Rev. Lett. 117). Droplets propel via interfacial Marangoni stresses powered by micellar solubilisation. Moreover, filled micelles act as a chemical repellent by diffusive phoretic gradient forces. We have studied these chemotactic effects in a series of microfluidic geometries, as published in Jin et al (2017 Proc. Natl Acad. Sci. 114 5089–94): first, droplets are guided along the shortest path through a maze by surfactant diffusing into the maze from the exit. Second, we let auto-chemotactic droplet swimmers pass through bifurcating microfluidic channels and record anticorrelations between the branch choices of consecutive droplets. We present an analytical Langevin model matching the experimental data. In a previously unpublished experiment, pillar arrays of variable sizes and shapes provide a convex wall interacting with the swimmer and, in the case of attachment, bending its trajectory and forcing it to revert to its own trail. We observe different behaviours based on the interplay of wall curvature and negative autochemotaxis, i.e. no attachment for highly curved interfaces, stable trapping at large pillars, and a narrow transition region where negative autochemotaxis makes the swimmers detach after a single orbit.
Chemotactic droplet swimmers in complex geometries.
Jin, Chenyu; Hokmabad, Babak V; Baldwin, Kyle A; Maass, Corinna C
2018-02-07
Chemotaxis 1 and auto-chemotaxis are key mechanisms in the dynamics of micro-organisms, e.g. in the acquisition of nutrients and in the communication between individuals, influencing the collective behaviour. However, chemical signalling and the natural environment of biological swimmers are generally complex, making them hard to access analytically. We present a well-controlled, tunable artificial model to study chemotaxis and autochemotaxis in complex geometries, using microfluidic assays of self-propelling oil droplets in an aqueous surfactant solution (Herminghaus et al 2014 Soft Matter 10 7008-22; Krüger et al 2016 Phys. Rev. Lett. 117). Droplets propel via interfacial Marangoni stresses powered by micellar solubilisation. Moreover, filled micelles act as a chemical repellent by diffusive phoretic gradient forces. We have studied these chemotactic effects in a series of microfluidic geometries, as published in Jin et al (2017 Proc. Natl Acad. Sci. 114 5089-94): first, droplets are guided along the shortest path through a maze by surfactant diffusing into the maze from the exit. Second, we let auto-chemotactic droplet swimmers pass through bifurcating microfluidic channels and record anticorrelations between the branch choices of consecutive droplets. We present an analytical Langevin model matching the experimental data. In a previously unpublished experiment, pillar arrays of variable sizes and shapes provide a convex wall interacting with the swimmer and, in the case of attachment, bending its trajectory and forcing it to revert to its own trail. We observe different behaviours based on the interplay of wall curvature and negative autochemotaxis, i.e. no attachment for highly curved interfaces, stable trapping at large pillars, and a narrow transition region where negative autochemotaxis makes the swimmers detach after a single orbit.
Generalized geometry and non-symmetric gravity
Jurco, Branislav; Khoo, Fech Scen; Schupp, Peter; Vysoky, Jan
2015-01-01
Generalized geometry provides the framework for a systematic approach to non-symmetric metric gravity theory and naturally leads to an Einstein-Kalb-Ramond gravity theory with totally anti-symmetric contortion. The approach is related to the study of the low-energy effective closed string gravity actions.
International conference on Algebraic and Complex Geometry
Kloosterman, Remke; Schütt, Matthias
2014-01-01
Several important aspects of moduli spaces and irreducible holomorphic symplectic manifolds were highlighted at the conference “Algebraic and Complex Geometry” held September 2012 in Hannover, Germany. These two subjects of recent ongoing progress belong to the most spectacular developments in Algebraic and Complex Geometry. Irreducible symplectic manifolds are of interest to algebraic and differential geometers alike, behaving similar to K3 surfaces and abelian varieties in certain ways, but being by far less well-understood. Moduli spaces, on the other hand, have been a rich source of open questions and discoveries for decades and still continue to be a hot topic in itself as well as with its interplay with neighbouring fields such as arithmetic geometry and string theory. Beyond the above focal topics this volume reflects the broad diversity of lectures at the conference and comprises 11 papers on current research from different areas of algebraic and complex geometry sorted in alphabetic order by the ...
Blow-Ups in Generalized Kähler Geometry
van der Leer Durán, J. L.
2018-02-01
We study blow-ups in generalized Kähler geometry. The natural candidates for submanifolds to be blown-up are those which are generalized Poisson submanifolds for one of the two generalized complex structures and can be blown up in a generalized complex manner. We show that the bi-Hermitian structure underlying the generalized Kähler pair lifts to a degenerate bi-Hermitian structure on this blow-up. Then, using a deformation procedure based on potentials in Kähler geometry, we identify two concrete situations in which one can deform the degenerate structure on the blow-up into a non-degenerate one. We end with a study of generalized Kähler Lie groups and give a concrete example on {(S^1)^n × (S^3)^m}, for n + m even.
An introduction to complex analysis and geometry
D'Angelo, John P
2010-01-01
An Introduction to Complex Analysis and Geometry provides the reader with a deep appreciation of complex analysis and how this subject fits into mathematics. The book developed from courses given in the Campus Honors Program at the University of Illinois Urbana-Champaign. These courses aimed to share with students the way many mathematics and physics problems magically simplify when viewed from the perspective of complex analysis. The book begins at an elementary level but also contains advanced material. The first four chapters provide an introduction to complex analysis with many elementary
Generalized geometry and partial supersymmetry breaking
Energy Technology Data Exchange (ETDEWEB)
Triendl, Hagen Mathias
2010-08-15
This thesis consists of two parts. In the first part we use the formalism of (exceptional) generalized geometry to derive the scalar field space of SU(2) x SU(2)-structure compactifications. We show that in contrast to SU(3) x SU(3) structures, there is no dynamical SU(2) x SU(2) structure interpolating between an SU(2) structure and an identity structure. Furthermore, we derive the scalar manifold of the low-energy effective action for consistent Kaluza-Klein truncations as expected from N = 4 supergravity. In the second part we then determine the general conditions for the existence of stable Minkowski and AdS N = 1 vacua in spontaneously broken gauged N = 2 supergravities and construct the general solution under the assumption that two appropriate commuting isometries exist in the hypermultiplet sector. Furthermore, we derive the low-energy effective action below the scale of partial supersymmetry breaking and show that it satisfies the constraints of N = 1 supergravity. We then apply the discussion to special quaternionic-Kaehler geometries which appear in the low-energy limit of SU(3) x SU(3)-structure compactifications and construct Killing vectors with the right properties. Finally we discuss the string theory realizations for these solutions. (orig.)
Generalized geometry and partial supersymmetry breaking
International Nuclear Information System (INIS)
Triendl, Hagen Mathias
2010-08-01
This thesis consists of two parts. In the first part we use the formalism of (exceptional) generalized geometry to derive the scalar field space of SU(2) x SU(2)-structure compactifications. We show that in contrast to SU(3) x SU(3) structures, there is no dynamical SU(2) x SU(2) structure interpolating between an SU(2) structure and an identity structure. Furthermore, we derive the scalar manifold of the low-energy effective action for consistent Kaluza-Klein truncations as expected from N = 4 supergravity. In the second part we then determine the general conditions for the existence of stable Minkowski and AdS N = 1 vacua in spontaneously broken gauged N = 2 supergravities and construct the general solution under the assumption that two appropriate commuting isometries exist in the hypermultiplet sector. Furthermore, we derive the low-energy effective action below the scale of partial supersymmetry breaking and show that it satisfies the constraints of N = 1 supergravity. We then apply the discussion to special quaternionic-Kaehler geometries which appear in the low-energy limit of SU(3) x SU(3)-structure compactifications and construct Killing vectors with the right properties. Finally we discuss the string theory realizations for these solutions. (orig.)
Conference on Complex Geometry and Mirror Symmetry
Vinet, Luc; Yau, Shing-Tung; Mirror Symmetry III
1999-01-01
This book presents surveys from a workshop held during the theme year in geometry and topology at the Centre de recherches mathématiques (CRM, University of Montréal). The volume is in some sense a sequel to Mirror Symmetry I (1998) and Mirror Symmetry II (1996), copublished by the AMS and International Press. Included are recent developments in the theory of mirror manifolds and the related areas of complex and symplectic geometry. The long introductory articles explain the key physical ideas and motivation, namely conformal field theory, supersymmetry, and string theory. Open problems are emphasized. Thus the book provides an efficient way for a very broad audience of mathematicians and physicists to reach the frontier of research in this fast expanding area. - See more at: http://bookstore.ams.org/amsip-10#sthash.DbxEFJDx.dpuf
Leibniz algebroids, twistings and exceptional generalized geometry
Baraglia, D.
2012-05-01
We investigate a class of Leibniz algebroids which are invariant under diffeomorphisms and symmetries involving collections of closed forms. Under appropriate assumptions we arrive at a classification which in particular gives a construction starting from graded Lie algebras. In this case the Leibniz bracket is a derived bracket and there are higher derived brackets resulting in an L∞-structure. The algebroids can be twisted by a non-abelian cohomology class and we prove that the twisting class is described by a Maurer-Cartan equation. For compact manifolds we construct a Kuranishi moduli space of this equation which is shown to be affine algebraic. We explain how these results are related to exceptional generalized geometry.
U-dual fluxes and Generalized Geometry
Aldazabal, G; Camara, Pablo G; Grana, M
2010-01-01
We perform a systematic analysis of generic string flux compactifications, making use of Exceptional Generalized Geometry (EGG) as an organizing principle. In particular, we establish the precise map between fluxes, gaugings of maximal 4d supergravity and EGG, identifying the complete set of gaugings that admit an uplift to 10d heterotic or type IIB supegravity backgrounds. Our results reveal a rich structure, involving new deformations of 10d supergravity backgrounds, such as the RR counterparts of the $\\beta$-deformation. These new deformations are expected to provide the natural extension of the $\\beta$-deformation to full-fledged F-theory backgrounds. Our analysis also provides some clues on the 10d origin of some of the particularly less understood gaugings of 4d supergravity. Finally, we derive the explicit expression for the effective superpotential in arbitrary N = 1 heterotic or type IIB orientifold compactifications, for all the allowed fluxes.
Discrete approach to complex planar geometries
International Nuclear Information System (INIS)
Cupini, E.; De Matteis, A.
1974-01-01
Planar regions in Monte Carlo transport problems have been represented by a finite set of points with a corresponding region index for each. The simulation of particle free-flight reduces then to the simple operations necessary for scanning appropriate grid points to determine whether a region other than the starting one is encountered. When the complexity of the geometry is restricted to only some regions of the assembly examined, a mixed discrete-continuous philosophy may be adopted. By this approach, the lattice of a thermal reactor has been treated, discretizing only the central regions of the cell containing the fuel rods. Excellent agreement with experimental results has been obtained in the computation of cell parameters in the energy range from fission to thermalization through the 238 U resonance region. (U.S.)
The Kerr geometry, complex world lines and hyperbolic strings
International Nuclear Information System (INIS)
Burinskii, A.Ya.
1994-01-01
In the Lind-Newman representation the Kerr geometry is created by a source moving along an analytical complex world line. An equivalence of the complex world line and complex (hyperbolic) string is considered. Therefore the hyperbolic string may play the role of the complex source of the Kerr geometry. The Kerr solution with the complex string source acquires Regge behavior of the angular momentum. (orig.)
Minimal length uncertainty and generalized non-commutative geometry
International Nuclear Information System (INIS)
Farmany, A.; Abbasi, S.; Darvishi, M.T.; Khani, F.; Naghipour, A.
2009-01-01
A generalized formulation of non-commutative geometry for the Bargmann-Fock space of quantum field theory is presented. The analysis is related to the symmetry of the simplistic space and a minimal length uncertainty.
Multigrid Methods for Aerodynamic Problems in Complex Geometries
Caughey, David A.
1995-01-01
Work has been directed at the development of efficient multigrid methods for the solution of aerodynamic problems involving complex geometries, including the development of computational methods for the solution of both inviscid and viscous transonic flow problems. The emphasis is on problems of complex, three-dimensional geometry. The methods developed are based upon finite-volume approximations to both the Euler and the Reynolds-Averaged Navier-Stokes equations. The methods are developed for use on multi-block grids using diagonalized implicit multigrid methods to achieve computational efficiency. The work is focused upon aerodynamic problems involving complex geometries, including advanced engine inlets.
Differential and complex geometry origins, abstractions and embeddings
Wells, Jr , Raymond O
2017-01-01
Differential and complex geometry are two central areas of mathematics with a long and intertwined history. This book, the first to provide a unified historical perspective of both subjects, explores their origins and developments from the sixteenth to the twentieth century. Providing a detailed examination of the seminal contributions to differential and complex geometry up to the twentieth century embedding theorems, this monograph includes valuable excerpts from the original documents, including works of Descartes, Fermat, Newton, Euler, Huygens, Gauss, Riemann, Abel, and Nash. Suitable for beginning graduate students interested in differential, algebraic or complex geometry, this book will also appeal to more experienced readers.
Introduction to the geometry of complex numbers
Deaux, Roland
2008-01-01
Geared toward readers unfamiliar with complex numbers, this text explains how to solve problems that frequently arise in the applied sciences and emphasizes constructions related to algebraic operations. 1956 edition.
On the Plane Geometry with Generalized Absolute Value Metric
Directory of Open Access Journals (Sweden)
A. Bayar
2008-01-01
Full Text Available Metric spaces are among the most important widely studied topics in mathematics. In recent years, Mathematicians began to investigate using other metrics different from Euclidean metric. These metrics also find their place computer age in addition to their importance in geometry. In this paper, we consider the plane geometry with the generalized absolute value metric and define trigonometric functions and norm and then give a plane tiling example for engineers underlying Schwarz's inequality in this plane.
International Nuclear Information System (INIS)
Yang Xue; Satvat, Nader
2012-01-01
Highlight: ► A two-dimensional numerical code based on the method of characteristics is developed. ► The complex arbitrary geometries are represented by constructive solid geometry and decomposed by unstructured meshing. ► Excellent agreement between Monte Carlo and the developed code is observed. ► High efficiency is achieved by parallel computing. - Abstract: A transport theory code MOCUM based on the method of characteristics as the flux solver with an advanced general geometry processor has been developed for two-dimensional rectangular and hexagonal lattice and full core neutronics modeling. In the code, the core structure is represented by the constructive solid geometry that uses regularized Boolean operations to build complex geometries from simple polygons. Arbitrary-precision arithmetic is also used in the process of building geometry objects to eliminate the round-off error from the commonly used double precision numbers. Then, the constructed core frame will be decomposed and refined into a Conforming Delaunay Triangulation to ensure the quality of the meshes. The code is fully parallelized using OpenMP and is verified and validated by various benchmarks representing rectangular, hexagonal, plate type and CANDU reactor geometries. Compared with Monte Carlo and deterministic reference solution, MOCUM results are highly accurate. The mentioned characteristics of the MOCUM make it a perfect tool for high fidelity full core calculation for current and GenIV reactor core designs. The detailed representation of reactor physics parameters can enhance the safety margins with acceptable confidence levels, which lead to more economically optimized designs.
Solar Proton Transport within an ICRU Sphere Surrounded by a Complex Shield: Combinatorial Geometry
Wilson, John W.; Slaba, Tony C.; Badavi, Francis F.; Reddell, Brandon D.; Bahadori, Amir A.
2015-01-01
The 3DHZETRN code, with improved neutron and light ion (Z (is) less than 2) transport procedures, was recently developed and compared to Monte Carlo (MC) simulations using simplified spherical geometries. It was shown that 3DHZETRN agrees with the MC codes to the extent they agree with each other. In the present report, the 3DHZETRN code is extended to enable analysis in general combinatorial geometry. A more complex shielding structure with internal parts surrounding a tissue sphere is considered and compared against MC simulations. It is shown that even in the more complex geometry, 3DHZETRN agrees well with the MC codes and maintains a high degree of computational efficiency.
Eddy Current Flexible Probes for Complex Geometries
Gilles-Pascaud, C.; Decitre, J. M.; Vacher, F.; Fermon, C.; Pannetier, M.; Cattiaux, G.
2006-03-01
The inspection of materials used in aerospace, nuclear or transport industry is a critical issue for the safety of components exposed to stress or/and corrosion. The industry claims for faster, more sensitive, and more flexible techniques. Technologies based on Eddy Current (EC) flexible array probe and magnetic sensor with high sensitivity such as giant magneto-resistance (GMR) could be a good solution to detect surface-breaking flaws in complex shaped surfaces. The CEA has recently developed, with support from the French Institute for Radiological Protection and Nuclear Safety (IRSN), a flexible array probe based on micro-coils etched on Kapton. The probe's performances have been assessed for the inspection of reactor residual heat removal pipes, and for aeronautical applications within the framework of the European project VERDICT. The experimental results confirm the very good detection of narrow cracks on plane and curve shaped surfaces. This paper also describes the recent progresses concerning the application of GMR sensors to EC testing, and the results obtained for the detection of small surface breaking flaws.
Development and Application of Agglomerated Multigrid Methods for Complex Geometries
Nishikawa, Hiroaki; Diskin, Boris; Thomas, James L.
2010-01-01
We report progress in the development of agglomerated multigrid techniques for fully un- structured grids in three dimensions, building upon two previous studies focused on efficiently solving a model diffusion equation. We demonstrate a robust fully-coarsened agglomerated multigrid technique for 3D complex geometries, incorporating the following key developments: consistent and stable coarse-grid discretizations, a hierarchical agglomeration scheme, and line-agglomeration/relaxation using prismatic-cell discretizations in the highly-stretched grid regions. A signi cant speed-up in computer time is demonstrated for a model diffusion problem, the Euler equations, and the Reynolds-averaged Navier-Stokes equations for 3D realistic complex geometries.
Self-dual geometry of generalized Hermitian surfaces
International Nuclear Information System (INIS)
Arsen'eva, O E; Kirichenko, V F
1998-01-01
Several results on the geometry of conformally semiflat Hermitian surfaces of both classical and hyperbolic types (generalized Hermitian surfaces) are obtained. Some of these results are generalizations and clarifications of already known results in this direction due to Koda, Itoh, and other authors. They reveal some unexpected beautiful connections between such classical characteristics of conformally semiflat (generalized) Hermitian surfaces as the Einstein property, the constancy of the holomorphic sectional curvature, and so on. A complete classification of compact self-dual Hermitian RK-surfaces that are at the same time generalized Hopf manifolds is obtained. This provides a complete solution of the Chen problem in this class of Hermitian surfaces
Generalization of the electronic susceptibility for arbitrary molecular geometries
Energy Technology Data Exchange (ETDEWEB)
Scherrer, Arne; Dreßler, Christian; Ahlert, Paul; Sebastiani, Daniel, E-mail: daniel.sebastiani@chemie.uni-halle.de [Institute of Chemistry, Martin-Luther-University Halle-Wittenberg, Von-Danckelmann-Platz 4, 06120 Halle (Saale) (Germany)
2016-04-14
We generalize the explicit representation of the electronic susceptibility χ{sub [R]}(r, r′) for arbitrary molecular geometries R. The electronic susceptibility is a response function that yields the response of the molecular electronic charge density at linear order to an arbitrary external perturbation. We address the dependence of this response function on the molecular geometry. The explicit representation of the molecular geometry dependence is achieved by means of a Taylor expansion in the nuclear coordinates. Our approach relies on a recently developed low-rank representation of the response function χ{sub [R]}(r, r′) which allows a highly condensed storage of the expansion and an efficient application within dynamical chemical environments. We illustrate the performance and accuracy of our scheme by computing the vibrationally induced variations of the response function of a water molecule and its resulting Raman spectrum.
Complex differential geometry and supermanifolds in strings and fields. Proceedings
Energy Technology Data Exchange (ETDEWEB)
Bongaarts, P.J.M. (Univ. of Leiden, Lorentz Inst. (Netherlands)); Martini, R. (Univ. of Twente, Faculty of Applied Mathematics, Enschede (Netherlands)) (eds.)
1988-01-01
This conference is the seventh in a series of meetings that started in 1973. All of these meetings have been centered around a few main topics of related interest and have been partly instructional in character, in order to stimulate further research. The last three conferences were devoted to aspects of differential geometry in mathematical physics, and this trend was continued in the present meeting. More specifically, the emphasis was this time on complex differential geometry (Kaehler manifolds), super and graded manifolds, and their applications to supersymmetry, strings and field theory. (orig.).
A generalized mechanical model for suture interfaces of arbitrary geometry
Li, Yaning; Ortiz, Christine; Boyce, Mary C.
2013-04-01
Suture interfaces with a triangular wave form commonly found in nature have recently been shown to exhibit exceptional mechanical behavior, where geometric parameters such as amplitude, frequency, and hierarchy can be used to nonlinearly tailor and amplify mechanical properties. In this study, using the principle of complementary virtual work, we formulate a generalized, composite mechanical model for arbitrarily-shaped interdigitating suture interfaces in order to more broadly investigate the influence of wave-form geometry on load transmission, deformation mechanisms, anisotropy, and stiffness, strength, and toughness of the suture interface for tensile and shear loading conditions. The application of this suture interface model is exemplified for the case of the general trapezoidal wave-form. Expressions for the in-plane stiffness, strength and fracture toughness and failure mechanisms are derived as nonlinear functions of shape factor β (which characterizes the general trapezoidal shape as triangular, trapezoidal, rectangular or anti-trapezoidal), the wavelength/amplitude ratio, the interface width/wavelength ratio, and the stiffness and strength ratios of the skeletal/interfacial phases. These results provide guidelines for choosing and tailoring interface geometry to optimize the mechanical performance in resisting different loads. The presented model provides insights into the relation between the mechanical function and the morphological diversity of suture interface geometries observed in natural systems.
KENO-VI: A Monte Carlo Criticality Program with generalized quadratic geometry
International Nuclear Information System (INIS)
Hollenbach, D.F.; Petrie, L.M.; Landers, N.F.
1993-01-01
This report discusses KENO-VI which is a new version of the KENO monte Carlo Criticality Safety developed at Oak Ridge National Laboratory. The purpose of KENO-VI is to provide a criticality safety code similar to KENO-V.a that possesses a more general and flexible geometry package. KENO-VI constructs and processes geometry data as sets of quadratic equations. A lengthy set of simple, easy-to-use geometric functions, similar to those provided in KENO-V.a., and the ability to build more complex geometric shapes represented by sets of quadratic equations are the heart of the geometry package in KENO-VI. The code's flexibility is increased by allowing intersecting geometry regions, hexagonal as well as cuboidal arrays, and the ability to specify an array boundary that intersects the array
String theory compactifications with fluxes, and generalized geometry
International Nuclear Information System (INIS)
Cassani, D.
2009-06-01
The topic of this thesis is compactifications in string theory and supergravity. We study dimensional reductions of type II theories on backgrounds with fluxes, using the techniques of Hitchin's generalized geometry. We start with an introduction of the needed mathematical tools, focusing on SU(3)xSU(3) structures on the generalized tangent bundle T+T * , and analyzing their deformations. Next we study the four dimensional N equals 2 gauged supergravity which can be defined reducing type II theories on SU(3)*SU(3) structure backgrounds with general NSNS and RR fluxes: we establish the complete bosonic action, and we show how its data are related to the generalized geometry formalism on T+T * . In particular, we derive a geometric expression for the full N = 2 scalar potential. Then we focus on the relations between the 10d and 4d descriptions of supersymmetric flux backgrounds: we spell out the N = 1 vacuum conditions within the 4d N = 2 theory, as well as from its N = 1 truncation, and we establish a precise matching with the equations characterizing the N = 1 backgrounds at the ten dimensional level. We conclude by presenting some concrete examples, based on coset spaces with SU(3) structure. We establish for these spaces the consistency of the truncation based on left-invariance, and we explore the landscape of vacua of the corresponding theory, taking string loop corrections into account. (author)
Geometry system used in the General Monte Carlo transport code SPARTAN
International Nuclear Information System (INIS)
Bending, R.C.; Easter, P.G.
1974-01-01
The geometry routines used in the general-purpose, three-dimensional particle transport code SPARTAN are described. The code is designed to deal with the very complex geometries encountered in lattice cell and fuel handling calculations, health physics, and shielding problems. Regions of the system being studied may be represented by simple shapes (spheres, cylinders, and so on) or by multinomial surfaces of any order, and many simple shapes may be combined to make up a complex layout. The geometry routines are designed to allow the program to carry out a number of tasks (such as sampling for a random point or tracking a path through several regions) in any order, so that the use of the routines is not restricted to a particular tracking or scoring method. Routines for reading, checking, and printing the data are included. (U.S.)
Complex quantum network geometries: Evolution and phase transitions
Bianconi, Ginestra; Rahmede, Christoph; Wu, Zhihao
2015-08-01
Networks are topological and geometric structures used to describe systems as different as the Internet, the brain, or the quantum structure of space-time. Here we define complex quantum network geometries, describing the underlying structure of growing simplicial 2-complexes, i.e., simplicial complexes formed by triangles. These networks are geometric networks with energies of the links that grow according to a nonequilibrium dynamics. The evolution in time of the geometric networks is a classical evolution describing a given path of a path integral defining the evolution of quantum network states. The quantum network states are characterized by quantum occupation numbers that can be mapped, respectively, to the nodes, links, and triangles incident to each link of the network. We call the geometric networks describing the evolution of quantum network states the quantum geometric networks. The quantum geometric networks have many properties common to complex networks, including small-world property, high clustering coefficient, high modularity, and scale-free degree distribution. Moreover, they can be distinguished between the Fermi-Dirac network and the Bose-Einstein network obeying, respectively, the Fermi-Dirac and Bose-Einstein statistics. We show that these networks can undergo structural phase transitions where the geometrical properties of the networks change drastically. Finally, we comment on the relation between quantum complex network geometries, spin networks, and triangulations.
The Geometry of Binary Collisions and Generalized Radon Transforms
Wennberg, Bernt
Elastic collisions are characterized by the conservation of momentum and energy. We consider some geometrical aspects of such collisions, when the energy of one particle can be expressed in terms of the moments as . The geometry of elastic collisions is essential for the regularizing property of the gain term in the Boltzmann equation, which was proved by P.-L. Lions. We show how such results can be deduced from a regularity theorem for generalized Radon transforms by Sogge & Stein. This is possible for and for ; we also show that the same technique cannot be used with other choices of .
ELECTRON CYCLOTRON CURRENT DRIVE EFFICIENCY IN GENERAL TOKAMAK GEOMETRY
International Nuclear Information System (INIS)
LIN-LUI, Y.R; CHAN, V.S; PRATER, R.
2003-01-01
Green's-function techniques are used to calculate electron cyclotron current drive (ECCD) efficiency in general tokamak geometry in the low-collisionality regime. Fully relativistic electron dynamics is employed in the theoretical formulation. The high-velocity collision model is used to model Coulomb collisions and a simplified quasi-linear rf diffusion operator describes wave-particle interactions. The approximate analytic solutions which are benchmarked with a widely used ECCD model, facilitate time-dependent simulations of tokamak operational scenarios using the non-inductive current drive of electron cyclotron waves
A dissipative particle dynamics method for arbitrarily complex geometries
Li, Zhen; Bian, Xin; Tang, Yu-Hang; Karniadakis, George Em
2018-02-01
Dissipative particle dynamics (DPD) is an effective Lagrangian method for modeling complex fluids in the mesoscale regime but so far it has been limited to relatively simple geometries. Here, we formulate a local detection method for DPD involving arbitrarily shaped geometric three-dimensional domains. By introducing an indicator variable of boundary volume fraction (BVF) for each fluid particle, the boundary of arbitrary-shape objects is detected on-the-fly for the moving fluid particles using only the local particle configuration. Therefore, this approach eliminates the need of an analytical description of the boundary and geometry of objects in DPD simulations and makes it possible to load the geometry of a system directly from experimental images or computer-aided designs/drawings. More specifically, the BVF of a fluid particle is defined by the weighted summation over its neighboring particles within a cutoff distance. Wall penetration is inferred from the value of the BVF and prevented by a predictor-corrector algorithm. The no-slip boundary condition is achieved by employing effective dissipative coefficients for liquid-solid interactions. Quantitative evaluations of the new method are performed for the plane Poiseuille flow, the plane Couette flow and the Wannier flow in a cylindrical domain and compared with their corresponding analytical solutions and (high-order) spectral element solution of the Navier-Stokes equations. We verify that the proposed method yields correct no-slip boundary conditions for velocity and generates negligible fluctuations of density and temperature in the vicinity of the wall surface. Moreover, we construct a very complex 3D geometry - the "Brown Pacman" microfluidic device - to explicitly demonstrate how to construct a DPD system with complex geometry directly from loading a graphical image. Subsequently, we simulate the flow of a surfactant solution through this complex microfluidic device using the new method. Its
Inspection of complex geometry pieces with an intelligent contact transducer
International Nuclear Information System (INIS)
Chatillon, S.; Roy, O.; Mahaut, St.
2000-01-01
A new multi-element contact transducer has been developed to improve the inspection of components with complex geometry. The emitting surface is flexible in order to optimize the contact with pieces. An algorithm, based on a simplified geometric model, has been used to determine the delays law which allows to control the focal characteristics of the transmitted field. Acquisition data lead in transmission with an articulated transducer validate the behavior provided by simulation. Thus the optimization of the delays law ensures the transmission of a beam which is homogeneous and controlled during the moving of the transducer. Inspections in echo-pulse mode are implemented on a sample simulating a component controlled on site. Results show that the dynamical adaptation of the delays law to the geometry of the piece leads to very good performances
C-spaces, generalized geometry and double field theory
International Nuclear Information System (INIS)
Papadopoulos, G.
2015-01-01
We construct a C-space associated with every closed 3-form on a spacetime M and show that it depends on the class of the form in H 3 (M,ℤ). We also demonstrate that C-spaces have a relation to generalized geometry and to gerbes. C-spaces are constructed after introducing additional coordinates at the open sets and at their double overlaps of a spacetime generalizing the standard construction of Kaluza-Klein spaces for 2-forms. C-spaces may not be manifolds and satisfy the topological geometrization condition. Double spaces arise as local subspaces of C-spaces that cannot be globally extended. This indicates that for the global definition of double field theories additional coordinates are needed. We explore several other aspect of C-spaces like their topology and relation to Whitehead towers, and also describe the construction of C-spaces for closed k-forms.
C-spaces, generalized geometry and double field theory
Energy Technology Data Exchange (ETDEWEB)
Papadopoulos, G. [Department of Mathematics, King’s College London,Strand, London WC2R 2LS (United Kingdom)
2015-09-07
We construct a C-space associated with every closed 3-form on a spacetime M and show that it depends on the class of the form in H{sup 3}(M,ℤ). We also demonstrate that C-spaces have a relation to generalized geometry and to gerbes. C-spaces are constructed after introducing additional coordinates at the open sets and at their double overlaps of a spacetime generalizing the standard construction of Kaluza-Klein spaces for 2-forms. C-spaces may not be manifolds and satisfy the topological geometrization condition. Double spaces arise as local subspaces of C-spaces that cannot be globally extended. This indicates that for the global definition of double field theories additional coordinates are needed. We explore several other aspect of C-spaces like their topology and relation to Whitehead towers, and also describe the construction of C-spaces for closed k-forms.
Unification of Electromagnetism and Gravitation in the Framework of General Geometry
Shahverdiyev, Shervgi
2005-01-01
A new geometry, called General geometry, is constructed. It is proven that its the most simplest special case is geometry underlying Electromagnetism. Another special case is Riemannian geometry. Action for electromagnetic field and Maxwell equations are derived from curvature function of geometry underlying Electromagnetism. It is shown that equation of motion for a particle interacting with electromagnetic field coincides exactly with equation for geodesics of geometry underlying Electromag...
Indian Academy of Sciences (India)
. In the previous article we looked at the origins of synthetic and analytic geometry. More practical minded people, the builders and navigators, were studying two other aspects of geometry- trigonometry and integral calculus. These are actually ...
Modelling and simulation of gas explosions in complex geometries
Energy Technology Data Exchange (ETDEWEB)
Saeter, Olav
1998-12-31
This thesis presents a three-dimensional Computational Fluid Dynamics (CFD) code (EXSIM94) for modelling and simulation of gas explosions in complex geometries. It gives the theory and validates the following sub-models : (1) the flow resistance and turbulence generation model for densely packed regions, (2) the flow resistance and turbulence generation model for single objects, and (3) the quasi-laminar combustion model. It is found that a simple model for flow resistance and turbulence generation in densely packed beds is able to reproduce the medium and large scale MERGE explosion experiments of the Commission of European Communities (CEC) within a band of factor 2. The model for a single representation is found to predict explosion pressure in better agreement with the experiments with a modified k-{epsilon} model. This modification also gives a slightly improved grid independence for realistic gas explosion approaches. One laminar model is found unsuitable for gas explosion modelling because of strong grid dependence. Another laminar model is found to be relatively grid independent and to work well in harmony with the turbulent combustion model. The code is validated against 40 realistic gas explosion experiments. It is relatively grid independent in predicting explosion pressure in different offshore geometries. It can predict the influence of ignition point location, vent arrangements, different geometries, scaling effects and gas reactivity. The validation study concludes with statistical and uncertainty analyses of the code performance. 98 refs., 96 figs, 12 tabs.
Surprising Coordination Geometry Differences in Ce(IV)- and Pu(IV)-Maltol Complexes
Energy Technology Data Exchange (ETDEWEB)
Lawrence Berkeley National Laboratory; Raymond, Kenneth; Szigethy, Geza; Xu, Jide; Gorden, Anne E.V.; Teat, Simon J.; Shuh, David K.; Raymond, Kenneth N.
2008-02-12
As part of a study to characterize the detailed coordination behavior of Pu(IV), single crystal X-ray diffraction structures have been determined for Pu(IV) and Ce(IV) complexes with the naturally-occurring ligand maltol (3-hydroxy-2-methyl-pyran-4-one) and its derivative bromomaltol (5-bromo-3-hydroxy-2-methyl-pyran-4-one). Although Ce(IV) is generally accepted as a structural analog for Pu(IV), and the maltol complexes of these two metals are isostructural, the corresponding bromomaltol complexes are strikingly different with respect to ligand orientation about the metal ion: All complexes exhibit trigonal dodecahedral coordination geometry but the Ce(IV)-bromomaltol complex displays an uncommon ligand arrangement not mirrored in the Pu(IV) complex, although the two metal species are generally accepted to be structural analogs.
Stability analysis of underground mining openings with complex geometry
Directory of Open Access Journals (Sweden)
Cała Marek
2016-03-01
Full Text Available Stability of mining openings requires consideration of a number of factors, such as: geological structure, the geometry of the underground mining workings, mechanical properties of the rock mass, changes in stress caused by the influence of neighbouring workings. Long-term prediction and estimation of workings state can be analysed with the use of numerical methods. Application of 3D numerical modelling in stability estimation of workings with complex geometry was described with the example of Crystal Caves in Wieliczka Salt Mine. Preservation of the Crystal Caves reserve is particularly important in view of their unique character and the protection of adjacent galleries which are a part of tourist attraction included in UNESCO list. A detailed 3D model of Crystal Caves and neighbouring workings was built. Application of FLAC3D modelling techniques enabled indication of the areas which are in danger of stability loss. Moreover, the area in which protective actions should be taken as well as recommendations concerning the convergence monitoring were proposed.
An adaptive fast multipole accelerated Poisson solver for complex geometries
Askham, T.; Cerfon, A. J.
2017-09-01
We present a fast, direct and adaptive Poisson solver for complex two-dimensional geometries based on potential theory and fast multipole acceleration. More precisely, the solver relies on the standard decomposition of the solution as the sum of a volume integral to account for the source distribution and a layer potential to enforce the desired boundary condition. The volume integral is computed by applying the FMM on a square box that encloses the domain of interest. For the sake of efficiency and convergence acceleration, we first extend the source distribution (the right-hand side in the Poisson equation) to the enclosing box as a C0 function using a fast, boundary integral-based method. We demonstrate on multiply connected domains with irregular boundaries that this continuous extension leads to high accuracy without excessive adaptive refinement near the boundary and, as a result, to an extremely efficient "black box" fast solver.
A study of complexity of oral mucosa using fractal geometry
Directory of Open Access Journals (Sweden)
S R Shenoi
2017-01-01
Full Text Available Background: The oral mucosa lining the oral cavity is composed of epithelium supported by connective tissue. The shape of the epithelial-connective tissue interface has traditionally been used to describe physiological and pathological changes in the oral mucosa. Aim: The aim is to evaluate the morphometric complexity in normal, dysplastic, well-differentiated, and moderately differentiated squamous cell carcinoma (SCC of the oral mucosa using fractal geometry. Materials and Methods: A total of 80 periodic acid–Schiff stained histological images of four groups: normal mucosa, dysplasia, well-differentiated SCC, and moderately differentiated SCC were verified by the gold standard. These images were then subjected to fractal analysis. Statistical Analysis: ANOVA and post hoc test: Bonferroni was applied. Results: Fractal dimension (FD increases as the complexity increases from normal to dysplasia and then to SCC. Normal buccal mucosa was found to be significantly different from dysplasia and the two grades of SCC (P < 0.05. ANOVA of fractal scores of four morphometrically different groups of buccal mucosa was significantly different with F (3,76 = 23.720 and P< 0.01. However, FD of dysplasia was not significantly different from well-differentiated and moderately differentiated SCC (P = 1.000 and P = 0.382, respectively. Conclusion: This study establishes FD as a newer tool in differentiating normal tissue from dysplastic and neoplastic tissue. Fractal geometry is useful in the study of both physiological and pathological changes in the oral mucosa. A new grading system based on FD may emerge as an adjuvant aid in cancer diagnosis.
Resistance projection welding of complex metal combinations and geometries
DEFF Research Database (Denmark)
Kristensen, Lars; Bay, Niels; Malberg, Michael Peter
Final report about the results and research in the MUPII-project "Pressvejsning af komplekse geometrier og materialer"......Final report about the results and research in the MUPII-project "Pressvejsning af komplekse geometrier og materialer"...
Spacetime and Geometry: An Introduction to General Relativity
International Nuclear Information System (INIS)
Poisson, E
2005-01-01
The ever growing relevance of general relativity to astrophysics and cosmology continues to motivate the publication of new textbooks which put the theory in a fresh perspective informed by recent developments. While the 1970s were the decade of Weinberg and Misner et al and the 80s the decade of Schutz and Wald, this is clearly the decade of Hartle and Carroll. Hartle has introduced a novel pedagogical approach to teaching general relativity, which he convincingly argues should be done in the standard undergraduate physics curriculum. His 'physics-first approach' emphasizes physical phenomena and minimizes mathematical formalism. Hartle achieves a lot by introducing only the spacetime metric and the geodesic equation, which are the main tools needed to explore curved spacetime and extract physical consequences. To be sure, to explain how the metric is obtained in the first place does require a background of differential geometry and the formulation of the Einstein field equations. But in Hartle's book this material is wisely presented at a later stage, after an ample sampling of the physics of curved spacetime has motivated the need for the advanced mathematics. Carroll follows instead the traditional route, what Hartle calls the 'math-first approach', in which one introduces first the required mathematical formalism and only then derives the physical consequences. He is, of course, in good company, as this is the method followed in all existing textbooks (with Hartle's being the sole exception). Carroll's approach may not be original, but it is tried and true, and the result of Carroll's efforts is an excellent introduction to general relativity. The book covers the standard topics that would be found in virtually all textbooks (differential geometry, the field equations, linearized theory, black holes, and cosmology), but in addition it contains topics (such as quantum field theory in curved spacetime) which can rarely be found in introductory texts. All these
Generalized functional formulation for multi-fractal representation of basin hydraulic geometry
Kim, JongChun; Paik, Kyungrock
2015-04-01
Natural rivers exhibit power-functional variability in their width, depth, and velocity with flow discharge (Leopold and Maddock, 1953). This relation named hydraulic geometry has been empirically supported by many field studies across the world (e.g., Leopold et al., 1964; Stall and Fok, 1968). The relationship appears either at a fixed cross-section, showing temporal variability, or along a downstream direction across an entire basin, showing spatial variability, the latter named downstream or basin hydraulic geometry. Theoretical studies that attempt to explain the power-law phenomenon (fractal), have assumed that the watershed is homogeneous hydrologically and geologically. Nevertheless, real watersheds are often subject to spatially heterogeneous conditions, due to various reasons including partial area storm coverage (Sólyom and Tucker, 2004) and transmission losses on bed and banks (Lane et al., 1997). In this setting, hydraulic geometry relationships are likely to deviate from monotonic power-law relationship and to follow rather more complex multi-fractal characteristics. In fact, deviation from single power-law was reported for at-a-station relationship of midwest rivers in US (Dodov and Foufoula-Georgiou, 2004). In the case of downstream variation, we identify significant multi-fractal characteristics over the Colorado River basin where strong heterogeneity in geological and hydrological settings presents. Conventional power-law hydraulic geometry relationships cannot express the functional variability for these cases. Motivated by this fact, we generalize the hydraulic geometry functional formulation in this study to express multi-fractal relationships. To do so, we couple the formulation of Paik and Kumar (2004), which generalized at-a-station and downstream relationships, with the formulation of Dodov and Foufoula-Georgiou (2004) which was proposed for multi-scaling in at-a-station relationship. The proposed formulation is successfully evaluated with
Pedoe, Dan
1988-01-01
""A lucid and masterly survey."" - Mathematics Gazette Professor Pedoe is widely known as a fine teacher and a fine geometer. His abilities in both areas are clearly evident in this self-contained, well-written, and lucid introduction to the scope and methods of elementary geometry. It covers the geometry usually included in undergraduate courses in mathematics, except for the theory of convex sets. Based on a course given by the author for several years at the University of Minnesota, the main purpose of the book is to increase geometrical, and therefore mathematical, understanding and to he
Multiphase flows in complex geometries: a UQ perspective
Icardi, Matteo
2015-01-07
Nowadays computer simulations are widely used in many multiphase flow applications involving interphases, dispersed particles, and complex geometries. Most of these problems are solved with mixed models composed of fundamental physical laws, rigorous mathematical upscaling, and empirical correlations/closures. This means that classical inference techniques or forward parametric studies, for example, becomes computationally prohibitive and must take into account the physical meaning and constraints of the equations. However mathematical techniques commonly used in Uncertainty Quantification can come to the aid for the (i) modeling, (ii) simulation, and (iii) validation steps. Two relevant applications for environmental, petroleum, and chemical engineering will be presented to highlight these aspects and the importance of bridging the gaps between engineering applications, computational physics and mathematical methods. The first example is related to the mathematical modeling of sub-grid/sub-scale information with Probability Density Function (PDF) models in problems involving flow, mixing, and reaction in random environment. After a short overview of the research field, some connections and similarities with Polynomial Chaos techniques, will be investigated. In the second example, averaged correlations laws and effective parameters for multiphase flow and their statistical fluctuations, will be considered and efficient computational techniques, borrowed from high-dimensional stochastic PDE problems, will be applied. In presence of interfacial flow, where small spatial scales and fast time scales are neglected, the assessment of robustness and predictive capabilities are studied. These illustrative examples are inspired by common problems arising, for example, from the modeling and simulation of turbulent and porous media flows.
MM99.81 Projection welding of complex geometries
DEFF Research Database (Denmark)
Kristensen, Lars
The objective of this work has been to establish a profound knowledge about design rules for projection welding geometries dependent of the actual material combination.Design rules and recommendations for geometries and projections in projection welding given in literature is summarised and these...
DEFF Research Database (Denmark)
Byg din egen boomerang, kast den, se den flyve, forstå hvorfor og hvordan den vender tilbage, og grib den. Det handler om opdriften på vingerne når du flyver, men det handler også og allermest om den mærkværdige gyroskop-effekt, du bruger til at holde balancen, når du kører på cykel. Vi vil bruge...... matematik, geometri, og fysik til at forstå, hvad det er, der foregår....
Directory of Open Access Journals (Sweden)
Drawert Brian
2012-06-01
Full Text Available Abstract Background Experiments in silico using stochastic reaction-diffusion models have emerged as an important tool in molecular systems biology. Designing computational software for such applications poses several challenges. Firstly, realistic lattice-based modeling for biological applications requires a consistent way of handling complex geometries, including curved inner- and outer boundaries. Secondly, spatiotemporal stochastic simulations are computationally expensive due to the fast time scales of individual reaction- and diffusion events when compared to the biological phenomena of actual interest. We therefore argue that simulation software needs to be both computationally efficient, employing sophisticated algorithms, yet in the same time flexible in order to meet present and future needs of increasingly complex biological modeling. Results We have developed URDME, a flexible software framework for general stochastic reaction-transport modeling and simulation. URDME uses Unstructured triangular and tetrahedral meshes to resolve general geometries, and relies on the Reaction-Diffusion Master Equation formalism to model the processes under study. An interface to a mature geometry and mesh handling external software (Comsol Multiphysics provides for a stable and interactive environment for model construction. The core simulation routines are logically separated from the model building interface and written in a low-level language for computational efficiency. The connection to the geometry handling software is realized via a Matlab interface which facilitates script computing, data management, and post-processing. For practitioners, the software therefore behaves much as an interactive Matlab toolbox. At the same time, it is possible to modify and extend URDME with newly developed simulation routines. Since the overall design effectively hides the complexity of managing the geometry and meshes, this means that newly developed methods
Advancing the manufacture of complex geometry GFRC for today's building envelopes
Directory of Open Access Journals (Sweden)
Thomas Henriksen
2017-06-01
With this research the current architectural knowledge base has been advanced in terms of complex geometry thin-walled GFRC for building envelopes. The identified solutions should allow building with complex geometries to be realised using thin-walled GFRC as the envelope cladding.
Algebrodynamics over complex space and phase extension of the Minkowski geometry
International Nuclear Information System (INIS)
Kassandrov, V. V.
2009-01-01
First principles should predetermine physical geometry and dynamics both together. In the 'algebrodynamics' they follow solely from the properties of biquaternion algebra B and the analysis over B. We briefly present the algebrodynamics over Minkowski background based on a nonlinear generalization to B of the Cauchi-Riemann analyticity conditions. Further, we consider the effective real geometry uniquely resulting from the structure of B multiplication and found it to be of the Minkowski type, with an additional phase invariant. Then we pass to study the primordial dynamics that takes place in the complex B space and brings into consideration a number of remarkable structures: an ensemble of identical correlated matter pre-elements ('duplicons'), caustic-like signals (interaction carriers), a concept of random complex time resulting in irreversibility of physical time at macrolevel, etc. In partucular, the concept of 'dimerous electron' naturally arises in the framework of complex algebrodynamics and, together with the above-mentioned phase invariant, allows for a novel approach to explanation of quantum interference phenomena alternative to recently accepted wave-particle dualism paradigm.
Sketching the General Quadratic Equation Using Dynamic Geometry Software
Stols, G. H.
2005-01-01
This paper explores a geometrical way to sketch graphs of the general quadratic in two variables with Geometer's Sketchpad. To do this, a geometric procedure as described by De Temple is used, bearing in mind that this general quadratic equation (1) represents all the possible conics (conics sections), and the fact that five points (no three of…
SCAP-82, Single Scattering, Albedo Scattering, Point-Kernel Analysis in Complex Geometry
International Nuclear Information System (INIS)
Disney, R.K.; Vogtman, S.E.
1987-01-01
1 - Description of problem or function: SCAP solves for radiation transport in complex geometries using the single or albedo scatter point kernel method. The program is designed to calculate the neutron or gamma ray radiation level at detector points located within or outside a complex radiation scatter source geometry or a user specified discrete scattering volume. Geometry is describable by zones bounded by intersecting quadratic surfaces within an arbitrary maximum number of boundary surfaces per zone. Anisotropic point sources are describable as pointwise energy dependent distributions of polar angles on a meridian; isotropic point sources may also be specified. The attenuation function for gamma rays is an exponential function on the primary source leg and the scatter leg with a build- up factor approximation to account for multiple scatter on the scat- ter leg. The neutron attenuation function is an exponential function using neutron removal cross sections on the primary source leg and scatter leg. Line or volumetric sources can be represented as a distribution of isotropic point sources, with un-collided line-of-sight attenuation and buildup calculated between each source point and the detector point. 2 - Method of solution: A point kernel method using an anisotropic or isotropic point source representation is used, line-of-sight material attenuation and inverse square spatial attenuation between the source point and scatter points and the scatter points and detector point is employed. A direct summation of individual point source results is obtained. 3 - Restrictions on the complexity of the problem: - The SCAP program is written in complete flexible dimensioning so that no restrictions are imposed on the number of energy groups or geometric zones. The geometric zone description is restricted to zones defined by boundary surfaces defined by the general quadratic equation or one of its degenerate forms. The only restriction in the program is that the total
Yang-Mills detour complexes and conformal geometry
Gover, A. Rod; Somberg, Petr; Soucek, Vladimir
2006-01-01
Working over a pseudo-Riemannian manifold, for each vector bundle with connection we construct a sequence of three differential operators which is a complex (termed a Yang-Mills detour complex) if and only if the connection satisfies the full Yang-Mills equations. A special case is a complex controlling the deformation theory of Yang-Mills connections. In the case of Riemannian signature the complex is elliptic. If the bundle connection respects a metric on the vector bundle then the complex ...
Modeling of Neoclassical Tearing Mode Stability for Generalized Toroidal Geometry
International Nuclear Information System (INIS)
A.L. Rosenberg; D.A. Gates; A. Pletzer; J.E. Menard; S.E. Kruger; C.C. Hegna; F. Paoletti; S. Sabbagh
2002-01-01
Neoclassical tearing modes (NTMs) can lead to disruption and loss of confinement. Previous analysis of these modes used large aspect ratio, low beta (plasma pressure/magnetic pressure) approximations to determine the effect of NTMs on tokamak plasmas. A more accurate tool is needed to predict the onset of these instabilities. As a follow-up to recent theoretical work, a code has been written which computes the tearing mode island growth rate for arbitrary tokamak geometry. It calls PEST-3 [A. Pletzer et al., J. Comput. Phys. 115, 530 (1994)] to compute delta prime, the resistive magnetohydrodynamic (MHD) matching parameter. The code also calls the FLUXGRID routines in NIMROD [A.H. Glasser et al., Plasma Phys. Controlled Fusion 41, A747 (1999)] for Dnc, DI and DR [C.C. Hegna, Phys. Plasmas 6, 3980 (1999); A.H. Glasser et al., Phys. Fluids 18, 875 (1975)], which are the bootstrap current driven term and the ideal and resistive interchange mode criterion, respectively. In addition to these components, the NIMROD routines calculate alphas-H, a new correction to the Pfirsch-Schlter term. Finite parallel transport effects were added and a National Spherical Torus Experiment (NSTX) [M. Ono et al., Nucl. Fusion 40, 557 (2000)] equilibrium was analyzed. Another program takes the output of PEST-3 and allows the user to specify the rational surface, island width, and amount of detail near the perturbed surface to visualize the total helical flux. The results of this work will determine the stability of NTMs in an spherical torus (ST) [Y.-K.M. Peng et al., Nucl. Fusion 26, 769 (1986)] plasma with greater accuracy than previously achieved
Yang-Mills Detour Complexes and Conformal Geometry
Gover, A. Rod; Somberg, Petr; Souček, Vladimír
2008-03-01
Working over a pseudo-Riemannian manifold, for each vector bundle with connection we construct a sequence of three differential operators which is a complex (termed a Yang-Mills detour complex) if and only if the connection satisfies the full Yang-Mills equations. A special case is a complex controlling the deformation theory of Yang-Mills connections. In the case of Riemannian signature the complex is elliptic. If the connection respects a metric on the bundle then the complex is formally self-adjoint. In dimension 4 the complex is conformally invariant and generalises, to the full Yang-Mills setting, the composition of (two operator) Yang-Mills complexes for (anti-)self-dual Yang-Mills connections. Via a prolonged system and tractor connection a diagram of differential operators is constructed which, when commutative, generates differential complexes of natural operators from the Yang-Mills detour complex. In dimension 4 this construction is conformally invariant and is used to yield two new sequences of conformal operators which are complexes if and only if the Bach tensor vanishes everywhere. In Riemannian signature these complexes are elliptic. In one case the first operator is the twistor operator and in the other sequence it is the operator for Einstein scales. The sequences are detour sequences associated to certain Bernstein-Gelfand-Gelfand sequences.
International Nuclear Information System (INIS)
Tang, X. Z.
2000-01-01
Subtleties of implementing the standard perfectly conducting wall boundary condition in a general toroidal geometry are clarified for a mixed scalar magnetic field representation. An iterative scheme based on Ohm's law is given
Statistical equilibrium and symplectic geometry in general relativity
International Nuclear Information System (INIS)
Iglesias, P.
1981-09-01
A geometrical construction is given of the statistical equilibrium states of a system of particles in the gravitational field in general relativity. By a method of localization variables, the expression of thermodynamic values is given and the compatibility of this description is shown with a macroscopic model of a relativistic continuous medium for a given value of the free-energy function [fr
Equilibrium between Different Coordination Geometries in Oxidovanadium(IV) Complexes
Ugone, Valeria; Garribba, Eugenio; Micera, Giovanni; Sanna, Daniele
2015-01-01
In this laboratory activity, the equilibrium between square pyramidal and octahedral V(IV)O[superscript 2+] complexes is described. We propose a set of experiments to synthesize and characterize two types of V(IV)O[superscript 2+] complexes. The experiment allows great flexibility and may be effectively used at a variety of levels and the activity…
4-dimensional General Relativity from the instrinsic spatial geometry of SO(3) Yang-Mills theory
International Nuclear Information System (INIS)
Ita, Eyo Eyo
2011-01-01
In this paper we derive 4-dimensional General Relativity from three dimensions, using the intrinsic spatial geometry inherent in Yang-Mills theory which has been exposed by previous authors as well as some properties of the Ashtekar variables. We provide various interesting relations, including the fact that General Relativity can be written as a Yang-Mills theory where the antiself-dual Weyl curvature replaces the Yang-Mills coupling constant. We have generalized the results of some previous authors, covering Einstein's spaces, to include more general spacetime geometries.
Depth estimation of complex geometry scenes from light fields
Si, Lipeng; Wang, Qing
2018-01-01
The surface camera (SCam) of light fields gathers angular sample rays passing through a 3D point. The consistency of SCams is evaluated to estimate the depth map of scene. But the consistency is affected by several limitations such as occlusions or non-Lambertian surfaces. To solve those limitations, the SCam is partitioned into two segments that one of them could satisfy the consistency constraint. The segmentation pattern of SCam is highly related to the texture of spatial patch, so we enforce a mask matching to describe the shape correlation between segments of SCam and spatial patch. To further address the ambiguity in textureless region, a global method with pixel-wise plane label is presented. Plane label inference at each pixel can recover not only depth value but also local geometry structure, that is suitable for light fields with sub-pixel disparities and continuous view variation. Our method is evaluated on public light field datasets and outperforms the state-of-the-art.
Development of a general method for obtaining the geometry of microfluidic networks
International Nuclear Information System (INIS)
Razavi, Mohammad Sayed; Salimpour, M. R.; Shirani, Ebrahim
2014-01-01
In the present study, a general method for geometry of fluidic networks is developed with emphasis on pressure-driven flows in the microfluidic applications. The design method is based on general features of network's geometry such as cross-sectional area and length of channels. Also, the method is applicable to various cross-sectional shapes such as circular, rectangular, triangular, and trapezoidal cross sections. Using constructal theory, the flow resistance, energy loss and performance of the network are optimized. Also, by this method, practical design strategies for the fabrication of microfluidic networks can be improved. The design method enables rapid prediction of fluid flow in the complex network of channels and is very useful for improving proper miniaturization and integration of microfluidic networks. Minimization of flow resistance of the network of channels leads to universal constants for consecutive cross-sectional areas and lengths. For a Y-shaped network, the optimal ratios of consecutive cross-section areas (A i+1 /A i ) and lengths (L i+1 /L i ) are obtained as A i+1 /A i = 2 −2/3 and L i+1 /L i = 2 −1/3 , respectively. It is shown that energy loss in the network is proportional to the volume of network. It is also seen when the number of channels is increased both the hydraulic resistance and the volume occupied by the network are increased in a similar manner. Furthermore, the method offers that fabrication of multi-depth and multi-width microchannels should be considered as an integral part of designing procedures. Finally, numerical simulations for the fluid flow in the network have been performed and results show very good agreement with analytic results
Geometry and quadratic nonlinearity of charge transfer complexes in solution: A theoretical study
International Nuclear Information System (INIS)
Mukhopadhyay, S.; Ramasesha, S.; Pandey, Ravindra; Das, Puspendu K.
2011-01-01
In this paper, we have computed the quadratic nonlinear optical (NLO) properties of a class of weak charge transfer (CT) complexes. These weak complexes are formed when the methyl substituted benzenes (donors) are added to strong acceptors like chloranil (CHL) or di-chloro-di-cyano benzoquinone (DDQ) in chloroform or in dichloromethane. The formation of such complexes is manifested by the presence of a broad absorption maximum in the visible range of the spectrum where neither the donor nor the acceptor absorbs. The appearance of this visible band is due to CT interactions, which result in strong NLO responses. We have employed the semiempirical intermediate neglect of differential overlap (INDO/S) Hamiltonian to calculate the energy levels of these CT complexes using single and double configuration interaction (SDCI). The solvent effects are taken into account by using the self-consistent reaction field (SCRF) scheme. The geometry of the complex is obtained by exploring different relative molecular geometries by rotating the acceptor with respect to the fixed donor about three different axes. The theoretical geometry that best fits the experimental energy gaps, β HRS and macroscopic depolarization ratios is taken to be the most probable geometry of the complex. Our studies show that the most probable geometry of these complexes in solution is the parallel displaced structure with a significant twist in some cases.
Haj-Ali, Rami; Marom, Gil; Ben Zekry, Sagit; Rosenfeld, Moshe; Raanani, Ehud
2012-09-21
The complex three-dimensional (3D) geometry of the native tricuspid aortic valve (AV) is represented by select parametric curves allowing for a general construction and representation of the 3D-AV structure including the cusps, commissures and sinuses. The proposed general mathematical description is performed by using three independent parametric curves, two for the cusp and one for the sinuses. These curves are used to generate different surfaces that form the structure of the AV. Additional dependent curves are also generated and utilized in this process, such as the joint curve between the cusps and the sinuses. The model's feasibility to generate patient-specific parametric geometry is examined against 3D-transesophageal echocardiogram (3D-TEE) measurements from a non-pathological AV. Computational finite-element (FE) mesh can then be easily constructed from these surfaces. Examples are given for constructing several 3D-AV geometries by estimating the needed parameters from echocardiographic measurements. The average distance (error) between the calculated geometry and the 3D-TEE measurements was only 0.78±0.63mm. The proposed general 3D parametric method is very effective in quantitatively representing a wide range of native AV structures, with and without pathology. It can also facilitate a methodical quantitative investigation over the effect of pathology and mechanical loading on these major AV parameters. Copyright © 2012 Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Keele, B.D.
2005-01-01
A collimated portable gamma-ray detector will be used to quantify the plutonium content of items that can be approximated as a point, line, or area geometry with respect to the detector. These items can include ducts, piping, glove boxes, isolated equipment inside of gloveboxes, and HEPA filters. The Generalized Geometry Holdup (GGH) model is used for the reduction of counting data. This document specifies the calculations to reduce counting data into contained plutonium and the associated total measurement uncertainty.
Solar Proton Transport Within an ICRU Sphere Surrounded by a Complex Shield: Ray-trace Geometry
Slaba, Tony C.; Wilson, John W.; Badavi, Francis F.; Reddell, Brandon D.; Bahadori, Amir A.
2015-01-01
A computationally efficient 3DHZETRN code with enhanced neutron and light ion (Z is less than or equal to 2) propagation was recently developed for complex, inhomogeneous shield geometry described by combinatorial objects. Comparisons were made between 3DHZETRN results and Monte Carlo (MC) simulations at locations within the combinatorial geometry, and it was shown that 3DHZETRN agrees with the MC codes to the extent they agree with each other. In the present report, the 3DHZETRN code is extended to enable analysis in ray-trace geometry. This latest extension enables the code to be used within current engineering design practices utilizing fully detailed vehicle and habitat geometries. Through convergence testing, it is shown that fidelity in an actual shield geometry can be maintained in the discrete ray-trace description by systematically increasing the number of discrete rays used. It is also shown that this fidelity is carried into transport procedures and resulting exposure quantities without sacrificing computational efficiency.
Giménez-Alventosa, V; Ballester, F; Vijande, J
2016-12-01
The design and construction of geometries for Monte Carlo calculations is an error-prone, time-consuming, and complex step in simulations describing particle interactions and transport in the field of medical physics. The software VoxelMages has been developed to help the user in this task. It allows to design complex geometries and to process DICOM image files for simulations with the general-purpose Monte Carlo code PENELOPE in an easy and straightforward way. VoxelMages also allows to import DICOM-RT structure contour information as delivered by a treatment planning system. Its main characteristics, usage and performance benchmarking are described in detail. Copyright © 2016 Elsevier Ltd. All rights reserved.
Geometry of real and complex canonical transformations in quantum mechanics
International Nuclear Information System (INIS)
Grossmann, A.
1977-08-01
Quantum mechanics of finitely many particles involves the group of linear (and affine) canonical transformations. A well-defined ray representation of this group acts in the space of states of any quantum-mechanical system with finitely many degrees of freedom and plays a central role in many different contexts. This representation appears quite naturally in quantum mechanics over phase space (Weyl-Wigner correspondence), that it becomes, when suitably written, just a matter of looking at one object from different symplectic reference frames. This is particularly interesting for complex canonical transformations which are represented by unbounded operators. The list of references gives an idea of the variety of motivations and points of view in the subject
Energy Technology Data Exchange (ETDEWEB)
DeHart, Mark David [Texas A & M Univ., College Station, TX (United States)
1992-12-01
A method for applying the discrete ordinates method for solution of the neutron transport equation in arbitary two-dimensional meshes has been developed. The finite difference approach normally used to approximate spatial derivatives in extrapolating angular fluxes across a cell is replaced by direct solution of the characteristic form of the transport equation for each discrete direction. Thus, computational cells are not restricted to the traditional shape of a mesh element within a given coordinate system. However, in terms of the treatment of energy and angular dependencies, this method resembles traditional discrete ordinates techniques. Using the method developed here, a general two-dimensional space can be approximated by an irregular mesh comprised of arbitrary polygons. The present work makes no assumptions about the orientations or the number of sides in a given cell, and computes all geometric relationships between each set of sides in each cell for each discrete direction. A set of non-reentrant polygons can therefore be used to represent any given two dimensional space. Results for a number of test problems have been compared to solutions obtained from traditional methods, with good agreement. Comparisons include benchmarks against analytical results for problems with simple geometry, as well numerical results obtained from traditional discrete ordinates methods by applying the ANISN and TWOTRAN computer programs. Numerical results were obtained for problems ranging from simple one-dimensional geometry to complicated multidimensional configurations. These results have demonstrated the ability of the developed method to closely approximate complex geometrical configurations and to obtain accurate results for problems that are extremely difficult to model using traditional methods.
4-Dimensional General Relativity from the instrinsic spatial geometry of SO(3) Yang--Mills theory
Ita III, Eyo Eyo
2007-01-01
In this paper we derive 4-dimensional General Relativity from three dimensions, using the intrinsic spatial geometry inherent in Yang--Mills theory which has been exposed by previous authors as well as as some properties of the Ashtekar variables. We provide various interesting relations, including the fact that General Relativity can be written as a Yang--Mills theory where the antiself-dual Weyl curvature replaces the Yang--Mills coupling constant. We have generalized the results of some pr...
Energy Technology Data Exchange (ETDEWEB)
Okumura, Y. [Dept. of Physics, Boston Univ., MA (United States); Kase, H. [Dept. of Physics, Daido Inst. of Technology, Nagoya (Japan); Morita, K. [Dept. of Physics, Nagoya Univ. (Japan)
2001-04-01
The standard model is reconstructed in a generalized differential geometry (GDG) based on the idea of a real structure as proposed by Coquereaux et al. and Connes. The GDG considered in this article is a kind of non-commutative geometry (NCG) on the discrete space that successfully reproduces the Higgs mechanism of the spontaneously broken gauge theory. Here, a GDG is a direct generalization of the differential geometry on an ordinary continuous manifold to the product space of this manifold with a discrete manifold. In a GDG, a one-form basis {chi} on the discrete space is incorporated in addition to the one-form basis dx{sup {mu}} on Minkowski space, rather than {gamma}{sup 5} as in Connes's original work. Although the Lagrangians obtained in this way are the same as those obtained in our previous formulation of GDG, the basic formalism becomes very simply and clear. (orig.)
Reactive flow simulation in complex 3D geometries using the COM3D code
International Nuclear Information System (INIS)
Breitung, W.; Kotchourko, A.; Veser, A.; Scholtyssek, W.
1999-01-01
The COM3D code, under development at the Forschungszentrum Karlsruhe (FZK), is a 3-d CFD code to describe turbulent combustion phenomena in complex geometries. It is intended to be part of the advanced integral code system for containment analysis (INCA) which includes in addition GASFLOW for distribution calculations, V3D for slow combustion and DET3D for detonation analysis. COM3D uses a TVD-solver and optional models for turbulence, chemistry and thermodynamics. The hydrodynamic model considers mass, momentum and energy conservation. Advanced procedures were provided to facilitate grid-development for complex 3-d structures. COM3D was validated on experiments performed on different scales with generally good agreement for important physical quantities. The code was applied to combustion analysis of a large PWR. The initial conditions were obtained from a GASFLOW distribution analysis for a LOOP scenario. Results are presented concerning flame propagation and pressure evolution in the containment which clearly demonstrate the effects of internal structures, their influence on turbulence formation and consequences for local loads. (author)
Energy Technology Data Exchange (ETDEWEB)
Chatillon, S.; Roy, O.; Mahaut, St
2000-07-01
A new multi-element contact transducer has been developed to improve the inspection of components with complex geometry. The emitting surface is flexible in order to optimize the contact with pieces. An algorithm, based on a simplified geometric model, has been used to determine the delays law which allows to control the focal characteristics of the transmitted field. Acquisition data lead in transmission with an articulated transducer validate the behavior provided by simulation. Thus the optimization of the delays law ensures the transmission of a beam which is homogeneous and controlled during the moving of the transducer. Inspections in echo-pulse mode are implemented on a sample simulating a component controlled on site. Results show that the dynamical adaptation of the delays law to the geometry of the piece leads to very good performances.
Directory of Open Access Journals (Sweden)
Mei Guo
2018-01-01
Full Text Available The syntheses, structural characterization, and magnetic properties of three lanthanide complexes with formulas [Ln(L13] (Ln = Dy (1Dy; Er (1Er; and [Dy(L22] (2Dy were reported. Complexes 1Dy and 1Er are isostructural with the metal ion in distorted trigonal-prismatic coordination geometry, but exhibit distinct magnetic properties due to the different shapes of electron density for DyIII (oblate and ErIII (prolate ions. Complex 1Dy shows obvious SMM behavior under a zero direct current (dc field with an effective energy barrier of 31.4 K, while complex 1Er only features SMM behavior under a 400 Oe external field with an effective energy barrier of 23.96 K. In stark contrast, complex 2Dy with the octahedral geometry only exhibits the frequency dependence of alternating current (ac susceptibility signals without χ″ peaks under a zero dc field.
Ay, Nihat; Lê, Hông Vân; Schwachhöfer, Lorenz
2017-01-01
The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. Parametrised measure models are defined as fundamental geometric objects, which can be both finite or infinite dimensional. Based on these models, canonical tensor fields are introduced and further studied, including the Fisher metric and the Amari-Chentsov tensor, and embeddings of statistical manifolds are investigated. This novel foundation then leads to application highlights, such as generalizations and extensions of the classical uniqueness result of Chentsov or the Cramér-Rao inequality. Additionally, several new application fields of information geometry are highlighted, for instance hierarchical and graphical models, complexity theory, population genetics, or Markov Chain Monte Carlo. The book will be of interest to mathematicians who are interested in geometry, inf...
User's manual for EVITS: a steady state fluids code for complex two-dimensional geometries
International Nuclear Information System (INIS)
Domanus, H.M.
1976-07-01
A 2-D computer code, EVITS, has been developed for estimating steady state, incompressible, isothermal flow fields in complex geometries. A vorticity-stream function formulation is used along with a model to resolve viscous effects at solid boundaries. Sufficient geometry and boundary type options are included within the code so that a large number of flow situations can be specified without modifying the program. All instructions to the code are via an input dataset. Detailed instructions for preparing the user oriented input, along with examples, are included in this users' manual
CIME school “Fully Nonlinear PDEs in Real and Complex Geometry and Optics”
Capogna, Luca; Gutiérrez, Cristian E; Montanari, Annamaria
2014-01-01
The purpose of this CIME summer school was to present current areas of research arising both in the theoretical and applied setting that involve fully nonlinear partial different equations. The equations presented in the school stem from the fields of Conformal Mapping Theory, Differential Geometry, Optics, and Geometric Theory of Several Complex Variables. The school consisted of four courses: Extremal problems for quasiconformal mappings in space by Luca Capogna, Fully nonlinear equations in geometry by Pengfei Guan, Monge-Ampere type equations and geometric optics by Cristian E. Gutiérrez, and On the Levi Monge Ampere equation by Annamaria Montanari.
Thermal plume above a simulated sitting person with different complexity of body geometry
DEFF Research Database (Denmark)
Zukowska, Daria; Melikov, Arsen Krikor; Popiolek, Zbigniew J.
2007-01-01
Occupants are one of the main heat sources in rooms. They generate thermal plumes with characteristics, which depend on geometry, surface temperature and area of the human body in contact with the surrounding air as well as temperature, velocity and turbulence intensity distribution in the room....... The characteristics of the thermal plume generated by a sitting person were studied using four human body simulators with different complexity of geometry but equal surface area: a vertical cylinder, a rectangular box, a dummy, and a thermal manikin. The results show that the dummy and the thermal manikin generate...
GPU-accelerated depth map generation for X-ray simulations of complex CAD geometries
Grandin, Robert J.; Young, Gavin; Holland, Stephen D.; Krishnamurthy, Adarsh
2018-04-01
Interactive x-ray simulations of complex computer-aided design (CAD) models can provide valuable insights for better interpretation of the defect signatures such as porosity from x-ray CT images. Generating the depth map along a particular direction for the given CAD geometry is the most compute-intensive step in x-ray simulations. We have developed a GPU-accelerated method for real-time generation of depth maps of complex CAD geometries. We preprocess complex components designed using commercial CAD systems using a custom CAD module and convert them into a fine user-defined surface tessellation. Our CAD module can be used by different simulators as well as handle complex geometries, including those that arise from complex castings and composite structures. We then make use of a parallel algorithm that runs on a graphics processing unit (GPU) to convert the finely-tessellated CAD model to a voxelized representation. The voxelized representation can enable heterogeneous modeling of the volume enclosed by the CAD model by assigning heterogeneous material properties in specific regions. The depth maps are generated from this voxelized representation with the help of a GPU-accelerated ray-casting algorithm. The GPU-accelerated ray-casting method enables interactive (> 60 frames-per-second) generation of the depth maps of complex CAD geometries. This enables arbitrarily rotation and slicing of the CAD model, leading to better interpretation of the x-ray images by the user. In addition, the depth maps can be used to aid directly in CT reconstruction algorithms.
Vanapalli, Siva; Suteria, Naureen; Nekouei, Mehdi
2017-11-01
We report a technique referred to as ``microfluidic bypass manometry'' for measurement of pressure drop versus flow rate (ΔP-Q) relations in a parallelized manner. It involves introducing co-flowing laminar streams into a microfluidic network that contains a series of loops, where each loop contains a test geometry and a bypass channel as a flow rate sensing element. To demonstrate the technique, we measure ΔP-Q relations simultaneously for forty test geometries ranging from linear to contraction-expansion to serpentine to pillar-laden microchannels. The measured Newtonian flow resistance of these different geometries is in excellent agreement with CFD simulations. To expand the capabilities of the method, we measured ΔP-Q relations for similar-sized oil droplets trapped in microcavities where the cavity geometry spans from prisms of 3 - 10 sides to cylinders. We find in all cases, ΔP-Q relation is nonlinear and the flow resistance is sensitive to drop confinement and weakly dependent on cavity geometry. We anticipate that microfluidic bypass manometry may find broad application in several areas including design of lab-on-chip devices, laminar drag reduction, rheology of complex fluids and mechanics of deformable particles.
Geometry modeling for SAM-CE Monte Carlo calculations
International Nuclear Information System (INIS)
Steinberg, H.A.; Troubetzkoy, E.S.
1980-01-01
Three geometry packages have been developed and incorporated into SAM-CE, for representing in three dimensions the transport medium. These are combinatorial geometry - a general (non-lattice) system, complex combinatorial geometry - a very general system with lattice capability, and special reactor geometry - a special purpose system for light water reactor geometries. Their different attributes are described
Steady-state and transient heat transfer through fins of complex geometry
Directory of Open Access Journals (Sweden)
Taler Dawid
2014-06-01
Full Text Available Various methods for steady-state and transient analysis of temperature distribution and efficiency of continuous-plate fins are presented. For a constant heat transfer coefficient over the fin surface, the plate fin can be divided into imaginary rectangular or hexangular fins. At first approximate methods for determining the steady-state fin efficiency like the method of equivalent circular fin and the sector method are discussed. When the fin geometry is complex, thus transient temperature distribution and fin efficiency can be determined using numerical methods. A numerical method for transient analysis of fins with complex geometry is developed. Transient temperature distributions in continuous fins attached to oval tubes is computed using the finite volume - finite element methods. The developed method can be used in the transient analysis of compact heat exchangers to calculate correctly the heat flow rate transferred from the finned tubes to the fluid.
Relaxed geometries and dipole moments of positron complexes with diatomic molecules
Energy Technology Data Exchange (ETDEWEB)
Assafrao, Denise; Mohallem, Jose R, E-mail: rachid@fisica.ufmg.b [Laboratorio de Atomos e Moleculas Especiais, Departamento de Fisica, ICEx, Universidade Federal de Minas Gerais, CP 702, 30123-970, Belo Horizonte, MG (Brazil)
2010-01-01
Relaxed geometries and dipole moments of diatomic molecules interacting with a slow positron are reported as functions of the positron distance to the more electronegative atom. A molecular model for the complex that allows applications to large systems is used. The electron population on the positron is proposed as a weighting function to calculate the average quantities. Results show Self-Consistent-Field quality or better.
Biparametric complexities and generalized Planck radiation law
Puertas-Centeno, David; Toranzo, I. V.; Dehesa, J. S.
2017-12-01
Complexity theory embodies some of the hardest, most fundamental and most challenging open problems in modern science. The very term complexity is very elusive, so the main goal of this theory is to find meaningful quantifiers for it. In fact, we need various measures to take into account the multiple facets of this term. Here, some biparametric Crámer–Rao and Heisenberg–Rényi measures of complexity of continuous probability distributions are defined and discussed. Then, they are applied to blackbody radiation at temperature T in a d-dimensional universe. It is found that these dimensionless quantities do not depend on T nor on any physical constants. So, they have a universal character in the sense that they only depend on spatial dimensionality. To determine these complexity quantifiers, we have calculated their dispersion (typical deviations) and entropy (Rényi entropies and the generalized Fisher information) constituents. They are found to have a temperature-dependent behavior similar to the celebrated Wien’s displacement law of the dominant frequency ν_max at which the spectrum reaches its maximum. Moreover, they allow us to gain insights into new aspects of the d-dimensional blackbody spectrum and the quantification of quantum effects associated with space dimensionality.
Phase-space Lagrangian derivation of electrostatic gyrokinetics in general geometry
Energy Technology Data Exchange (ETDEWEB)
Parra, Felix I [Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford, OX1 3NP (United Kingdom); Calvo, Ivan, E-mail: f.parradiaz1@physics.ox.ac.uk, E-mail: ivan.calvo@ciemat.es [Isaac Newton Institute for Mathematical Sciences, University of Cambridge, Cambridge, CB3 0EH (United Kingdom)
2011-04-15
Gyrokinetic theory is based on an asymptotic expansion in the small parameter {epsilon}, defined as the ratio of the gyroradius and the characteristic length of variation of the magnetic field. In this paper, this ordering is strictly implemented to compute the electrostatic gyrokinetic phase-space Lagrangian in general magnetic geometry to order {epsilon}{sup 2}. In particular, a new expression for the complete second-order gyrokinetic Hamiltonian is provided, showing that in a rigorous treatment of gyrokinetic theory magnetic geometry and turbulence cannot be dealt with independently. The new phase-space gyrokinetic Lagrangian gives a Vlasov equation accurate to order {epsilon}{sup 2} and a Poisson equation accurate to order {epsilon}. The final expressions are explicit and can be implemented into any simulation without further computations.
From Stein to Weinstein and back symplectic geometry of affine complex manifolds
Cieliebak, Kai
2013-01-01
A beautiful and comprehensive introduction to this important field. -Dusa McDuff, Barnard College, Columbia University This excellent book gives a detailed, clear, and wonderfully written treatment of the interplay between the world of Stein manifolds and the more topological and flexible world of Weinstein manifolds. Devoted to this subject with a long history, the book serves as a superb introduction to this area and also contains the authors' new results. -Tomasz Mrowka, MIT This book is devoted to the interplay between complex and symplectic geometry in affine complex manifolds. Affine co
Solar optical codes evaluation for modeling and analyzing complex solar receiver geometries
Yellowhair, Julius; Ortega, Jesus D.; Christian, Joshua M.; Ho, Clifford K.
2014-09-01
Solar optical modeling tools are valuable for modeling and predicting the performance of solar technology systems. Four optical modeling tools were evaluated using the National Solar Thermal Test Facility heliostat field combined with flat plate receiver geometry as a benchmark. The four optical modeling tools evaluated were DELSOL, HELIOS, SolTrace, and Tonatiuh. All are available for free from their respective developers. DELSOL and HELIOS both use a convolution of the sunshape and optical errors for rapid calculation of the incident irradiance profiles on the receiver surfaces. SolTrace and Tonatiuh use ray-tracing methods to intersect the reflected solar rays with the receiver surfaces and construct irradiance profiles. We found the ray-tracing tools, although slower in computation speed, to be more flexible for modeling complex receiver geometries, whereas DELSOL and HELIOS were limited to standard receiver geometries such as flat plate, cylinder, and cavity receivers. We also list the strengths and deficiencies of the tools to show tool preference depending on the modeling and design needs. We provide an example of using SolTrace for modeling nonconventional receiver geometries. The goal is to transfer the irradiance profiles on the receiver surfaces calculated in an optical code to a computational fluid dynamics code such as ANSYS Fluent. This approach eliminates the need for using discrete ordinance or discrete radiation transfer models, which are computationally intensive, within the CFD code. The irradiance profiles on the receiver surfaces then allows for thermal and fluid analysis on the receiver.
Modelling of turbulence and combustion for simulation of gas explosions in complex geometries
Energy Technology Data Exchange (ETDEWEB)
Arntzen, Bjoern Johan
1998-12-31
This thesis analyses and presents new models for turbulent reactive flows for CFD (Computational Fluid Dynamics) simulation of gas explosions in complex geometries like offshore modules. The course of a gas explosion in a complex geometry is largely determined by the development of turbulence and the accompanying increased combustion rate. To be able to model the process it is necessary to use a CFD code as a starting point, provided with a suitable turbulence and combustion model. The modelling and calculations are done in a three-dimensional finite volume CFD code, where complex geometries are represented by a porosity concept, which gives porosity on the grid cell faces, depending on what is inside the cell. The turbulent flow field is modelled with a k-{epsilon} turbulence model. Subgrid models are used for production of turbulence from geometry not fully resolved on the grid. Results from laser doppler anemometry measurements around obstructions in steady and transient flows have been analysed and the turbulence models have been improved to handle transient, subgrid and reactive flows. The combustion is modelled with a burning velocity model and a flame model which incorporates the burning velocity into the code. Two different flame models have been developed: SIF (Simple Interface Flame model), which treats the flame as an interface between reactants and products, and the {beta}-model where the reaction zone is resolved with about three grid cells. The flame normally starts with a quasi laminar burning velocity, due to flame instabilities, modelled as a function of flame radius and laminar burning velocity. As the flow field becomes turbulent, the flame uses a turbulent burning velocity model based on experimental data and dependent on turbulence parameters and laminar burning velocity. The laminar burning velocity is modelled as a function of gas mixture, equivalence ratio, pressure and temperature in reactant. Simulations agree well with experiments. 139
Directory of Open Access Journals (Sweden)
Giuseppe eMercurio
2014-01-01
Full Text Available We present an analysis method of normal incidence x-ray standing wave (NIXSW data that allows detailed adsorption geometries of complex molecules to be retrieved. This method (Fourier vector analysis is based on the comparison of both the coherence and phase of NIXSW data to NIXSW simulations of different molecular geometries as the relevant internal degrees of freedom are tuned. We introduce this analysis method using the prototypical molecular switch azobenzene (AB adsorbed on the Ag(111 surface as a model system. The application of the Fourier vector analysis to AB/Ag(111 provides, on the one hand, detailed adsorption geometries including dihedral angles, and on the other hand, insights into the dynamics of molecules and their bonding to the metal substrate. This analysis scheme is generally applicable to any adsorbate, it is necessary for molecules with potentially large distortions, and will be particularly valuable for molecules whose distortion on adsorption can be mapped on a limited number of internal degrees of freedom.
Generalized q-deformed correlation functions as spectral functions of hyperbolic geometry
Energy Technology Data Exchange (ETDEWEB)
Bonora, L. [International School for Advanced Studies (SISSA/ISAS), Trieste (Italy); INFN, Sezione di Trieste, Trieste (Italy); Bytsenko, A.A. [Universidade Estadual de Londrina, Departamento de Fisica, Caixa Postal 6001, Londrina, Parana (Brazil); Guimaraes, M.E.X. [Universidade Federal Fluminense, Instituto de Fisica, Niteroi-RJ CEP (Brazil)
2014-08-15
We analyze the role of vertex operator algebra and 2d amplitudes from the point of view of the representation theory of infinite-dimensional Lie algebras, MacMahon and Ruelle functions. By definition p-dimensional MacMahon function, with p ≤ 3, is the generating function of p-dimensional partitions of integers. These functions can be represented as amplitudes of a two-dimensional c = 1 CFT, and, as such, they can be generalized to p > 3. With some abuse of language we call the latter amplitudes generalized MacMahon functions. In this paper we show that generalized p-dimensional MacMahon functions can be rewritten in terms of Ruelle spectral functions, whose spectrum is encoded in the Patterson-Selberg function of three-dimensional hyperbolic geometry. (orig.)
International Nuclear Information System (INIS)
Dalvit, C.; Tennant, L.; Wright, P.E.
1987-01-01
A straightforward strategy for assignment of the C ε H, C δ H, N δ H proton resonances of the proximal histidine ligand in diamagnetic complexes of monomeric hemoglobins and myoglobins is reported. These resonances are subject to large ring current shifts and are highly sensitive to coordination geometry. There are no significant differences between the CO complexes of myoglobin, leghemoglobin or hemoglobin α-subunits in proximal His coordination geometry or hydrogen bonding to the backbone at Leu F4. Ring current calculations show that the His F8 coordination geometry in the CO complexes of myoglobin and hemoglobin α-subunits is very similar in crystal and solution. (Auth.)
Norbisrath, Jan Henrik
Carbonate rocks are known to have complex and heterogeneous pore structures, which result from their biogenic origin and strong affinity for diagenetic processes that change their pore structure after burial. The combination of sheer endless variations of precursor biogenic material, depositional environments, and diagenetic effects results in rocks that are interesting to study but intricate to understand. Many schemes to categorize the diversity of carbonate rocks are in use today; most are based on the macropore structure and qualitative thin-section analysis. Many studies, however, acknowledge that micropores have a significant influence on the macroscopic petrophysical rock properties, which are essential to determine reservoir quality. Micropores are, by definition, smaller than the thickness of a thin-section (kerogen and pyrite content. Results show that the nanopore geometry here has little influence on cementation factors, and instead porosity is the main control on m in mudrocks. Cementation factors are crucial for estimates of oil-in-place and water saturation in a wireline application, and a slight change of (assumed) cementation factor can change the interpreter's evaluation from dry hole to discovery. Therefore, accurate determination of cementation factors is a critical task in formation evaluation, similar to accurate estimates of permeability. To achieve this goal, this dissertation utilizes a new approach of using complex resistivity spectra (CRS) to assess the pore geometry and its resulting electrical and fluid flow properties. Specifically, frequency dispersion of complex resistivity in the kHz range is used as input for a new model to predict cementation factor and permeability in a wide variety of core plug samples. The underlying concept that relates CRS to flow properties is that both are related to pore geometry. CRS are linked to pore geometry by interfacial polarization effects at the fluid-rock boundary that control the phase and
DEFF Research Database (Denmark)
Pradera-Mallabiabarrena, Ainara; Jacobsen, Finn; Svendsen, Christian
2013-01-01
was applied to low Mach number flow past a circular cylinder in free-field, where the Green's function and its derivative were obtained analytically. In this paper, the method will be applied to the case of low Mach number flow past a complex confined scattering geometry where both compact and non......The purpose of this paper is to demonstrate that a recently published methodology for predicting flow generated noise by compact surfaces under free-field conditions [1] can be extended to a different and more complex configuration of industrial interest. In the previous paper, the methodology...... are generated by use of a Computational Fluid Dynamics (CFD) simulation. Due to the complexity of the scattering surfaces, the derivative of the Green's function must be obtained numerically through a Computational Acoustics (CA) simulation. The results have been validated through comparison with sound power...
National Aeronautics and Space Administration — The focus of this analysis was the development of a complex geometry test fixture and test method for determining solvent cleaning efficiency. AK-225 belongs to a...
Motivation for Using Generalized Geometry in the Time Dependent Transport Code TDKENO
Energy Technology Data Exchange (ETDEWEB)
Dustin Popp; Zander Mausolff; Sedat Goluoglu
2016-04-01
We are proposing to use the code, TDKENO, to model TREAT. TDKENO solves the time dependent, three dimensional Boltzmann transport equation with explicit representation of delayed neutrons. Instead of directly integrating this equation, the neutron flux is factored into two components – a rapidly varying amplitude equation and a slowly varying shape equation and each is solved separately on different time scales. The shape equation is solved using the 3D Monte Carlo transport code KENO, from Oak Ridge National Laboratory’s SCALE code package. Using the Monte Carlo method to solve the shape equation is still computationally intensive, but the operation is only performed when needed. The amplitude equation is solved deterministically and frequently, so the solution gives an accurate time-dependent solution without having to repeatedly We have modified TDKENO to incorporate KENO-VI so that we may accurately represent the geometries within TREAT. This paper explains the motivation behind using generalized geometry, and provides the results of our modifications. TDKENO uses the Improved Quasi-Static method to accomplish this. In this method, the neutron flux is factored into two components. One component is a purely time-dependent and rapidly varying amplitude function, which is solved deterministically and very frequently (small time steps). The other is a slowly varying flux shape function that weakly depends on time and is only solved when needed (significantly larger time steps).
DEFF Research Database (Denmark)
Torralba, Marta; Jiménez, Roberto; Yagüe-Fabra, José A.
2018-01-01
micro-geometries as well (i.e., in the sub-mm dimensional range). However, there are different factors that may influence the CT process performance, being one of them the surface extraction technique used. In this paper, two different extraction techniques are applied to measure a complex miniaturized...... Canny algorithm. This algorithm has proven to provide accurate results in parts with simple geometries, but its suitability for 3D complex geometries has not been proven so far. To verify the measurement results and compare both techniques, reference measurements are performed on an optical coordinate...
A Framework for the Interactive Handling of High-Dimensional Simulation Data in Complex Geometries
Benzina, Amal
2013-01-01
Flow simulations around building infrastructure models involve large scale complex geometries, which when discretized in adequate detail entail high computational cost. Moreover, tasks such as simulation insight by steering or optimization require many such costly simulations. In this paper, we illustrate the whole pipeline of an integrated solution for interactive computational steering, developed for complex flow simulation scenarios that depend on a moderate number of both geometric and physical parameters. A mesh generator takes building information model input data and outputs a valid cartesian discretization. A sparse-grids-based surrogate model—a less costly substitute for the parameterized simulation—uses precomputed data to deliver approximated simulation results at interactive rates. Furthermore, a distributed multi-display visualization environment shows building infrastructure together with flow data. The focus is set on scalability and intuitive user interaction.
Complexity-action duality of the shock wave geometry in a massive gravity theory
Miao, Yan-Gang; Zhao, Long
2018-01-01
On the holographic complexity dual to the bulk action, we investigate the action growth for a shock wave geometry in a massive gravity theory within the Wheeler-DeWitt (WDW) patch at the late time limit. For a global shock wave, the graviton mass does not affect the action growth in the bulk, i.e., the complexity on the boundary, showing that the action growth (complexity) is the same for both the Einstein gravity and the massive gravity. Nevertheless, for a local shock wave that depends on transverse coordinates, the action growth (complexity) caused by the boundary disturbance (perturbation) is proportional to the butterfly velocity for the two gravity theories, but the butterfly velocity of the massive gravity theory is smaller than that of the Einstein gravity theory, indicating that the action growth (complexity) of the massive gravity is depressed by the graviton mass. In addition, we extend the black hole thermodynamics of the massive gravity and obtain the right Smarr formula.
Qamar, Shamsul; Uche, David U; Khan, Farman U; Seidel-Morgenstern, Andreas
2017-05-05
This work is concerned with the analytical solutions and moment analysis of a linear two-dimensional general rate model (2D-GRM) describing the transport of a solute through a chromatographic column of cylindrical geometry. Analytical solutions are derived through successive implementation of finite Hankel and Laplace transformations for two different sets of boundary conditions. The process is further analyzed by deriving analytical temporal moments from the Laplace domain solutions. Radial gradients are typically neglected in liquid chromatography studies which are particularly important in the case of non-perfect injections. Several test problems of single-solute transport are considered. The derived analytical results are validated against the numerical solutions of a high resolution finite volume scheme. The derived analytical results can play an important role in further development of liquid chromatography. Copyright © 2017 Elsevier B.V. All rights reserved.
Directory of Open Access Journals (Sweden)
Alexander Burinskii
2013-01-01
Full Text Available The 4D Kerr geometry displays many wonderful relations with quantum world and, in particular, with superstring theory. The lightlike structure of fields near the Kerr singular ring is similar to the structure of Sen solution for a closed heterotic string. Another string, open and complex, appears in the complex representation of the Kerr geometry initiated by Newman. Combination of these strings forms a membrane source of the Kerr geometry which is parallel to the structure of M-theory. In this paper we give one more evidence of this relationship, emergence of the Calabi-Yau twofold (K3 surface in twistorial structure of the Kerr geometry as a consequence of the Kerr theorem. Finally, we indicate that the Kerr stringy system may correspond to a complex embedding of the critical N = 2 superstring.
Variational P1 approximations of general-geometry multigroup transport problems
International Nuclear Information System (INIS)
Rulko, R.P.; Tomasevic, D.; Larsen, E.W.
1995-01-01
A variational approximation is developed for general-geometry multigroup transport problems with arbitrary anisotropic scattering. The variational principle is based on a functional that approximates a reaction rate in a subdomain of the system. In principle, approximations that result from this functional ''optimally'' determine such reaction rates. The functional contains an arbitrary parameter α and requires the approximate solutions of a forward and an adjoint transport problem. If the basis functions for the forward and adjoint solutions are chosen to be linear functions of the angular variable Ω, the functional yields the familiar multigroup P 1 equations for all values of α. However, the boundary conditions that result from the functional depend on α. In particular, for problems with vacuum boundaries, one obtains the conventional mixed boundary condition, but with an extrapolation distance that depends continuously on α. The choice α = 0 yields a generalization of boundary conditions derived earlier by Federighi and Pomraning for a more limited class of problems. The choice α = 1 yields a generalization of boundary conditions derived previously by Davis for monoenergetic problems. Other boundary conditions are obtained by choosing different values of α. The authors discuss this indeterminancy of α in conjunction with numerical experiments
Energy Technology Data Exchange (ETDEWEB)
Yokuda, Satoru T.; Poloski, Adam P.; Adkins, Harold E.; Casella, Andrew M.; Hohimer, Ryan E.; Karri, Naveen K.; Luna, Maria; Minette, Michael J.; Tingey, Joel M.
2009-05-11
The External Flowsheet Review Team (EFRT) has identified the issues relating to the Waste Treatment and Immobilization Plant (WTP) pipe plugging. Per the review’s executive summary, “Piping that transports slurries will plug unless it is properly designed to minimize this risk. This design approach has not been followed consistently, which will lead to frequent shutdowns due to line plugging.” To evaluate the potential for plugging, testing was performed to determine critical velocities for the complex WTP piping layout. Critical velocity is defined as the point at which a moving bed of particles begins to form on the pipe bottom during slurry-transport operations. Pressure drops across the fittings of the test pipeline were measured with differential pressure transducers, from which the critical velocities were determined. A WTP prototype flush system was installed and tested upon the completion of the pressure-drop measurements. We also provide the data for the overflow relief system represented by a WTP complex piping geometry with a non-Newtonian slurry. A waste simulant composed of alumina (nominally 50 μm in diameter) suspended in a kaolin clay slurry was used for this testing. The target composition of the simulant was 10 vol% alumina in a suspending medium with a yield stress of 3 Pa. No publications or reports are available to confirm the critical velocities for the complex geometry evaluated in this testing; therefore, for this assessment, the results were compared to those reported by Poloski et al. (2008) for which testing was performed for a straight horizontal pipe. The results of the flush test are compared to the WTP design guide 24590-WTP-GPG-M-0058, Rev. 0 (Hall 2006) in an effort to confirm flushing-velocity requirements.
McBride, D.; Cross, M.; Croft, N.; Bennett, C.; Gebhardt, J.
2006-03-01
A computational procedure is presented for solving complex variably saturated flows in porous media, that may easily be implemented into existing conventional finite-volume-based computational fluid dynamics codes, so that their functionality might be geared upon to readily enable the modelling of a complex suite of interacting fluid, thermal and chemical reaction process physics. This procedure has been integrated within a multi-physics finite volume unstructured mesh framework, allowing arbitrarily complex three-dimensional geometries to be modelled. The model is particularly targeted at ore heap-leaching processes, which encounter complex flow problems, such as infiltration into dry soil, drainage, perched water tables and flow through heterogeneous materials, but is equally applicable to any process involving flow through porous media, such as in environmental recovery processes. The computational procedure is based on the mixed form of the classical Richards equation, employing an adaptive transformed mixed algorithm that is numerically robust and significantly reduces compute (or CPU) time. The computational procedure is accurate (compares well with other methods and analytical data), comprehensive (representing any kind of porous flow model), and is computationally efficient. As such, this procedure provides a suitable basis for the implementation of large-scale industrial heap-leach models.
Critical Parameters of Complex Geometry Intersecting Cylinders Containing Uranyl Nitrate Solution
Energy Technology Data Exchange (ETDEWEB)
Rothe, Robert Emil; Briggs, Joseph Blair
1999-06-01
About three dozen previously unreported critical configurations are presented for very complex geometries filled with high concentration enriched uranyl nitrate solution. These geometries resemble a tall, thin Central Column (or trunk of a "tree") having long, thin arms (or "branches") extending up to four directions off the column. Arms are equally spaced from one another in vertical planes; and that spacing ranges from arms in contact to quite wide spacings. Both the Central Column and the many different arms are critically safe by themselves when each, alone, is filled with fissile solution; but, in combination, criticality occurs due to the interactions between arms and the column. Such neutronic interactions formed the principal focus of this study. While these results are fresh to the nuclear criticality safety industry and to those seeking novel experiments against which to validate computer codes, the experiments, themselves, are not recent. Over 100 experiments were performed at the Rocky Flats Critical Mass Laboratory between September, 1967, and February of the following year.
Energy Technology Data Exchange (ETDEWEB)
J. B. Briggs (INEEL POC); R. E. Rothe
1999-06-14
About three dozen previously unreported critical configurations are presented for very complex geometries filled with high concentration enriched uranyl nitrate solution. These geometries resemble a tall, thin Central Column (or trunk of a ''tree'') having long, thin arms (or ''branches'') extending up to four directions off the column. Arms are equally spaced from one another in vertical planes, and that spacing ranges from arms in contact to quite wide spacings. Both the Central Column and the many different arms are critically safe by themselves with each, alone, is filled with fissile solution; but, in combination, criticality occurs due to the interactions between arms and the column. Such neutronic interactions formed the principal focus of this study. While these results are fresh to the nuclear criticality safety industry and to those seeking novel experiments against which to validate computer codes, the experiments, themselves, are not recent. Over 100 experiments were performed at the Rocky Flats Critical Mass Laboratory between September, 1967, and February of the following year.
Modeling of Bio-Fluids Flow with Complex Geometry Using Immersed Boundary Method
Mao, Shaolin; Celik, Ismail
2007-11-01
Fluid dynamics problems in the area of bio-fluids involve complex geometries and moving boundaries in addition to strong transients. The applications of CFD to such problems traditionally employ boundary fitted coordinates, which require generation of complicated computational grids. The alternative approach utilizing Cartesian coordinates with embedded virtual force method (immersed boundary method) avoids the problem of expensive and time consuming boundary fitted grid. The simple orthogonal grids directly benefit numerical accuracy and computational efficiency. An immediate application of immersed boundary method (IB) is to modify in-house CFD DREAM code for bio-engineering applications using domain decomposition methodology. Several benchmarks are tested and numerical results for gas-droplet two-phase flow are shown to examine the transport and dispersion of germ-laden droplets in a room. This modeling effort provides valuable information for ventilation control strategies to improve airflow patterns to reduce indoor airborne infection risk.
López-Sánchez, Erick J.; Romero, Juan M.; Yépez-Martínez, Huitzilin
2017-09-01
Different experimental studies have reported anomalous diffusion in brain tissues and notably this anomalous diffusion is expressed through fractional derivatives. Axons are important to understand neurodegenerative diseases such as multiple sclerosis, Alzheimer's disease, and Parkinson's disease. Indeed, abnormal accumulation of proteins and organelles in axons is a hallmark of these diseases. The diffusion in the axons can become anomalous as a result of this abnormality. In this case the voltage propagation in axons is affected. Another hallmark of different neurodegenerative diseases is given by discrete swellings along the axon. In order to model the voltage propagation in axons with anomalous diffusion and swellings, in this paper we propose a fractional cable equation for a general geometry. This generalized equation depends on fractional parameters and geometric quantities such as the curvature and torsion of the cable. For a cable with a constant radius we show that the voltage decreases when the fractional effect increases. In cables with swellings we find that when the fractional effect or the swelling radius increases, the voltage decreases. Similar behavior is obtained when the number of swellings and the fractional effect increase. Moreover, we find that when the radius swelling (or the number of swellings) and the fractional effect increase at the same time, the voltage dramatically decreases.
International Nuclear Information System (INIS)
Trebotich, David
2007-01-01
We have developed a simulation capability to model multiscale flow and transport in complex biological systems based on algorithms and software infrastructure developed under the SciDAC APDEC CET. The foundation of this work is a new hybrid fluid-particle method for modeling polymer fluids in irregular microscale geometries that enables long-time simulation of validation experiments. Both continuum viscoelastic and discrete particle representations have been used to model the constitutive behavior of polymer fluids. Complex flow environment geometries are represented on Cartesian grids using an implicit function. Direct simulation of flow in the irregular geometry is then possible using embedded boundary/volume-of-fluid methods without loss of geometric detail. This capability has been used to simulate biological flows in a variety of application geometries including biomedical microdevices, anatomical structures and porous media
Development of a numerical methodology for flowforming process simulation of complex geometry tubes
Varela, Sonia; Santos, Maite; Arroyo, Amaia; Pérez, Iñaki; Puigjaner, Joan Francesc; Puigjaner, Blanca
2017-10-01
Nowadays, the incremental flowforming process is widely explored because of the usage of complex tubular products is increasing due to the light-weighting trend and the use of expensive materials. The enhanced mechanical properties of finished parts combined with the process efficiency in terms of raw material and energy consumption are the key factors for its competitiveness and sustainability, which is consistent with EU industry policy. As a promising technology, additional steps for extending the existing flowforming limits in the production of tubular products are required. The objective of the present research is to further expand the current state of the art regarding limitations on tube thickness and diameter, exploring the feasibility to flowform complex geometries as tubes of elevated thickness of up to 60 mm. In this study, the analysis of the backward flowforming process of 7075 aluminum tubular preform is carried out to define the optimum process parameters, machine requirements and tooling geometry as demonstration case. Numerical simulation studies on flowforming of thin walled tubular components have been considered to increase the knowledge of the technology. The calculation of the rotational movement of the mesh preform, the high ratio thickness/length and the thermomechanical condition increase significantly the computation time of the numerical simulation model. This means that efficient and reliable tools able to predict the forming loads and the quality of flowformed thick tubes are not available. This paper aims to overcome this situation by developing a simulation methodology based on FEM simulation code including new strategies. Material characterization has also been performed through tensile test to able to design the process. Finally, to check the reliability of the model, flowforming tests at industrial environment have been developed.
Talebi, A.
2008-01-01
Key words: Hillslope geometry, Hillslope hydrology, Hillslope stability, Complex hillslopes, Modeling shallow landslides, HSB model, HSB-SM model.
The hydrologic response of a hillslope to rainfall involves a complex, transient saturated-unsaturated interaction that usually leads to a
Directory of Open Access Journals (Sweden)
Mikdam Jamal
2017-12-01
Full Text Available Metal additive manufacturing (AM is increasingly used to create complex 3D components at near net shape. However, the surface finish (SF of the metal AM part is uneven, with surface roughness being variable over the facets of the design. Standard post-processing methods such as grinding and linishing often meet with major challenges in finishing parts of complex shape. This paper reports on research that demonstrated that mass finishing (MF processes are able to deliver high-quality surface finishes (Ra and Sa on AM-generated parts of a relatively complex geometry (both internal features and external facets under select conditions. Four processes were studied in this work: stream finishing, high-energy (HE centrifuge, drag finishing and disc finishing. Optimisation of the drag finishing process was then studied using a structured design of experiments (DOE. The effects of a range of finishing parameters were evaluated and optimal parameters and conditions were determined. The study established that the proposed method can be successfully applied in drag finishing to optimise the surface roughness in an industrial application and that it is an economical way of obtaining the maximum amount of information in a short period of time with a small number of tests. The study has also provided an important step in helping understand the requirements of MF to deliver AM-generated parts to a target quality finish and cycle time.
International Nuclear Information System (INIS)
Ali, S A; Kim, D-H; Cafaro, C; Giffin, A
2012-01-01
Information geometric techniques and inductive inference methods hold great promise for solving computational problems of interest in classical and quantum physics, especially with regard to complexity characterization of dynamical systems in terms of their probabilistic description on curved statistical manifolds. In this paper, we investigate the possibility of describing the macroscopic behavior of complex systems in terms of the underlying statistical structure of their microscopic degrees of freedom by the use of statistical inductive inference and information geometry. We review the maximum relative entropy formalism and the theoretical structure of the information geometrodynamical approach to chaos on statistical manifolds M S . Special focus is devoted to a description of the roles played by the sectional curvature K M S , the Jacobi field intensity J M S and the information geometrodynamical entropy S M S . These quantities serve as powerful information-geometric complexity measures of information-constrained dynamics associated with arbitrary chaotic and regular systems defined on M S . Finally, the application of such information-geometric techniques to several theoretical models is presented.
An extended step characteristic method for solving the transport equation in general geometries
International Nuclear Information System (INIS)
DeHart, M.D.; Pevey, R.E.; Parish, T.A.
1994-01-01
A method for applying the discrete ordinates method to solve the Boltzmann transport equation on arbitrary two-dimensional meshes has been developed. The finite difference approach normally used to approximate spatial derivatives in extrapolating angular fluxes across a cell is replaced by direct solution of the characteristic form of the transport equation for each discrete direction. Thus, computational cells are not restricted to the geometrical shape of a mesh element characteristic of a given coordinate system. However, in terms of the treatment of energy and angular dependencies, this method resembles traditional discrete ordinates techniques. By using the method developed here, a general two-dimensional space can be approximated by an irregular mesh comprised of arbitrary polygons. Results for a number of test problems have been compared with solutions obtained from traditional methods, with good agreement. Comparisons include benchmarks against analytical results for problems with simple geometry, as well as numerical results obtained from traditional discrete ordinates methods by applying the ANISN and TWOTRAN-II computer programs
The relation between geometry and function of the ankle joint complex: a biomechanical review.
Kleipool, Roeland P; Blankevoort, Leendert
2010-05-01
This review deals with the relation between the anatomy and function of the ankle joint complex. The questions addressed are how high do the forces in the ankle joint get, where can the joints go (range of motion) and where do they go during walking and running. Finally the role of the ligaments and the articular surfaces is discussed, i.e. how does it happen. The magnitude of the loads on the ankle joint complex are primarily determined by muscle activity and can be as high as four times the body weight during walking. For the maximal range of motion, plantar and dorsiflexion occurs in the talocrural joint and marginally at the subtalar joint. In-eversion takes place at both levels. The functional range of motion is well within the limits of the maximal range of motion. The ligaments do not contribute to the forces for the functional range of motion but determine the maximal range of motion together with the articular surfaces. The geometry of the articular surfaces primarily determines the kinematics. Clinical studies must include these anatomical aspects to better understand the mechanism of injury, recovery, and interventions. Models can elucidate the mechanism by which the anatomy relates to the function. The relation between the anatomy and mechanical properties of the joint structures and joint function should be considered for diagnosis and treatment of ankle joint pathology.
Westerly, David C; Mo, Xiaohu; Tomé, Wolfgang A; Mackie, Thomas R; DeLuca, Paul M
2013-06-01
Pencil beam algorithms are commonly used for proton therapy dose calculations. Szymanowski and Oelfke ["Two-dimensional pencil beam scaling: An improved proton dose algorithm for heterogeneous media," Phys. Med. Biol. 47, 3313-3330 (2002)] developed a two-dimensional (2D) scaling algorithm which accurately models the radial pencil beam width as a function of depth in heterogeneous slab geometries using a scaled expression for the radial kernel width in water as a function of depth and kinetic energy. However, an assumption made in the derivation of the technique limits its range of validity to cases where the input expression for the radial kernel width in water is derived from a local scattering power model. The goal of this work is to derive a generalized form of 2D pencil beam scaling that is independent of the scattering power model and appropriate for use with any expression for the radial kernel width in water as a function of depth. Using Fermi-Eyges transport theory, the authors derive an expression for the radial pencil beam width in heterogeneous slab geometries which is independent of the proton scattering power and related quantities. The authors then perform test calculations in homogeneous and heterogeneous slab phantoms using both the original 2D scaling model and the new model with expressions for the radial kernel width in water computed from both local and nonlocal scattering power models, as well as a nonlocal parameterization of Molière scattering theory. In addition to kernel width calculations, dose calculations are also performed for a narrow Gaussian proton beam. Pencil beam width calculations indicate that both 2D scaling formalisms perform well when the radial kernel width in water is derived from a local scattering power model. Computing the radial kernel width from a nonlocal scattering model results in the local 2D scaling formula under-predicting the pencil beam width by as much as 1.4 mm (21%) at the depth of the Bragg peak for a 220
Zhao, Xujun; Li, Jiyuan; Jiang, Xikai; Karpeev, Dmitry; Heinonen, Olle; Smith, Barry; Hernandez-Ortiz, Juan P.; de Pablo, Juan J.
2017-06-01
An efficient parallel Stokes' solver has been developed for complete description of hydrodynamic interactions between Brownian particles in bulk and confined geometries. A Langevin description of the particle dynamics is adopted, where the long-range interactions are included using a Green's function formalism. A scalable parallel computational approach is presented, where the general geometry Stokeslet is calculated following a matrix-free algorithm using the general geometry Ewald-like method. Our approach employs a highly efficient iterative finite-element Stokes' solver for the accurate treatment of long-range hydrodynamic interactions in arbitrary confined geometries. A combination of mid-point time integration of the Brownian stochastic differential equation, the parallel Stokes' solver, and a Chebyshev polynomial approximation for the fluctuation-dissipation theorem leads to an O(N) parallel algorithm. We illustrate the new algorithm in the context of the dynamics of confined polymer solutions under equilibrium and non-equilibrium conditions. The method is then extended to treat suspended finite size particles of arbitrary shape in any geometry using an immersed boundary approach.
Stallings, William M.
It was hypothesized that instruction in descriptive geometry produces an increase in SRT scores. The resultant data do not firmly support this hypothesis. It is suggested that this study be replicated with the use of randomly selected control groups. (MS)
Heat leak analysis on a cryostat suspension system with complex geometry
International Nuclear Information System (INIS)
Zhang, B.
1994-01-01
An internal suspension system is designed for the cryostat of the SSC sector cryogenic shaft transfer line. The suspension system supports seven cryogenic circuits of three temperature levels at 4, 20, and 80 K. Due to strict strength requirements and space constraints, the designed suspension system has complex geometry which makes the estimate of heat leaks into the cryogenic circuits rather difficult. Numerical analysis is performed on three subassemblies of the suspension system using a finite element analysis package by Algor. Typical temperature distributions in key elements are graphically presented, and heat leaks into the circuit tubes at three temperature levels are summarized. The results of the analysis indicate that the current suspension system design, while meeting the strength requirements, significantly reduces the heat leaks into the 4 and 20 K helium circuits compared to the conventional design which uses a single spacer to support the cryogenic circuits. The results also provide good reference for the final design of the suspension system, and can be readily verified experimentally
Validation and Analysis of Forward Osmosis CFD Model in Complex 3D Geometries
Directory of Open Access Journals (Sweden)
Lars Yde
2012-11-01
Full Text Available In forward osmosis (FO, an osmotic pressure gradient generated across a semi-permeable membrane is used to generate water transport from a dilute feed solution into a concentrated draw solution. This principle has shown great promise in the areas of water purification, wastewater treatment, seawater desalination and power generation. To ease optimization and increase understanding of membrane systems, it is desirable to have a comprehensive model that allows for easy investigation of all the major parameters in the separation process. Here we present experimental validation of a computational fluid dynamics (CFD model developed to simulate FO experiments with asymmetric membranes. Simulations are compared with experimental results obtained from using two distinctly different complex three-dimensional membrane chambers. It is found that the CFD model accurately describes the solute separation process and water permeation through membranes under various flow conditions. It is furthermore demonstrated how the CFD model can be used to optimize membrane geometry in such as way as to promote the mass transfer.
An immersed-boundary finite-volume method for simulation of heat transfer in complex geometries
International Nuclear Information System (INIS)
Kim, Jung Woo; Choi, Hae Cheon
2004-01-01
An immersed boundary method for solving the Navier-Stokes and thermal energy equations is developed to compute the heat transfer over or inside the complex geometries in the cartesian or cylindrical coordinates by introducing the momentum forcing, mass source/sink, and heat source/sink. The present method is based on the finite volume approach on a staggered mesh together with a fractional step method. The method of applying the momentum forcing and mass source/sink to satisfy the no-slip condition on the body surface is explained in detail in Kim, Kim and Choi (2001, Journal of Computational Physics). In this paper, the heat source/sink is introduced on the body surface or inside the body to satisfy the iso-thermal or iso-heat-flux condition on the immersed boundary. The present method is applied to three different problems : forced convection around a circular cylinder, mixed convection around a pair of circular cylinders, and forced convection around a main cylinder with a secondary small cylinder. The results show good agreements with those obtained by previous experiments and numerical simulations, verifying the accuracy of the present method
A versatile embedded boundary adaptive mesh method for compressible flow in complex geometry
Almarouf, Mohamad Abdulilah Alhusain Alali
2017-02-25
We present an embedded ghost-fluid method for numerical solutions of the compressible Navier Stokes (CNS) equations in arbitrary complex domains. A PDE multidimensional extrapolation approach is used to reconstruct the solution in the ghost-fluid regions and imposing boundary conditions on the fluid-solid interface, coupled with a multi-dimensional algebraic interpolation for freshly cleared cells. The CNS equations are numerically solved by the second order multidimensional upwind method. Block-structured adaptive mesh refinement, implemented with the Chombo framework, is utilized to reduce the computational cost while keeping high resolution mesh around the embedded boundary and regions of high gradient solutions. The versatility of the method is demonstrated via several numerical examples, in both static and moving geometry, ranging from low Mach number nearly incompressible flows to supersonic flows. Our simulation results are extensively verified against other numerical results and validated against available experimental results where applicable. The significance and advantages of our implementation, which revolve around balancing between the solution accuracy and implementation difficulties, are briefly discussed as well.
A shallow-flow model for the propagation of tsunamis over complex geometries and mobile beds
Directory of Open Access Journals (Sweden)
D. A. S. Conde
2013-10-01
Full Text Available A distinguishable feature of overland tsunami propagation is the incorporation of solids within the flow column, either sediment from the natural environment or remains from built infrastructure. This article describes a 2DH (two-dimensional horizontal mathematical model particularly suited for tsunami propagation over complex and dynamic geometries, such as river and estuarine mobile beds. The discretization scheme is based on a finite-volume method using a flux-splitting technique featuring a reviewed Roe–Riemann solver, with appropriate source-term formulations to ensure full conservativeness. The model is validated with laboratory data and paleo-tsunami evidence. As a forecasting application, it is applied to a tsunami scenario in the Tagus estuary, an effort justified by the numerous catastrophic tsunamis that are known to have struck this location over the past two millennia. The obtained results show that, despite the significant differences in Lisbon's layout and morphology, a 1755-like tsunami would still inflict a devastating impact on this major city.
Validation and Analysis of Forward Osmosis CFD Model in Complex 3D Geometries
Gruber, Mathias F.; Johnson, Carl J.; Tang, Chuyang; Jensen, Mogens H.; Yde, Lars; Hélix-Nielsen, Claus
2012-01-01
In forward osmosis (FO), an osmotic pressure gradient generated across a semi-permeable membrane is used to generate water transport from a dilute feed solution into a concentrated draw solution. This principle has shown great promise in the areas of water purification, wastewater treatment, seawater desalination and power generation. To ease optimization and increase understanding of membrane systems, it is desirable to have a comprehensive model that allows for easy investigation of all the major parameters in the separation process. Here we present experimental validation of a computational fluid dynamics (CFD) model developed to simulate FO experiments with asymmetric membranes. Simulations are compared with experimental results obtained from using two distinctly different complex three-dimensional membrane chambers. It is found that the CFD model accurately describes the solute separation process and water permeation through membranes under various flow conditions. It is furthermore demonstrated how the CFD model can be used to optimize membrane geometry in such as way as to promote the mass transfer. PMID:24958428
Ghoneim, Mohamed T.
2017-02-01
A highly manufacturable deep reactive ion etching based process involving a hybrid soft/hard mask process technology shows high aspect ratio complex geometry Lego-like silicon electronics formation enabling free-form (physically flexible, stretchable, and reconfigurable) electronic systems.
The Cyclic Sieving Phenomenon for Faces of Generalized Cluster Complexes
Eu, Sen-Peng; Fu, Tung-Shan
2006-01-01
The notion of cyclic sieving phenomenon is introduced by Reiner, Stanton, and White as a generalization of Stembridge's $q=-1$ phenomenon. The generalized cluster complexes associated to root systems are given by Fomin and Reading as a generalization of the cluster complexes found by Fomin and Zelevinsky. In this paper, the faces of various dimensions of the generalized cluster complexes in type $A_n$, $B_n$, $D_n$, and $I_2(a)$ are shown to exhibit the cyclic sieving phenomenon under a cycli...
International Nuclear Information System (INIS)
Degtyarev, I.I.; Lokhovitskij, A.E.; Maslov, M.A.; Yazynin, I.A.
1994-01-01
The first version of integrative shell of the program complex MARS is written for calculating radiation transfer in the three-dimensional geometries. The integrative shell allows the user to work in convenient form with complex MARS, creat input files data and get graphic visualization of calculated functions. Version 1.0 is adapted for personal computers of types IBM-286,386,486 with operative size memory not smaller than 500K. 5 refs
Impulsive generalized function synchronization of complex dynamical networks
International Nuclear Information System (INIS)
Zhang, Qunjiao; Chen, Juan; Wan, Li
2013-01-01
This Letter investigates generalized function synchronization of continuous and discrete complex networks by impulsive control. By constructing the reasonable corresponding impulsively controlled response networks, some criteria and corollaries are derived for the generalized function synchronization between the impulsively controlled complex networks, continuous and discrete networks are both included. Furthermore, the generalized linear synchronization and nonlinear synchronization are respectively illustrated by several examples. All the numerical simulations demonstrate the correctness of the theoretical results
Rodger, Alison
1995-01-01
Molecular Geometry discusses topics relevant to the arrangement of atoms. The book is comprised of seven chapters that tackle several areas of molecular geometry. Chapter 1 reviews the definition and determination of molecular geometry, while Chapter 2 discusses the unified view of stereochemistry and stereochemical changes. Chapter 3 covers the geometry of molecules of second row atoms, and Chapter 4 deals with the main group elements beyond the second row. The book also talks about the complexes of transition metals and f-block elements, and then covers the organometallic compounds and trans
Simulation and Validation of a Storm Surge in Bays and Estuaries With Complex Coastline Geometry
Dukhovskoy, D. S.; Morey, S. L.
2008-12-01
Simulation of nearshore ocean dynamics in a region with a complex coastline, commonly found along bays and estuaries, has been a challenging task for modelers. Over the last decade, unstructured grid models based on finite-element and finite-volume methods have been gaining popularity within the ocean modeling community. Application of this type of model facilitates accurate representation of the nearshore processes in model domains with bays, estuaries, and river channels. This study demonstrates the utility of applying an unstructured grid model for simulation and analysis of a storm surge in such a region. A high-resolution storm surge model of Apalachee Bay in the northeastern Gulf of Mexico is developed using an unstructured grid Finite-Volume Coastal Ocean Model (FVCOM) with wetting and drying capabilities. The model is applied to the case of Hurricane Dennis (July 2005). This storm caused underpredicted severe flooding of the Apalachee Bay coastal area and communities located inland up rivers that has yet to be adequately explained. Accurate resolution of the complicated geometry of the coastal region and waterways in the model reveals substantial spatial variability in the amplitude and timing of the maximum water level and processes responsible for the unanticipated high storm tide in the area. In this study, a methodology of validating a storm surge simulations using high-water marks is illustrated. Model experiments suggest that excessive flooding in the coastal zone during Dennis was caused by additive effects of coincident high tides, wave setup, and a propagating shelf wave that added to the locally wind generated surge.
Spinor formalism and complex-vector formalism of general relativity
International Nuclear Information System (INIS)
Han-ying, G.; Yong-shi, W.; Gendao, L.
1974-01-01
In this paper, using E. Cartan's exterior calculus, we give the spinor form of the structure equations, which leads naturally to the Newman--Penrose equations. Furthermore, starting from the spinor spaces and the el (2C) algebra, we construct the general complex-vector formalism of general relativity. We find that both the Cahen--Debever--Defrise complex-vector formalism and that of Brans are its special cases. Thus, the spinor formalism and the complex-vector formalism of general relativity are unified on the basis of the uni-modular group SL(2C) and its Lie algebra
Energy Technology Data Exchange (ETDEWEB)
Manolescu, M.; Sperandio, M.; Allard, F. [La Rochelle Universite, 17 - La Rochelle, LEPTAB (France)
1996-12-31
Bibliographic studies in the domain of radiant heat transfers in complex geometries demonstrate the impossibility of resolving such problems using classical analytical methods. The numerical analysis can theoretically be performed successfully but requires enormous computer means. The contribution of this study consists in using computerized graphical techniques to treat general problems of radiant heat transfers in complex geometries. This paper presents the model used, the calculation technique and the optimizations that allow to greatly reduce the computer memory required and the calculation time. The code developed uses evocative images for the synthetic presentation of results which facilitate the searcher`s and conceiver`s choices. Finally, an application to the characterization of thermal comfort in residential environments is developed to illustrate the potentialities of this method. (J.S.) 19 refs.
Flow MRI simulation in complex 3D geometries: Application to the cerebral venous network.
Fortin, Alexandre; Salmon, Stéphanie; Baruthio, Joseph; Delbany, Maya; Durand, Emmanuel
2018-02-05
Develop and evaluate a complete tool to include 3D fluid flows in MRI simulation, leveraging from existing software. Simulation of MR spin flow motion is of high interest in the study of flow artifacts and angiography. However, at present, only a few simulators include this option and most are restricted to static tissue imaging. An extension of JEMRIS, one of the most advanced high performance open-source simulation platforms to date, was developed. The implementation of a Lagrangian description of the flow allows simulating any MR experiment, including both static tissues and complex flow data from computational fluid dynamics. Simulations of simple flow models are compared with real experiments on a physical flow phantom. A realistic simulation of 3D flow MRI on the cerebral venous network is also carried out. Simulations and real experiments are in good agreement. The generality of the framework is illustrated in 2D and 3D with some common flow artifacts (misregistration and inflow enhancement) and with the three main angiographic techniques: phase contrast velocimetry (PC), time-of-flight, and contrast-enhanced imaging MRA. The framework provides a versatile and reusable tool for the simulation of any MRI experiment including physiological fluids and arbitrarily complex flow motion. © 2018 International Society for Magnetic Resonance in Medicine.
Hely, Clement
During the past 50 years, the use of composite materials drastically increase, mainly thanks to the interest of aeronautical industries for these strong and lightweight materials. To improve the productivity of composite materials manufacturing some of the largest aeronautics companies began to develop automated processes such as Automated Fibre Placement (AFP). The AFP workcells currently used by the industry were mainly developed for production of large, nearly flat, plates with low curvatures such as aircraft fuselages. However, the fields of aeronautics and sport goods production begin nowadays to show an interest for manufacturing of smaller and more complex parts. The aim of the project in which this research takes place is to design a new AFP workcell and to develop new techniques allowing production of parts with small size and complex geometry. The work presented in this thesis focuses on the path planning on multi-axial revolution surfaces, e.g. Y-shaped tubes of constant circular cross section. Several path planning algorithms will be presented aiming at the exhaustive coverage of a mandrel with pre-impregnated (prepreg) composite tape. The methodology used in two of these algorithms is to individually cover each branch of the Y-shaped part with paths deriving from a helix. In the first one, the helix will be cut at the boundary between a branch and the junction region (algorithm HD) while in the second (algorithm HA) the pseudo-helix path can be adjusted to follow this boundary. These two methods were shown to have some drawbacks compromising their practical use and possibly leading to parts with diminished mechanical properties. To avoid these drawbacks, two others algorithms were developed with a new methodology. With them, the aim is to cover two branches of the Y-shape with a continuous course (i.e. without cut). The first one uses a well known strategy which defines plies with a constant fibre orientation. Parallel paths are then computed to
Directory of Open Access Journals (Sweden)
Esteban A. Agudo-Adriani
2016-04-01
Full Text Available In the past decade, significant efforts have been made to describe fish-habitat associations. However, most studies have oversimplified actual connections between fish assemblages and their habitats by using univariate correlations. The purpose of this study was to identify the features of habitat forming corals that facilitate and influences assemblages of associated species such as fishes. For this we developed three-dimensional models of colonies of Acropora cervicornis to estimate geometry (length and height, structural complexity (i.e., volume, density of branches, etc. and biological features of the colonies (i.e., live coral tissue, algae. We then correlated these colony characteristics with the associated fish assemblage using multivariate analyses. We found that geometry and complexity were better predictors of the structure of fish community, compared to other variables such as percentage of live coral tissue or algae. Combined, the geometry of each colony explained 40% of the variability of the fish assemblage structure associated with this coral species; 61% of the abundance and 69% of fish richness, respectively. Our study shows that three-dimensional reconstructions of discrete colonies of Acropora cervicornis provides a useful description of the colonial structural complexity and may explain a great deal of the variance in the structure of the associated coral reef fish community. This demonstration of the strongly trait-dependent ecosystem role of this threatened species has important implications for restoration and conservation efforts.
Directory of Open Access Journals (Sweden)
Haci Mehmet Baskonus
2016-07-01
Full Text Available In this paper, we apply the sine-Gordon expansion method which is one of the powerful methods to the generalized-Zakharov equation with complex structure. This algorithm yields new complex hyperbolic function solutions to the generalized-Zakharov equation with complex structure. Wolfram Mathematica 9 has been used throughout the paper for plotting two- and three-dimensional surface of travelling wave solutions obtained.
Beyond Crossing Fibers: Bootstrap Probabilistic Tractography Using Complex Subvoxel Fiber Geometries
Campbell, Jennifer S. W.; MomayyezSiahkal, Parya; Savadjiev, Peter; Leppert, Ilana R.; Siddiqi, Kaleem; Pike, G. Bruce
2014-01-01
Diffusion magnetic resonance imaging fiber tractography is a powerful tool for investigating human white matter connectivity in vivo. However, it is prone to false positive and false negative results, making interpretation of the tractography result difficult. Optimal tractography must begin with an accurate description of the subvoxel white matter fiber structure, includes quantification of the uncertainty in the fiber directions obtained, and quantifies the confidence in each reconstructed fiber tract. This paper presents a novel and comprehensive pipeline for fiber tractography that meets the above requirements. The subvoxel fiber geometry is described in detail using a technique that allows not only for straight crossing fibers but for fibers that curve and splay. This technique is repeatedly performed within a residual bootstrap statistical process in order to efficiently quantify the uncertainty in the subvoxel geometries obtained. A robust connectivity index is defined to quantify the confidence in the reconstructed connections. The tractography pipeline is demonstrated in the human brain. PMID:25389414
International Nuclear Information System (INIS)
Robinson, I.; Trautman, A.
1988-01-01
The geometry of classical physics is Lorentzian; but weaker geometries are often more appropriate: null geodesics and electromagnetic fields, for example, are well known to be objects of conformal geometry. To deal with a single null congruence, or with the radiative electromagnetic fields associated with it, even less is needed: flag geometry for the first, optical geometry, with which this paper is chiefly concerned, for the second. The authors establish a natural one-to-one correspondence between optical geometries, considered locally, and three-dimensional Cauchy-Riemann structures. A number of Lorentzian geometries are shown to be equivalent from the optical point of view. For example the Goedel universe, the Taub-NUT metric and Hauser's twisting null solution have an optical geometry isomorphic to the one underlying the Robinson congruence in Minkowski space. The authors present general results on the problem of lifting a CR structure to a Lorentz manifold and, in particular, to Minkowski space; and exhibit the relevance of the deviation form to this problem
Grau Galofre, Anna; Jellinek, A. Mark
2017-04-01
The morphology of channel networks related to long-term erosion reflects the mechanisms involved in their formation. This study aims to identify quantitative metrics, drawn from topographic data and satellite imagery, that are diagnostic of the distinctive styles of erosion by rivers, glaciers, subglacial meltwater, and groundwater sapping. From digital elevation models, we identify three geometric metrics: the minimum channel width, channel aspect ratio (longest length to channel width at the outlet), and tributary junction angle. We also characterize channel network complexity in terms of its stream order and fractal dimension. To validate our approach, we perform a principal component analysis (PCA) on measurements of these five metrics on 70 channel networks. We build understanding of these results, in turn using scaling analyses of appropriate physical models. We show that rivers, glaciers, and groundwater sapping erode the landscape in rigorously distinguishable ways. Whereas rivers are characterized by nearly constant minimum width, variable aspect ratio, and high stream orders, glaciers have highly variable minimum widths and aspect ratios and much smaller stream orders. Erosion by subglacial meltwater remains poorly understood, and we argue that we require an additional metric to fully characterize these systems. Our methodology can more generally be applied to identify the contributions of different processes involved in carving a channel network. In particular, we are able to identify transitions from fluvial to glaciated landscapes or vice versa.
Faulkner, Thomas Ewan
1952-01-01
This text explores the methods of the projective geometry of the plane. Some knowledge of the elements of metrical and analytical geometry is assumed; a rigorous first chapter serves to prepare readers. Following an introduction to the methods of the symbolic notation, the text advances to a consideration of the theory of one-to-one correspondence. It derives the projective properties of the conic and discusses the representation of these properties by the general equation of the second degree. A study of the relationship between Euclidean and projective geometry concludes the presentation. Nu
Schreyer, W.; Kikawa, T.; Losekamm, M. J.; Paul, S.; Picker, R.
2017-06-01
Modern precision experiments trapping low-energy particles require detailed simulations of particle trajectories and spin precession to determine systematic measurement limitations and apparatus deficiencies. We developed PENTrack, a tool that allows to simulate trajectories of ultracold neutrons and their decay products-protons and electrons-and the precession of their spins in complex geometries and electromagnetic fields. The interaction of ultracold neutrons with matter is implemented with the Fermi-potential formalism and diffuse scattering using Lambert and microroughness models. The results of several benchmark simulations agree with STARucn v1.2, uncovered several flaws in Geant4 v10.2.2, and agree with experimental data. Experiment geometry and electromagnetic fields can be imported from commercial computer-aided-design and finite-element software. All simulation parameters are defined in simple text files allowing quick changes. The simulation code is written in C++ and is freely available at github.com/wschreyer/PENTrack.git.
Ghikas, Demetris P. K.; Oikonomou, Fotios D.
2018-04-01
Using the generalized entropies which depend on two parameters we propose a set of quantitative characteristics derived from the Information Geometry based on these entropies. Our aim, at this stage, is to construct first some fundamental geometric objects which will be used in the development of our geometrical framework. We first establish the existence of a two-parameter family of probability distributions. Then using this family we derive the associated metric and we state a generalized Cramer-Rao Inequality. This gives a first two-parameter classification of complex systems. Finally computing the scalar curvature of the information manifold we obtain a further discrimination of the corresponding classes. Our analysis is based on the two-parameter family of generalized entropies of Hanel and Thurner (2011).
Learning with Generalization Capability by Kernel Methods of Bounded Complexity
Czech Academy of Sciences Publication Activity Database
Kůrková, Věra; Sanguineti, M.
2005-01-01
Roč. 21, č. 3 (2005), s. 350-367 ISSN 0885-064X R&D Projects: GA AV ČR 1ET100300419 Institutional research plan: CEZ:AV0Z10300504 Keywords : supervised learning * generalization * model complexity * kernel methods * minimization of regularized empirical errors * upper bounds on rates of approximate optimization Subject RIV: BA - General Mathematics Impact factor: 1.186, year: 2005
Huemul: a two dimensional multigroup collision probability code for general geometries
International Nuclear Information System (INIS)
Calabrese, C.R.; Grant, C.R.
1990-01-01
The control rod calculation and the necessity of having a 2-D transport code able to calculate geometries as different as pool reactor or power reactor control rods resulted in the development of a new tool according to these requirements. This new tool permits a 2-D spatial representation, and the calculation mesh is formed by circumferential arcs segments not necessarily parallel to the coordinate axis. It includes the possibility of considering boundary conditions in the form of an albedo matrix (J + /J - ) as well as different external currents for each face of the model. It also allows an arbitrary number of energy groups compatible with computer limitations. These possibilities make HUEMUL a useful tool for a great variety of control rod or supercell type calculations. HUEMUL has been tested with copper activity measurements performed in the Canadian D2O facility ZED-2 with stainless-steel adjuster rods obtaining a very good agreement (better than 2%). Also manganese activity measurements in RA-2 pool reactor were used to compare calculated and measured values inside a MTR fuel element calculations, (better than 1%). Comparisons with results from the WIMS code for a light water cell with 3% enriched UO 2 has also shown a very good agreement in fluxes and multiplication constant (better than 1.5% in fluxes and 50 pcm in k-infinity). (Author) [es
Energy Technology Data Exchange (ETDEWEB)
Stark, R.H.
1977-05-01
This report is a non-technical exposition on the ambiguities in conventional specification of the shape of a part to be manufactured and on various alternatives for representing its geometry for computer processing. It touches lightly on wire-frame and bounded surface representations and on the concept of design by volumes. It concludes that no existing computer-aided design system has yet shown its long-range superiority over he spectrum of parts and of uses to which its information base should be applicable. 9 figures.
On the general procedure for modelling complex ecological systems
International Nuclear Information System (INIS)
He Shanyu.
1987-12-01
In this paper, the principle of a general procedure for modelling complex ecological systems, i.e. the Adaptive Superposition Procedure (ASP) is shortly stated. The result of application of ASP in a national project for ecological regionalization is also described. (author). 3 refs
Symplectic geometry on moduli spaces of holomorphic bundles over complex surfaces
Khesin, Boris; Rosly, Alexei
2000-01-01
We give a comparative description of the Poisson structures on the moduli spaces of flat connections on real surfaces and holomorphic Poisson structures on the moduli spaces of holomorphic bundles on complex surfaces. The symplectic leaves of the latter are classified by restrictions of the bundles to certain divisors. This can be regarded as fixing a "complex analogue of the holonomy" of a connection along a "complex analogue of the boundary" in analogy with the real case.
International Nuclear Information System (INIS)
Bakshi, P.; Kalman, G.
1976-02-01
A new approach for the solution of the Vlasov equation for complex magnetic field geometries has been developed using operator techniques. The general approach is illustrated by determining the perturbed distribution function and density operator for the problem of shear stabilization of drift waves for transverse and arbitrary directions of propagation. The ensuing corrections to stability criteria of current theories are obtained for certain domains of physical parameters. Preliminary work on the integral equation approach to the dispersion relation has been initiated. As a prelude to the study of particle orbits in complex mirror geometries, the adiabatic and non-adiabatic behavior of a harmonic oscillator has been studied using operator methods. High-β, high shear plasma sheath configurations have been studied with the full ion dynamics taken into account and electrons treated in the zero and first order approximation, in the ratio of the electron Larmor radius to the scale length. The resulting sheath structure equation in the lowest order approximation has been solved for certain entering ion distributions, and prepared for computer analysis for others. In this approximation the electron current parallel to magnetic field lines has to be assumed suppressed or predetermined. Equations in the next order approximation include the finite Larmor radius stress tensor. This equation is under study
Generalized vector products, duality, and octonionic identities in D = 8 geometry
International Nuclear Information System (INIS)
Duendarer, R.; Guersey, F.; Tze, C.
1984-01-01
In an explicit, unified, and covariant formulation, we study and generalize the exceptional vector products in R 8 of Zvengrowski, Gray, and Kleinfeld. We derive the associated general quadratic, cubic, and quartic G 2 invariant algebraic identities and uncover an octonionic counterpart to the d = 4 quaternionic duality. When restricted to seven dimensions the latter is an algebraic statement of absolute parallelism on S 7 . We further link up with the Ogievetski--Tzeitlin vector product and obtain explicit tensor forms of the SO(7) and G 2 structure constants. SO(8) transformations related by Triality are characterized by means of invariant tensors. Possible physical applications are discussed
Stiffeners in variational-difference method for calculating shells with complex geometry
Directory of Open Access Journals (Sweden)
Ivanov Vyacheslav Nikolaevich
2014-05-01
Full Text Available We have already considered an introduction of reinforcements in the variational-difference method (VDM of shells analysis with complex shape. At the moment only ribbed shells of revolution and shallow shells can be calculated with the help of developed analytical and finite-difference methods. Ribbed shells of arbitrary shape can be calculated only using the finite element method (FEM. However there are problems, when using FEM, which are absent in finite- and variational-difference methods: rigid body motion; conforming trial functions; parameterization of a surface; independent stress strain state. In this regard stiffeners are entered in VDM. VDM is based on the Lagrange principle - the principle of minimum total potential energy. Stress-strain state of ribs is described by the Kirchhoff-Clebsch theory of curvilinear bars: tension, bending and torsion of ribs are taken into account. Stress-strain state of shells is described by the Kirchhoff-Love theory of thin elastic shells. A position of points of the middle surface is defined by curvilinear orthogonal coordinates α, β. Curved ribs are situated along coordinate lines. Strain energy of ribs is added into the strain energy to account for ribs. A matrix form of strain energy of ribs is formed similar to a matrix form of the strain energy of the shell. A matrix of geometrical characteristics of a rib is formed from components of matrices of geometric characteristics of a shell. A matrix of mechanical characteristics of a rib contains rib’s eccentricity and geometrical characteristics of a rib’s section. Derivatives of displacements in the strain vector are replaced with finite-difference relations after the middle surface of a shell gets covered with a grid (grid lines coincide with the coordinate lines of principal curvatures. By this case the total potential energy functional becomes a function of strain nodal displacements. Partial derivatives of unknown nodal displacements are
Programming While Construction of Engineering 3D Models of Complex Geometry
Kheyfets, A. L.
2017-11-01
The capabilities of geometrically accurate computational 3D models construction with the use of programming are presented. The construction of models of an architectural arch and a glo-boid worm gear is considered as an example. The models are designed in the AutoCAD pack-age. Three programs of construction are given. The first program is for designing a multi-section architectural arch. The control of the arch’s geometry by impacting its main parameters is shown. The second program is for designing and studying the working surface of a globoid gear’s worm. The article shows how to make the animation for this surface’s formation. The third program is for formation of a worm gear cavity surface. The cavity formation dynamics is studied. The programs are written in the AutoLisp programming language. The program texts are provided.
Complexity analysis based on generalized deviation for financial markets
Li, Chao; Shang, Pengjian
2018-03-01
In this paper, a new modified method is proposed as a measure to investigate the correlation between past price and future volatility for financial time series, known as the complexity analysis based on generalized deviation. In comparison with the former retarded volatility model, the new approach is both simple and computationally efficient. The method based on the generalized deviation function presents us an exhaustive way showing the quantization of the financial market rules. Robustness of this method is verified by numerical experiments with both artificial and financial time series. Results show that the generalized deviation complexity analysis method not only identifies the volatility of financial time series, but provides a comprehensive way distinguishing the different characteristics between stock indices and individual stocks. Exponential functions can be used to successfully fit the volatility curves and quantify the changes of complexity for stock market data. Then we study the influence for negative domain of deviation coefficient and differences during the volatile periods and calm periods. after the data analysis of the experimental model, we found that the generalized deviation model has definite advantages in exploring the relationship between the historical returns and future volatility.
Zervas, Ioannis; Olakunle Omosanya, Kamaldeen; Lippard, Stephen John; Johansen, Ståle Emil; Marfo, George
2017-04-01
Several inversion structures have been reported in the Southwestern Barents Sea, however such structures are poorly understood in the Troms-Finnmark Fault Complex (TFFC). This study interpreted three-dimensional (3-D) seismic data mainly in the TFFC and several adjoining structural elements, such as the Harstad and Tromsø Basins, the Finnmark Platform and the Ringvassøy Loppa Fault Complex. The methods used here include detailed seismic interpretation, analysis of structural maps, and fault displacement characterization. Our results show several evidences of localized partial positive inversion, intermittent with rifting events of Middle Jurassic to Early Cretaceous age. The inversion structures are of Middle/Late Triassic to Early Cretaceous age and include snakehead geometries of inverted wedge structures, folds associated with extensional faults, small-scale stratigraphic inversion in a fault network and reverse drag geometries along planar to rotated fault planes. The axial planes of folds associated with extensional faults in the study area revealed two different episodes of contraction linked to either compressional or shearing movements. Causes of inversion may also include far-field stresses related to halokinesis in the Tromsø Basin and uplift of the Loppa High. Inversion structures have had an impact on hydrocarbon prospectivity and accumulation in the TFFC and surrounding basins. Our work shows that localized folds close to extensional faults positively change the geometries of traps within the Stø Fm. (reservoir) and the Hekkingen Fm. (cap rock). In contrast, folding observed in the potential source rock of the Hekkingen Fm. post-dates the timing of petroleum generation and migration. Reactivated faults in the TFFC can act as conduits for hydrocarbons or compromise the sealing integrity of the traps.
Spinning geometry = Twisted geometry
International Nuclear Information System (INIS)
Freidel, Laurent; Ziprick, Jonathan
2014-01-01
It is well known that the SU(2)-gauge invariant phase space of loop gravity can be represented in terms of twisted geometries. These are piecewise-linear-flat geometries obtained by gluing together polyhedra, but the resulting geometries are not continuous across the faces. Here we show that this phase space can also be represented by continuous, piecewise-flat three-geometries called spinning geometries. These are composed of metric-flat three-cells glued together consistently. The geometry of each cell and the manner in which they are glued is compatible with the choice of fluxes and holonomies. We first remark that the fluxes provide each edge with an angular momentum. By studying the piecewise-flat geometries which minimize edge lengths, we show that these angular momenta can be literally interpreted as the spin of the edges: the geometries of all edges are necessarily helices. We also show that the compatibility of the gluing maps with the holonomy data results in the same conclusion. This shows that a spinning geometry represents a way to glue together the three-cells of a twisted geometry to form a continuous geometry which represents a point in the loop gravity phase space. (paper)
A Renewed Approach for Large Eddy Simulation of Complex Geometries, Phase II
National Aeronautics and Space Administration — The potential benefits of Large Eddy Simulation (LES) for aerodynamics and combustion simulation hvae largely been missed, due to the complexity of generating grids...
N=1 domain wall solutions of massive type II supergravity as generalized geometries
International Nuclear Information System (INIS)
Louis, J.
2006-05-01
We study N=1 domain wall solutions of type IIB supergravity compactified on a Calabi-Yau manifold in the presence of RR and NS electric and magnetic fluxes. We show that the dynamics of the scalar fields along the direction transverse to the domain wall is described by gradient flow equations controlled by a superpotential W. We then provide a geometrical interpretation of the gradient flow equations in terms of the mirror symmetric compactification of type IIA. They correspond to a set of generalized Hitchin flow equations of a manifold with SU(3) x SU(3)structure which is fibered over the direction transverse to the domain wall. (Orig.)
A note on generalized metrics on complex manifolds
International Nuclear Information System (INIS)
Rastogi, S.C.
1986-08-01
In 1981, Hojo introduced a generalized metric function Φ (P) , p(≠1) is a real number in a Finsler space and studied some beautiful consequences of such a metric function. The aim of this paper is to investigate the possibility of introducing a similar metric function on a complex manifold studied by Rund. It is interesting to note that such an introduction is unnatural for values of p other than 2, which corresponds to the metric function introduced by Rund. (author)
Contextual interactions in a generalized energy model of complex cells
Dellen, Babette; Clark, John W.; Wessel, Ralf
2009-01-01
We propose a generalized energy model of complex cells to describe modulatory contextual influences on the responses of neurons in the primary visual cortex (V1). Many orientationselective cells in V1 respond to contrast of orientation and motion of stimuli exciting the classical receptive field (CRF) and the non-CRF, or surround. In the proposed model, a central spatiotemporal filter, defining the CRF, is nonlinearly combined with a spatiotemporal filter extending into the non- ...
Stability of the complex generalized Hartree-Fock equations.
Goings, Joshua J; Ding, Feizhi; Frisch, Michael J; Li, Xiaosong
2015-04-21
For molecules with complex and competing magnetic interactions, it is often the case that the lowest energy Hartree-Fock solution may only be obtained by removing the spin and time-reversal symmetry constraints of the exact non-relativistic Hamiltonian. To do so results in the complex generalized Hartree-Fock (GHF) method. However, with the loss of variational constraints comes the greater possibility of converging to higher energy minima. Here, we report the implementation of stability test of the complex GHF equations, along with an orbital update scheme should an instability be found. We apply the methodology to finding the local minima of several spin-frustrated hydrogen rings, as well as the non-collinear molecular magnet Cr3, illustrating the utility of the broken symmetry GHF method and some of its lesser-known nuances.
Contextual interactions in a generalized energy model of complex cells.
Dellen, Babette K; Clark, John W; Wessel, Ralf
2009-01-01
We propose a generalized energy model of complex cells to describe modulatory contextual influences on the responses of neurons in the primary visual cortex (V1). Many orientation-selective cells in V1 respond to contrast of orientation and motion of stimuli exciting the classical receptive field (CRF) and the non-CRF, or surround. In the proposed model, a central spatiotemporal filter, defining the CRF, is nonlinearly combined with a spatiotemporal filter extending into the non-CRF. These filters are assumed to describe simple-cell responses, while the nonlinear combination of their responses describes the responses of complex cells. This mathematical operation accounts for the inherent nonlinearity of complex cells, such as phase independence and frequency doubling, and for nonlinear interactions between stimuli in the CRF and surround of the cell, including sensitivity to feature contrast. If only the CRF of the generalized complex cell is stimulated by a drifting grating, the model reduces to the standard energy model. The theoretical predictions of the model are supported by computer simulations and compared with experimental data from V1.
3D simulation of polyurethane foam injection and reacting mold flow in a complex geometry
Özdemir, İ. Bedii; Akar, Fırat
2017-11-01
The aim of the present work is to develop a flow model which can be used to determine the paths of the polyurethane foam in the mold filling process of a refrigerator cabinet so that improvements in the distribution and the size of the venting holes can be achieved without the expensive prototyping and experiments. For this purpose, the multi-component, two-phase chemically reacting flow is described by Navier Stokes and 12 scalar transport equations. The air and the multi-component foam zones are separated by an interface, which moves only with advection since the mass diffusion of species are set zero in the air zone. The inverse density, viscosity and other diffusion coefficients are calculated by a mass fraction weighted average of the corresponding temperature-dependent values of all species. Simulations are performed in a real refrigerator geometry, are able to reveal the problematical zones where air bubbles and voids trapped in the solidified foam are expected to occur. Furthermore, the approach proves itself as a reliable design tool to use in deciding the locations of air vents and sizing the channel dimensions.
3D simulation of polyurethane foam injection and reacting mold flow in a complex geometry
Özdemir, İ. Bedii; Akar, Fırat
2018-05-01
The aim of the present work is to develop a flow model which can be used to determine the paths of the polyurethane foam in the mold filling process of a refrigerator cabinet so that improvements in the distribution and the size of the venting holes can be achieved without the expensive prototyping and experiments. For this purpose, the multi-component, two-phase chemically reacting flow is described by Navier Stokes and 12 scalar transport equations. The air and the multi-component foam zones are separated by an interface, which moves only with advection since the mass diffusion of species are set zero in the air zone. The inverse density, viscosity and other diffusion coefficients are calculated by a mass fraction weighted average of the corresponding temperature-dependent values of all species. Simulations are performed in a real refrigerator geometry, are able to reveal the problematical zones where air bubbles and voids trapped in the solidified foam are expected to occur. Furthermore, the approach proves itself as a reliable design tool to use in deciding the locations of air vents and sizing the channel dimensions.
The accuracy of geometries for iron porphyrin complexes from density functional theory
DEFF Research Database (Denmark)
Rydberg, Patrik Åke Anders; Olsen, Lars
2009-01-01
Iron porphyrin complexes are cofactors in many important proteins such as cytochromes P450, hemoglobin, heme peroxidases, etc. Many computational studies on these systems have been done over the past decade. In this study, the performance of some of the most commonly used density functional theor...
Evaluation of 2D shallow-water model for spillway flow with a complex geometry
Although the two-dimensional (2D) shallow water model is formulated based on several assumptions such as hydrostatic pressure distribution and vertical velocity is negligible, as a simple alternative to the complex 3D model, it has been used to compute water flows in which these assumptions may be ...
Composite structured mesh generation with automatic domain decomposition in complex geometries
This paper presents a novel automatic domain decomposition method to generate quality composite structured meshes in complex domains with arbitrary shapes, in which quality structured mesh generation still remains a challenge. The proposed decomposition algorithm is based on the analysis of an initi...
High performance parallel computing of flows in complex geometries: II. Applications
International Nuclear Information System (INIS)
Gourdain, N; Gicquel, L; Staffelbach, G; Vermorel, O; Duchaine, F; Boussuge, J-F; Poinsot, T
2009-01-01
Present regulations in terms of pollutant emissions, noise and economical constraints, require new approaches and designs in the fields of energy supply and transportation. It is now well established that the next breakthrough will come from a better understanding of unsteady flow effects and by considering the entire system and not only isolated components. However, these aspects are still not well taken into account by the numerical approaches or understood whatever the design stage considered. The main challenge is essentially due to the computational requirements inferred by such complex systems if it is to be simulated by use of supercomputers. This paper shows how new challenges can be addressed by using parallel computing platforms for distinct elements of a more complex systems as encountered in aeronautical applications. Based on numerical simulations performed with modern aerodynamic and reactive flow solvers, this work underlines the interest of high-performance computing for solving flow in complex industrial configurations such as aircrafts, combustion chambers and turbomachines. Performance indicators related to parallel computing efficiency are presented, showing that establishing fair criterions is a difficult task for complex industrial applications. Examples of numerical simulations performed in industrial systems are also described with a particular interest for the computational time and the potential design improvements obtained with high-fidelity and multi-physics computing methods. These simulations use either unsteady Reynolds-averaged Navier-Stokes methods or large eddy simulation and deal with turbulent unsteady flows, such as coupled flow phenomena (thermo-acoustic instabilities, buffet, etc). Some examples of the difficulties with grid generation and data analysis are also presented when dealing with these complex industrial applications.
Equivalence of the generalized and complex Kohn variational methods
Energy Technology Data Exchange (ETDEWEB)
Cooper, J N; Armour, E A G [School of Mathematical Sciences, University Park, Nottingham NG7 2RD (United Kingdom); Plummer, M, E-mail: pmxjnc@googlemail.co [STFC Daresbury Laboratory, Daresbury, Warrington, Cheshire WA4 4AD (United Kingdom)
2010-04-30
For Kohn variational calculations on low energy (e{sup +} - H{sub 2}) elastic scattering, we prove that the phase shift approximation, obtained using the complex Kohn method, is precisely equal to a value which can be obtained immediately via the real-generalized Kohn method. Our treatment is sufficiently general to be applied directly to arbitrary potential scattering or single open channel scattering problems, with exchange if required. In the course of our analysis, we develop a framework formally to describe the anomalous behaviour of our generalized Kohn calculations in the regions of the well-known Schwartz singularities. This framework also explains the mathematical origin of the anomaly-free singularities we reported in a previous article. Moreover, we demonstrate a novelty: that explicit solutions of the Kohn equations are not required in order to calculate optimal phase shift approximations. We relate our rigorous framework to earlier descriptions of the Kohn-type methods.
Equivalence of the generalized and complex Kohn variational methods
International Nuclear Information System (INIS)
Cooper, J N; Armour, E A G; Plummer, M
2010-01-01
For Kohn variational calculations on low energy (e + - H 2 ) elastic scattering, we prove that the phase shift approximation, obtained using the complex Kohn method, is precisely equal to a value which can be obtained immediately via the real-generalized Kohn method. Our treatment is sufficiently general to be applied directly to arbitrary potential scattering or single open channel scattering problems, with exchange if required. In the course of our analysis, we develop a framework formally to describe the anomalous behaviour of our generalized Kohn calculations in the regions of the well-known Schwartz singularities. This framework also explains the mathematical origin of the anomaly-free singularities we reported in a previous article. Moreover, we demonstrate a novelty: that explicit solutions of the Kohn equations are not required in order to calculate optimal phase shift approximations. We relate our rigorous framework to earlier descriptions of the Kohn-type methods.
A Parallel Cartesian Approach for External Aerodynamics of Vehicles with Complex Geometry
Aftosmis, M. J.; Berger, M. J.; Adomavicius, G.
2001-01-01
This workshop paper presents the current status in the development of a new approach for the solution of the Euler equations on Cartesian meshes with embedded boundaries in three dimensions on distributed and shared memory architectures. The approach uses adaptively refined Cartesian hexahedra to fill the computational domain. Where these cells intersect the geometry, they are cut by the boundary into arbitrarily shaped polyhedra which receive special treatment by the solver. The presentation documents a newly developed multilevel upwind solver based on a flexible domain-decomposition strategy. One novel aspect of the work is its use of space-filling curves (SFC) for memory efficient on-the-fly parallelization, dynamic re-partitioning and automatic coarse mesh generation. Within each subdomain the approach employs a variety reordering techniques so that relevant data are on the same page in memory permitting high-performance on cache-based processors. Details of the on-the-fly SFC based partitioning are presented as are construction rules for the automatic coarse mesh generation. After describing the approach, the paper uses model problems and 3- D configurations to both verify and validate the solver. The model problems demonstrate that second-order accuracy is maintained despite the presence of the irregular cut-cells in the mesh. In addition, it examines both parallel efficiency and convergence behavior. These investigations demonstrate a parallel speed-up in excess of 28 on 32 processors of an SGI Origin 2000 system and confirm that mesh partitioning has no effect on convergence behavior.
Fast laser systems for measuring the geometry of complex-shaped objects
Galiulin, Ravil M.; Galiulin, Rishat M.; Bakirov, J. M.; Vorontsov, A. V.; Ponomarenko, I. V.
1999-01-01
The technical characteristics, advantages and applications of an automated optoelectronic measuring system designed by 'Optel' company, State Aviation University of Ufa, are presented in this paper. The measuring apparatus can be applied for industrial development and research, for example, in rapid prototyping, and for obtaining geometrical parameters in medicine and criminalistics. It essentially is a non-contact and rapid scanning system, allowing measurements of complex shaped objects like metal and plastic workpieces or parts of human body.
Sainath, Kamalesh; Teixeira, Fernando; Donderici, Burkay
2013-01-01
We propose the complex-plane generalization of a powerful algebraic sequence acceleration algorithm, the Method of Weighted Averages (MWA), to guarantee exponential-cum-algebraic convergence of Fourier and Fourier-Hankel (F-H) integral transforms. This "complex-plane" MWA, effected via a linear-path detour in the complex plane, results in rapid, absolute convergence of field/potential solutions in multi-layered environments regardless of the source-observer geometry and anisotropy/loss of the...
Geant4-DNA simulations using complex DNA geometries generated by the DnaFabric tool
Meylan, S.; Vimont, U.; Incerti, S.; Clairand, I.; Villagrasa, C.
2016-07-01
Several DNA representations are used to study radio-induced complex DNA damages depending on the approach and the required level of granularity. Among all approaches, the mechanistic one requires the most resolved DNA models that can go down to atomistic DNA descriptions. The complexity of such DNA models make them hard to modify and adapt in order to take into account different biological conditions. The DnaFabric project was started to provide a tool to generate, visualise and modify such complex DNA models. In the current version of DnaFabric, the models can be exported to the Geant4 code to be used as targets in the Monte Carlo simulation. In this work, the project was used to generate two DNA fibre models corresponding to two DNA compaction levels representing the hetero and the euchromatin. The fibres were imported in a Geant4 application where computations were performed to estimate the influence of the DNA compaction on the amount of calculated DNA damage. The relative difference of the DNA damage computed in the two fibres for the same number of projectiles was found to be constant and equal to 1.3 for the considered primary particles (protons from 300 keV to 50 MeV). However, if only the tracks hitting the DNA target are taken into account, then the relative difference is more important for low energies and decreases to reach zero around 10 MeV. The computations were performed with models that contain up to 18,000 DNA nucleotide pairs. Nevertheless, DnaFabric will be extended to manipulate multi-scale models that go from the molecular to the cellular levels.
Bailey, B.; Stoll, R., II; Miller, N. E.; Pardyjak, E.; Mahaffee, W.
2014-12-01
Plants cover the majority of Earth's land surface, and thus play a critical role in the surface energy balance. Within individual plant communities, the leaf energy balance is a fundamental component of most biophysical processes. Absorbed radiation drives the energy balance and provides the means by which plants produce food. Available energy is partitioned into sensible and latent heat fluxes to determine surface temperature, which strongly influences rates of metabolic activity and growth. The energy balance of an individual leaf is coupled with other leaves in the community through longwave radiation emission and advection through the air. This complex coupling can make scaling models from leaves to whole-canopies difficult, specifically in canopies with complex, heterogeneous geometries. We present a new three-dimensional canopy model that simultaneously resolves sub-tree to whole-canopy scales. The model provides spatially explicit predictions of net radiation exchange, boundary-layer and stomatal conductances, evapotranspiration rates, and ultimately leaf surface temperature. The radiation model includes complex physics such as anisotropic emission and scattering. Radiation calculations are accelerated by leveraging graphics processing unit (GPU) technology, which allows canopy-scale problems to be performed on a standard desktop workstation. Since validating the three-dimensional distribution of leaf temperature can be extremely challenging, we used several independent measurement techniques to quantify errors in measured and modeled values. When compared with measured leaf temperatures, the model gave a mean error of about 2°C, which was close to the estimated measurement uncertainty.
An Embedded Ghost-Fluid Method for Compressible Flow in Complex Geometry
Almarouf, Mohamad Abdulilah Alhusain Alali
2016-06-03
We present an embedded ghost-fluid method for numerical solutions of the compressible Navier Stokes (CNS) equations in arbitrary complex domains. The PDE multidimensional extrapolation approach of Aslam [1] is used to reconstruct the solution in the ghost-fluid regions and impose boundary conditions at the fluid-solid interface. The CNS equations are numerically solved by the second order multidimensional upwind method of Colella [2] and Saltzman [3]. Block-structured adaptive mesh refinement implemented under the Chombo framework is utilized to reduce the computational cost while keeping high-resolution mesh around the embedded boundary and regions of high gradient solutions. Numerical examples with different Reynolds numbers for low and high Mach number flow will be presented. We compare our simulation results with other reported experimental and computational results. The significance and advantages of our implementation, which revolve around balancing between the solution accuracy and implementation difficulties, are briefly discussed as well. © 2016 Trans Tech Publications.
Peaks, plateaus, canyons, and craters: The complex geometry of simple mid-domain effect models
DEFF Research Database (Denmark)
Colwell, Robert K.; Gotelli, Nicholas J.; Rahbek, Carsten
2009-01-01
dye algorithm to place assemblages of species of uniform We used a spreading dye algorithm to place assemblages of species of uniform range size in one-dimensional or two-dimensional bounded domains. In some models, we allowed dispersal to introduce range discontinuity. Results: As uniform range size...... increases from small to medium, a flat pattern of species As uniform range size increases from small to medium, a flat pattern of species richness is replaced by a pair of peripheral peaks, separated by a valley (one-dimensional models), or by a cratered ring (two-dimensional models) of species richness...... of a uniform size generate more complex patterns, including peaks, plateaus, canyons, and craters of species richness....
Numerical simulation of the neutrally stratified ABL flow over complex geometry
Beneš, L.; Bodnár, T.; Kozel, K.
2012-12-01
The paper deals with a mathematical and numerical study of the Atmospheric Boundary Layer (ABL) flow over a complex topography represented either by part of the Giant mountains or by a surface brown coal mine and a coal depot, both located in the North Bohemia. Various types of protective obstacles have been tested and compared, mainly with respect to the reduction of dustiness in the latter case. The mathematical model is based on system of Reynolds Averaged Navier-Stokes (RANS) equations for viscous and incompressible flow. The artificial compressibility method was used. The numerical method is based either on the finite-volume explicit scheme or on a semi-implicit finite-difference scheme. A simple algebraic turbulence model is applied to close the governing system of equations. Moreover, an additional transport equation for a passive pollutant has been considered.
Wing geometry as a tool for studying the Lutzomyia longipalpis (Diptera: Psychodidae complex
Directory of Open Access Journals (Sweden)
J De la Riva
2001-11-01
Full Text Available Toro Toro (T and Yungas (Y have been described as genetically well differentiated populations of the Lutzomyia longipalpis (Lutz & Neiva, 1912 complex in Bolivia. Here we use geometric morphometrics to compare samples from these populations and new populations (Bolivia and Nicaragua, representing distant geographical origins, qualitative morphological variation ("one-spot" or "two-spots" phenotypes, ecologically distinct traits (peridomestic and silvatic populations, and possibly different epidemiological roles (transmitting or nor transmitting Leishmania chagasi. The Nicaragua (N (Somotillo sample was "one-spot" phenotype and a possible peridomestic vector. The Bolivian sample of the Y was also "one-spot" phenotype and a demonstrated peridomestic vector of visceral leishmaniasis (VL. The three remaining samples were silvatic, "two-spots" phenotypes. Two of them (Uyuni and T were collected in the highlands of Bolivian where VL never has been reported. The last one (Robore, R came from the lowlands of Bolivia, where human cases of VL are sporadically reported. The decomposition of metric variation into size and shape by geometric morphometric techniques suggests the existence of two groups (N/Y/R, and U/T. Several arguments indicate that such subdivision of Lu. longipalpis could correspond to different evolutionary units.
DEFF Research Database (Denmark)
Jiménez, Roberto; Torralba, Marta; Yagüe-Fabra, José A.
2017-01-01
The dimensional verification of miniaturized components with 3D complex geometries is particularly challenging. Computed Tomography (CT) can represent a suitable alternative solution to micro metrology tools based on optical and tactile techniques. However, the establishment of CT systems......’ traceability when measuring 3D complex geometries is still an open issue. In this work, an alternative method for the measurement uncertainty assessment of 3D complex geometries by using CT is presented. The method is based on the micro-CT system Maximum Permissible Error (MPE) estimation, determined...... experimentally by using several calibrated reference artefacts. The main advantage of the presented method is that a previous calibration of the component by a more accurate Coordinate Measuring System (CMS) is not needed. In fact, such CMS would still hold all the typical limitations of optical and tactile...
Patel, Anita; Pulugundla, Gautam; Smolentsev, Sergey; Abdou, Mohamed; Bhattacharyay, Rajendraprasad
2018-04-01
Following the magnetohydrodynamic (MHD) code validation and verification proposal by Smolentsev et al. (Fusion Eng Des 100:65-72, 2015), we perform code to code and code to experiment comparisons between two computational solvers, FLUIDYN and HIMAG, which are presently considered as two of the prospective CFD tools for fusion blanket applications. In such applications, an electrically conducting breeder/coolant circulates in the blanket ducts in the presence of a strong plasma-confining magnetic field at high Hartmann numbers, it{Ha} (it{Ha}^2 is the ratio between electromagnetic and viscous forces) and high interaction parameters, it{N} (it{N} is the ratio of electromagnetic to inertial forces). The main objective of this paper is to provide the scientific and engineering community with common references to assist fusion researchers in the selection of adequate computational means to be used for blanket design and analysis. As an initial validation case, the two codes are applied to the classic problem of a laminar fully developed MHD flows in a rectangular duct. Both codes demonstrate a very good agreement with the analytical solution for it{Ha} up to 15, 000. To address the capabilities of the two codes to properly resolve complex geometry flows, we consider a case of three-dimensional developing MHD flow in a geometry comprising of a series of interconnected electrically conducting rectangular ducts. The computed electric potential distributions for two flows (Case A) it{Ha}=515, it{N}=3.2 and (Case B) it{Ha}=2059, it{N}=63.8 are in very good agreement with the experimental data, while the comparisons for the MHD pressure drop are still unsatisfactory. To better interpret the observed differences, the obtained numerical data are analyzed against earlier theoretical and experimental studies for flows that involve changes in the relative orientation between the flow and the magnetic field.
International Nuclear Information System (INIS)
Reynolds, J. M.; Lopez-Bruna, D.
2009-01-01
This report is the first of a series dedicated to the numerical calculation of the evolution of fusion plasmas in general toroidal geometry, including TJ-II plasmas. A kinetic treatment has been chosen: the evolution equation of the distribution function of one or several plasma species is solved in guiding center coordinates. The distribution function is written as a Maxwellian one modulated by polynomial series in the kinetic coordinates with no other approximations than those of the guiding center itself and the computation capabilities. The code allows also for the inclusion of the three-dimensional electrostatic potential in a self-consistent manner, but the initial objective has been set to solving only the neoclassical transport. A high order conservative method (Spectral Difference Method) has been chosen in order to discretized the equation for its numerical solution. In this first report, in addition to justifying the work, the evolution equation and its approximations are described, as well as the baseline of the numerical procedures. (Author) 28 refs
Berends, Hans-Martin; Manke, Anne-Marie; Näther, Christian; Tuczek, Felix; Kurz, Philipp
2012-05-28
In this work the synthesis of the novel manganese complex [Mn(2)(III,III)(tpdm)(2)(μ-O)(μ-OAc)(2)](2+) (1) is reported, containing two manganese centres ligated to the unusual, facially coordinating, all-pyridine ligand tpdm (tris(2-pyridyl)methane). The geometric and electronic properties of complex 1 were characterised by X-ray crystallography, vibrational (IR and Raman) and optical spectroscopy (UV/Vis and MCD). Cyclic voltammograms of 1 showed a quasi-reversible oxidation event at 950 mV and an irreversible reduction wave at -250 mV vs. Ag/Ag(+). The redox behaviour of the compound was investigated in detail by UV/Vis- and X-band EPR-spectroelectrochemistry. Both electrochemical (+1200 mV) and chemical (tBuOOH) oxidations transform 1 into the singly oxidized di-μ-oxido species [Mn(2)(III,IV)(tpdm)(2)(μ-O)(2)(μ-OAc)](2+). Further electrochemical oxidation at the same potential results in the removal of a second electron to obtain a Mn(2)(IV,IV)-species. The ability of compound 1 to evolve O(2) was studied using different reaction agents. While reactions with both hydrogen peroxide and peroxomonosulfate yield O(2), homogeneous water-oxidation using Ce(IV) was not observed. Nevertheless, the oxidation reactions of 1 are very interesting model processes for oxidation state (S-state) transitions of the natural manganese water-oxidation catalyst in photosynthesis. However, despite its favourable coordination geometry and multielectron redox chemistry, complex 1 fails to be a catalytically active model for natural water-oxidation.
SAM-CE, Time-Dependent 3-D Neutron Transport, Gamma Transport in Complex Geometry by Monte-Carlo
International Nuclear Information System (INIS)
2003-01-01
1 - Nature of physical problem solved: The SAM-CE system comprises two Monte Carlo codes, SAM-F and SAM-A. SAM-F supersedes the forward Monte Carlo code, SAM-C. SAM-A is an adjoint Monte Carlo code designed to calculate the response due to fields of primary and secondary gamma radiation. The SAM-CE system is a FORTRAN Monte Carlo computer code designed to solve the time-dependent neutron and gamma-ray transport equations in complex three-dimensional geometries. SAM-CE is applicable for forward neutron calculations and for forward as well as adjoint primary gamma-ray calculations. In addition, SAM-CE is applicable for the gamma-ray stage of the coupled neutron-secondary gamma ray problem, which may be solved in either the forward or the adjoint mode. Time-dependent fluxes, and flux functionals such as dose, heating, count rates, etc., are calculated as functions of energy, time and position. Multiple scoring regions are permitted and these may be either finite volume regions or point detectors or both. Other scores of interest, e.g., collision and absorption densities, etc., are also made. 2 - Method of solution: A special feature of SAM-CE is its use of the 'combinatorial geometry' technique which affords the user geometric capabilities exceeding those available with other commonly used geometric packages. All nuclear interaction cross section data (derived from the ENDF for neutrons and from the UNC-format library for gamma-rays) are tabulated in point energy meshes. The energy meshes for neutrons are internally derived, based on built-in convergence criteria and user- supplied tolerances. Tabulated neutron data for each distinct nuclide are in unique and appropriate energy meshes. Both resolved and unresolved resonance parameters from ENDF data files are treated automatically, and extremely precise and detailed descriptions of cross section behaviour is permitted. Such treatment avoids the ambiguities usually associated with multi-group codes, which use flux
International Nuclear Information System (INIS)
Chatillon, S.
2000-01-01
This work is devoted to the enhancement of the ultrasonic non destructive testing in contact of nuclear components with complex geometry. In service inspections of such components performed with conventional probes present limited performances: variations in sensitivity, due to unmatched contact, incorrect characterization of the defect, because of the disorientations of the transducer during its displacement, and uncovered scan area when the geometry of the components disturbs the displacement of the transducer. We propose a new concept of smart transducer to improve the performances of such inspections. The radiating surface is flexible to optimize the sensitivity of the testing. Using the measure of the radiating surface distortion, performed by a specific instrumentation, phased array techniques allow the control of the transmitted beam to optimize the defect localization and characterization. Thus, this system is self-contained. We present the different steps involved to develop this system and its experimental validation. A computing model is extended to predict the field transmitted by a flexible contact transducer. This model is used to optimize the radiating surface of a jointed transducer. A delay law optimizing algorithm is developed to ensure the control of the transmitted beam. At last, a method and the associated instrumentation designed to measure the radiating surface distortion are proposed. Experimental Measures in the through-transmission mode validate the ability of this system to control the field transmitted through complex interfaces. At last, inspections in the pulse-echo mode are performed on a specimen with an irregular profile, representative of a real component inspected on site, and artificial embedded reflectors. Two control configurations are used. In the first one, the transducer is displaced along the surface, in the second one, the transducer is fixed and the region of interest is scanned using beam steering. The results show that
Generalized Optical Theorem Detection in Random and Complex Media
Tu, Jing
The problem of detecting changes of a medium or environment based on active, transmit-plus-receive wave sensor data is at the heart of many important applications including radar, surveillance, remote sensing, nondestructive testing, and cancer detection. This is a challenging problem because both the change or target and the surrounding background medium are in general unknown and can be quite complex. This Ph.D. dissertation presents a new wave physics-based approach for the detection of targets or changes in rather arbitrary backgrounds. The proposed methodology is rooted on a fundamental result of wave theory called the optical theorem, which gives real physical energy meaning to the statistics used for detection. This dissertation is composed of two main parts. The first part significantly expands the theory and understanding of the optical theorem for arbitrary probing fields and arbitrary media including nonreciprocal media, active media, as well as time-varying and nonlinear scatterers. The proposed formalism addresses both scalar and full vector electromagnetic fields. The second contribution of this dissertation is the application of the optical theorem to change detection with particular emphasis on random, complex, and active media, including single frequency probing fields and broadband probing fields. The first part of this work focuses on the generalization of the existing theoretical repertoire and interpretation of the scalar and electromagnetic optical theorem. Several fundamental generalizations of the optical theorem are developed. A new theory is developed for the optical theorem for scalar fields in nonhomogeneous media which can be bounded or unbounded. The bounded media context is essential for applications such as intrusion detection and surveillance in enclosed environments such as indoor facilities, caves, tunnels, as well as for nondestructive testing and communication systems based on wave-guiding structures. The developed scalar
Complex Environmental Data Modelling Using Adaptive General Regression Neural Networks
Kanevski, Mikhail
2015-04-01
The research deals with an adaptation and application of Adaptive General Regression Neural Networks (GRNN) to high dimensional environmental data. GRNN [1,2,3] are efficient modelling tools both for spatial and temporal data and are based on nonparametric kernel methods closely related to classical Nadaraya-Watson estimator. Adaptive GRNN, using anisotropic kernels, can be also applied for features selection tasks when working with high dimensional data [1,3]. In the present research Adaptive GRNN are used to study geospatial data predictability and relevant feature selection using both simulated and real data case studies. The original raw data were either three dimensional monthly precipitation data or monthly wind speeds embedded into 13 dimensional space constructed by geographical coordinates and geo-features calculated from digital elevation model. GRNN were applied in two different ways: 1) adaptive GRNN with the resulting list of features ordered according to their relevancy; and 2) adaptive GRNN applied to evaluate all possible models N [in case of wind fields N=(2^13 -1)=8191] and rank them according to the cross-validation error. In both cases training were carried out applying leave-one-out procedure. An important result of the study is that the set of the most relevant features depends on the month (strong seasonal effect) and year. The predictabilities of precipitation and wind field patterns, estimated using the cross-validation and testing errors of raw and shuffled data, were studied in detail. The results of both approaches were qualitatively and quantitatively compared. In conclusion, Adaptive GRNN with their ability to select features and efficient modelling of complex high dimensional data can be widely used in automatic/on-line mapping and as an integrated part of environmental decision support systems. 1. Kanevski M., Pozdnoukhov A., Timonin V. Machine Learning for Spatial Environmental Data. Theory, applications and software. EPFL Press
International Nuclear Information System (INIS)
Strominger, A.
1990-01-01
A special manifold is an allowed target manifold for the vector multiplets of D=4, N=2 supergravity. These manifolds are of interest for string theory because the moduli spaces of Calabi-Yau threefolds and c=9, (2,2) conformal field theories are special. Previous work has given a local, coordinate-dependent characterization of special geometry. A global description of special geometries is given herein, and their properties are studied. A special manifold M of complex dimension n is characterized by the existence of a holomorphic Sp(2n+2,R)xGL(1,C) vector bundle over M with a nowhere-vanishing holomorphic section Ω. The Kaehler potential on M is the logarithm of the Sp(2n+2,R) invariant norm of Ω. (orig.)
Condensation in complex geometries
International Nuclear Information System (INIS)
Lauro, F.
1975-01-01
A mathematical evaluation of the condensation exchange coefficient can only succeds for well specified cases: small upright or inclined plates, horizontal tubes, small height vertical tubes. Among the main hypotheses accounted for this mathematical development in the case of the condensate, a laminar flow and uniform surface temperature are always considered. In practice certain shapes of surfaces significantly increase the heat transfer during the vapor condensation on a surface wet by the condensate. Such surfaces are rough surfaces such as the condensate is submitted to surface tension effects, negligeable for plane or large curvature surfaces, and the nature of the material may play an important role (temperature gradients). Results from tests on tubes with special shapes, performed in France or out of France, are given [fr
Energy Technology Data Exchange (ETDEWEB)
Chien-Chih Liu, James [Univ. of California, Berkeley, CA (United States)
1993-01-01
The work presented here investigates the phenomenon of shock wave propagation in gas continuous, two-phase media. The motivation for this work stems from the need to understand blast venting consequences in the HYLIFE inertial confinement fusion (ICF) reactor. The HYLIFE concept utilizes lasers or heavy ion beams to rapidly heat and compress D-T targets injected into the center of a reactor chamber. A segmented blanket of falling molten lithium or Li_{2}BeF_{4} (Flibe) jets encircles the reactor`s central cavity, shielding the reactor structure from radiation damage, absorbing the fusion energy, and breeding more tritium fuel. X-rays from the fusion microexplosion will ablate a thin layer of blanket material from the surfaces which face toward the fusion site. This generates a highly energetic vapor, which mostly coalesces in the central cavity. The blast expansion from the central cavity generates a shock which propagates through the segmented blanket - a complex geometry, gas-continuous two-phase medium. The impulse that the blast gives to the liquid as it vents past, the gas shock on the chamber wall, and ultimately the liquid impact on the wall are all important quantities to the HYLIFE structural designers.
Petersen, Peter
2016-01-01
Intended for a one year course, this text serves as a single source, introducing readers to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few Works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory. The book will appeal to a readership that have a basic knowledge of standard manifold theory, including tensors, forms, and Lie groups. Important revisions to the third edition include: a substantial addition of unique and enriching exercises scattered throughout the text; inclusion of an increased number of coordinate calculations of connection and curvature; addition of general formulas for curvature on Lie Groups and submersions; integration of variational calculus into the text allowing for an early treatment of the Sphere theorem using a proof by Berger; incorporation of several recent results about manifolds with posit...
Bergmann, Ryan
general 3D geometries on GPUs, but compared to production codes like Serpent and MCNP, WARP has limited capabilities. Despite WARP's lack of features, its novel algorithm implementations show that high performance can be achieved on a GPU despite the inherently divergent program flow and sparse data access patterns. WARP is not ready for everyday nuclear reactor calculations, but is a good platform for further development of GPU-accelerated Monte Carlo neutron transport. In it's current state, it may be a useful tool for multiplication factor searches, i.e. determining reactivity coefficients by perturbing material densities or temperatures, since these types of calculations typically do not require many flux tallies. (Abstract shortened by UMI.)
Energy Technology Data Exchange (ETDEWEB)
Eigestad, Geir Terje
2003-04-01
The thesis is divided into two main parts. Part I gives an overview and summary of the theory that lies behind the flow equations and the discretization principles used in the work. Part II is a collection of research papers that have been written by the candidate (in collaboration with others). The main objective of this thesis is the discretization of an elliptic PDE which describes the pressure in a porous medium. The porous medium will in general be described by permeability tensors which are heterogeneous and anisotropic. In addition, the geometry is often complex for practical applications. This requires discretization approaches that are suited for the problems in mind. The discretization approaches used here are based on imposed flux and potential continuity, and will be discussed in detail in Chapter 3 of Part I. These methods are called Multi Point Flux Approximation Methods, and the acronym MPFA will be used for them. Issues related to these methods will be the main issue of this thesis. The rest of this thesis is organised as follows: Part I: Chapter 1 gives a brief overview of the physics and mathematics behind reservoir simulation. The standard mass balance equations are presented, and we try to explain what reservoir simulation is. Some standard discretization s methods are briefly discussed in Chapter 2. The main focus in Part I is on the MPFA discretization approach for various geometries, and is given in Chapter 3. Some details may have been left out in the papers of Part II, and the section serves both as a summary of the discretization method(s), as well as a more detailed description than what is found in the papers. In Chapter 4, extensions to handle time dependent and nonlinear problems are discussed. Some of the numerical examples presented in Part II deal with two phase flow, and are based on the extension given in this chapter. Chapter 5 discusses numerical results that have been obtained for the MPFA methods for elliptic problems, and
Directory of Open Access Journals (Sweden)
Виктор Семенович Корнилов
2013-12-01
Full Text Available In article methodical aspects, components of fundamental training of students of physical and mathematical specialties of higher educational institutions of fractal geometry are discussed. The attention to use in the course of such training of means of informatization is paid.
Delcey, Mickaël G; Freitag, Leon; Pedersen, Thomas Bondo; Aquilante, Francesco; Lindh, Roland; González, Leticia
2014-05-07
We present a formulation of analytical energy gradients at the complete active space self-consistent field (CASSCF) level of theory employing density fitting (DF) techniques to enable efficient geometry optimizations of large systems. As an example, the ground and lowest triplet state geometries of a ruthenium nitrosyl complex are computed at the DF-CASSCF level of theory and compared with structures obtained from density functional theory (DFT) using the B3LYP, BP86, and M06L functionals. The average deviation of all bond lengths compared to the crystal structure is 0.042 Å at the DF-CASSCF level of theory, which is slightly larger but still comparable with the deviations obtained by the tested DFT functionals, e.g., 0.032 Å with M06L. Specifically, the root-mean-square deviation between the DF-CASSCF and best DFT coordinates, delivered by BP86, is only 0.08 Å for S0 and 0.11 Å for T1, indicating that the geometries are very similar. While keeping the mean energy gradient errors below 0.25%, the DF technique results in a 13-fold speedup compared to the conventional CASSCF geometry optimization algorithm. Additionally, we assess the singlet-triplet energy vertical and adiabatic differences with multiconfigurational second-order perturbation theory (CASPT2) using the DF-CASSCF and DFT optimized geometries. It is found that the vertical CASPT2 energies are relatively similar regardless of the geometry employed whereas the adiabatic singlet-triplet gaps are more sensitive to the chosen triplet geometry.
Supersymmetric Sigma Model Geometry
Directory of Open Access Journals (Sweden)
Ulf Lindström
2012-08-01
Full Text Available This is a review of how sigma models formulated in Superspace have become important tools for understanding geometry. Topics included are: The (hyperkähler reduction; projective superspace; the generalized Legendre construction; generalized Kähler geometry and constructions of hyperkähler metrics on Hermitian symmetric spaces.
Jana, Subrata; Santra, Ramesh Chandra; Das, Saurabh; Chattopadhyay, Shouvik
2014-09-01
Two new copper(II) complexes, [Cu(L)(OCN)] (1) and [CuL(dca)]n (2), where HL = 2-(-(2-(diethylamino)ethylimino)methyl)naphthalen-1-ol, dca = N(CN)2-, have been synthesized and characterized by elemental analysis, IR, UV-VIS spectroscopy and single crystal X-ray diffraction studies. Complex 1 has square planar and complex 2 square pyramidal geometries in solid state around metal centre. Interactions of the complexes with calf thymus DNA (CT DNA) were studied by UV-VIS spectroscopy. Binding constant and site size of interaction were determined. Binding site size and intrinsic binding constant K revealed complex 1 interacted with calf thymus DNA better than complex 2.
Drozda, Tomasz G.; Quinlan, Jesse R.; Pisciuneri, Patrick H.; Yilmaz, S. Levent
2012-01-01
Significant progress has been made in the development of subgrid scale (SGS) closures based on a filtered density function (FDF) for large eddy simulations (LES) of turbulent reacting flows. The FDF is the counterpart of the probability density function (PDF) method, which has proven effective in Reynolds averaged simulations (RAS). However, while systematic progress is being made advancing the FDF models for relatively simple flows and lab-scale flames, the application of these methods in complex geometries and high speed, wall-bounded flows with shocks remains a challenge. The key difficulties are the significant computational cost associated with solving the FDF transport equation and numerically stiff finite rate chemistry. For LES/FDF methods to make a more significant impact in practical applications a pragmatic approach must be taken that significantly reduces the computational cost while maintaining high modeling fidelity. An example of one such ongoing effort is at the NASA Langley Research Center, where the first generation FDF models, namely the scalar filtered mass density function (SFMDF) are being implemented into VULCAN, a production-quality RAS and LES solver widely used for design of high speed propulsion flowpaths. This effort leverages internal and external collaborations to reduce the overall computational cost of high fidelity simulations in VULCAN by: implementing high order methods that allow reduction in the total number of computational cells without loss in accuracy; implementing first generation of high fidelity scalar PDF/FDF models applicable to high-speed compressible flows; coupling RAS/PDF and LES/FDF into a hybrid framework to efficiently and accurately model the effects of combustion in the vicinity of the walls; developing efficient Lagrangian particle tracking algorithms to support robust solutions of the FDF equations for high speed flows; and utilizing finite rate chemistry parametrization, such as flamelet models, to reduce
Energy Technology Data Exchange (ETDEWEB)
Arnaud, F.X. [Université Toulouse III-Paul Sabatier, INPT, LAPLACE, F-31062 Toulouse (France); CNRS, LAPLACE, F-31062 Toulouse (France); Paillas, S. [IRCM, Institut de Recherche en Cancérologie de Montpellier, Montpellier F-34298 (France); INSERM, U1194, Montpellier F-34298 (France); Pouget, J.P [IRCM, Institut de Recherche en Cancérologie de Montpellier, Montpellier F-34298 (France); INSERM, U1194, Montpellier F-34298 (France); Université de Montpelllier, F-34090 Montpellier (France); Institut régional du Cancer de Montpellier, F-34298 Montpellier (France); Incerti, S. [Université Bordeaux, CENBG, UMR 5797, F-33170 Gradignan (France); CNRS, IN2P3, CENBG, UMR 5797, F-33170 Gradignan (France); Bardiès, M. [Inserm, UMR1037 CRCT, F-31000 Toulouse (France); Université Toulouse III-Paul Sabatier, UMR1037 CRCT, F-31000 Toulouse (France); Bordage, M.C., E-mail: marie-claude.bordage@inserm.fr [Université Toulouse III-Paul Sabatier, INPT, LAPLACE, F-31062 Toulouse (France); CNRS, LAPLACE, F-31062 Toulouse (France); Inserm, UMR1037 CRCT, F-31000 Toulouse (France); Université Toulouse III-Paul Sabatier, UMR1037 CRCT, F-31000 Toulouse (France)
2016-01-01
In cellular dosimetry, common assumptions consider concentric spheres for nucleus and cell and uniform radionuclides distribution. These approximations do not reflect reality, specially in the situation of radioimmunotherapy with Auger emitters, where very short-ranged electrons induce hyper localised energy deposition. A realistic cellular dosimetric model was generated to give account of the real geometry and activity distribution, for non-internalizing and internalizing antibodies (mAbs) labelled with Auger emitter I-125. The impact of geometry was studied by comparing the real geometry obtained from confocal microscopy for both cell and nucleus with volume equivalent concentric spheres. Non-uniform and uniform source distributions were considered for each mAbs distribution. Comparisons in terms of mean deposited energy per decay, energy deposition spectra and energy-volume histograms were calculated using Geant4. We conclude that realistic models are needed, especially when energy deposition is highly non-homogeneous due to source distribution.
Complex Wedge-Shaped Matrices: A Generalization of Jacobi Matrices
Czech Academy of Sciences Publication Activity Database
Hnětynková, Iveta; Plešinger, M.
2015-01-01
Roč. 487, 15 December (2015), s. 203-219 ISSN 0024-3795 R&D Projects: GA ČR GA13-06684S Keywords : eigenvalues * eigenvector * wedge-shaped matrices * generalized Jacobi matrices * band (or block) Krylov subspace methods Subject RIV: BA - General Mathematics Impact factor: 0.965, year: 2015
DEFF Research Database (Denmark)
Jalaal, M.; Soleimani, Soheil; Domairry, G.
2011-01-01
In this paper the meshless Local Multi Quadrics-based Differential Quadrature (MQ-DQ) method is applied to obtain the electric field distribution for different applicable irregular geometries. This method is the combination of Differential Quadrature approximation of derivatives and function...... approximation of MQ-Radial Basis Function (RBF). Three different geometries with irregular boundaries are considered and the obtained results are compared with those gained by Finite Element (FE) solutions achieved by COMSOL commercial code. Outcomes prove that current technique is in very good agreement...
Fabanich, William A., Jr.
2014-01-01
SpaceClaim/TD Direct has been used extensively in the development of the Advanced Stirling Radioisotope Generator (ASRG) thermal model. This paper outlines the workflow for that aspect of the task and includes proposed best practices and lessons learned. The ASRG thermal model was developed to predict component temperatures and power output and to provide insight into the prime contractor's thermal modeling efforts. The insulation blocks, heat collectors, and cold side adapter flanges (CSAFs) were modeled with this approach. The model was constructed using mostly TD finite difference (FD) surfaces/solids. However, some complex geometry could not be reproduced with TD primitives while maintaining the desired degree of geometric fidelity. Using SpaceClaim permitted the import of original CAD files and enabled the defeaturing/repair of those geometries. TD Direct (a SpaceClaim add-on from CRTech) adds features that allowed the "mark-up" of that geometry. These so-called "mark-ups" control how finite element (FE) meshes are to be generated through the "tagging" of features (e.g. edges, solids, surfaces). These tags represent parameters that include: submodels, material properties, material orienters, optical properties, and radiation analysis groups. TD aliases were used for most tags to allow analysis to be performed with a variety of parameter values. "Domain-tags" were also attached to individual and groups of surfaces and solids to allow them to be used later within TD to populate objects like, for example, heaters and contactors. These tools allow the user to make changes to the geometry in SpaceClaim and then easily synchronize the mesh in TD without having to redefine the objects each time as one would if using TDMesher. The use of SpaceClaim/TD Direct helps simplify the process for importing existing geometries and in the creation of high fidelity FE meshes to represent complex parts. It also saves time and effort in the subsequent analysis.
Fabanich, William
2014-01-01
SpaceClaim/TD Direct has been used extensively in the development of the Advanced Stirling Radioisotope Generator (ASRG) thermal model. This paper outlines the workflow for that aspect of the task and includes proposed best practices and lessons learned. The ASRG thermal model was developed to predict component temperatures and power output and to provide insight into the prime contractors thermal modeling efforts. The insulation blocks, heat collectors, and cold side adapter flanges (CSAFs) were modeled with this approach. The model was constructed using mostly TD finite difference (FD) surfaces solids. However, some complex geometry could not be reproduced with TD primitives while maintaining the desired degree of geometric fidelity. Using SpaceClaim permitted the import of original CAD files and enabled the defeaturing repair of those geometries. TD Direct (a SpaceClaim add-on from CRTech) adds features that allowed the mark-up of that geometry. These so-called mark-ups control how finite element (FE) meshes were generated and allowed the tagging of features (e.g. edges, solids, surfaces). These tags represent parameters that include: submodels, material properties, material orienters, optical properties, and radiation analysis groups. TD aliases were used for most tags to allow analysis to be performed with a variety of parameter values. Domain-tags were also attached to individual and groups of surfaces and solids to allow them to be used later within TD to populate objects like, for example, heaters and contactors. These tools allow the user to make changes to the geometry in SpaceClaim and then easily synchronize the mesh in TD without having to redefine these objects each time as one would if using TD Mesher.The use of SpaceClaim/TD Direct has helped simplify the process for importing existing geometries and in the creation of high fidelity FE meshes to represent complex parts. It has also saved time and effort in the subsequent analysis.
The Generalization Complexity Measure for Continuous Input Data
Directory of Open Access Journals (Sweden)
Iván Gómez
2014-01-01
defined in Boolean space, quantifies the complexity of data in relationship to the prediction accuracy that can be expected when using a supervised classifier like a neural network, SVM, and so forth. We first extend the original measure for its use with continuous functions to later on, using an approach based on the use of the set of Walsh functions, consider the case of having a finite number of data points (inputs/outputs pairs, that is, usually the practical case. Using a set of trigonometric functions a model that gives a relationship between the size of the hidden layer of a neural network and the complexity is constructed. Finally, we demonstrate the application of the introduced complexity measure, by using the generated model, to the problem of estimating an adequate neural network architecture for real-world data sets.
DEFF Research Database (Denmark)
Müller, Stefan; Feliu, Elisenda; Regensburger, Georg
2016-01-01
We give necessary and sufficient conditions in terms of sign vectors for the injectivity of families of polynomials maps with arbitrary real exponents defined on the positive orthant. Our work relates and extends existing injectivity conditions expressed in terms of Jacobian matrices and determin...... and determinants. In the context of chemical reaction networks with power-law kinetics, our results can be used to preclude as well as to guarantee multiple positive steady states. In the context of real algebraic geometry, our results reveal the first ...
Synchronization of general complex networks via adaptive control ...
Indian Academy of Sciences (India)
2014-03-07
Mar 7, 2014 ... networks with derivative coupling and time-delay coupling was investigated by adaptive control schemes [42]. However ... [41], the synchronization of complex dynamical networks with non-derivative coupling and derivative coupling .... For any symmetric positive definite matrix. M ∈ Rn×n and x,y ∈ Rn, ...
Holme, Audun
1988-01-01
This volume presents selected papers resulting from the meeting at Sundance on enumerative algebraic geometry. The papers are original research articles and concentrate on the underlying geometry of the subject.
Some properties of complex matrix-variate generalized Dirichlet ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
Abstract. Dirichlet integrals and the associated Dirichlet statistical densities are widely used in various areas. Generalizations of Dirichlet integrals and Dirichlet models to matrix-variate cases, when the matrices are real symmetric positive definite or hermi- tian positive definite, are available [4]. Real scalar variables case of ...
Some properties of complex matrix-variate generalized Dirichlet ...
Indian Academy of Sciences (India)
Dirichlet integrals and the associated Dirichlet statistical densities are widely used in various areas. Generalizations of Dirichlet integrals and Dirichlet models to matrix-variate cases, when the matrices are real symmetric positive definite or hermitian positive definite, are available [4]. Real scalar variables case of the ...
DEFF Research Database (Denmark)
Obeidat, Anas Hassan MohD
devel-oping a computational method which can deal with complex fluid structure, simulate complex geometers that change topology is particular challenging as the connectivity of the computational domain may change dynamically, and still eÿcient is important. In this thesis we are presenting a remeshed......Turbulence modelling is a key issue in many industrial application, as the com-putational power of direct numerical simulation (DNS) is insuÿcient to deal with complex flow structures with high Reynolds number. Also in Industrial applications often involve turbulent flow in complex geometries. Thus...... a state-of-the art eulerian methods to study the turbulent flow in a model diesel engine. the goals of this study include validation of large eddy simulations (LES) turbulence models....
van den Broek, P.M.
1984-01-01
The aim of this paper is to give a detailed exposition of the relation between the geometry of twistor space and the geometry of Minkowski space. The paper has a didactical purpose; no use has been made of differential geometry and cohomology.
Directory of Open Access Journals (Sweden)
Mónica Andrea Gordillo Varela
2016-09-01
Full Text Available The molecular geometry of (E-4-dimethylamino-N′-[(pyridin-2-ylmethylidene- N]benzohydrazide (C15H16N4O complexed with M2+ (M=Zn, Cu, Ni, Fe, Mn, Ca and Co ions were calculated, using density functional theory (B3LYP with 6-31G(d, p basis set. Vibrational frequencies were computed in order to verify the absence of imaginary vibrational frequencies, fact that confirms the global minimum in geometry optimization. Molecular geometry parameters (bond lengths and angles for Cu2+ and Zn2+ complexes were compared with crystallographic data previously reported, showing good correlation. Binding energies for all complexes were computed at B3LYP/6-31G++(d, p level of theory. These calculations indicate that Cu-L is the lowest favorable complex, Cu2+ corresponds to the smallest cation on the present study. In the other hand, Ca-L, one of the less favorable complex, corresponds to the biggest cation analyzed in the present study. Molecular orbital analysis was carried out showing variations in energy differences between HOMO-LUMO values in function of the metallic ion employed.
DEFF Research Database (Denmark)
Zukowska, Daria; Melikov, Arsen Krikor; Popiolek, Zbigniew
2008-01-01
The impact of thermal plumes generated by human body simulators with different geometry on the airflow pattern in a full scale room with displacement ventilation (supply air temperature 21.6°C, total flow rate 80 L/s) was studied when two seated occupants were simulated first by two thermal...... manikins resembling accurately human body shape and then by two heated cylinders. The manikins and the cylinders had the same surface area of 1.63 m2 and the same heat generation of 73 W. CO2 supplied from the top of the heat sources was used for simulating bio-effluents. CO2 concentration was measured...
Discrete quantum geometries and their effective dimension
International Nuclear Information System (INIS)
Thuerigen, Johannes
2015-01-01
In several approaches towards a quantum theory of gravity, such as group field theory and loop quantum gravity, quantum states and histories of the geometric degrees of freedom turn out to be based on discrete spacetime. The most pressing issue is then how the smooth geometries of general relativity, expressed in terms of suitable geometric observables, arise from such discrete quantum geometries in some semiclassical and continuum limit. In this thesis I tackle the question of suitable observables focusing on the effective dimension of discrete quantum geometries. For this purpose I give a purely combinatorial description of the discrete structures which these geometries have support on. As a side topic, this allows to present an extension of group field theory to cover the combinatorially larger kinematical state space of loop quantum gravity. Moreover, I introduce a discrete calculus for fields on such fundamentally discrete geometries with a particular focus on the Laplacian. This permits to define the effective-dimension observables for quantum geometries. Analysing various classes of quantum geometries, I find as a general result that the spectral dimension is more sensitive to the underlying combinatorial structure than to the details of the additional geometric data thereon. Semiclassical states in loop quantum gravity approximate the classical geometries they are peaking on rather well and there are no indications for stronger quantum effects. On the other hand, in the context of a more general model of states which are superposition over a large number of complexes, based on analytic solutions, there is a flow of the spectral dimension from the topological dimension d on low energy scales to a real number between 0 and d on high energy scales. In the particular case of 1 these results allow to understand the quantum geometry as effectively fractal.
The complex etiology of schizophrenia - general state of the art.
Hosák, Ladislav; Hosakova, Jirina
2015-12-01
The etiology of schizophrenia is complex. The aim of this article is to present a global view of the causes of schizophrenia and their interconnectivity. Recent genetic research into schizophrenia is based on genome-wide association studies, the assessment of DNA copy number variations, and the concept of endophenotypes. A lot of suspected genes have already been identified, mostly relating to neurodevelopment, neuroplasticity, immunology and neuroendocrinology. Gene-environment interactions (G×E) reflect genetic variation in susceptibility to the environment. Psychosocial stress and cannabis abuse seem to be the most important environmental factors in schizophrenia etiology. Epigenetic mechanisms, particularly DNA methylation, histone modifications, and non-coding RNAs are the most important linking factor among the genetic and prenatal environmental variables in the etiology of schizophrenia. Postnatal risk factors (e.g., stress, urbanicity, cannabis use) may also affect the risk of schizophrenia via the potentiation of vulnerable brain pathways. Many questionable issues pertaining to G×E assessment of schizophrenia still persist and relate to the exact assessment of environmental agents as well as psychopathology. In future research concerning G×E in schizophrenia, the study samples should be adequately large, schizophrenia endophenotypes should be involved, prospective studies should be supported, environmental causative factors as well as psychopathology should be assessed in a quantitative way, the multiple interactions among the variety of environmental and genetic variables should be evaluated, and epigenetic factors should not be neglected. The EU-GEI project of the European Network of National Schizophrenia Networks Studying Gene-Environment Interactions (2010-2015) may become a milestone in the schizophrenia G×E research.
Kyriakopoulos, C.; Tarnowski, J. M.; Oglesby, D. D.
2016-12-01
We use 3D dynamic finite element models to investigate potential rupture paths of earthquakes propagating along faults in the western San Gorgonio Pass (SGP) region. The SGP is a structurally complex region along the San Andreas fault system (SAF) in southern California. We focus on the San Bernardino strand of the SAF, the San Gorgonio Pass Fault Zone, and a portion of the Garnet Hill strand of the SAF. The San Bernardino and Garnet Hill strands are predominately right-lateral strike-slip faults. Thrust faults dominate the San Gorgonio Pass Fault Zone, with small right-lateral tear faults between the thrust faults. We use the finite element code FaultMod (Barall, 2009) to observe differences in rupture propagation along a meshed fault geometry that reflects most of the surface trace complexity. We test three different types of pre-stress assumptions: 1) constant tractions, 2) regional stress regimes, and 3) long-term stressing rates from quasi-static crustal deformation modeling. Models with constant tractions assume pure right-lateral strike-slip motion on the San Bernardino and Garnet Hill strands and oblique thrust/right-lateral strike-slip motion on the San Gorgonio Pass Fault Zone. Preliminary results from models with constant tractions suggest that the complexity of the fault geometry may inhibit rupture propagation, depending on nucleation location.
International Nuclear Information System (INIS)
Xu Yuhua; Zhou Wuneng; Fang Jian'an; Lu Hongqian
2009-01-01
This Letter proposes an approach to identify the topological structure and unknown parameters for uncertain general complex networks simultaneously. By designing effective adaptive controllers, we achieve synchronization between two complex networks. The unknown network topological structure and system parameters of uncertain general complex dynamical networks are identified simultaneously in the process of synchronization. Several useful criteria for synchronization are given. Finally, an illustrative example is presented to demonstrate the application of the theoretical results.
Energy Technology Data Exchange (ETDEWEB)
Xu Yuhua, E-mail: yuhuaxu2004@163.co [College of Information Science and Technology, Donghua University, Shanghai 201620 (China) and Department of Maths, Yunyang Teacher' s College, Hubei 442000 (China); Zhou Wuneng, E-mail: wnzhou@163.co [College of Information Science and Technology, Donghua University, Shanghai 201620 (China); Fang Jian' an [College of Information Science and Technology, Donghua University, Shanghai 201620 (China); Lu Hongqian [Shandong Institute of Light Industry, Shandong Jinan 250353 (China)
2009-12-28
This Letter proposes an approach to identify the topological structure and unknown parameters for uncertain general complex networks simultaneously. By designing effective adaptive controllers, we achieve synchronization between two complex networks. The unknown network topological structure and system parameters of uncertain general complex dynamical networks are identified simultaneously in the process of synchronization. Several useful criteria for synchronization are given. Finally, an illustrative example is presented to demonstrate the application of the theoretical results.
Ronchin, Erika; Masterlark, Timothy; Dawson, John; Saunders, Steve; Martì Molist, Joan
2017-06-01
We test an innovative inversion scheme using Green's functions from an array of pressure sources embedded in finite-element method (FEM) models to image, without assuming an a-priori geometry, the composite and complex shape of a volcano deformation source. We invert interferometric synthetic aperture radar (InSAR) data to estimate the pressurization and shape of the magma reservoir of Rabaul caldera, Papua New Guinea. The results image the extended shallow magmatic system responsible for a broad and long-term subsidence of the caldera between 2007 February and 2010 December. Elastic FEM solutions are integrated into the regularized linear inversion of InSAR data of volcano surface displacements in order to obtain a 3-D image of the source of deformation. The Green's function matrix is constructed from a library of forward line-of-sight displacement solutions for a grid of cubic elementary deformation sources. Each source is sequentially generated by removing the corresponding cubic elements from a common meshed domain and simulating the injection of a fluid mass flux into the cavity, which results in a pressurization and volumetric change of the fluid-filled cavity. The use of a single mesh for the generation of all FEM models avoids the computationally expensive process of non-linear inversion and remeshing a variable geometry domain. Without assuming an a-priori source geometry other than the configuration of the 3-D grid that generates the library of Green's functions, the geodetic data dictate the geometry of the magma reservoir as a 3-D distribution of pressure (or flux of magma) within the source array. The inversion of InSAR data of Rabaul caldera shows a distribution of interconnected sources forming an amorphous, shallow magmatic system elongated under two opposite sides of the caldera. The marginal areas at the sides of the imaged magmatic system are the possible feeding reservoirs of the ongoing Tavurvur volcano eruption of andesitic products on the
International Nuclear Information System (INIS)
Kalligiannaki, Evangelia; Harmandaris, Vagelis; Katsoulakis, Markos A.; Plecháč, Petr
2015-01-01
Using the probabilistic language of conditional expectations, we reformulate the force matching method for coarse-graining of molecular systems as a projection onto spaces of coarse observables. A practical outcome of this probabilistic description is the link of the force matching method with thermodynamic integration. This connection provides a way to systematically construct a local mean force and to optimally approximate the potential of mean force through force matching. We introduce a generalized force matching condition for the local mean force in the sense that allows the approximation of the potential of mean force under both linear and non-linear coarse graining mappings (e.g., reaction coordinates, end-to-end length of chains). Furthermore, we study the equivalence of force matching with relative entropy minimization which we derive for general non-linear coarse graining maps. We present in detail the generalized force matching condition through applications to specific examples in molecular systems
Energy Technology Data Exchange (ETDEWEB)
Kalligiannaki, Evangelia, E-mail: ekalligian@tem.uoc.gr [Department of Mathematics and Applied Mathematics, University of Crete, 70013 Heraklion (Greece); Harmandaris, Vagelis, E-mail: harman@uoc.gr [Department of Mathematics and Applied Mathematics, University of Crete, 70013 Heraklion (Greece); Institute of Applied and Computational Mathematics (IACM), Foundation for Research and Technology Hellas (FORTH), IACM/FORTH, GR-71110 Heraklion (Greece); Katsoulakis, Markos A., E-mail: markos@math.umass.edu [Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003 (United States); Plecháč, Petr, E-mail: plechac@math.udel.edu [Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716 (United States)
2015-08-28
Using the probabilistic language of conditional expectations, we reformulate the force matching method for coarse-graining of molecular systems as a projection onto spaces of coarse observables. A practical outcome of this probabilistic description is the link of the force matching method with thermodynamic integration. This connection provides a way to systematically construct a local mean force and to optimally approximate the potential of mean force through force matching. We introduce a generalized force matching condition for the local mean force in the sense that allows the approximation of the potential of mean force under both linear and non-linear coarse graining mappings (e.g., reaction coordinates, end-to-end length of chains). Furthermore, we study the equivalence of force matching with relative entropy minimization which we derive for general non-linear coarse graining maps. We present in detail the generalized force matching condition through applications to specific examples in molecular systems.
Kalligiannaki, Evangelia; Harmandaris, Vagelis; Katsoulakis, Markos A; Plecháč, Petr
2015-08-28
Using the probabilistic language of conditional expectations, we reformulate the force matching method for coarse-graining of molecular systems as a projection onto spaces of coarse observables. A practical outcome of this probabilistic description is the link of the force matching method with thermodynamic integration. This connection provides a way to systematically construct a local mean force and to optimally approximate the potential of mean force through force matching. We introduce a generalized force matching condition for the local mean force in the sense that allows the approximation of the potential of mean force under both linear and non-linear coarse graining mappings (e.g., reaction coordinates, end-to-end length of chains). Furthermore, we study the equivalence of force matching with relative entropy minimization which we derive for general non-linear coarse graining maps. We present in detail the generalized force matching condition through applications to specific examples in molecular systems.
2010-10-01
... testing; cytology general supervisor. 493.1467 Section 493.1467 Public Health CENTERS FOR MEDICARE....1467 Condition: Laboratories performing high complexity testing; cytology general supervisor. For the subspecialty of cytology, the laboratory must have a general supervisor who meets the qualification...
Selvaraj, Tamilmani; Rajalingam, Renganathan; Balasubramanian, Viswanathan
2018-03-01
A detailed comparative Density Functional Theory (DFT) study is made to understand the structural changes of the guest complex due to steric and electronic interactions with the host framework. In this study, Ru(III) benzimidazole and 2- ethyl Ru(III) benzimidazole complexes encapsulated in a supercage of zeolite Y. The zeolitic framework integrity is not disturbed by the intrusion of the large guest complex. A blue shift in the d-d transition observed in the UV-Visible spectroscopic studies of the zeolite encapsulated complexes and they shows a higher catalytic efficiency. Encapsulation of zeolite matrix makes the metal center more viable to nucleophilic attack and favors the phenol oxidation reaction. Based on the theoretical calculations, transition states and structures of reaction intermediates involved in the catalytic cycles are derived.
Structural Behavioral Study on the General Aviation Network Based on Complex Network
Zhang, Liang; Lu, Na
2017-12-01
The general aviation system is an open and dissipative system with complex structures and behavioral features. This paper has established the system model and network model for general aviation. We have analyzed integral attributes and individual attributes by applying the complex network theory and concluded that the general aviation network has influential enterprise factors and node relations. We have checked whether the network has small world effect, scale-free property and network centrality property which a complex network should have by applying degree distribution of functions and proved that the general aviation network system is a complex network. Therefore, we propose to achieve the evolution process of the general aviation industrial chain to collaborative innovation cluster of advanced-form industries by strengthening network multiplication effect, stimulating innovation performance and spanning the structural hole path.
International Nuclear Information System (INIS)
Altın, İsmail; Bilgin, Atilla
2015-01-01
This study builds on a previous parametric investigation using a thermodynamic-based quasi-dimensional (QD) cycle simulation of a spark-ignition (SI) engine with dual-spark plugs. The previous work examined the effects of plug-number and location on some performance parameters considering an engine with a simple cylindrical disc-shaped combustion chamber. In order to provide QD thermodynamic models applicable to complex combustion chamber geometries, a novel approach is considered here: flame-maps, which utilizes a computer aided design (CAD) software (SolidWorks). Flame maps are produced by the CAD software, which comprise all the possible flame radiuses with an increment of one-mm between them, according to the spark plug positions, spark timing, and piston position near the top dead center. The data are tabulated and stored as matrices. Then, these tabulated data are adapted to the previously reported cycle simulation. After testing for simple disc-shaped chamber geometries, the simulation is applied to a real production automobile (Honda-Fit) engine to perform the parametric study. - Highlights: • QD model was applied in dual plug engine with complex realistic combustion chamber. • This method successfully modeled the combustion in the dual-plug Honda-Fit engine. • The same combustion chamber is tested for various spark plug(s) locations. • The centrally located single spark-plug results in the fastest combustion
Jin, BoCheng
2011-12-01
Organic and inorganic fiber reinforced composites with innumerable fiber orientation distributions and fiber geometries are abundantly available in several natural and synthetic structures. Inorganic glass fiber composites have been introduced to numerous applications due to their economical fabrication and tailored structural properties. Numerical characterization of such composite material systems is necessitated due to their intrinsic statistical nature, which renders extensive experimentation prohibitively time consuming and costly. To predict various mechanical behavior and characterizations of Uni-Directional Fiber Composites (UDFC) and Random Fiber Composites (RaFC), we numerically developed Representative Volume Elements (RVE) with high accuracy and efficiency and with complex fiber geometric representations encountered in uni-directional and random fiber networks. In this thesis, the numerical simulations of unidirectional RaFC fiber strand RVE models (VF>70%) are first presented by programming in ABAQUS PYTHON. Secondly, when the cross sectional aspect ratios (AR) of the second phase fiber inclusions are not necessarily one, various types of RVE models with different cross sectional shape fibers are simulated and discussed. A modified random sequential absorption algorithm is applied to enhance the volume fraction number (VF) of the RVE, which the mechanical properties represents the composite material. Thirdly, based on a Spatial Segment Shortest Distance (SSSD) algorithm, a 3-Dimentional RaFC material RVE model is simulated in ABAQUS PYTHON with randomly oriented and distributed straight fibers of high fiber aspect ratio (AR=100:1) and volume fraction (VF=31.8%). Fourthly, the piecewise multi-segments fiber geometry is obtained in MATLAB environment by a modified SSSD algorithm. Finally, numerical methods including the polynomial curve fitting and piecewise quadratic and cubic B-spline interpolation are applied to optimize the RaFC fiber geometries
Energy Technology Data Exchange (ETDEWEB)
Grotz, Andreas
2011-10-07
In this thesis, a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems is proposed. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry: the spin space, the tangent space endowed with a Lorentzian metric, connection and curvature. In order to get the correspondence to classical differential geometry, we construct examples of causal fermion systems by regularizing Dirac sea configurations in Minkowski space and on a globally hyperbolic Lorentzian manifold. When removing the regularization, the objects of our quantum geometry reduce to the common objects of spin geometry on Lorentzian manifolds, up to higher order curvature corrections.
Pottmann, Helmut
2014-11-26
Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.
Sinnott, Jan D.
This paper discusses the utility of a general systems theory paradigm for psychology. The paradigm can be used for conceptualizing such complex phenomena as change over time in living systems, person-society interactions, and the epistemology of multiply determined changes. Consideration is also given to applications of the approach to…
Caglayan, Gunhan
2016-01-01
This qualitative research, drawing on the theoretical frameworks by Even (1990, 1993) and Sfard (2007), investigated five high school mathematics teachers' geometric interpretations of complex number multiplication along with the roots of unity. The main finding was that mathematics teachers constructed the modulus, the argument, and the conjugate…
Operationalization of biopsychosocial case complexity in general health care : the INTERMED project
de Jonge, P; Huyse, FJ; Slaets, JPJ; Sollner, W; Stiefel, FC
Objective: Lack of operationalization of the biopsychosocial model hinders its effective application to the increasingly prevalent problems of comorbidities in clinical presentations. Here, we describe the INTERMED, an instrument to assess biopsychosocial case complexity in general health care, and
Maor, Eli
2014-01-01
If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by acclaimed math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configur
International Nuclear Information System (INIS)
Hennart, J.P.; Valle, E. del.
1995-01-01
A generalized nodal finite element formalism is presented, which covers virtually all known finit difference approximation to the discrete ordinates equations in slab geometry. This paper (Part 1) presents the theory of the so called open-quotes continuous moment methodsclose quotes, which include such well-known methods as the open-quotes diamond differenceclose quotes and the open-quotes characteristicclose quotes schemes. In a second paper (hereafter referred to as Part II), the authors will present the theory of the open-quotes discontinuous moment methodsclose quotes, consisting in particular of the open-quotes linear discontinuousclose quotes scheme as well as of an entire new class of schemes. Corresponding numerical results are available for all these schemes and will be presented in a third paper (Part III). 12 refs
Traoré, Philippe; Ahipo, Yves Marcel; Louste, Christophe
2009-08-01
In this paper an improved finite volume scheme to discretize diffusive flux on a non-orthogonal mesh is proposed. This approach, based on an iterative technique initially suggested by Khosla [P.K. Khosla, S.G. Rubin, A diagonally dominant second-order accurate implicit scheme, Computers and Fluids 2 (1974) 207-209] and known as deferred correction, has been intensively utilized by Muzaferija [S. Muzaferija, Adaptative finite volume method for flow prediction using unstructured meshes and multigrid approach, Ph.D. Thesis, Imperial College, 1994] and later Fergizer and Peric [J.H. Fergizer, M. Peric, Computational Methods for Fluid Dynamics, Springer, 2002] to deal with the non-orthogonality of the control volumes. Using a more suitable decomposition of the normal gradient, our scheme gives accurate solutions in geometries where the basic idea of Muzaferija fails. First the performances of both schemes are compared for a Poisson problem solved in quadrangular domains where control volumes are increasingly skewed in order to test their robustness and efficiency. It is shown that convergence properties and the accuracy order of the solution are not degraded even on extremely skewed mesh. Next, the very stable behavior of the method is successfully demonstrated on a randomly distorted grid as well as on an anisotropically distorted one. Finally we compare the solution obtained for quadrilateral control volumes to the ones obtained with a finite element code and with an unstructured version of our finite volume code for triangular control volumes. No differences can be observed between the different solutions, which demonstrates the effectiveness of our approach.
Sahraei, Atefeh; Kargar, Hadi; Hakimi, Mohammad; Tahir, Muhammad Nawaz
2017-12-01
A series of zirconium (IV) Schiff-base complexes formulated as [Zr (Lx)2] and [Zr (Lx‧)2] were synthesized by reaction of tetradentate salicylaldimine Schiff-base ligands with [Zr (acac)4] in methanol. These ligands are as follows: H2Lx and H2Lx‧ (x = x‧ = 1,2,3,4). The new complexes have been characterized using FT-IR, lH NMR, 13C{1H} NMR spectroscopic techniques, elemental analyses (CHN) and the crystal structure of Zr (L3)2, Zr (L1‧)2 and Zr (L3‧)2 were determined by X-ray crystallography. The crystal structure analysis revealed that the coordination environment of the metal in all complexes is eight-coordinate occupied by N2O2 sets of the coordinated ligands in distorted square-antiprism geometry. The in vitro biological screening effects of the synthesized compounds were tested against different microbial kinds and the zirconium (IV) complexes exhibit antimicrobial activity.
Lefschetz, Solomon
2005-01-01
An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.
Sturmberg, Joachim P; Martin, Carmel M; Katerndahl, David A
2014-01-01
Over the past 7 decades, theories in the systems and complexity sciences have had a major influence on academic thinking and research. We assessed the impact of complexity science on general practice/family medicine. We performed a historical integrative review using the following systematic search strategy: medical subject heading [humans] combined in turn with the terms complex adaptive systems, nonlinear dynamics, systems biology, and systems theory, limited to general practice/family medicine and published before December 2010. A total of 16,242 articles were retrieved, of which 49 were published in general practice/family medicine journals. Hand searches and snowballing retrieved another 35. After a full-text review, we included 56 articles dealing specifically with systems sciences and general/family practice. General practice/family medicine engaged with the emerging systems and complexity theories in 4 stages. Before 1995, articles tended to explore common phenomenologic general practice/family medicine experiences. Between 1995 and 2000, articles described the complex adaptive nature of this discipline. Those published between 2000 and 2005 focused on describing the system dynamics of medical practice. After 2005, articles increasingly applied the breadth of complex science theories to health care, health care reform, and the future of medicine. This historical review describes the development of general practice/family medicine in relation to complex adaptive systems theories, and shows how systems sciences more accurately reflect the discipline's philosophy and identity. Analysis suggests that general practice/family medicine first embraced systems theories through conscious reorganization of its boundaries and scope, before applying empirical tools. Future research should concentrate on applying nonlinear dynamics and empirical modeling to patient care, and to organizing and developing local practices, engaging in community development, and influencing
Noble, J. H.; Lubasch, M.; Stevens, J.; Jentschura, U. D.
2017-12-01
We describe a matrix diagonalization algorithm for complex symmetric (not Hermitian) matrices, A ̲ =A̲T, which is based on a two-step algorithm involving generalized Householder reflections based on the indefinite inner product 〈 u ̲ , v ̲ 〉 ∗ =∑iuivi. This inner product is linear in both arguments and avoids complex conjugation. The complex symmetric input matrix is transformed to tridiagonal form using generalized Householder transformations (first step). An iterative, generalized QL decomposition of the tridiagonal matrix employing an implicit shift converges toward diagonal form (second step). The QL algorithm employs iterative deflation techniques when a machine-precision zero is encountered "prematurely" on the super-/sub-diagonal. The algorithm allows for a reliable and computationally efficient computation of resonance and antiresonance energies which emerge from complex-scaled Hamiltonians, and for the numerical determination of the real energy eigenvalues of pseudo-Hermitian and PT-symmetric Hamilton matrices. Numerical reference values are provided.
Common Fixed Points of Generalized Cocyclic Mappings in Complex Valued Metric Spaces
Directory of Open Access Journals (Sweden)
Mujahid Abbas
2015-01-01
Full Text Available We present fixed point results of mappings satisfying generalized contractive conditions in complex valued metric spaces. As an application, we obtain a common fixed point of a pair of weakly compatible mappings. Some common fixed point results of generalized contractive-type mappings involved in cocyclic representation of a nonempty subset of a complex valued metric space are also obtained. Some examples are also presented to support the results proved herein. These results extend and generalize many results in the existing literature.
Energy Technology Data Exchange (ETDEWEB)
Hook, D W [Blackett Laboratory, Imperial College of Science Technology and Medicine, University of London, Prince Consort Road, London, SW7 2BW (United Kingdom)
2008-01-11
A geometric framework for quantum mechanics arose during the mid 1970s when authors such as Cantoni explored the notion of generalized transition probabilities, and Kibble promoted the idea that the space of pure quantum states provides a natural quantum mechanical analogue for classical phase space. This central idea can be seen easily since the projection of Schroedinger's equation from a Hilbert space into the space of pure spaces is a set of Hamilton's equations. Over the intervening years considerable work has been carried out by a variety of authors and a mature description of quantum mechanics in geometric terms has emerged with many applications. This current offering would seem ideally placed to review the last thirty years of progress and relate this to the most recent work in quantum entanglement. Bengtsson and Zyczkowski's beautifully illustrated volume, Geometry of Quantum States (referred to as GQS from now on) attempts to cover considerable ground in its 466 pages. Its topics range from colour theory in Chapter 1 to quantum entanglement in Chapter 15-to say that this is a whirlwind tour is, perhaps, no understatement. The use of the work 'introduction' in the subtitle of GQS, might suggest to the reader that this work be viewed as a textbook and I think that this interpretation would be incorrect. The authors have chosen to present a survey of different topics with the specific aim to introduce entanglement in geometric terms-the book is not intended as a pedagogical introduction to the geometric approach to quantum mechanics. Each of the fifteen chapters is a short, and mostly self-contained, essay on a particular aspect or application of geometry in the context of quantum mechanics with entanglement being addressed specifically in the final chapter. The chapters fall into three classifications: those concerned with the mathematical background, those which discuss quantum theory and the foundational aspects of the geometric
The existence of generalized synchronization of chaotic systems in complex networks.
Hu, Aihua; Xu, Zhenyuan; Guo, Liuxiao
2010-03-01
The paper studies the existence of generalized synchronization in complex networks, which consist of chaotic systems. When a part of modified nodes are chaotic, and the others have asymptotically stable equilibriums or orbital asymptotically stable periodic solutions, under certain conditions, the existence of generalized synchronization can be turned to the problem of contractive fixed point in the family of Lipschitz functions. In addition, theoretical proofs are proposed to the exponential attractive property of generalized synchronization manifold. Numerical simulations validate the theory.
Introduction to tropical geometry
Maclagan, Diane
2015-01-01
Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewise-linear functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of information about their classical counterparts. Tropical geometry is a young subject that has undergone a rapid development since the beginning of the 21st century. While establishing itself as an area in its own right, deep connections have been made to many branches of pure and applied mathematics. This book offers a self-contained introduction to tropical geometry, suitable as a course text for beginning graduate students. Proofs are provided for the main results, such as the Fundamental Theorem and the Structure Theorem. Numerous examples and explicit computations illustrate the main concepts. Each of t...
Lectures on Symplectic Geometry
Silva, Ana Cannas
2001-01-01
The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and cl...
Wiesner, Valerie L.; Youngblood, Jeffrey; Trice, Rodney
2014-01-01
Room-temperature injection molding is proposed as a novel, low-cost and more energy efficient manufacturing process capable of forming complex-shaped zirconium diboride (ZrB2) parts. This innovative processing method utilized aqueous suspensions with high powder loading and a minimal amount (5 vol.) of water-soluble polyvinylpyrrolidone (PVP), which was used as a viscosity modifier. Rheological characterization was performed to evaluate the room-temperature flow properties of ZrB2-PVP suspensions. ZrB2 specimens were fabricated with high green body strength and were machinable prior to binder removal despite their low polymer content. After binder burnout and pressureless sintering, the bulk density and microstructure of specimens were characterized using Archimedes technique and scanning electron microscopy. X-Ray Diffraction was used to determine the phase compositions present in sintered specimens. Ultimate strength of sintered specimens will be determined using ASTM C1323-10 compressive C-ring test.
Energy Technology Data Exchange (ETDEWEB)
Lacaze, Guilhem [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Oefelein, Joseph [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-03-01
Large-eddy-simulation (LES) is quickly becoming a method of choice for studying complex thermo-physics in a wide range of propulsion and power systems. It provides a means to study coupled turbulent combustion and flow processes in parameter spaces that are unattainable using direct-numerical-simulation (DNS), with a degree of fidelity that can be far more accurate than conventional engineering methods such as the Reynolds-averaged Navier-Stokes (RANS) approx- imation. However, development of predictive LES is complicated by the complex interdependence of different type of errors coming from numerical methods, algorithms, models and boundary con- ditions. On the other hand, control of accuracy has become a critical aspect in the development of predictive LES for design. The objective of this project is to create a framework of metrics aimed at quantifying the quality and accuracy of state-of-the-art LES in a manner that addresses the myriad of competing interdependencies. In a typical simulation cycle, only 20% of the computational time is actually usable. The rest is spent in case preparation, assessment, and validation, because of the lack of guidelines. This work increases confidence in the accuracy of a given solution while min- imizing the time obtaining the solution. The approach facilitates control of the tradeoffs between cost, accuracy, and uncertainties as a function of fidelity and methods employed. The analysis is coupled with advanced Uncertainty Quantification techniques employed to estimate confidence in model predictions and calibrate model's parameters. This work has provided positive conse- quences on the accuracy of the results delivered by LES and will soon have a broad impact on research supported both by the DOE and elsewhere.
Sridhar, Balasubramanian; Nanubolu, Jagadeesh Babu; Ravikumar, Krishnan
2014-09-01
The anticonvulsant and antiepileptic drug lamotrigine was crystallized with three aromatic acids viz., 2,5-dihydroxybenzoic acid (I), para-toluenesulfonic acid (II) and 4-bromobenzoic acid (III), with the objective of understanding the formation of a salt or co-crystal in the solid state. Single crystal X-ray diffraction and FT-infrared spectroscopic measurements were carried out for all of them. The asymmetric units of I and II contain two lamotriginium cations and two anions (2,5-dihydroxybenzoate in I and para-toluenesulfonate in II), respectively, and additionally II contains one water molecule. The asymmetric unit of III comprises one lamotriginium cation, one 4-bromobenzoate anion and one dimethylformamide (DMF) solvate. In all three complexes the protonation occurs at the N2 atom of the triazine ring. In I and II, the complete proton transfer is observed. However in III, only partial proton transfer is inferred from O to N because of the acidic H atom disorder. The protonation of lamotrigine is also confirmed by the unambiguous location of H atom from the difference Fourier map and as well as from the geometrical bond analysis. Further, various lamotrigine-acid complexes from the CSD were analyzed to establish a correlation between different ionization states (neutral, intermediate and ionic) and changes in the geometrical parameters. The bond angles of triazine ring in lamotrigine and bond distances of carboxylic acid are found to be the best descriptors for distinguishing all three ionization states, whereas, the bond angles of carboxylic acid have to failed to distinguish intermediate state from ionic. From hydrogen bonding point of view, only the lamotrigine-acid heterosynthon is observed in I and II, whereas in III, both lamotrigine-lamotrigine homosynthon and lamotrigine-acid heterosynthon are observed. In I, the cation-anion and anion-anion interactions form a supramolecular two-dimension hydrogen-bonded square grid network, while the water molecule
Differential geometry based multiscale models.
Wei, Guo-Wei
2010-08-01
Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atomistic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier-Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson-Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson-Nernst-Planck equations that are
Differential Geometry Based Multiscale Models
Wei, Guo-Wei
2010-01-01
Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atom-istic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier–Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson–Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson–Nernst–Planck equations that
Discovering Neural Nets with Low Kolmogorov Complexity and High Generalization Capability.
Schmidhuber, Jurgen
1997-07-01
Many neural net learning algorithms aim at finding "simple" nets to explain training data. The expectation is that the "simpler" the networks, the better the generalization on test data (--> Occam's razor). Previous implementations, however, use measures for "simplicity" that lack the power, universality and elegance of those based on Kolmogorov complexity and Solomonoff's algorithmic probability. Likewise, most previous approaches (especially those of the "Bayesian" kind) suffer from the problem of choosing appropriate priors. This paper addresses both issues. It first reviews some basic concepts of algorithmic complexity theory relevant to machine learing, and how the Solomonoff-Levin distribution (or universal prior) deals with the prior problem. The universal prior leads to a probabilistic method for finding "algorithmically simple" problem solutions with high generalization capability. The method is based on Levin complexity (a time-bounded generalization of Kolmogorov complexity) and inspired by Levin's optimal universal search algorithm. For a given problem, solution candidates are computed by efficient "self-sizing" programs that influence their own runtime and storage size. The probabilistic search algorithm finds the "good" programs (the ones quickly computing algorithmically probable solutions fitting the training data). Simulations focus on the task of discovering "algorithmically simple" neural networks with low Kolmogorov complexity and high generalization capability. It is demonstrated that the method, at least with certain toy problems where it is computationally feasible, can lead to generalization results unmatchable by previous neural network algorithms. Much remains to be done, however, to make large scale applications and "incremental learning" feasible. Copyright 1997 Elsevier Science Ltd.
Berger, Marcel
2010-01-01
Both classical geometry and modern differential geometry have been active subjects of research throughout the 20th century and lie at the heart of many recent advances in mathematics and physics. The underlying motivating concept for the present book is that it offers readers the elements of a modern geometric culture by means of a whole series of visually appealing unsolved (or recently solved) problems that require the creation of concepts and tools of varying abstraction. Starting with such natural, classical objects as lines, planes, circles, spheres, polygons, polyhedra, curves, surfaces,
Robinson, Gilbert de B
2011-01-01
This brief undergraduate-level text by a prominent Cambridge-educated mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement for Gilbert de B. Robinson's text, which is the result of several years of teaching and learning the most effective methods from discussions with students. Topics include lines and planes, determinants and linear equations, matrices, groups and linear transformations, and vectors and vector spaces. Additional subjects range from conics and quadrics to homogeneous coordinates and projective geom
Burdette, A C
1971-01-01
Analytic Geometry covers several fundamental aspects of analytic geometry needed for advanced subjects, including calculus.This book is composed of 12 chapters that review the principles, concepts, and analytic proofs of geometric theorems, families of lines, the normal equation of the line, and related matters. Other chapters highlight the application of graphing, foci, directrices, eccentricity, and conic-related topics. The remaining chapters deal with the concept polar and rectangular coordinates, surfaces and curves, and planes.This book will prove useful to undergraduate trigonometric st
Cecil, Thomas E
2015-01-01
This exposition provides the state-of-the art on the differential geometry of hypersurfaces in real, complex, and quaternionic space forms. Special emphasis is placed on isoparametric and Dupin hypersurfaces in real space forms as well as Hopf hypersurfaces in complex space forms. The book is accessible to a reader who has completed a one-year graduate course in differential geometry. The text, including open problems and an extensive list of references, is an excellent resource for researchers in this area. Geometry of Hypersurfaces begins with the basic theory of submanifolds in real space forms. Topics include shape operators, principal curvatures and foliations, tubes and parallel hypersurfaces, curvature spheres and focal submanifolds. The focus then turns to the theory of isoparametric hypersurfaces in spheres. Important examples and classification results are given, including the construction of isoparametric hypersurfaces based on representations of Clifford algebras. An in-depth treatment of Dupin hy...
Desseyn, H. O.; And Others
1985-01-01
Compares linear-nonlinear and planar-nonplanar geometry through the valence-shell electron pairs repulsion (V.S.E.P.R.), Mulliken-Walsh, and electrostatic force theories. Indicates that although the V.S.E.P.R. theory has more advantages for elementary courses, an explanation of the best features of the different theories offers students a better…
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 8. Geometry VI - Space-the Final Frontier. Kapil H Paranjape. Series Article Volume 1 Issue 8 August 1996 pp 28-33. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/001/08/0028-0033 ...
Geometry -----------~--------------RESONANCE
Indian Academy of Sciences (India)
Mathematicians were at war with one another because Euclid's axioms for geometry were not entirely acceptable to all. Archi- medes, Pasch and others introduced further axioms as they thought that Euclid had missed a few, while other mathematicians were bothered by the non-elementary nature of the parallel axiom.
On Generalized Stam Inequalities and Fisher–Rényi Complexity Measures
Directory of Open Access Journals (Sweden)
Steeve Zozor
2017-09-01
Full Text Available Information-theoretic inequalities play a fundamental role in numerous scientific and technological areas (e.g., estimation and communication theories, signal and information processing, quantum physics, … as they generally express the impossibility to have a complete description of a system via a finite number of information measures. In particular, they gave rise to the design of various quantifiers (statistical complexity measures of the internal complexity of a (quantum system. In this paper, we introduce a three-parametric Fisher–Rényi complexity, named ( p , β , λ -Fisher–Rényi complexity, based on both a two-parametic extension of the Fisher information and the Rényi entropies of a probability density function ρ characteristic of the system. This complexity measure quantifies the combined balance of the spreading and the gradient contents of ρ , and has the three main properties of a statistical complexity: the invariance under translation and scaling transformations, and a universal bounding from below. The latter is proved by generalizing the Stam inequality, which lowerbounds the product of the Shannon entropy power and the Fisher information of a probability density function. An extension of this inequality was already proposed by Bercher and Lutwak, a particular case of the general one, where the three parameters are linked, allowing to determine the sharp lower bound and the associated probability density with minimal complexity. Using the notion of differential-escort deformation, we are able to determine the sharp bound of the complexity measure even when the three parameters are decoupled (in a certain range. We determine as well the distribution that saturates the inequality: the ( p , β , λ -Gaussian distribution, which involves an inverse incomplete beta function. Finally, the complexity measure is calculated for various quantum-mechanical states of the harmonic and hydrogenic systems, which are the two main
Self-designing parametric geometries
Sobester, Andras
2015-01-01
The thesis of this paper is that script-based geometry modelling offers the possibility of building `self-designing' intelligence into parametric airframe geometries. We show how sophisticated heuristics (such as optimizers and complex decision structures) can be readily integrated into the parametric geometry model itself using a script-driven modelling architecture. The result is an opportunity for optimization with the scope of conceptual design and the fidelity of preliminary design. Addi...
International Nuclear Information System (INIS)
Toppan, Francesco
2004-01-01
Relying upon the division-algebra classification of Clifford algebras and spinors, a classification of generalized supersymmetries (or, with a slight abuse of language,'generalized supertranslations') is provided. In each given space-time the maximal, saturated, generalized supersymmetry, compatible with the division-algebra constraint that can be consistently imposed on spinors and on superalgebra generators, is furnished. Constraining the superalgebra generators in both the complex and the quaternionic cases gives rise to the two classes of constrained hermitean and holomorphic generalized supersymmetries. In the complex case these two classes of generalized supersymmetries can be regarded as complementary. The quaternionic holomorphic supersymmetry only exists in certain space-time dimensions and can admit at most a single bosonic scalar central charge. The results here presented pave the way for a better understanding of the various M algebra-type of structures which can be introduced in different space-time signatures and in association with different division algebras, as well as their mutual relations. In a previous work, e.g., the introduction of a complex holomorphic generalized supersymmetry was shown to be necessary in order to perform the analytic continuation of the standard M-theory to the 11-dimensional euclidean space. As an application of the present results, it is shown that the above algebra also admits a 12-dimensional, euclidean, F-algebra presentation. (author)
International Nuclear Information System (INIS)
Toppan, Francesco
2004-06-01
Relying upon the division-algebra classification of Clifford algebras and spinors, a classification of generalized supersymmetries (or, with a slight abuse of language, 'generalized super translations') is provided. In each given space-time the maximal, saturated, generalized supersymmetry, compatible with the division-algebra constraint that can be consistently imposed on spinors and on superalgebra generators, is furnished. Constraining the superalgebra generators in both the complex and the quaternionic cases gives rise to the two classes of constrained hermitian and holomorphic generalized supersymmetries. In the complex case these two classes of generalized supersymmetries can be regarded as complementary. The quaternionic holomorphic supersymmetry only exists in certain space-time dimensions and can admit at most a single bosonic scalar central charge. The results here presented pave the way for a better understanding of the various M algebra-type of structures which can be introduced in different space-time signatures and in association with different division algebras, as well as their mutual relations. In a previous work, e.g., the introduction of a complex holomorphic generalized supersymmetry was shown to be necessary in order to perform the analytic continuation of the standard M-theory to the 11-dimensional Euclidean space. As an application of the present results, it is shown that the above algebra also admits a 12-dimensional, Euclidean, F-algebra presentation. (author)
Introduction to combinatorial geometry
International Nuclear Information System (INIS)
Gabriel, T.A.; Emmett, M.B.
1985-01-01
The combinatorial geometry package as used in many three-dimensional multimedia Monte Carlo radiation transport codes, such as HETC, MORSE, and EGS, is becoming the preferred way to describe simple and complicated systems. Just about any system can be modeled using the package with relatively few input statements. This can be contrasted against the older style geometry packages in which the required input statements could be large even for relatively simple systems. However, with advancements come some difficulties. The users of combinatorial geometry must be able to visualize more, and, in some instances, all of the system at a time. Errors can be introduced into the modeling which, though slight, and at times hard to detect, can have devastating effects on the calculated results. As with all modeling packages, the best way to learn the combinatorial geometry is to use it, first on a simple system then on more complicated systems. The basic technique for the description of the geometry consists of defining the location and shape of the various zones in terms of the intersections and unions of geometric bodies. The geometric bodies which are generally included in most combinatorial geometry packages are: (1) box, (2) right parallelepiped, (3) sphere, (4) right circular cylinder, (5) right elliptic cylinder, (6) ellipsoid, (7) truncated right cone, (8) right angle wedge, and (9) arbitrary polyhedron. The data necessary to describe each of these bodies are given. As can be easily noted, there are some subsets included for simplicity
Wang, Haoyu; Sun, Yingxian; Li, Zhao; Guo, Xiaofan; Chen, Shuang; Ye, Ning; Tian, Yichen; Zhang, Lijun
2018-04-10
Despite current interest in the unfavorable impact of cardiometabolic index (CMI) and lipid accumulation product (LAP) on diabetes and cardiovascular risk, information regarding the relation of CMI and LAP to left ventricular (LV) geometry has not been specifically addressed. We aimed to examine the hypothesis: (1) CMI and LAP represent an independent determinant of LV remodeling in general population of rural China; (2) there are gender differences in obesity-related alterations in terms of LV morphology. The sample for this cross-sectional analysis included 11,258 participants (mean age 53.9 years; 54.0% females) who underwent assessment of basic metabolic and anthropometric parameters in rural areas of northeast China. Comprehensive echocardiography-defined LV geometric pattern was determined according to left ventricular mass index and relative wall thickness. The prevalence rate of eccentric and concentric LV hypertrophy (LVH) presented a proportional increase with elevated quartiles of CMI and LAP in a dose-response manner (all P < 0.005). When CMI and LAP were entered as a continuous variable in multivariable adjusted model, we observed the independent effect of 1 SD increment in CMI and LAP with the probability of eccentric and concentric LVH, while this relationship was more pronounced in females than in males. Likewise, the odds ratio comparing the top versus bottom quartiles of CMI were 2.105 (95%CI:1.600-2.768) for eccentric LVH and 2.236 (95%CI:1.419-3.522) for concentric LVH in females. Males in the highest CMI quartile exhibited a nearly doubled (OR:1.724, 95%CI:1.287-2.311) and 1.523-fold (95%CI:1.003-2.313) greater risk of eccentric and concentric LVH, respectively. Increasing LAP entailed a higher possibility of eccentric LVH by a factor of 3.552 and 1.768 in females and males, respectively. In contrast to females, where LAP fourth quartile and concentric LVH were positively associated (OR:2.544, 95%CI:1.537-4.209), higher LAP did not
Directory of Open Access Journals (Sweden)
Leonardo Paris
2012-06-01
Full Text Available Lo studio degli ingranaggi si basa sulle geometrie coniugate in cui due curve o due superfici si mantengono costantemente in contatto pur se in movimento reciproco. La teoria geometrica degli ingranaggi fino alla fine del XIX secolo era uno dei molteplici rami nelle applicazioni della Geometria Descrittiva. Lo studio si basa sulla conoscenza delle principali proprietà delle curve piane e gobbe e delle loro derivate. La specificità del tema è che queste geometrie nel momento in cui si devono relazionare con le loro coniugate, devono rispettare dei vincoli che altrimenti non avrebbero. Si vuole evidenziare attraverso casi concreti il ruolo della geometria descrittiva nel passaggio dal teorico al pratico riproponendo in chiave informatica, temi e procedure di indagine spesso passati in secondo piano se non addirittura dimenticati.
Low Complexity Sparse Bayesian Learning for Channel Estimation Using Generalized Mean Field
DEFF Research Database (Denmark)
Pedersen, Niels Lovmand; Manchón, Carles Navarro; Fleury, Bernard Henri
2014-01-01
We derive low complexity versions of a wide range of algorithms for sparse Bayesian learning (SBL) in underdetermined linear systems. The proposed algorithms are obtained by applying the generalized mean field (GMF) inference framework to a generic SBL probabilistic model. In the GMF framework, we...
Generalization of the Activated Complex Theory of Reaction Rates. II. Classical Mechanical Treatment
Marcus, R. A.
1964-01-01
In its usual classical form activated complex theory assumes a particular expression for the kinetic energy of the reacting system -- one associated with a rectilinear motion along the reaction coordinate. The derivation of the rate expression given in the present paper is based on the general kinetic energy expression.
Latour-Delfgaauw, C.H.M.; van der Windt, D.A.W.M.; de Jonge, P.; Riphagen, II; Vos, R.; Huyse, F.J.; Stalman, W.A.B.
2007-01-01
Objective: The aim of this study was to summarize the available literature on the effectiveness of ambulatory nurse-led case management for complex patients in general health care. Method: We searched MEDLINE, EMBASE, the Cochrane Controlled Trials Register, and Cinahl. We included randomized
Heath, Elizabeth M; English, Jeryl D; Johnson, Cleverick D; Swearingen, Elizabeth B; Akyalcin, Sercan
2017-02-01
Our aims were to assess the perceptions of orthodontic case complexity among orthodontists, general dentists, orthodontic residents, and dental students and to compare their perceptions with the American Board of Orthodontics Discrepancy Index (DI). Orthodontists, general dentists, orthodontic residents, and dental students (n = 343) participated in a Web-based survey. Pretreatment orthodontic records of 29 cases with varying DI scores were obtained. Respondents were asked to evaluate case complexity on a 100-point visual analog scale. Additional information was collected on participants' orthodontic education and orthodontic treatment preferences. Pearson correlation coefficients were used to assess the relationship between the average complexity score and the DI score. Repeated measures analysis with linear mixed models was used to assess the association between the average complexity score and the DI score and whether the association between the 2 scores varied by level of difficulty or panel group. The level of significance for all analyses was set at P clear aligners. DI score was significantly associated with complexity perceptions (P = 0.0168). Associations between average complexity and DI score varied significantly by provider group (P = 0.0033), with orthodontists and residents showing the strongest associations. When the DI score was greater than 15, orthodontists and residents perceived cases as more complex than did the other provider groups. Orthodontists and orthodontic residents had better judgments for evaluating orthodontic case complexity. The high correlation between orthodontic professionals' perceptions and DI scores suggested that additional orthodontic education and training have an influence on the ability to recognize case complexity. Copyright © 2017 American Association of Orthodontists. Published by Elsevier Inc. All rights reserved.
Atiyah, M.; Dijkgraaf, R.; Hitchin, N.
2010-01-01
We review the remarkably fruitful interactions between mathematics and quantum physics in the past decades, pointing out some general trends and highlighting several examples, such as the counting of curves in algebraic geometry, invariants of knots and four-dimensional topology.
International Nuclear Information System (INIS)
Sainath, Kamalesh; Teixeira, Fernando L.; Donderici, Burkay
2014-01-01
We propose the complex-plane generalization of a powerful algebraic sequence acceleration algorithm, the method of weighted averages (MWA), to guarantee exponential-cum-algebraic convergence of Fourier and Fourier–Hankel (F–H) integral transforms. This “complex-plane” MWA, effected via a linear-path detour in the complex plane, results in rapid, absolute convergence of field and potential solutions in multi-layered environments regardless of the source-observer geometry and anisotropy/loss of the media present. In this work, we first introduce a new integration path used to evaluate the field contribution arising from the radiation spectra. Subsequently, we (1) exhibit the foundational relations behind the complex-plane extension to a general Levin-type sequence convergence accelerator, (2) specialize this analysis to one member of the Levin transform family (the MWA), (3) address and circumvent restrictions, arising for two-dimensional integrals associated with wave dynamics problems, through minimal complex-plane detour restrictions and a novel partition of the integration domain, (4) develop and compare two formulations based on standard/real-axis MWA variants, and (5) present validation results and convergence characteristics for one of these two formulations
Directory of Open Access Journals (Sweden)
A. V. Skrypnikov
2015-01-01
Full Text Available Summary. In this work the general ideas of a method of V. I. Skurikhin taking into account the specified features develop and questions of the analysis and synthesis of a complex of technical means, with finishing them to the level suitable for use in engineering practice of design of information management systems are in more detail considered. In work the general system approach to the solution of questions of a choice of technical means of the information management system is created, the general technique of the sys tem analysis and synthesis of a complex of the technical means and its subsystems providing achievement of extreme value of criterion of efficiency of functioning of a technical complex of the information management system is developed. The main attention is paid to the applied party of system researches of complex technical providing, in particular, to definition of criteria of quality of functioning of a technical complex, development of methods of the analysis of information base of the information management system and definition of requirements to technical means, and also methods of structural synthesis of the main subsystems of complex technical providing. Thus, the purpose is research on the basis of system approach of complex technical providing the information management system and development of a number of methods of the analysis and the synthesis of complex technical providing suitable for use in engineering practice of design of systems. The well-known paradox of development of management information consists of that parameters of the system, and consequently, and requirements to the complex hardware, can not be strictly reasonable to development of algorithms and programs, and vice versa. The possible method of overcoming of these difficulties is prognostication of structure and parameters of complex hardware for certain management informations on the early stages of development, with subsequent clarification and
2002-01-01
Discrete geometry investigates combinatorial properties of configurations of geometric objects. To a working mathematician or computer scientist, it offers sophisticated results and techniques of great diversity and it is a foundation for fields such as computational geometry or combinatorial optimization. This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections and thus it can serve as a collection of surveys in several narrower subfields. The main topics include: basics on convex sets, convex polytopes, and hyperplane arrangements; combinatorial complexity of geometric configurations; intersection patterns and transversals of convex sets; geometric Ramsey-type results; polyhedral combinatorics and high-dimensional convexity; and lastly, embeddings of finite metric spaces into normed spaces. Jiri Matousek is Professor of Com...
A general exit strategy of monoheme cytochromes c and c2 in electron transfer complexes?
De March, Matteo; Brancatelli, Giovanna; Demitri, Nicola; De Zorzi, Rita; Hickey, Neal; Geremia, Silvano
2015-09-01
Using our previously reported maps of the electrostatic surface of horse heart ferri- and ferro-cyt c, comparisons were made between the complementary electrostatic surfaces of three cyt c peroxidase-cyt c complexes and the photosynthetic reaction center-cyt c complex, considering both iron oxidation states. The results obtained were consistent with a sliding mechanism for the electron shuttle on the surface of the protein complexes, promoted by the change in iron oxidation state. This mechanism was found to be in agreement with theoretical and NMR studies reported in the literature. Importantly, the analysis also provided a rationale for recognition of nonproductive associations. As we have previously reported the same conclusion on examination of redox partners of cyt c in the mitochondrial respiratory pathway, our hypothesis is that the proposed mechanism could represent a general exit strategy of monoheme cyts c and c2 in electron transfer complexes. © 2015 International Union of Biochemistry and Molecular Biology.
International Nuclear Information System (INIS)
Bakshi, P.; Kalman, G.
1977-02-01
The new approach for the solution of the Vlasov equation for complex magnetic field geometries and for the determination of ensuing stability criteria for microinstabilities has been developed further by estimation of various parameters in the contexts of Tokamak and Tormac regimes, by carrying out analytically the averaging over the fast cyclotron motion to obtain a compact expression for the dispersion equation, and by considering the ensuing results for stability of the drift wave in various parameter domains. The study of high-β, high shear plasma sheath structures has continued both analytically and through computation work. Results in the Vlasov-fluid model for simple ion distribution functions indicate a relation for maximum shear the sheath can support for a given β. The effect of the rotation of the main plasma on the sheath structure, the coupling of the main plasma to the sheath and its rotational damping, and the formation of a viscous boundary layer between the sheath and the plasma have been investigated
International Nuclear Information System (INIS)
Bergmann, Ryan M.; Vujić, Jasmina L.
2015-01-01
Highlights: • WARP, a GPU-accelerated Monte Carlo neutron transport code, has been developed. • The NVIDIA OptiX high-performance ray tracing library is used to process geometric data. • The unionized cross section representation is modified for higher performance. • Reference remapping is used to keep the GPU busy as neutron batch population reduces. • Reference remapping is done using a key-value radix sort on neutron reaction type. - Abstract: In recent supercomputers, general purpose graphics processing units (GPGPUs) are a significant faction of the supercomputer’s total computational power. GPGPUs have different architectures compared to central processing units (CPUs), and for Monte Carlo neutron transport codes used in nuclear engineering to take advantage of these coprocessor cards, transport algorithms must be changed to execute efficiently on them. WARP is a continuous energy Monte Carlo neutron transport code that has been written to do this. The main thrust of WARP is to adapt previous event-based transport algorithms to the new GPU hardware; the algorithmic choices for all parts of which are presented in this paper. It is found that remapping history data references increases the GPU processing rate when histories start to complete. The main reason for this is that completed data are eliminated from the address space, threads are kept busy, and memory bandwidth is not wasted on checking completed data. Remapping also allows the interaction kernels to be launched concurrently, improving efficiency. The OptiX ray tracing framework and CUDPP library are used for geometry representation and parallel dataset-side operations, ensuring high performance and reliability
Higher geometry an introduction to advanced methods in analytic geometry
Woods, Frederick S
2005-01-01
For students of mathematics with a sound background in analytic geometry and some knowledge of determinants, this volume has long been among the best available expositions of advanced work on projective and algebraic geometry. Developed from Professor Woods' lectures at the Massachusetts Institute of Technology, it bridges the gap between intermediate studies in the field and highly specialized works.With exceptional thoroughness, it presents the most important general concepts and methods of advanced algebraic geometry (as distinguished from differential geometry). It offers a thorough study
Ciarlet, Philippe G
2007-01-01
This book gives the basic notions of differential geometry, such as the metric tensor, the Riemann curvature tensor, the fundamental forms of a surface, covariant derivatives, and the fundamental theorem of surface theory in a selfcontained and accessible manner. Although the field is often considered a classical one, it has recently been rejuvenated, thanks to the manifold applications where it plays an essential role. The book presents some important applications to shells, such as the theory of linearly and nonlinearly elastic shells, the implementation of numerical methods for shells, and
Geometry of discrete quantum computing
Hanson, Andrew J.; Ortiz, Gerardo; Sabry, Amr; Tai, Yu-Tsung
2013-05-01
Conventional quantum computing entails a geometry based on the description of an n-qubit state using 2n infinite precision complex numbers denoting a vector in a Hilbert space. Such numbers are in general uncomputable using any real-world resources, and, if we have the idea of physical law as some kind of computational algorithm of the universe, we would be compelled to alter our descriptions of physics to be consistent with computable numbers. Our purpose here is to examine the geometric implications of using finite fields Fp and finite complexified fields \\mathbf {F}_{p^2} (based on primes p congruent to 3 (mod4)) as the basis for computations in a theory of discrete quantum computing, which would therefore become a computable theory. Because the states of a discrete n-qubit system are in principle enumerable, we are able to determine the proportions of entangled and unentangled states. In particular, we extend the Hopf fibration that defines the irreducible state space of conventional continuous n-qubit theories (which is the complex projective space \\mathbf {CP}^{2^{n}-1}) to an analogous discrete geometry in which the Hopf circle for any n is found to be a discrete set of p + 1 points. The tally of unit-length n-qubit states is given, and reduced via the generalized Hopf fibration to \\mathbf {DCP}^{2^{n}-1}, the discrete analogue of the complex projective space, which has p^{2^{n}-1} (p-1)\\,\\prod _{k=1}^{n-1} ( p^{2^{k}}+1) irreducible states. Using a measure of entanglement, the purity, we explore the entanglement features of discrete quantum states and find that the n-qubit states based on the complexified field \\mathbf {F}_{p^2} have pn(p - 1)n unentangled states (the product of the tally for a single qubit) with purity 1, and they have pn + 1(p - 1)(p + 1)n - 1 maximally entangled states with purity zero.
Initiation to global Finslerian geometry
Akbar-Zadeh, Hassan
2006-01-01
After a brief description of the evolution of thinking on Finslerian geometry starting from Riemann, Finsler, Berwald and Elie Cartan, the book gives a clear and precise treatment of this geometry. The first three chapters develop the basic notions and methods, introduced by the author, to reach the global problems in Finslerian Geometry. The next five chapters are independent of each other, and deal with among others the geometry of generalized Einstein manifolds, the classification of Finslerian manifolds of constant sectional curvatures. They also give a treatment of isometric, affine, p
Synchronization stability of general complex dynamical networks with time-varying delays
International Nuclear Information System (INIS)
Li Kun; Guan Shuguang; Gong Xiaofeng; Lai, C.-H.
2008-01-01
The synchronization problem of some general complex dynamical networks with time-varying delays is investigated. Both time-varying delays in the network couplings and time-varying delays in the dynamical nodes are considered. The novel delay-dependent criteria in terms of linear matrix inequalities (LMI) are derived based on free-weighting matrices technique and appropriate Lyapunov functional proposed recently. Numerical examples are given to illustrate the effectiveness and advantage of the proposed synchronization criteria
General-Purpose Computation with Neural Networks: A Survey of Complexity Theoretic Results
Czech Academy of Sciences Publication Activity Database
Šíma, Jiří; Orponen, P.
2003-01-01
Roč. 15, č. 12 (2003), s. 2727-2778 ISSN 0899-7667 R&D Projects: GA AV ČR IAB2030007; GA ČR GA201/02/1456 Institutional research plan: AV0Z1030915 Keywords : computational power * computational complexity * perceptrons * radial basis functions * spiking neurons * feedforward network s * reccurent network s * probabilistic computation * analog computation Subject RIV: BA - General Mathematics Impact factor: 2.747, year: 2003
Directory of Open Access Journals (Sweden)
Theocharis Theofanidis
2016-01-01
Full Text Available Real hypersurfaces satisfying the condition ϕl=lϕ(l=R(·,ξξ have been studied by many authors under at least one more condition, since the class of these hypersurfaces is quite tough to be classified. The aim of the present paper is the classification of real hypersurfaces in complex projective plane CP2 satisfying a generalization of ϕl=lϕ under an additional restriction on a specific function.
Solutions of Riccati-Abel equation in terms of characteristics of general complex algebra
International Nuclear Information System (INIS)
Yamaleev, R.M.
2012-01-01
The Riccati-Abel differential equation defined as an equation between the first order derivative and the cubic polynomial is explored. In the case of constant coefficients this equation is reduced into an algebraic equation. A method of derivation of a summation formula for solutions of the Riccati-Abel equation is elaborated. The solutions of the Riccati-Abel equation are expressed in terms of the characteristic functions of general complex algebra of the third order
An introduction to incidence geometry
De Bruyn, Bart
2016-01-01
This book gives an introduction to the field of Incidence Geometry by discussing the basic families of point-line geometries and introducing some of the mathematical techniques that are essential for their study. The families of geometries covered in this book include among others the generalized polygons, near polygons, polar spaces, dual polar spaces and designs. Also the various relationships between these geometries are investigated. Ovals and ovoids of projective spaces are studied and some applications to particular geometries will be given. A separate chapter introduces the necessary mathematical tools and techniques from graph theory. This chapter itself can be regarded as a self-contained introduction to strongly regular and distance-regular graphs. This book is essentially self-contained, only assuming the knowledge of basic notions from (linear) algebra and projective and affine geometry. Almost all theorems are accompanied with proofs and a list of exercises with full solutions is given at the end...
Directory of Open Access Journals (Sweden)
M. Sánchez Noa
2001-07-01
Full Text Available En el presente trabajo se exponen los resultados del análisis realizado en árboles de compleja geometría pertenecientes a unmultiplicador planetario tipo 2KH-A destinado a emplearse en aerogeneradores de electricidad. En el mismo, se presentanlos modelos físico-matemáticos de dichos árboles para ser analizados mediante el método de los elementos finitos,considerando el estado de carga que surge al funcionar el mecanismo y contemplando el efecto adicional de las cargasgiroscópicas. Se muestran las zonas de conflicto de tensiones y se analizan propuestas de diseño que permitan, garantizandola resistencia y rigidez, realizar variaciones dimensionales y mejorar la compacidad de los elementos, disminuyendo a lavez el peso de los mismos.Palabras claves: Elementos finitos, multiplicador planetario, diseño de árbol, resistencia mecánica.____________________________________________________________________________AbstractThe results of the analysis in shafts of complex geometry, belonging to a planetary multiplier type 2KH-AM to be usedin wind generators is presented. The physical-mathematical models of these shafts are analyzed by means of finiteelement method. Can increasing of load when the mechanism is working and contemplating the additional effect of thegyroscopic loads. The tension distribution are shown and design proposals are analyzed to improve the resistance, rigidityand to improve the compactness of the elements. This analysis constitutes an application of the the finite element methodof which reference doesn't existKey Words: Finite elements method, planetary gear unit, shaft design, mechanical strength.
Positive geometries and canonical forms
Arkani-Hamed, Nima; Bai, Yuntao; Lam, Thomas
2017-11-01
Recent years have seen a surprising connection between the physics of scattering amplitudes and a class of mathematical objects — the positive Grassmannian, positive loop Grassmannians, tree and loop Amplituhedra — which have been loosely referred to as "positive geometries". The connection between the geometry and physics is provided by a unique differential form canonically determined by the property of having logarithmic singularities (only) on all the boundaries of the space, with residues on each boundary given by the canonical form on that boundary. The structures seen in the physical setting of the Amplituhedron are both rigid and rich enough to motivate an investigation of the notions of "positive geometries" and their associated "canonical forms" as objects of study in their own right, in a more general mathematical setting. In this paper we take the first steps in this direction. We begin by giving a precise definition of positive geometries and canonical forms, and introduce two general methods for finding forms for more complicated positive geometries from simpler ones — via "triangulation" on the one hand, and "push-forward" maps between geometries on the other. We present numerous examples of positive geometries in projective spaces, Grassmannians, and toric, cluster and flag varieties, both for the simplest "simplex-like" geometries and the richer "polytope-like" ones. We also illustrate a number of strategies for computing canonical forms for large classes of positive geometries, ranging from a direct determination exploiting knowledge of zeros and poles, to the use of the general triangulation and push-forward methods, to the representation of the form as volume integrals over dual geometries and contour integrals over auxiliary spaces. These methods yield interesting representations for the canonical forms of wide classes of positive geometries, ranging from the simplest Amplituhedra to new expressions for the volume of arbitrary convex
Abhyankar, Shreeram Shankar
1964-01-01
This book provides, for use in a graduate course or for self-study by graduate students, a well-motivated treatment of several topics, especially the following: (1) algebraic treatment of several complex variables; (2) geometric approach to algebraic geometry via analytic sets; (3) survey of local algebra; (4) survey of sheaf theory. The book has been written in the spirit of Weierstrass. Power series play the dominant role. The treatment, being algebraic, is not restricted to complex numbers, but remains valid over any complete-valued field. This makes it applicable to situations arising from
Differential geometry curves, surfaces, manifolds
Kühnel, Wolfgang
2015-01-01
This carefully written book is an introduction to the beautiful ideas and results of differential geometry. The first half covers the geometry of curves and surfaces, which provide much of the motivation and intuition for the general theory. The second part studies the geometry of general manifolds, with particular emphasis on connections and curvature. The text is illustrated with many figures and examples. The prerequisites are undergraduate analysis and linear algebra. This new edition provides many advancements, including more figures and exercises, and-as a new feature-a good number of so
International Nuclear Information System (INIS)
Weinhorst, Bastian; Fischer, Ulrich; Lu, Lei; Qiu, Yuefeng; Wilson, Paul
2015-01-01
Highlights: • Comparison of different approaches for the use of CAD geometry for Monte Carlo transport calculations. • Comparison with regard to user-friendliness and computation performance. • Three approaches, namely conversion with McCad, unstructured mesh feature of MCN6 and DAGMC. • Installation most complex for DAGMC, model preparation worst for McCad, computation performance worst for MCNP6. • Installation easiest for McCad, model preparation best for MCNP6, computation speed fastest for McCad. - Abstract: Computer aided design (CAD) is an important industrial way to produce high quality designs. Therefore, CAD geometries are in general used for engineering and the design of complex facilities like the ITER tokamak. Although Monte Carlo codes like MCNP are well suited to handle the complex 3D geometry of ITER for transport calculations, they rely on their own geometry description and are in general not able to directly use the CAD geometry. In this paper, three different approaches for the use of CAD geometries with MCNP calculations are investigated and assessed with regard to calculation performance and user-friendliness. The first method is the conversion of the CAD geometry into MCNP geometry employing the conversion software McCad developed by KIT. The second approach utilizes the MCNP6 mesh geometry feature for the particle tracking and relies on the conversion of the CAD geometry into a mesh model. The third method employs DAGMC, developed by the University of Wisconsin-Madison, for the direct particle tracking on the CAD geometry using a patched version of MCNP. The obtained results show that each method has its advantages depending on the complexity and size of the model, the calculation problem considered, and the expertise of the user.
Geometry of lattice field theory
International Nuclear Information System (INIS)
Honan, T.J.
1986-01-01
Using some tools of algebraic topology, a general formalism for lattice field theory is presented. The lattice is taken to be a simplicial complex that is also a manifold and is referred to as a simplicial manifold. The fields on this lattice are cochains, that are called lattice forms to emphasize the connections with differential forms in the continuum. This connection provides a new bridge between lattice and continuum field theory. A metric can be put onto this simplicial manifold by assigning lengths to every link or I-simplex of the lattice. Regge calculus is a way of defining general relativity on this lattice. A geometric discussion of Regge calculus is presented. The Regge action, which is a discrete form of the Hilbert action, is derived from the Hilbert action using distribution valued forms. This is a new derivation that emphasizes the underlying geometry. Kramers-Wannier duality in statistical mechanics is discussed in this general setting. Nonlinear field theories, which include gauge theories and nonlinear sigma models are discussed in the continuum and then are put onto a lattice. The main new result here is the generalization to curved spacetime, which consists of making the theory compatible with Regge calculus
Low-complexity blind equalization for OFDM systems with general constellations
Al-Naffouri, Tareq Y.
2012-12-01
This paper proposes a low-complexity algorithm for blind equalization of data in orthogonal frequency division multiplexing (OFDM)-based wireless systems with general constellations. The proposed algorithm is able to recover the transmitted data even when the channel changes on a symbol-by-symbol basis, making it suitable for fast fading channels. The proposed algorithm does not require any statistical information about the channel and thus does not suffer from latency normally associated with blind methods. The paper demonstrates how to reduce the complexity of the algorithm, which becomes especially low at high signal-to-noise ratio (SNR). Specifically, it is shown that in the high SNR regime, the number of operations is of the order O(LN), where L is the cyclic prefix length and N is the total number of subcarriers. Simulation results confirm the favorable performance of the proposed algorithm. © 2012 IEEE.
The generalization of Plackett-Burman design based on fractional calculus of complex order
Ibrahim, Rabha W.; Jalab, Hamid A.
2014-12-01
Response surface attitude was working to optimize the degradation situations of Aflatoxin B1(AFB1) by Rhodococcus erythropolis in liquid culture. The interesting factors that influence the degradation, as identified by a Plackett-Burman design with six variables, were temperature, liquid volume, pH, inoculums size, agitation speed and incubation time. In this work, we generalize the Plackett-Burman design, based on fractional calculus of complex order, to describe correlation between the six variables and the degradation rate of AFB1. The experimental results show the influence of the proposed method. The results demonstrated that the degradation efficiency of R. erythropolis could extent 99% in liquid culture.
Cowan, E. Jun
1999-06-01
Interpreted either as a folded igneous sheet or a basin-shaped intrusion, the origin of the Palaeoproterozoic Sudbury Igneous Complex (SIC), Ontario, Canada, has been debated by geologists for over a century. Most recent proposals view the SIC to have been emplaced as a horizontal impact melt and subsequently folded after solidification. This requires the SIC to have folded from an originally horizontal sheet, to the present basinal geometry, with dips of 30° in the North Range and 70° in the East Range. The fold scenario would require the sharply curved juncture between the North and East Ranges (North Lobe) to be deformed in the solid-state due to folding. In order to test the fold model, the rock fabric was investigated in the East and North Ranges and the North Lobe of SIC at 256 sites with the aid of anisotropy of magnetic susceptibility (AMS). A sampling transect through an undeformed portion of the SIC in the western North Range reveals that the gabbro-norite exhibits SIC contact-parallel magnetic foliation and down-dip magnetic lineation, both of which, respectively, correlate to an igneous foliation and lineation. The granophyre, in contrast, features spatially consistent magnetic lineation that is oriented orthogonal to the SIC contact. This magnetic lineation can be correlated to a mineral fabric characterised by aligned acicular crystals of plagioclase, and is interpreted to be a wall-orthogonal crystallisation texture. The East and North Ranges in the eastern SIC reveal similar patterns of AMS fabrics. The magnetic lineation of the granophyre is orthogonal to the basal contact of the SIC in the East and North Ranges, and in the fold-like North Lobe between the two ranges. An axial-planar magnetic foliation is developed in the granophyre as the North Lobe is approached, but the magnetic lineation is nevertheless contact-orthogonal and well-defined. This AMS fabric is interpreted to be a combination of an original igneous contact-orthogonal lineation
Optical geometry across the horizon
International Nuclear Information System (INIS)
Jonsson, Rickard
2006-01-01
In a recent paper (Jonsson and Westman 2006 Class. Quantum Grav. 23 61), a generalization of optical geometry, assuming a non-shearing reference congruence, is discussed. Here we illustrate that this formalism can be applied to (a finite four-volume) of any spherically symmetric spacetime. In particular we apply the formalism, using a non-static reference congruence, to do optical geometry across the horizon of a static black hole. While the resulting geometry in principle is time dependent, we can choose the reference congruence in such a manner that an embedding of the geometry always looks the same. Relative to the embedded geometry the reference points are then moving. We discuss the motion of photons, inertial forces and gyroscope precession in this framework
Global affine differential geometry of hypersurfaces
Li, An-Min; Zhao, Guosong; Hu, Zejun
2015-01-01
This book draws a colorful and widespread picture of global affine hypersurface theory up to the most recent state. Moreover, the recent development revealed that affine differential geometry- as differential geometry in general- has an exciting intersection area with other fields of interest, like partial differential equations, global analysis, convex geometry and Riemann surfaces.
Energy Technology Data Exchange (ETDEWEB)
Toh, K.C.; Trefethen, L.N. [Cornell Univ., Ithaca, NY (United States)
1994-12-31
What properties of a nonsymmetric matrix A determine the convergence rate of iterations such as GMRES, QMR, and Arnoldi? If A is far from normal, should one replace the usual Ritz values {r_arrow} eigenvalues notion of convergence of Arnoldi by alternative notions such as Arnoldi lemniscates {r_arrow} pseudospectra? Since Krylov subspace iterations can be interpreted as minimization processes involving polynomials of matrices, the answers to questions such as these depend upon mathematical problems of the following kind. Given a polynomial p(z), how can one bound the norm of p(A) in terms of (1) the size of p(z) on various sets in the complex plane, and (2) the locations of the spectrum and pseudospectra of A? This talk reports some progress towards solving these problems. In particular, the authors present theorems that generalize the Kreiss matrix theorem from the unit disk (for the monomial A{sup n}) to a class of general complex domains (for polynomials p(A)).
Vázquez-Fernández, M Ángeles; Bermejo, Manuel R; Fernández-García, M Isabel; González-Riopedre, Gustavo; Rodríguez-Doutón, M Jesús; Maneiro, Marcelino
2011-12-01
The peroxidase and catalase activities of eighteen manganese-Schiff base complexes have been studied. A correlation between the structure of the complexes and their catalytic activity is discussed on the basis of the variety of systems studied. Complexes 1-18 have the general formulae [MnL(n)(D)(2)](X)(H(2)O/CH(3)OH)(m), where L(n)=L(1)-L(13); D=H(2)O, CH(3)OH or Cl; m=0-2.5 and X=NO(3)(-), Cl(-), ClO(4)(-), CH(3)COO(-), C(2)H(5)COO(-) or C(5)H(11)COO(-). The dianionic tetradentate Schiff base ligands H(2)L(n) are the result of the condensation of different substituted (OMe-, OEt-, Br-, Cl-) hydroxybenzaldehyde with diverse diamines (1,2-diaminoethane for H(2)L(1)-H(2)L(2); 1,2-diamino-2-methylethane for H(2)L(3)-H(2)L(4); 1,2-diamino-2,2-dimethylethane for H(2)L(5); 1,2-diphenylenediamine for H(2)L(6)-H(2)L(7); 1,3-diaminopropane for H(2)L(8)-H(2)L(11); 1,3-diamino-2,2-dimethylpropane for H(2)L(12)-H(2)L(13)). The new Mn(III) complexes [MnL(1)(H(2)O)Cl](H(2)O)(2.5) (2), [MnL(2)(H(2)O)(2)](NO(3))(H(2)O) (4), [MnL(6)(H(2)O)(2)][MnL(6)(CH(3)OH)(H(2)O)](NO(3))(2)(CH(3)OH) (8), [MnL(6)(H(2)O)(OAc)](H(2)O) (9) and [MnL(7)(H(2)O)(2)](NO(3))(CH(3)OH)(2) (12) were isolated and characterised by elemental analysis, magnetic susceptibility and conductivity measurements, redox studies, ESI spectrometry and UV, IR, paramagnetic (1)H NMR, and EPR spectroscopies. X-ray crystallographic studies of these complexes and of the ligand H(2)L(6) are also reported. The crystal structures of the rest of the complexes have been previously published and herein we have only revised their study by those techniques still not reported (EPR and (1)H NMR for some of these compounds) and which help to establish their structures in solution. Complexes 1-12 behave as more efficient mimics of peroxidase or catalase in contrast with 13-18. The analysis between the catalytic activity and the structure of the compounds emphasises the significance of the existence of a vacant or a labile position in the
Bennett, C.; Poole, G. C.; Kimball, J. S.; Stanford, J. A.; O'Daniel, S. J.; Mertes, L. A.
2005-05-01
Historically, physical scientists have developed models with highly accurate governing equations, while biologists have excelled at abstraction (the strategic simplification of system complexity). These different modeling paradigms yield biological (e.g. food web) and physical (e.g. hydrologic) models that can be difficult to integrate. Complex biological dynamics may be impossible to represent with governing equations. Conversely, physical processes may be oversimplified in biological models. Using agent-based modeling, a technique applied widely in social sciences and economics, we are developing a general modeling system to integrate accurate representations of physical dynamics such as water and heat flux with abstracted biological processes such as nutrient transformations. The modeling system represents an ecosystem as a complex integrated network of intelligent physical and biological "agents" that store, transform, and trade ecosystem resources (e.g., water, heat, nutrients, carbon) using equations that describe either abstracted concepts and/or physical laws. The modular design of the system allows resource submodels to be developed independently and installed into the simulation architecture. The modeling system provides a useful heuristic tool to support integrated physical and biological research topics, such as the influence of hydrologic dynamics and spatio-temporal physical heterogeneity on trophic (food web) dynamics and/or nutrient cycling.
General surgeon management of complex hepatopancreatobiliary trauma at a level I trauma center.
Kilen, Peter; Greenbaum, Alissa; Miskimins, Richard; Rojo, Manuel; Preda, Razvan; Howdieshell, Thomas; Lu, Stephen; West, Sonlee
2017-09-01
The impact of general surgeons (GS) taking trauma call on patient outcomes has been debated. Complex hepatopancreatobiliary (HPB) injuries present a particular challenge and often require specialized care. We predicted no difference in the initial management or outcomes of complex HPB trauma between GS and trauma/critical care (TCC) specialists. A retrospective review of patients who underwent operative intervention for complex HPB trauma from 2008 to 2015 at an ACS-verified level I trauma center was performed. Chart review was used to obtain variables pertaining to demographics, clinical presentation, operative management, and outcomes. Patients were grouped according to whether their index operation was performed by a GS or TCC provider and compared. 180 patients met inclusion criteria. The GS (n = 43) and TCC (n = 137) cohorts had comparable patient demographics and clinical presentations. Most injuries were hepatic (73.3% GS versus 72.6% TCC) and TCC treated more pancreas injuries (15.3% versus GS 13.3%; P = 0.914). No significant differences were found in HPB-directed interventions at the initial operation (41.9% GS versus 56.2% TCC; P = 0.100), damage control laparotomy with temporary abdominal closure (69.8% versus 69.3%; P = 0.861), LOS, septic complications or 30-day mortality (13.9% versus 10.2%; P = 0.497). TCC were more likely to place an intraabdominal drain than GS (52.6% versus 34.9%; P = 0.043). We found no significant differences between GS and TCC specialists in initial operative management or clinical outcomes of complex HPB trauma. The frequent and proper use of damage control laparotomy likely contribute to these findings. Copyright © 2017 Elsevier Inc. All rights reserved.
Kendig, Keith
2015-01-01
Designed to make learning introductory algebraic geometry as easy as possible, this text is intended for advanced undergraduates and graduate students who have taken a one-year course in algebra and are familiar with complex analysis. This newly updated second edition enhances the original treatment's extensive use of concrete examples and exercises with numerous figures that have been specially redrawn in Adobe Illustrator. An introductory chapter that focuses on examples of curves is followed by a more rigorous and careful look at plane curves. Subsequent chapters explore commutative ring th
GEOMETRY – AN IMPORTANT MEANS OF EDUCATION IN THE CIVILISATION SCOPE
Liliana TOCARIU, PhD
2017-01-01
Geometry (from the Greek: γεωμετρία; geo = earth, metria = measure) is a genuine science, rooted in mathematics, which studies the plane and spatial forms of bodies from the objective or conceptual reality and the nature of the relationship that exists between them. Due to its complexity, geometry is divided into: Euclidian geometry, analytical geometry, descriptive geometry, projective geometry, kinematic geometry, surface and curve differential geometry, axiomatic geometry,...
Synthesis and characterization of a chiral dimeric copper(II) complex ...
Indian Academy of Sciences (India)
Unknown
midal geometry. Generally, the dichloro-bridged square- pyramidal copper complexes with square pyramid geometry exhibit three different geometries with re- gard to the relative arrangement of square pyramids, viz. perpendicular bases (type I), parallel bases (type. II) and coplanar bases (type III).12 The asymmetric.
Eisenhart, Luther Pfahler
2005-01-01
This concise text by a prominent mathematician deals chiefly with manifolds dominated by the geometry of paths. Topics include asymmetric and symmetric connections, the projective geometry of paths, and the geometry of sub-spaces. 1927 edition.
Complex analysis I entire and meromorphic functions polyanalytic functions and their generalizations
Havin, V; Nikolski, N
1997-01-01
The first part of the volume contains a comprehensive description of the theory of entire and meromorphic functions of one complex variable and its applications. It includes the fundamental notions, methods and results on the growth of entire functions and the distribution of their zeros, the Rolf Nevanlinna theory of distribution of values of meromorphic functions including the inverse problem, the theory of completely regular growth, the concept of limit sets for entire and subharmonic functions. The authors describe the interpolation by entire functions, to entire and meromorphic solutions of ordinary differential equations, to the Riemann boundary problem with an infinite index and to the arithmetic of the convolution semigroup of probability distributions. Polyanalytic functions form one of the most natural generalizations of analytic functions and are described in Part II. They emerged for the first time in plane elasticity theory where they found important applications (due to Kolossof, Mushelishvili e...
Moments of generalized Husimi distributions and complexity of many-body quantum states
International Nuclear Information System (INIS)
Sugita, Ayumu
2003-01-01
We consider generalized Husimi distributions for many-body systems, and show that their moments are good measures of complexity of many-body quantum states. Our construction of the Husimi distribution is based on the coherent state of the single-particle transformation group. Then the coherent states are independent-particle states, and, at the same time, the most localized states in the Husimi representation. Therefore delocalization of the Husimi distribution, which can be measured by the moments, is a sign of many-body correlation (entanglement). Since the delocalization of the Husimi distribution is also related to chaoticity of the dynamics, it suggests a relation between entanglement and chaos. Our definition of the Husimi distribution can be applied not only to systems of distinguishable particles, but also to those of identical particles, i.e., fermions and bosons. We derive an algebraic formula to evaluate the moments of the Husimi distribution
Reliability and Efficiency of Generalized Rumor Spreading Model on Complex Social Networks
International Nuclear Information System (INIS)
Naimi, Yaghoob; Naimi, Mohammad
2013-01-01
We introduce the generalized rumor spreading model and investigate some properties of this model on different complex social networks. Despite pervious rumor models that both the spreader-spreader (SS) and the spreader-stifler (SR) interactions have the same rate α, we define α (1) and α (2) for SS and SR interactions, respectively. The effect of variation of α (1) and α (2) on the final density of stiflers is investigated. Furthermore, the influence of the topological structure of the network in rumor spreading is studied by analyzing the behavior of several global parameters such as reliability and efficiency. Our results show that while networks with homogeneous connectivity patterns reach a higher reliability, scale-free topologies need a less time to reach a steady state with respect the rumor. (interdisciplinary physics and related areas of science and technology)
Reliability and Efficiency of Generalized Rumor Spreading Model on Complex Social Networks
Yaghoob, Naimi; Mohammad, Naimi
2013-07-01
We introduce the generalized rumor spreading model and investigate some properties of this model on different complex social networks. Despite pervious rumor models that both the spreader-spreader (SS) and the spreader-stifler (SR) interactions have the same rate α, we define α(1) and α(2) for SS and SR interactions, respectively. The effect of variation of α(1) and α(2) on the final density of stiflers is investigated. Furthermore, the influence of the topological structure of the network in rumor spreading is studied by analyzing the behavior of several global parameters such as reliability and efficiency. Our results show that while networks with homogeneous connectivity patterns reach a higher reliability, scale-free topologies need a less time to reach a steady state with respect the rumor.
International Nuclear Information System (INIS)
Gurevich, L.Eh.; Gliner, Eh.B.
1978-01-01
Problems of investigating the Universe space-time geometry are described on a popular level. Immediate space-time geometries, corresponding to three cosmologic models are considered. Space-time geometry of a closed model is the spherical Riemann geonetry, of an open model - is the Lobachevskij geometry; and of a plane model - is the Euclidean geometry. The Universe real geometry in the contemporary epoch of development is based on the data testifying to the fact that the Universe is infinitely expanding
The geometry description markup language
International Nuclear Information System (INIS)
Chytracek, R.
2001-01-01
Currently, a lot of effort is being put on designing complex detectors. A number of simulation and reconstruction frameworks and applications have been developed with the aim to make this job easier. A very important role in this activity is played by the geometry description of the detector apparatus layout and its working environment. However, no real common approach to represent geometry data is available and such data can be found in various forms starting from custom semi-structured text files, source code (C/C++/FORTRAN), to XML and database solutions. The XML (Extensible Markup Language) has proven to provide an interesting approach for describing detector geometries, with several different but incompatible XML-based solutions existing. Therefore, interoperability and geometry data exchange among different frameworks is not possible at present. The author introduces a markup language for geometry descriptions. Its aim is to define a common approach for sharing and exchanging of geometry description data. Its requirements and design have been driven by experience and user feedback from existing projects which have their geometry description in XML
Visuospatial Working Memory in Intuitive Geometry, and in Academic Achievement in Geometry
Giofre, David; Mammarella, Irene C.; Ronconi, Lucia; Cornoldi, Cesare
2013-01-01
A study was conducted on the involvement of visuospatial working memory (VSWM) in intuitive geometry and in school performance in geometry at secondary school. A total of 166 pupils were administered: (1) six VSWM tasks, comprising simple storage and complex span tasks; and (2) the intuitive geometry task devised by Dehaene, Izard, Pica, and…
Plucker, Jonathan A; Shelton, Amy L
2015-01-01
Current technology has dramatically increased the prevalence of studies to establish the genetic correlates of a wide variety of human characteristics, including not only the physical attributes that determine what we look like and the risk of physiological disease but also the psychological and cognitive characteristics that often define who we are as individuals. Perhaps one of the most deeply personal and often controversial characteristics is the concept of general intelligence, known in the psychological literature as "g." As with the genetic study of any complex trait, the first step in studying the genetics of g is to carefully define the characteristic of interest. For g, this entails establishing what intelligence means and providing a clear operational definition for how it will be measured. In this paper, we provide a brief historical and theoretical overview of the construct of general intelligence, describe its relationship to the contemporary measurement of intelligence, and discuss these concepts in light of the challenges associated with defining g as a characteristic in the study of genetics. © 2015 The Hastings Center.
Generalized additive models reveal the intrinsic complexity of wood formation dynamics.
Cuny, Henri E; Rathgeber, Cyrille B K; Kiessé, Tristan Senga; Hartmann, Felix P; Barbeito, Ignacio; Fournier, Meriem
2013-04-01
The intra-annual dynamics of wood formation, which involves the passage of newly produced cells through three successive differentiation phases (division, enlargement, and wall thickening) to reach the final functional mature state, has traditionally been described in conifers as three delayed bell-shaped curves followed by an S-shaped curve. Here the classical view represented by the 'Gompertz function (GF) approach' was challenged using two novel approaches based on parametric generalized linear models (GLMs) and 'data-driven' generalized additive models (GAMs). These three approaches (GFs, GLMs, and GAMs) were used to describe seasonal changes in cell numbers in each of the xylem differentiation phases and to calculate the timing of cell development in three conifer species [Picea abies (L.), Pinus sylvestris L., and Abies alba Mill.]. GAMs outperformed GFs and GLMs in describing intra-annual wood formation dynamics, showing two left-skewed bell-shaped curves for division and enlargement, and a right-skewed bimodal curve for thickening. Cell residence times progressively decreased through the season for enlargement, whilst increasing late but rapidly for thickening. These patterns match changes in cell anatomical features within a tree ring, which allows the separation of earlywood and latewood into two distinct cell populations. A novel statistical approach is presented which renews our understanding of xylogenesis, a dynamic biological process in which the rate of cell production interplays with cell residence times in each developmental phase to create complex seasonal patterns.
Advances in discrete differential geometry
2016-01-01
This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, ...
Results from field trial of a low-cost solar cooker with novel concentrator geometry
Berryman, Ian; Jelley, Nick; Stone, Richard; Dadd, Mike
2016-05-01
Solar cookers are generally of either box-type or make use of parabolic dishes, including approximations thereof. The former are cheap but operate at low solar concentrations and temperatures, whilst the latter often require complex mirror geometries and can be prohibitively expensive to manufacture. This paper will present the results from a field trial of a prototype solar cooker which use of a novel concentrator geometry to achieve high temperatures.
Riparian meadow complexes found in mountain ranges of the Central Great Basin physiographic region (western United States) are of interest to researchers as they contain significant biodiversity relative to the surrounding basin areas. These meadow complexes are currently degradi...
Flegg, H Graham
2001-01-01
This excellent introduction to topology eases first-year math students and general readers into the subject by surveying its concepts in a descriptive and intuitive way, attempting to build a bridge from the familiar concepts of geometry to the formalized study of topology. The first three chapters focus on congruence classes defined by transformations in real Euclidean space. As the number of permitted transformations increases, these classes become larger, and their common topological properties become intuitively clear. Chapters 4-12 give a largely intuitive presentation of selected topics.
Dooner, David B
2012-01-01
Building on the first edition published in 1995 this new edition of Kinematic Geometry of Gearing has been extensively revised and updated with new and original material. This includes the methodology for general tooth forms, radius of torsure', cylinder of osculation, and cylindroid of torsure; the author has also completely reworked the '3 laws of gearing', the first law re-written to better parallel the existing 'Law of Gearing" as pioneered by Leonard Euler, expanded from Euler's original law to encompass non-circular gears and hypoid gears, the 2nd law of gearing describing a unique relat
A new experiment-independent mechanism to persistify and serve the detector geometry of ATLAS
Bianchi, Riccardo Maria; Boudreau, Joseph; Vukotic, Ilija
2017-10-01
The complex geometry of the whole detector of the ATLAS experiment at LHC is currently stored only in custom online databases, from which it is built on-the-fly on request. Accessing the online geometry guarantees accessing the latest version of the detector description, but requires the setup of the full ATLAS software framework “Athena”, which provides the online services and the tools to retrieve the data from the database. This operation is cumbersome and slows down the applications that need to access the geometry. Moreover, all applications that need to access the detector geometry need to be built and run on the same platform as the ATLAS framework, preventing the usage of the actual detector geometry in stand-alone applications. Here we propose a new mechanism to persistify (in software development in general, and in HEP computing in particular, persistifying means taking an object which lives in memory only - for example because it was built on-the-fly while processing the experimental data, - serializing it and storing it on disk as a persistent object) and serve the geometry of HEP experiments. The new mechanism is composed by a new file format and the modules to make use of it. The new file format allows to store the whole detector description locally in a file, and it is especially optimized to describe large complex detectors with the minimum file size, making use of shared instances and storing compressed representations of geometry transformations. Then, the detector description can be read back in, to fully restore the in-memory geometry tree. Moreover, a dedicated REST API is being designed and developed to serve the geometry in standard exchange formats like JSON, to let users and applications download specific partial geometry information. With this new geometry persistification a new generation of applications could be developed, which can use the actual detector geometry while being platform-independent and experiment-independent.
The complexity of managing COPD exacerbations: a grounded theory study of European general practice.
Risør, Mette Bech; Spigt, Mark; Iversen, R; Godycki-Cwirko, M; Francis, N; Altiner, A; Andreeva, E; Kung, K; Melbye, H
2013-12-05
To understand the concerns and challenges faced by general practitioners (GPs) and respiratory physicians about primary care management of acute exacerbations in patients with chronic obstructive pulmonary disease (COPD). 21 focus group discussions (FGDs) were performed in seven countries with a Grounded Theory approach. Each country performed three rounds of FGDs. Primary and secondary care in Norway, Germany, Wales, Poland, Russia, The Netherlands, China (Hong Kong). 142 GPs and respiratory physicians were chosen to include urban and rural GPs as well as hospital-based and out patient-clinic respiratory physicians. Management of acute COPD exacerbations is dealt with within a scope of concerns. These concerns range from 'dealing with comorbidity' through 'having difficult patients' to 'confronting a hopeless disease'. The first concern displays medical uncertainty regarding diagnosis, medication and hospitalisation. These clinical processes become blurred by comorbidity and the social context of the patient. The second concern shows how patients receive the label 'difficult' exactly because they need complex attention, but even more because they are time consuming, do not take responsibility and are non-compliant. The third concern relates to the emotional reactions by the physicians when confronted with 'a hopeless disease' due to the fact that most of the patients do not improve and the treatment slows down the process at best. GPs and respiratory physicians balance these concerns with medical knowledge and practical, situational knowledge, trying to encompass the complexity of a medical condition. Knowing the patient is essential when dealing with comorbidities as well as with difficult relations in the consultations on exacerbations. This study suggests that it is crucial to improve the collaboration between primary and secondary care, in terms of, for example, shared consultations and defined work tasks, which may enhance shared knowledge of patients
Simmons, Charles J; Stratemeier, Horst; Hitchman, Michael A; Reinen, Dirk; Masters, Vanessa M; Riley, Mark J
2011-06-06
The crystal structures of trans-diaquabis(methoxyacetato)copper(II) and the isostructural nickel(II) complex have been determined over a wide temperature range. In conjunction with the reported behavior of the g-values, the structural data suggest that the copper(II) compound exhibits a thermal equilibrium between three structural forms, two having orthorhombically distorted, tetragonally elongated geometries but with the long and intermediate bonds to different atoms, and the third with a tetragonally compressed geometry. This is apparently the first reported example of a copper(II) complex undergoing an equilibrium between tetragonally elongated and compressed forms. The optical spectrum of single crystals of the copper(II) compound is used to obtain metal-ligand bonding parameters which yield the g-values of the compressed form of the complex and hence the proportions of the complex in each structural form at every temperature. When combined with estimates of the Jahn-Teller distortions of the different forms, the latter produce excellent agreement with the observed temperature dependence of the bond lengths. The behavior of an infrared combination band is consistent with such a thermal equilibrium, as is the temperature dependence of the thermal ellipsoid parameters and the XAFS. The potential surfaces of the different forms of the copper(II) complex have been calculated by a model based upon Jahn-Teller coupling. It is suggested that cooperative effects may cause the development of the population of tetragonally compressed complexes, and the crystal packing is consistent with this hypothesis, though the present model may oversimplify the diversity of structural forms present at high temperature. © 2011 American Chemical Society
Zonal wavefront reconstruction in quadrilateral geometry for phase measuring deflectometry.
Huang, Lei; Xue, Junpeng; Gao, Bo; Zuo, Chao; Idir, Mourad
2017-06-20
There are wide applications for zonal reconstruction methods in slope-based metrology due to its good capability of reconstructing the local details on surface profile. It was noticed in the literature that large reconstruction errors occur when using zonal reconstruction methods designed for rectangular geometry to process slopes in a quadrilateral geometry, which is a more general geometry with phase measuring deflectometry. In this work, we present a new idea for the zonal methods for quadrilateral geometry. Instead of employing the intermediate slopes to set up height-slope equations, we consider the height increment as a more general connector to establish the height-slope relations for least-squares regression. The classical zonal methods and interpolation-assisted zonal methods are compared with our proposal. Results of both simulation and experiment demonstrate the effectiveness of the proposed idea. In implementation, the modification on the classical zonal methods is addressed. The new methods preserve many good aspects of the classical ones, such as the ability to handle a large incomplete slope dataset in an arbitrary aperture, and the low computational complexity comparable with the classical zonal method. Of course, the accuracy of the new methods is much higher when integrating the slopes in quadrilateral geometry.
Domain-general neural correlates of dependency formation: Using complex tones to simulate language.
Brilmayer, Ingmar; Sassenhagen, Jona; Bornkessel-Schlesewsky, Ina; Schlesewsky, Matthias
2017-08-01
There is an ongoing debate whether the P600 event-related potential component following syntactic anomalies reflects syntactic processes per se, or if it is an instance of the P300, a domain-general ERP component associated with attention and cognitive reorientation. A direct comparison of both components is challenging because of the huge discrepancy in experimental designs and stimulus choice between language and 'classic' P300 experiments. In the present study, we develop a new approach to mimic the interplay of sequential position as well as categorical and relational information in natural language syntax (word category and agreement) in a non-linguistic target detection paradigm using musical instruments. Participants were instructed to (covertly) detect target tones which were defined by instrument change and pitch rise between subsequent tones at the last two positions of four-tone sequences. We analysed the EEG using event-related averaging and time-frequency decomposition. Our results show striking similarities to results obtained from linguistic experiments. We found a P300 that showed sensitivity to sequential position and a late positivity sensitive to stimulus type and position. A time-frequency decomposition revealed significant effects of sequential position on the theta band and a significant influence of stimulus type on the delta band. Our results suggest that the detection of non-linguistic targets defined via complex feature conjunctions in the present study and the detection of syntactic anomalies share the same underlying processes: attentional shift and memory based matching processes that act upon multi-feature conjunctions. We discuss the results as supporting domain-general accounts of the P600 during natural language comprehension. Copyright © 2017 Elsevier Ltd. All rights reserved.
Tak, E C P M; van Meurs, J B; Bierma-Zeinstra, S M A; Hofman, A; Hopman-Rock, M
2017-12-01
The aim of the present study was to report on factors associated with changes in disability after 5 years, with a focus on physical activity (PA) in community-dwelling older adults with generalized radiographic osteoarthritis (GROA). Assessment of GROA (hand, knee, hip) and disability (Health Assessment Questionnaire) in the Rotterdam Study (cohort RS-1, N = 7,983; with GROA, n = 821). A good outcome at follow-up was defined as improved or mild disability, and a poor outcome as worsened or severe disability. Factors potentially associated with outcome were demographics, joint complaints, other chronic health problems or limitations (body mass index, number of chronic conditions, cognition), and level of different types of PA. Some of these assessments were repeated in between 1997 and 1999 (RS-3), and between 2002 and 2004 (RS-4). A total of 309 older adults with GROA and valid measures on RS-3 and RS-4 showed mild to moderate disability, with minor increases over 5 years (follow-up N = 287 RS-3 to RS-4). PA levels decreased with increasing disability, especially in sport and walking. PA was univariately associated with a better outcome at follow-up but when adjusted for other factors (higher age, having knee pain and stiffness, and having more than two other chronic conditions) was associated with negative changes in general and lower limb disability, although not with upper limb disability. This was the first study to report that community-dwelling older adults with GROA show moderate levels of disability, and that reduced levels of disability are associated with higher levels of PA, but when adjusted for other confounders this association is lost. Further research is needed to study the complex relationships between PA and other determinants of disability. Copyright © 2017 John Wiley & Sons, Ltd.
Energy Technology Data Exchange (ETDEWEB)
Curbelo, Jesus P.; Silva, Odair P. da; Barros, Ricardo C. [Universidade do Estado do Rio de Janeiro (UERJ), Nova Friburgo, RJ (Brazil). Instituto Politecnico. Programa de Pos-graduacao em Modelagem Computacional; Garcia, Carlos R., E-mail: cgh@instec.cu [Departamento de Ingenieria Nuclear, Instituto Superior de Tecnologias y Ciencias Aplicadas (InSTEC), La Habana (Cuba)
2017-07-01
Presented here is the application of the adjoint technique for solving source-detector discrete ordinates (S{sub N}) transport problems by using a spectral nodal method. For slab-geometry adjoint S-N model, the adjoint spectral Green's function method (SGF{sup †}) is extended to multigroup problems considering arbitrary L'th-order of scattering anisotropy, and the possibility of non-zero prescribed boundary conditions for the forward S{sub N} transport problems. The SGF{sup †} method converges numerical solutions that are completely free from spatial truncation errors. In order to generate numerical solutions of the SGF{sup †} equations, we use the partial adjoint one-node block inversion (NBI) iterative scheme. Partial adjoint NBI scheme uses the most recent estimates for the node-edge adjoint angular Fluxes in the outgoing directions of a given discretization node, to solve the resulting adjoint SN problem in that node for all the adjoint angular fluxes in the incoming directions, which constitute the outgoing adjoint angular fluxes for the adjacent node in the sweeping directions. Numerical results are given to illustrate the present spectral nodal method features and some advantages of using the adjoint technique in source-detector problems. author)
International Nuclear Information System (INIS)
Curbelo, Jesus P.; Silva, Odair P. da; Barros, Ricardo C.
2017-01-01
Presented here is the application of the adjoint technique for solving source{detector discrete ordinates (S N ) transport problems by using a spectral nodal method. For slab-geometry adjoint S-N model, the adjoint spectral Green's function method (SGF † ) is extended to multigroup problems considering arbitrary L'th-order of scattering anisotropy, and the possibility of non{zero prescribed boundary conditions for the forward S N transport problems. The SGF † method converges numerical solutions that are completely free from spatial truncation errors. In order to generate numerical solutions of the SGF † equations, we use the partial adjoint one{node block inversion (NBI) iterative scheme. Partial adjoint NBI scheme uses the most recent estimates for the node-edge adjoint angular Fluxes in the outgoing directions of a given discretization node, to solve the resulting adjoint SN problem in that node for all the adjoint angular fluxes in the incoming directions, which constitute the outgoing adjoint angular fluxes for the adjacent node in the sweeping directions. Numerical results are given to illustrate the present spectral nodal method features and some advantages of using the adjoint technique in source-detector problems. author)
Deep graphs—A general framework to represent and analyze heterogeneous complex systems across scales
Traxl, Dominik; Boers, Niklas; Kurths, Jürgen
2016-06-01
Network theory has proven to be a powerful tool in describing and analyzing systems by modelling the relations between their constituent objects. Particularly in recent years, a great progress has been made by augmenting "traditional" network theory in order to account for the multiplex nature of many networks, multiple types of connections between objects, the time-evolution of networks, networks of networks and other intricacies. However, existing network representations still lack crucial features in order to serve as a general data analysis tool. These include, most importantly, an explicit association of information with possibly heterogeneous types of objects and relations, and a conclusive representation of the properties of groups of nodes as well as the interactions between such groups on different scales. In this paper, we introduce a collection of definitions resulting in a framework that, on the one hand, entails and unifies existing network representations (e.g., network of networks and multilayer networks), and on the other hand, generalizes and extends them by incorporating the above features. To implement these features, we first specify the nodes and edges of a finite graph as sets of properties (which are permitted to be arbitrary mathematical objects). Second, the mathematical concept of partition lattices is transferred to the network theory in order to demonstrate how partitioning the node and edge set of a graph into supernodes and superedges allows us to aggregate, compute, and allocate information on and between arbitrary groups of nodes. The derived partition lattice of a graph, which we denote by deep graph, constitutes a concise, yet comprehensive representation that enables the expression and analysis of heterogeneous properties, relations, and interactions on all scales of a complex system in a self-contained manner. Furthermore, to be able to utilize existing network-based methods and models, we derive different representations of
Rajab, Ghada Z; Suh, Soh Youn; Demer, Joseph L
2017-06-01
Dissociated strabismus complex (DSC) is an enigmatic form of strabismus that includes dissociated vertical deviation (DVD) and dissociated horizontal deviation (DHD). We employed magnetic resonance imaging (MRI) to evaluate the extraocular muscles in DSC. We studied 5 patients with DSC and mean age of 25 years (range, 12-42 years), and 15 age-matched, orthotropic control subjects. All patients had DVD; 4 also had DHD. We employed high-resolution, surface coil MRI with thin, 2 mm slices and central target fixation. Volumes of the rectus and superior oblique muscles in the region 12 mm posterior to 4 mm anterior to the globe-optic nerve junction were measured in quasi-coronal planes in central gaze. Patients with DSC had no structural abnormalities of rectus muscles or rectus pulleys or the superior oblique muscle but exhibited modest, statistically significant increased volume of all rectus muscles ranging from 20% for medial rectus to 9% for lateral rectus (P muscles. DSC is associated with generalized rectus extraocular muscle hypertrophy in the absence of other orbital abnormalities. Copyright © 2017 American Association for Pediatric Ophthalmology and Strabismus. Published by Elsevier Inc. All rights reserved.
A general theoretical model for electron transfer reactions in complex systems.
Amadei, Andrea; Daidone, Isabella; Aschi, Massimiliano
2012-01-28
In this paper we present a general theoretical-computational model for treating electron transfer reactions in complex atomic-molecular systems. The underlying idea of the approach, based on unbiased first-principles calculations at the atomistic level, utilizes the definition and the construction of the Diabatic Perturbed states of the involved reactive partners (i.e. the quantum centres in our perturbation approach) as provided by the interaction with their environment, including their mutual interaction. In this way we reconstruct the true Adiabatic states of the reactive partners characterizing the electron transfer process as the fluctuation of the electronic density due to the fluctuating perturbation. Results obtained by using a combination of Molecular Dynamics simulation and the Perturbed Matrix Method on a prototypical intramolecular electron transfer (from 2-(9,9'-dimethyl)fluorene to the 2-naphthalene group separated by a steroidal 5-α-androstane skeleton) well illustrate the accuracy of the method in reproducing both the thermodynamics and the kinetics of the process.
Quantum groups: Geometry and applications
International Nuclear Information System (INIS)
Chu, C.S.
1996-01-01
The main theme of this thesis is a study of the geometry of quantum groups and quantum spaces, with the hope that they will be useful for the construction of quantum field theory with quantum group symmetry. The main tool used is the Faddeev-Reshetikhin-Takhtajan description of quantum groups. A few content-rich examples of quantum complex spaces with quantum group symmetry are treated in details. In chapter 1, the author reviews some of the basic concepts and notions for Hopf algebras and other background materials. In chapter 2, he studies the vector fields of quantum groups. A compact realization of these vector fields as pseudodifferential operators acting on the linear quantum spaces is given. In chapter 3, he describes the quantum sphere as a complex quantum manifold by means of a quantum stereographic projection. A covariant calculus is introduced. An interesting property of this calculus is the existence of a one-form realization of the exterior differential operator. The concept of a braided comodule is introduced and a braided algebra of quantum spheres is constructed. In chapter 4, the author considers the more general higher dimensional quantum complex projective spaces and the quantum Grassman manifolds. Differential calculus, integration and braiding can be introduced as in the one dimensional case. Finally, in chapter 5, he studies the framework of quantum principal bundle and construct the q-deformed Dirac monopole as a quantum principal bundle with a quantum sphere as the base and a U(1) with non-commutative calculus as the fiber. The first Chern class can be introduced and integrated to give the monopole charge
Indian Academy of Sciences (India)
Page S20: NMR compound 4i. Page S22: NMR compound 4j. General: Chemicals were purchased from Fluka, Merck and Aldrich Chemical Companies. All the products were characterized by comparison of their IR, 1H NMR and 13C NMR spectroscopic data and their melting points with reported values. General procedure ...
DeGrand, Michael J.; Abrams, M. Leigh; Jenkins, Judith L.; Welch, Lawrence E.
2011-01-01
By adding a large quantity of Cl[superscript -] to an aqueous solution of CoCl[subscript 2][multiplied by]6H[subscript 2]O, a mixture containing a red octahedral cobalt complex and a blue tetrahedral complex is produced. When the solution temperature is modified, the equilibrium constant, K[subscript eq], of the complexation reaction is shifted…
Mahé, Louis; Roy, Marie-Françoise
1992-01-01
Ten years after the first Rennes international meeting on real algebraic geometry, the second one looked at the developments in the subject during the intervening decade - see the 6 survey papers listed below. Further contributions from the participants on recent research covered real algebra and geometry, topology of real algebraic varieties and 16thHilbert problem, classical algebraic geometry, techniques in real algebraic geometry, algorithms in real algebraic geometry, semialgebraic geometry, real analytic geometry. CONTENTS: Survey papers: M. Knebusch: Semialgebraic topology in the last ten years.- R. Parimala: Algebraic and topological invariants of real algebraic varieties.- Polotovskii, G.M.: On the classification of decomposing plane algebraic curves.- Scheiderer, C.: Real algebra and its applications to geometry in the last ten years: some major developments and results.- Shustin, E.L.: Topology of real plane algebraic curves.- Silhol, R.: Moduli problems in real algebraic geometry. Further contribu...
Functional integration over geometries
International Nuclear Information System (INIS)
Mottola, E.
1995-01-01
The geometric construction of the functional integral over coset spaces M/G is reviewed. The inner product on the cotangent space of infinitesimal deformations of M defines an invariant distance and volume form, or functional integration measure on the full configuration space. Then, by a simple change of coordinates parameterizing the gauge fiber G, the functional measure on the coset space M/G is deduced. This change of integration variables leads to a Jacobian which is entirely equivalent to the Faddeev--Popov determinant of the more traditional gauge fixed approach in non-abelian gauge theory. If the general construction is applied to the case where G is the group of coordinate reparameterizations of spacetime, the continuum functional integral over geometries, i.e. metrics modulo coordinate reparameterizations may be defined. The invariant functional integration measure is used to derive the trace anomaly and effective action for the conformal part of the metric in two and four dimensional spacetime. In two dimensions this approach generates the Polyakov--Liouville action of closed bosonic non-critical string theory. In four dimensions the corresponding effective action leads to novel conclusions on the importance of quantum effects in gravity in the far infrared, and in particular, a dramatic modification of the classical Einstein theory at cosmological distance scales, signaled first by the quantum instability of classical de Sitter spacetime. Finite volume scaling relations for the functional integral of quantum gravity in two and four dimensions are derived, and comparison with the discretized dynamical triangulation approach to the integration over geometries are discussed. Outstanding unsolved problems in both the continuum definition and the simplicial approach to the functional integral over geometries are highlighted
Bochnak, Jacek; Roy, Marie-Françoise
1998-01-01
This book is a systematic treatment of real algebraic geometry, a subject that has strong interrelation with other areas of mathematics: singularity theory, differential topology, quadratic forms, commutative algebra, model theory, complexity theory etc. The careful and clearly written account covers both basic concepts and up-to-date research topics. It may be used as text for a graduate course. The present edition is a substantially revised and expanded English version of the book "Géometrie algébrique réelle" originally published in French, in 1987, as Volume 12 of ERGEBNISSE. Since the publication of the French version the theory has made advances in several directions. Many of these are included in this English version. Thus the English book may be regarded as a completely new treatment of the subject.
Algebraic Methods in Plane Geometry
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 13; Issue 10. Algebraic Methods in Plane Geometry - The Use of Conic Sections. Shailesh A Shirali. General Article Volume 13 Issue 10 October 2008 pp 916-928. Fulltext. Click here to view fulltext PDF. Permanent link:
Multivariable calculus and differential geometry
Walschap, Gerard
2015-01-01
This text is a modern in-depth study of the subject that includes all the material needed from linear algebra. It then goes on to investigate topics in differential geometry, such as manifolds in Euclidean space, curvature, and the generalization of the fundamental theorem of calculus known as Stokes' theorem.
Generalization of the Activated Complex Theory of Reaction Rates. I. Quantum Mechanical Treatment
Marcus, R. A.
1964-01-01
In its usual form activated complex theory assumes a quasi-equilibrium between reactants and activated complex, a separable reaction coordinate, a Cartesian reaction coordinate, and an absence of interaction of rotation with internal motion in the complex. In the present paper a rate expression is derived without introducing the Cartesian assumption. The expression bears a formal resemblance to the usual one and reduces to it when the added assumptions of the latter are introduced.
Meyer, Walter J
2006-01-01
Meyer''s Geometry and Its Applications, Second Edition, combines traditional geometry with current ideas to present a modern approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, and introduces axiomatic, Euclidean geometry, non-Euclidean geometry, and transformational geometry. The text integrates applications and examples throughout and includes historical notes in many chapters. The Second Edition of Geometry and Its Applications is a significant text for any college or university that focuses on geometry''s usefulness in other disciplines. It is especially appropriate for engineering and science majors, as well as future mathematics teachers.* Realistic applications integrated throughout the text, including (but not limited to): - Symmetries of artistic patterns- Physics- Robotics- Computer vision- Computer graphics- Stability of architectural structures- Molecular biology- Medicine- Pattern recognition* Historical notes included in many chapters...
International Nuclear Information System (INIS)
Tyurin, A N
2000-01-01
The special geometry of calibrated cycles, which is closely related to the mirror symmetry among Calabi-Yau 3-manifolds, is in fact only a specialization of a more general geometry, which may naturally be called slightly deformed algebraic geometry or phase geometry. On the other hand, both of these geometries are parallel to classical gauge theory and its complexification. This article explains this parallelism. Hence the appearance of new invariants in complexified gauge theory is accompanied by the appearance of analogous invariants in the theory of special Lagrangian cycles, whose development is at present much more modest. Algebraic geometry is transformed into special Lagrangian geometry by the geometric Fourier transform (GFT). Roughly speaking, this construction coincides with the well-known 'spectral curve' constructions plus phase geometry
Cvetic, Mirjam; Piragua, Hernan; Taylor, Washington
2015-01-01
We construct the general form of an F-theory compactification with two U(1) factors based on a general elliptically fibered Calabi-Yau manifold with Mordell-Weil group of rank two. This construction produces broad classes of models with diverse matter spectra, including many that are not realized in earlier F-theory constructions with U(1)xU(1) gauge symmetry. Generic U(1)xU(1) models can be related to a Higgsed non-Abelian model with gauge group SU(2)xSU(2)xSU(3), SU(2)^3xSU(3), or a subgroup thereof. The nonlocal horizontal divisors of the Mordell-Weil group are replaced with local vertical divisors associated with the Cartan generators of non-Abelian gauge groups from Kodaira singularities. We give a global resolution of codimension two singularities of the Abelian model; we identify the full anomaly free matter content, and match it to the unHiggsed non-Abelian model. The non-Abelian Weierstrass model exhibits a new algebraic description of the singularities in the fibration that results in the first expl...
Modern differential geometry for physicists
Isham, C J
1989-01-01
These notes are the content of an introductory course on modern, coordinate-free differential geometry which is taken by the first-year theoretical physics PhD students, or by students attending the one-year MSc course "Fundamental Fields and Forces" at Imperial College. The book is concerned entirely with mathematics proper, although the emphasis and detailed topics have been chosen with an eye to the way in which differential geometry is applied these days to modern theoretical physics. This includes not only the traditional area of general relativity but also the theory of Yang-Mills fields
Diabetic retinopathy and complexity of retinal surgery in a general hospital.
Mijangos-Medina, Laura Fanny; Hurtado-Noriega, Blanca Esmeralda; Lima-Gómez, Virgilio
2012-01-01
Usual retinal surgery (vitrectomy or surgery for retinal detachment) may require additional procedures to deal with complex cases, which increase time and resource use and delay access to treatment. We undertook this study to identify the proportion of primary retinal surgeries that required complex procedures and the associated causes. We carried out an observational, descriptive, cross-sectional, retrospective study. Patients with primary retinal surgery were evaluated (January 2007-December 2010). The proportion and 95% confidence intervals (CI) of preoperative diagnosis and cause of the disease requiring retinal surgery as well as the causes for complex retinal surgery were identified. Complex retinal surgery was defined as that requiring lens extraction, intraocular lens implantation, heavy perfluorocarbon liquids, silicone oil tamponade or intravitreal drugs, in addition to the usual surgical retinal procedure. The proportion of complex retinal surgeries was compared among preoperative diagnoses and among causes (χ(2), odds ratio [OR]). We studied 338 eyes. Mean age of subjects was 53.7 years, and there were 49% females. The most common diagnoses were vitreous hemorrhage (27.2%) and rhegmatogenous retinal detachment (24.6%). The most common cause was diabetes (50.6%); 273 eyes required complex surgery (80.8%, 95% CI: 76.6-85). The proportion did not differ among diagnoses but was higher in diabetic retinopathy (89%, p diabetic retinopathy increased by 3-fold the probability of requiring these complex procedures. Early treatment of diabetic retinopathy may reduce the proportion of complex retinal surgery by 56%.
Automorphisms in Birational and Affine Geometry
Ciliberto, Ciro; Flenner, Hubert; McKernan, James; Prokhorov, Yuri; Zaidenberg, Mikhail
2014-01-01
The main focus of this volume is on the problem of describing the automorphism groups of affine and projective varieties, a classical subject in algebraic geometry where, in both cases, the automorphism group is often infinite dimensional. The collection covers a wide range of topics and is intended for researchers in the fields of classical algebraic geometry and birational geometry (Cremona groups) as well as affine geometry with an emphasis on algebraic group actions and automorphism groups. It presents original research and surveys and provides a valuable overview of the current state of the art in these topics. Bringing together specialists from projective, birational algebraic geometry and affine and complex algebraic geometry, including Mori theory and algebraic group actions, this book is the result of ensuing talks and discussions from the conference “Groups of Automorphisms in Birational and Affine Geometry” held in October 2012, at the CIRM, Levico Terme, Italy. The talks at the conference high...
Electrodynamics and Spacetime Geometry: Foundations
Cabral, Francisco; Lobo, Francisco S. N.
2017-02-01
We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic structure of electromagnetism, clearly formulated via integration theory and differential forms. We review the foundations of classical electromagnetism based on charge and magnetic flux conservation, the Lorentz force and the constitutive relations. These relations introduce the conformal part of the metric and allow the study of electrodynamics for specific spacetime geometries. At the foundational level, we discuss the possibility of generalizing the vacuum constitutive relations, by relaxing the fixed conditions of homogeneity and isotropy, and by assuming that the symmetry properties of the electro-vacuum follow the spacetime isometries. The implications of this extension are briefly discussed in the context of the intimate connection between electromagnetism and the geometry (and causal structure) of spacetime.
Czech Academy of Sciences Publication Activity Database
Khusniyarov, M. M.; Harms, K.; Burghaus, O.; Sundermayer, J.; Sarkar, B.; Kaim, W.; van Slageren, J.; Duboc, C.; Fiedler, Jan
-, č. 10 (2008), s. 1355-1365 ISSN 1477-9226 R&D Projects: GA MŠk OC 139; GA MŠk OC 140 Institutional research plan: CEZ:AV0Z40400503 Keywords : metal complexes * non-innocent N,N’-Bis(pentafluorophenyl)-o-phenylenediamido ligand * electronic structure Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 3.580, year: 2008
Special metrics and group actions in geometry
Fino, Anna; Musso, Emilio; Podestà, Fabio; Vezzoni, Luigi
2017-01-01
The volume is a follow-up to the INdAM meeting “Special metrics and quaternionic geometry” held in Rome in November 2015. It offers a panoramic view of a selection of cutting-edge topics in differential geometry, including 4-manifolds, quaternionic and octonionic geometry, twistor spaces, harmonic maps, spinors, complex and conformal geometry, homogeneous spaces and nilmanifolds, special geometries in dimensions 5–8, gauge theory, symplectic and toric manifolds, exceptional holonomy and integrable systems. The workshop was held in honor of Simon Salamon, a leading international scholar at the forefront of academic research who has made significant contributions to all these subjects. The articles published here represent a compelling testimony to Salamon’s profound and longstanding impact on the mathematical community. Target readership includes graduate students and researchers working in Riemannian and complex geometry, Lie theory and mathematical physics.
Geometry essentials for dummies
Ryan, Mark
2011-01-01
Just the critical concepts you need to score high in geometry This practical, friendly guide focuses on critical concepts taught in a typical geometry course, from the properties of triangles, parallelograms, circles, and cylinders, to the skills and strategies you need to write geometry proofs. Geometry Essentials For Dummies is perfect for cramming or doing homework, or as a reference for parents helping kids study for exams. Get down to the basics - get a handle on the basics of geometry, from lines, segments, and angles, to vertices, altitudes, and diagonals Conque
Introduction to projective geometry
Wylie, C R
2008-01-01
This lucid introductory text offers both an analytic and an axiomatic approach to plane projective geometry. The analytic treatment builds and expands upon students' familiarity with elementary plane analytic geometry and provides a well-motivated approach to projective geometry. Subsequent chapters explore Euclidean and non-Euclidean geometry as specializations of the projective plane, revealing the existence of an infinite number of geometries, each Euclidean in nature but characterized by a different set of distance- and angle-measurement formulas. Outstanding pedagogical features include w
Advances in the study of the environmental fate, transport, and ecotoxicological effects of engineered nanomaterials (ENMs) have been hampered by a lack of adequate techniques for the detection and quantification of ENMs at environmentally relevant concentrations in complex media...
A General Non-Radioactive ATPase Assay for Chromatin Remodeling Complexes
Stanton, Benjamin Z.; Hodges, Courtney; Crabtree, Gerald R.; Zhao, Keji
2016-01-01
Chromatin remodeling complexes couple the energy released from ATP hydrolysis to facilitate transcription, recombination and repair mechanisms essential for a wide variety of biologic responses. While recombinant expression of the regulatory subunits of these enzymes is possible, measuring catalytic (ATPase) activity of the intact complexes recovered from normal or mutant cells is critical for understanding their mechanisms. SWI/SNF-like remodeling complexes can be megadaltons in size and include many regulatory subunits, making reconstitution of purified subunits challenging for recapitulating in vivo function. The protocol in this article defines the first highly quantitative ATPase assay for intact remodeling complexes that does not require radiation or reconstitution of recombinantly expressed subunits. This protocol is specifically useful for defining the catalytic role of active-site mutations in the context of other regulatory subunits and quantitatively rank-ordering inactivating catalytic-site mutations. PMID:28253434
Geometry of surfaces a practical guide for mechanical engineers
Radzevich, Stephen P
2012-01-01
Presents an in-depth analysis of geometry of part surfaces and provides the tools for solving complex engineering problems Geometry of Surfaces: A Practical Guide for Mechanical Engineers is a comprehensive guide to applied geometry of surfaces with focus on practical applications in various areas of mechanical engineering. The book is divided into three parts on Part Surfaces, Geometry of Contact of Part Surfaces and Mapping of the Contacting Part Surfaces. Geometry of Surfaces: A Practical Guide for Mechanical Engineers combines differential geometry and gearing theory and presents new developments in the elementary theory of enveloping surfaces. Written by a leading expert of the field, this book also provides the reader with the tools for solving complex engineering problems in the field of mechanical engineering. Presents an in-depth analysis of geometry of part surfaces Provides tools for solving complex engineering problems in the field of mechanical engineering Combines differential geometry an...
Robotic general surgery experience: a gradual progress from simple to more complex procedures.
Al-Naami, M; Anjum, M N; Aldohayan, A; Al-Khayal, K; Alkharji, H
2013-12-01
Robotic surgery was introduced at our institution in 2003, and we used a progressive approach advancing from simple to more complex procedures. A retrospective chart review. Cases included totalled 129. Set-up and operative times have improved over time and with experience. Conversion rates to standard laparoscopic or open techniques were 4.7% and 1.6%, respectively. Intraoperative complications (6.2%), blood loss and hospital stay were directly proportional to complexity. There were no mortalities and the postoperative complication rate (13.2%) was within accepted norms. Our findings suggest that robot technology is presently most useful in cases tailored toward its advantages, i.e. those confined to a single space, those that require performance of complex tasks, and re-do procedures. Copyright © 2013 John Wiley & Sons, Ltd.
Principles of algebraic geometry
Griffiths, Phillip A
1994-01-01
A comprehensive, self-contained treatment presenting general results of the theory. Establishes a geometric intuition and a working facility with specific geometric practices. Emphasizes applications through the study of interesting examples and the development of computational tools. Coverage ranges from analytic to geometric. Treats basic techniques and results of complex manifold theory, focusing on results applicable to projective varieties, and includes discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex as well as special top
A Statistical Evaluation of Atmosphere-Ocean General Circulation Models: Complexity vs. Simplicity
Robert K. Kaufmann; David I. Stern
2004-01-01
The principal tools used to model future climate change are General Circulation Models which are deterministic high resolution bottom-up models of the global atmosphere-ocean system that require large amounts of supercomputer time to generate results. But are these models a cost-effective way of predicting future climate change at the global level? In this paper we use modern econometric techniques to evaluate the statistical adequacy of three general circulation models (GCMs) by testing thre...
Directory of Open Access Journals (Sweden)
Yanning Zeng
2016-12-01
Full Text Available A new pair of plladium complexes (Pd4 and Pd5 ligated with constrained N-(5,6,7-trihydroquinolin-8-ylidenearylamine ligands have been prepared and well characterized by 1H-, 13C-NMR and FTIR spectroscopies as well as elemental analysis. The molecular structure of Pd4 and Pd5 in solid state have also been determined by X-ray diffraction, showing slightly distorted square planar geometry around the palladium metal center. All complexes Pd1–Pd5 are revealed highly efficient catalyst in methyl acrylate (MA polymerization as well as methyl acrylate/norbornene (MA/NB copolymerization. In the case of MA polymerization, as high as 98.4% conversion with high molecular weight up to 6282 kg·mol−1 was achieved. Likewise, Pd3 complex has good capability to incorporate about 18% NB content into MA polymer chains. Furthermore, low catalyst loadings (0.002 mol % of Pd4 or Pd5 are able to efficiently mediate the coupling of haloarenes with styrene affording up to 98% conversion.
General treatment of conjugate acid-base, redox and complexation equilibria.
Elenkova, N G
1980-09-01
Acid-base, redox and complexation reactions are treated uniformly in terms of particle transfer. As a result, a single set of mathematical equations can be used to describe all three types of reaction and to perform the usual calculations for these systems.
A general method for computing the total solar radiation force on complex spacecraft structures
Chan, F. K.
1981-01-01
The method circumvents many of the existing difficulties in computational logic presently encountered in the direct analytical or numerical evaluation of the appropriate surface integral. It may be applied to complex spacecraft structures for computing the total force arising from either specular or diffuse reflection or even from non-Lambertian reflection and re-radiation.
De Rham complexes of q-analogue of general linear group GLq(N)
International Nuclear Information System (INIS)
Sun Xiaodong; Wang Shikun
1993-07-01
In this paper we give a set of De Rham complexes of quantum group GL q (N) determined by one parameter r, and prove that the differential calculi on the quantum group GL q (N) given in this paper are bicovariant. The noncommutative differential calculi on the quantum groups SL q (N) and SU q (N) are also discussed. (author). 15 refs
Vossos, Spyridon; Vossos, Elias
2016-08-01
closed LSTT is reduced, if one RIO has small velocity wrt another RIO. Thus, we have infinite number of closed LSTTs, each one with the corresponding SR theory. In case that we relate accelerated observers with variable metric of spacetime, we have the case of General Relativity (GR). For being that clear, we produce a generalized Schwarzschild metric, which is in accordance with any SR based on this closed complex LSTT and Einstein equations. The application of this kind of transformations to the SR and GR is obvious. But, the results may be applied to any linear space of dimension four endowed with steady or variable metric, whose elements (four- vectors) have spatial part (vector) with Euclidean metric.
International Nuclear Information System (INIS)
Vossos, Spyridon; Vossos, Elias
2016-01-01
any other closed LSTT is reduced, if one RIO has small velocity wrt another RIO. Thus, we have infinite number of closed LSTTs, each one with the corresponding SR theory. In case that we relate accelerated observers with variable metric of spacetime, we have the case of General Relativity (GR). For being that clear, we produce a generalized Schwarzschild metric, which is in accordance with any SR based on this closed complex LSTT and Einstein equations. The application of this kind of transformations to the SR and GR is obvious. But, the results may be applied to any linear space of dimension four endowed with steady or variable metric, whose elements (four- vectors) have spatial part (vector) with Euclidean metric. (paper)
Bárány, Imre; Vilcu, Costin
2016-01-01
This volume presents easy-to-understand yet surprising properties obtained using topological, geometric and graph theoretic tools in the areas covered by the Geometry Conference that took place in Mulhouse, France from September 7–11, 2014 in honour of Tudor Zamfirescu on the occasion of his 70th anniversary. The contributions address subjects in convexity and discrete geometry, in distance geometry or with geometrical flavor in combinatorics, graph theory or non-linear analysis. Written by top experts, these papers highlight the close connections between these fields, as well as ties to other domains of geometry and their reciprocal influence. They offer an overview on recent developments in geometry and its border with discrete mathematics, and provide answers to several open questions. The volume addresses a large audience in mathematics, including researchers and graduate students interested in geometry and geometrical problems.
On the Analyticity for the Generalized Quadratic Derivative Complex Ginzburg-Landau Equation
Directory of Open Access Journals (Sweden)
Chunyan Huang
2014-01-01
Full Text Available We study the analytic property of the (generalized quadratic derivative Ginzburg-Landau equation (1/2⩽α⩽1 in any spatial dimension n⩾1 with rough initial data. For 1/2<α⩽1, we prove the analyticity of local solutions to the (generalized quadratic derivative Ginzburg-Landau equation with large rough initial data in modulation spaces Mp,11-2α(1⩽p⩽∞. For α=1/2, we obtain the analytic regularity of global solutions to the fractional quadratic derivative Ginzburg-Landau equation with small initial data in B˙∞,10(ℝn∩M∞,10(ℝn. The strategy is to develop uniform and dyadic exponential decay estimates for the generalized Ginzburg-Landau semigroup e-a+it-Δα to overcome the derivative in the nonlinear term.
Generalized random walk algorithm for the numerical modeling of complex diffusion processes
Vamos, C; Vereecken, H
2003-01-01
A generalized form of the random walk algorithm to simulate diffusion processes is introduced. Unlike the usual approach, at a given time all the particles from a grid node are simultaneously scattered using the Bernoulli repartition. This procedure saves memory and computing time and no restrictions are imposed for the maximum number of particles to be used in simulations. We prove that for simple diffusion the method generalizes the finite difference scheme and gives the same precision for large enough number of particles. As an example, simulations of diffusion in random velocity field are performed and the main features of the stochastic mathematical model are numerically tested.
International Nuclear Information System (INIS)
Landman, U.
1984-01-01
Since the beginning of this project, our group has been involved in theoretical studies of surface phenomena and processes, aimed toward increasing our understanding of fundamental processes which govern the properties of material surfaces. Our studies cover a wide spectrum of surface phenomena: surface reactivity, surface crystallography, electronic and vibrational structure, dynamical processes, phase transformations and phase change, the properties of interfaces and investigations of material processing and novel materials preparation techniques. In these investigations we develop and employ analytical and novel numerical, simulation, methods for the study of complex surface phenomena. Our recent surface molecular dynamics studies and simulations of laser annealing phenomena opened new avenues for the investigation of the microscopic dynamics and evolution of equilibrium and non-equilibrium processes at surfaces and interfaces. Our current studies of metallic glasses using a new langrangian formulation which includes all components of the total energy (density dependent electron gas, single particle and pair interactions) of the system, represents a novel approach for theoretical studies of this important class of systems
Euclidean geometry and transformations
Dodge, Clayton W
1972-01-01
This introduction to Euclidean geometry emphasizes transformations, particularly isometries and similarities. Suitable for undergraduate courses, it includes numerous examples, many with detailed answers. 1972 edition.
International Nuclear Information System (INIS)
Hrivnacova, I; Viren, B
2008-01-01
The Virtual Geometry Model (VGM) was introduced at CHEP in 2004 [1], where its concept, based on the abstract interfaces to geometry objects, has been presented. Since then, it has undergone a design evolution to pure abstract interfaces, it has been consolidated and completed with more advanced features. Currently it is used in Geant4 VMC for the support of TGeo geometry definition with Geant4 native geometry navigation and recently it has been used in the validation of the G4Root tool. The implementation of the VGM for a concrete geometry model represents a small layer between the VGM and the particular native geometry. In addition to the implementations for Geant4 and Root TGeo geometry models, there is now added the third one for AGDD, which together with the existing XML exporter makes the VGM the most advanced tool for exchanging geometry formats providing 9 ways of conversions between Geant4, TGeo, AGDD and GDML models. In this presentation we will give the overview and the present status of the tool, we will review the supported features and point to possible limits in converting geometry models
O'Leary, Michael
2010-01-01
Guides readers through the development of geometry and basic proof writing using a historical approach to the topic. In an effort to fully appreciate the logic and structure of geometric proofs, Revolutions of Geometry places proofs into the context of geometry's history, helping readers to understand that proof writing is crucial to the job of a mathematician. Written for students and educators of mathematics alike, the book guides readers through the rich history and influential works, from ancient times to the present, behind the development of geometry. As a result, readers are successfull
Fundamental concepts of geometry
Meserve, Bruce E
1983-01-01
Demonstrates relationships between different types of geometry. Provides excellent overview of the foundations and historical evolution of geometrical concepts. Exercises (no solutions). Includes 98 illustrations.
Algorithms in Algebraic Geometry
Dickenstein, Alicia; Sommese, Andrew J
2008-01-01
In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric computation. Some of these algorithms were originally designed for abstract algebraic geometry, but now are of interest for use in applications and some of these algorithms were originally designed for applications, but now are of interest for use in abstract algebraic geometry. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its
Tak, E.C.; Meurs, J.B. van; Bierma-Zeinstra, S.M.; Hofman, A.; Hopman-Rock, M.
2017-01-01
OBJECTIVE: The aim of the present study was to report on factors associated with changes in disability after 5 years, with a focus on physical activity (PA) in community-dwelling older adults with generalized radiographic osteoarthritis (GROA). METHODS: Assessment of GROA (hand, knee, hip) and
DEFF Research Database (Denmark)
Gutin, Gregory; Kim, Eun Jung; Soleimanfallah, Arezou
2012-01-01
The NP-hard general factor problem asks, given a graph and for each vertex a list of integers, whether the graph has a spanning subgraph where each vertex has a degree that belongs to its assigned list. The problem remains NP-hard even if the given graph is bipartite with partition U V, and each ...
Estimation of Complex Generalized Linear Mixed Models for Measurement and Growth
Jeon, Minjeong
2012-01-01
Maximum likelihood (ML) estimation of generalized linear mixed models (GLMMs) is technically challenging because of the intractable likelihoods that involve high dimensional integrations over random effects. The problem is magnified when the random effects have a crossed design and thus the data cannot be reduced to small independent clusters. A…
Leibniz algebroids, twistings and exceptional generalized geometry
Baraglia, David
2011-01-01
We investigate a class of Leibniz algebroids which are invariant under diffeomorphisms and symmetries involving collections of closed forms. Under appropriate assumptions we arrive at a classification which in particular gives a construction starting from graded Lie algebras. In this case the Leibniz bracket is a derived bracket and there are higher derived brackets resulting in an $L_\\infty$-structure. The algebroids can be twisted by a non-abelian cohomology class and we prove that the twis...
The transport equation in general geometry
International Nuclear Information System (INIS)
Pomraning, G.C.
1990-01-01
As stated in the introduction to the paper, the motivation for this work was to obtain an explicit form for the streaming operator in the transport equation, which could be used to compute curvature effects in an asymptotic analysis leading to diffusion theory. This sign error was discovered while performing this analysis
Needle decompositions in Riemannian geometry
Klartag, Bo'az
2017-01-01
The localization technique from convex geometry is generalized to the setting of Riemannian manifolds whose Ricci curvature is bounded from below. In a nutshell, the author's method is based on the following observation: When the Ricci curvature is non-negative, log-concave measures are obtained when conditioning the Riemannian volume measure with respect to a geodesic foliation that is orthogonal to the level sets of a Lipschitz function. The Monge mass transfer problem plays an important role in the author's analysis.
Needle decompositions in riemannian geometry
Klartag, Bo'az
2017-01-01
The localization technique from convex geometry is generalized to the setting of Riemannian manifolds whose Ricci curvature is bounded from below. In a nutshell, the author's method is based on the following observation: When the Ricci curvature is non-negative, log-concave measures are obtained when conditioning the Riemannian volume measure with respect to a geodesic foliation that is orthogonal to the level sets of a Lipschitz function. The Monge mass transfer problem plays an important role in the author's analysis.
Pinning synchronization of two general complex networks with periodically intermittent control
Directory of Open Access Journals (Sweden)
Meng Fanyu
2015-12-01
Full Text Available In this paper, the method of periodically pinning intermittent control is introduced to solve the problem of outer synchronization between two complex networks. Based on the Lyapunov stability theory, differential inequality method and adaptive technique, some simple synchronous criteria have been derived analytically. At last, both the theoretical and numerical analysis illustrate the effectiveness of the proposed control methodology. This method not only reduces the conservatism of control gain but also saves the cost of production.These advantages make this method having a large application scope in the real production process.
The complexity of managing COPD exacerbations: a grounded theory study of European general practice
Ris?r, Mette Bech; Spigt, Mark; Iversen, R; Godycki-Cwirko, M; Francis, N; Altiner, A; Andreeva, E; Kung, K; Melbye, H
2013-01-01
Objectives To understand the concerns and challenges faced by general practitioners (GPs) and respiratory physicians about primary care management of acute exacerbations in patients with chronic obstructive pulmonary disease (COPD). Design 21 focus group discussions (FGDs) were performed in seven countries with a Grounded Theory approach. Each country performed three rounds of FGDs. Setting Primary and secondary care in Norway, Germany, Wales, Poland, Russia, The Netherlands, China (Hong Kong...
Energy Technology Data Exchange (ETDEWEB)
Chatillon, S
2000-07-01
This work is devoted to the enhancement of the ultrasonic non destructive testing in contact of nuclear components with complex geometry. In service inspections of such components performed with conventional probes present limited performances: variations in sensitivity, due to unmatched contact, incorrect characterization of the defect, because of the disorientations of the transducer during its displacement, and uncovered scan area when the geometry of the components disturbs the displacement of the transducer. We propose a new concept of smart transducer to improve the performances of such inspections. The radiating surface is flexible to optimize the sensitivity of the testing. Using the measure of the radiating surface distortion, performed by a specific instrumentation, phased array techniques allow the control of the transmitted beam to optimize the defect localization and characterization. Thus, this system is self-contained. We present the different steps involved to develop this system and its experimental validation. A computing model is extended to predict the field transmitted by a flexible contact transducer. This model is used to optimize the radiating surface of a jointed transducer. A delay law optimizing algorithm is developed to ensure the control of the transmitted beam. At last, a method and the associated instrumentation designed to measure the radiating surface distortion are proposed. Experimental Measures in the through-transmission mode validate the ability of this system to control the field transmitted through complex interfaces. At last, inspections in the pulse-echo mode are performed on a specimen with an irregular profile, representative of a real component inspected on site, and artificial embedded reflectors. Two control configurations are used. In the first one, the transducer is displaced along the surface, in the second one, the transducer is fixed and the region of interest is scanned using beam steering. The results show that
Kaufmann, Matthew L.; Bomer, Megan A.; Powell, Nancy Norem
2009-01-01
Students enter the geometry classroom with a strong concept of fairness and a sense of what it means to "play by the rules," yet many students have difficulty understanding the postulates, or rules, of geometry and their implications. Although they may never have articulated the properties of an axiomatic system, they have gained a practical…
Foundations of algebraic geometry
Weil, A
1946-01-01
This classic is one of the cornerstones of modern algebraic geometry. At the same time, it is entirely self-contained, assuming no knowledge whatsoever of algebraic geometry, and no knowledge of modern algebra beyond the simplest facts about abstract fields and their extensions, and the bare rudiments of the theory of ideals.
Geometry of multihadron production
International Nuclear Information System (INIS)
Bjorken, J.D.
1994-10-01
This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions
1996-01-01
Designs and Finite Geometries brings together in one place important contributions and up-to-date research results in this important area of mathematics. Designs and Finite Geometries serves as an excellent reference, providing insight into some of the most important research issues in the field.
General strategy for the ab initio calculation of exchange coupling in polynuclear complexes
Handrick, K.; Malrieu, J. P.; Castell, O.
1994-08-01
A general strategy for the calculation of energy differences between states of different total spin is proposed. The procedure goes through the definition of a minimal model space and a set of energy-difference contributing determinants is established through the second-order development of the corresponding Hamiltonian in the framework of the quasidegenerate perturbation theory. The forementioned determinants are treated variationally in a so-called differential configuration interaction (CI). Several test calculations for simple model Li clusters have been carried out, and the results of the differential CI compare favorably with those of the exact solution in the full CI procedure.
Foliation theory in algebraic geometry
McKernan, James; Pereira, Jorge
2016-01-01
Featuring a blend of original research papers and comprehensive surveys from an international team of leading researchers in the thriving fields of foliation theory, holomorphic foliations, and birational geometry, this book presents the proceedings of the conference "Foliation Theory in Algebraic Geometry," hosted by the Simons Foundation in New York City in September 2013. Topics covered include: Fano and del Pezzo foliations; the cone theorem and rank one foliations; the structure of symmetric differentials on a smooth complex surface and a local structure theorem for closed symmetric differentials of rank two; an overview of lifting symmetric differentials from varieties with canonical singularities and the applications to the classification of AT bundles on singular varieties; an overview of the powerful theory of the variety of minimal rational tangents introduced by Hwang and Mok; recent examples of varieties which are hyperbolic and yet the Green-Griffiths locus is the whole of X; and a classificati...
Bender, C L; Otamendi, A; Calfa, G D; Molina, V A
2018-04-20
Fear generalization occurs when a response, previously acquired with a threatening stimulus, is transferred to a similar one. However, it could be maladaptive when stimuli that do not represent a real threat are appraised as dangerous, which is a hallmark of several anxiety disorders. Stress exposure is a major risk factor for the occurrence of anxiety disorders and it is well established that it influences different phases of fear memory; nevertheless, its impact on the generalization of contextual fear memories has been less studied. In the present work, we have characterized the impact of acute restraint stress prior to contextual fear conditioning on the generalization of this fear memory, and the role of the GABAergic signaling within the basolateral amygdala complex (BLA) on the stress modulatory effects. We have found that a single stress exposure promoted the generalization of this memory trace to a different context that was well discriminated in unstressed conditioned animals. Moreover, this effect was dependent on the formation of a contextual associative memory and on the testing order (i.e., conditioning context first vs generalization context first). Furthermore, we observed that increasing GABA-A signaling by intra-BLA midazolam administration prior to the stressful session exposure prevented the generalization of fear memory, whereas intra-BLA administration of the GABA-A antagonist (Bicuculline), prior to fear conditioning, induced the generalization of fear memory in unstressed rats. We concluded that stress exposure, prior to contextual fear conditioning, promotes the generalization of fear memory and that the GABAergic transmission within the BLA has a critical role in this phenomenon. Copyright © 2017 Elsevier Inc. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Youn, Sam Son; Lee, Soon Bok [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of); Kim, Jong Bum; Lee, Hyung Yeon; Yoo, Bong [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)
2000-05-01
The prediction of the inelastic behavior of the structure is an essential part of reliability assessment procedure, because most of the failures are induced by the inelastic deformation, such as creep and plastic deformation. During decades, there has been much progress in understanding of the inelastic behavior of the materials and a lot of inelastic constitutive equations have been developed. These equations consist of the definition of inelastic strain and the evolution of the state variables introduced to quantify the irreversible processes occurred in the material. With respect to the definition of the inelastic strain, the inelastic constitutive models can be categorized into elastoplastic model, unified viscoplastic model and separated viscoplastic model and the different integration methods have been applied to each category. In the present investigation, the generalized integration method applicable for various types of constitutive equations is developed and implemented into ABAQUS by means of UMAT subroutine. The solution of the non-linear system of algebraic equations arising from time discretization with the generalized midpoint rule is determined using line-search technique in combination with Newton method. The strategy to control the time increment for the improvement of the accuracy of the numerical integration is proposed. Several numerical examples are considered to demonstrate the efficiency and applicably of the present method.
SABRINA, Geometry Plot Program for MCNP
International Nuclear Information System (INIS)
SEIDL, Marcus
2003-01-01
1 - Description of program or function: SABRINA is an interactive, three-dimensional, geometry-modeling code system, primarily for use with CCC-200/MCNP. SABRINA's capabilities include creation, visualization, and verification of three-dimensional geometries specified by either surface- or body-base combinatorial geometry; display of particle tracks are calculated by MCNP; and volume fraction generation. 2 - Method of solution: Rendering is performed by ray tracing or an edge and intersection algorithm. Volume fraction calculations are made by ray tracing. 3 - Restrictions on the complexity of the problem: A graphics display with X Window capability is required
Planetary Image Geometry Library
Deen, Robert C.; Pariser, Oleg
2010-01-01
The Planetary Image Geometry (PIG) library is a multi-mission library used for projecting images (EDRs, or Experiment Data Records) and managing their geometry for in-situ missions. A collection of models describes cameras and their articulation, allowing application programs such as mosaickers, terrain generators, and pointing correction tools to be written in a multi-mission manner, without any knowledge of parameters specific to the supported missions. Camera model objects allow transformation of image coordinates to and from view vectors in XYZ space. Pointing models, specific to each mission, describe how to orient the camera models based on telemetry or other information. Surface models describe the surface in general terms. Coordinate system objects manage the various coordinate systems involved in most missions. File objects manage access to metadata (labels, including telemetry information) in the input EDRs and RDRs (Reduced Data Records). Label models manage metadata information in output files. Site objects keep track of different locations where the spacecraft might be at a given time. Radiometry models allow correction of radiometry for an image. Mission objects contain basic mission parameters. Pointing adjustment ("nav") files allow pointing to be corrected. The object-oriented structure (C++) makes it easy to subclass just the pieces of the library that are truly mission-specific. Typically, this involves just the pointing model and coordinate systems, and parts of the file model. Once the library was developed (initially for Mars Polar Lander, MPL), adding new missions ranged from two days to a few months, resulting in significant cost savings as compared to rewriting all the application programs for each mission. Currently supported missions include Mars Pathfinder (MPF), MPL, Mars Exploration Rover (MER), Phoenix, and Mars Science Lab (MSL). Applications based on this library create the majority of operational image RDRs for those missions. A
Gravitation. [Book on general relativity
Misner, C. W.; Thorne, K. S.; Wheeler, J. A.
1973-01-01
This textbook on gravitation physics (Einstein's general relativity or geometrodynamics) is designed for a rigorous full-year course at the graduate level. The material is presented in two parallel tracks in an attempt to divide key physical ideas from more complex enrichment material to be selected at the discretion of the reader or teacher. The full book is intended to provide competence relative to the laws of physics in flat space-time, Einstein's geometric framework for physics, applications with pulsars and neutron stars, cosmology, the Schwarzschild geometry and gravitational collapse, gravitational waves, experimental tests of Einstein's theory, and mathematical concepts of differential geometry.
Geometry on the space of geometries
International Nuclear Information System (INIS)
Christodoulakis, T.; Zanelli, J.
1988-06-01
We discuss the geometric structure of the configuration space of pure gravity. This is an infinite dimensional manifold, M, where each point represents one spatial geometry g ij (x). The metric on M is dictated by geometrodynamics, and from it, the Christoffel symbols and Riemann tensor can be found. A ''free geometry'' tracing a geodesic on the manifold describes the time evolution of space in the strong gravity limit. In a regularization previously introduced by the authors, it is found that M does not have the same dimensionality, D, everywhere, and that D is not a scalar, although it is covariantly constant. In this regularization, it is seen that the path integral measure can be absorbed in a renormalization of the cosmological constant. (author). 19 refs
Geometry of quantum computation with qutrits.
Li, Bin; Yu, Zu-Huan; Fei, Shao-Ming
2013-01-01
Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum computation with n qutrits. We show that the optimal quantum circuits are essentially equivalent to the shortest path between two points in a certain curved geometry of SU(3(n)). As an example, three-qutrit systems are investigated in detail.
Perspectives in Analysis, Geometry, and Topology
Itenberg, I V; Passare, Mikael
2012-01-01
The articles in this volume are invited papers from the Marcus Wallenberg symposium and focus on research topics that bridge the gap between analysis, geometry, and topology. The encounters between these three fields are widespread and often provide impetus for major breakthroughs in applications. Topics include new developments in low dimensional topology related to invariants of links and three and four manifolds; Perelman's spectacular proof of the Poincare conjecture; and the recent advances made in algebraic, complex, symplectic, and tropical geometry.
PREFACE: Water in confined geometries
Rovere, Mauro
2004-11-01
The study of water confined in complex systems in solid or gel phases and/or in contact with macromolecules is relevant to many important processes ranging from industrial applications such as catalysis and soil chemistry, to biological processes such as protein folding or ionic transport in membranes. Thermodynamics, phase behaviour and the molecular mobility of water have been observed to change upon confinement depending on the properties of the substrate. In particular, polar substrates perturb the hydrogen bond network of water, inducing large changes in the properties upon freezing. Understanding how the connected random hydrogen bond network of bulk water is modified when water is confined in small cavities inside a substrate material is very important for studies of stability and the enzymatic activity of proteins, oil recovery or heterogeneous catalysis, where water-substrate interactions play a fundamental role. The modifications of the short-range order in the liquid depend on the nature of the water-substrate interaction, hydrophilic or hydrophobic, as well as on its spatial range and on the geometry of the substrate. Despite extensive study, both experimentally and by computer simulation, there remain a number of open problems. In the many experimental studies of confined water, those performed on water in Vycor are of particular interest for computer simulation and theoretical studies since Vycor is a porous silica glass characterized by a quite sharp distribution of pore sizes and a strong capability to absorb water. It can be considered as a good candidate for studying the general behaviour of water in hydrophilic nanopores. But there there have been a number of studies of water confined in more complex substrates, where the interpretation of experiments and computer simulation is more difficult, such as in zeolites or in aerogels or in contact with membranes. Of the many problems to consider we can mention the study of supercooled water. It is
Energy Technology Data Exchange (ETDEWEB)
Reynolds, J. M.; Lopez-Bruna, D.
2009-12-11
This report is the first of a series dedicated to the numerical calculation of the evolution of fusion plasmas in general toroidal geometry, including TJ-II plasmas. A kinetic treatment has been chosen: the evolution equation of the distribution function of one or several plasma species is solved in guiding center coordinates. The distribution function is written as a Maxwellian one modulated by polynomial series in the kinetic coordinates with no other approximations than those of the guiding center itself and the computation capabilities. The code allows also for the inclusion of the three-dimensional electrostatic potential in a self-consistent manner, but the initial objective has been set to solving only the neoclassical transport. A high order conservative method (Spectral Difference Method) has been chosen in order to discretized the equation for its numerical solution. In this first report, in addition to justifying the work, the evolution equation and its approximations are described, as well as the baseline of the numerical procedures. (Author) 28 refs.
Estimation of wind velocity over a complex terrain using the Generalized Mapping Regressor
Energy Technology Data Exchange (ETDEWEB)
Beccali, M.; Marvuglia, A. [Dipartimento di Ricerche Energetiche ed Ambientali (DREAM), Universita degli Studi di Palermo, Viale delle Scienze - edificio 9, 90128 Palermo (Italy); Cirrincione, G. [Department de Genie Electrique, Universite de Picardie Jules Verne, 33, Rue Saint Leu, 80039 Amiens (France); Serporta, C. [ISSIA-CNR (Institute on Intelligent Systems for the Automation), Section of Palermo, Via Dante12, Palermo (Italy)
2010-03-15
Wind energy evaluation is an important goal in the conversion of energy systems to more environmentally friendly solutions. In this paper, we present a novel approach to wind speed spatial estimation on the isle of Sicily (Italy): an incremental self-organizing neural network (Generalized Mapping Regressor - GMR) is coupled with exploratory data analysis techniques in order to obtain a map of the spatial distribution of the average wind speed over the entire region. First, the topographic surface of the island was modelled using two different neural techniques and by exploiting the information extracted from a digital elevation model of the region. Then, GMR was used for automatic modelling of the terrain roughness. Afterwards, a statistical analysis of the wind data allowed for the estimation of the parameters of the Weibull wind probability distribution function. In the last sections of the paper, the expected values of the Weibull distributions were regionalized using the GMR neural network. (author)
Cole, Jacqueline M; Chan, Michael C W; Gibson, Vernon C; Howard, Judith A K
2011-10-01
The synthesis, chemical and structural characterization of a series of pentamethylcyclopentadienyl (Cp*) tantalum imido complexes and aryloxide derivatives are presented. Specifically, the imido complexes Cp*Ta(N(t)Bu)(CH(2)R)(2), where R = Ph [dibenzyl(tert-butylamido) (η(5)-pentamethylcyclopentadienyl)tantalum(IV) (1)], Me(2)Ph [tert-butylamido)bis(2-methyl-2-phenylpropyl) (η(5)-pentamethylcyclopentadienyl)tantalum(IV) (2)], CMe(3) [(tert-butylamido)bis(2,2-dimethylpropyl) (η(5)-pentamethylcyclopentadienyl)tantalum(IV) (3)], are reported. The crystal structure of (3) reveals α-agostic interactions with the Ta atom. The resulting increase in the tantalum core coordination improves electronic stability. As such it does not react with pentafluorophenol, in contrast to the other two reported imido complexes [(1) and (2)]. Addition of C(6)F(5)OH to (1) yields a dimeric aryl-oxide derivative, [Cp*Ta(CH(2)Ph)(OC(6)H(5))(μ-O)](2) [di-μ-oxido-bis[benzyl(pentafluorophenolato) (η(5)-pentamethylcyclopentadienyl)tantalum(V)] (4)]. Its crystal structure reveals long Ta-O(C(6)H(5)) bonds but short oxo-bridging Ta-O bonds. This is explained by accounting for the fierce electronic competition for the vacant d(π) orbitals of the electrophilic Ta(V) centre. Steric congestion around each metal is alleviated by a large twist angle (77.1°) between the benzyl and pentafluorophenyl ligands and the ordering of each of these groups into stacked pairs. The imido complex (2) reacts with C(6)F(5)OH to produce a mixture of Cp*Ta(OC(6)F(5))(4) [tetrakis(pentafluorophenolato)(η(5)-pentamethylcyclopentadienyl)tantalum(V) (5)] and [Cp*Ta(OC(6)F(5))(2)(μ-O)](2) [di-μ-oxido-bis[bis(pentafluorophenolato)(η(5)-pentamethylcyclopentadienyl)tantalum(V)] (6)]. Steric congestion is offset in both cases by the twisting of its pentafluorophenyl ligands. Particularly strong electronic competition for the empty d(π) metal orbitals in (6) is reflected in its bond geometry, and owes itself to the
Kulczycki, Stefan
2008-01-01
This accessible approach features two varieties of proofs: stereometric and planimetric, as well as elementary proofs that employ only the simplest properties of the plane. A short history of geometry precedes a systematic exposition of the principles of non-Euclidean geometry.Starting with fundamental assumptions, the author examines the theorems of Hjelmslev, mapping a plane into a circle, the angle of parallelism and area of a polygon, regular polygons, straight lines and planes in space, and the horosphere. Further development of the theory covers hyperbolic functions, the geometry of suff
Fractal geometry and computer graphics
Sakas, Georgios; Peitgen, Heinz-Otto; Englert, Gabriele
1992-01-01
Fractal geometry has become popular in the last 15 years, its applications can be found in technology, science, or even arts. Fractal methods and formalism are seen today as a general, abstract, but nevertheless practical instrument for the description of nature in a wide sense. But it was Computer Graphics which made possible the increasing popularity of fractals several years ago, and long after their mathematical formulation. The two disciplines are tightly linked. The book contains the scientificcontributions presented in an international workshop in the "Computer Graphics Center" in Darmstadt, Germany. The target of the workshop was to present the wide spectrum of interrelationships and interactions between Fractal Geometry and Computer Graphics. The topics vary from fundamentals and new theoretical results to various applications and systems development. All contributions are original, unpublished papers.The presentations have been discussed in two working groups; the discussion results, together with a...
A General Multiscale Hybrid Method for Transport through Complex Porous Media
Yousefzadeh, M.; Battiato, I.
2015-12-01
Porous media flow and transport in the subsurface can be described over a hierarchy of scales ranging from atomistic to continuum. Depending on the physics of the problem we ought to incorporate all relevant scales. Often the behavior of the system is controlled by the phenomena at the pore-scale. Therefore accurate and efficient modeling of any large domain requires simulating parts of it at the pore-scale (i.e., wherein continuum models become invalid) and the rest at the continuum scale. Hybrid models combine pore-scale and continuum-scale representations. Desirable features of hybrid models are: 1) their ability to track where and when to use pore-scale models, i.e. their adaptability to time- and space-dependent phenomena, 2) their flexibility in implementing coupling boundary conditions, and 3) significant computational speed-up when the sub-domain wherein pore-scale simulations are required is much smaller than the total computational domain. Moreover, coupling conditions should be physics-based in order reduce the overall number of assumptions. We propose a general, robust and non-overlapping hybrid scheme based on IBM to model flow and reactive transport in porous media. The suggested algorithm has been numerically tested for several transport and flow scenarios.
Modelling Complex Inlet Geometries in CFD
DEFF Research Database (Denmark)
Skovgaard, M.; Nielsen, Peter V.
field. In order to apply CFD for this purpose it is essential to be able to model the inlet conditions precisely and effectively, in a way which is comprehensible to the manufacturer of inlet devices and in a way which can be coped with by the computer. In this paper a universal method is presented...
Fractal geometry mathematical foundations and applications
Falconer, Kenneth
2013-01-01
The seminal text on fractal geometry for students and researchers: extensively revised and updated with new material, notes and references that reflect recent directions. Interest in fractal geometry continues to grow rapidly, both as a subject that is fascinating in its own right and as a concept that is central to many areas of mathematics, science and scientific research. Since its initial publication in 1990 Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals. The book introduces and develops the general theory and applica
Differential geometry and topology of curves
Animov, Yu
2001-01-01
Differential geometry is an actively developing area of modern mathematics. This volume presents a classical approach to the general topics of the geometry of curves, including the theory of curves in n-dimensional Euclidean space. The author investigates problems for special classes of curves and gives the working method used to obtain the conditions for closed polygonal curves. The proof of the Bakel-Werner theorem in conditions of boundedness for curves with periodic curvature and torsion is also presented. This volume also highlights the contributions made by great geometers. past and present, to differential geometry and the topology of curves.
Busemann, Herbert
2005-01-01
A comprehensive approach to qualitative problems in intrinsic differential geometry, this text examines Desarguesian spaces, perpendiculars and parallels, covering spaces, the influence of the sign of the curvature on geodesics, more. 1955 edition. Includes 66 figures.
Melzak, Z A
2008-01-01
Intended for students of many different backgrounds with only a modest knowledge of mathematics, this text features self-contained chapters that can be adapted to several types of geometry courses. 1983 edition.
Rudiments of algebraic geometry
Jenner, WE
2017-01-01
Aimed at advanced undergraduate students of mathematics, this concise text covers the basics of algebraic geometry. Topics include affine spaces, projective spaces, rational curves, algebraic sets with group structure, more. 1963 edition.
DEFF Research Database (Denmark)
Kokkendorff, Simon Lyngby
2002-01-01
The subject of this Ph.D.-thesis is somewhere in between continuous and discrete geometry. Chapter 2 treats the geometry of finite point sets in semi-Riemannian hyperquadrics,using a matrix whose entries are a trigonometric function of relative distances in a given point set. The distance...... to the geometry of a simplex in a semi-Riemannian hyperquadric. In chapter 3 we study which finite metric spaces that are realizable in a hyperbolic space in the limit where curvature goes to -∞. We show that such spaces are the so called leaf spaces, the set of degree 1 vertices of weighted trees. We also...... establish results on the limiting geometry of such an isometrically realized leaf space simplex in hyperbolic space, when curvature goes to -∞. Chapter 4 discusses negative type of metric spaces. We give a measure theoretic treatment of this concept and related invariants. The theory developed...
Geometry and physics of branes
International Nuclear Information System (INIS)
Gal'tsov, D V
2003-01-01
theory on open and unoriented surfaces. This topic is not a recent discovery but it attracted much attention after the discovery of D-branes and led to the construction of a large number of different new models. After reviewing generalities of two-dimensional CFTs, current algebras, the Knizhnik-Zamolodchikov equation and braid-invariant Green functions, CFT on surfaces with holes and crosscaps is discussed. Then the method of Sagnotti, which allows one to calculate partition functions in the presence of boundaries or crosscaps if the modular matrices are known, is introduced, with explicit examples of the annulus, the Klein bottle and the Moebius strip. The contribution by C Gomez and P Resco treats several topics in string tachyon dynamics. In recent years, a new understanding of the dynamic role of tachyons in string theory has started to emerge, in particular due to A Sen. Starting with a general discussion of tachyon instabilities, the authors explain the Fischler--Susskind mechanism of absorbing the (genus-one) string loop divergences by a renormalization of the worldsheet sigma-model for closed strings. Then the open string contribution to the cosmological constant is considered and the tachyon condensation conjecture is formulated. The tachyon potential calculation is discussed via the beta function computation for an open string. The lectures end up with the K-theory approach to D-branes and the K-version of Sen's conjecture. The third part of the book, which occupies more than half of the volume, is at the advanced level and is addressed to a more mathematically oriented audience. It consists of lectures by K Fukaya (Deformation theory, homological algebra and mirror symmetry), and by A Grassi and M Rossi (Large N dualities and transitions in geometry). The main theme of Fukaya's lectures is the relation between deformation theory and mirror symmetry - more precisely, the part of this direction related to moduli theory. The first part contains the classical
Implosions and hypertoric geometry
DEFF Research Database (Denmark)
Dancer, A.; Kirwan, F.; Swann, A.
2013-01-01
The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion.......The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion....
Intermediate algebra & analytic geometry
Gondin, William R
1967-01-01
Intermediate Algebra & Analytic Geometry Made Simple focuses on the principles, processes, calculations, and methodologies involved in intermediate algebra and analytic geometry. The publication first offers information on linear equations in two unknowns and variables, functions, and graphs. Discussions focus on graphic interpretations, explicit and implicit functions, first quadrant graphs, variables and functions, determinate and indeterminate systems, independent and dependent equations, and defective and redundant systems. The text then examines quadratic equations in one variable, system
Conformal Lorentz geometry revisited
Teleman, Kostake
1996-02-01
. We also show that Mach's principle on inertial motions receives an explanation in our theory by considering the particular geodesic paths, for which one of the partners of an interacting pair is fixed and sent to infinity. In fact we study a dynamical system (W,L) which presents some formal and topological similarities with a system of two particles interacting gravitationally. (W,L) is the only conformally invariant relativistic two-point dynamical system. At the end we show that W can be naturally regarded as the base of a principal GL(2,C)-bundle which comes with a natural connection. We study this bundle from differential geometric point of view. Physical interpretations will be discussed in a future paper. This text is an improvement of a previous version, which was submitted under the title ``Hypertwistor Geometry.'' [See, K. Teleman, ``Hypertwistor Geometry (abstract),'' 14th International Conference on General Relativity and Gravitation, Florence, Italy, 1995.] The change of the title and many other improvements are due to the valuable comments of the referee, who also suggested the author to avoid hazardous interpretations.
Coordinate geometry method for capturing and evaluating crown preparation geometry.
Tiu, Janine; Waddell, J Neil; Al-Amleh, Basil; Jansen van Vuuren, Wendy-Ann; Swain, Michael V
2014-09-01
A validated universal method requiring no human input is needed to capture and evaluate preparation geometries in a manner that can be used to see the correlation of different parameters. The purpose of this study was to present a method of capturing and evaluating crown preparation geometry. One manually machined acrylic resin block and 9 randomly selected preparations for ceramic complete crowns prepared by general dentists were selected and prepared. The specimens were scanned (3D scanner; Nobel Biocare), and buccolingual and mesiodistal cross section images were collected. The images were imported into digitizing software (Engauge Digitizer 4.1) to convert the outlines into x and y coordinates. Six points were chosen by using a set of algorithms, and the resulting parameters were calculated. The acrylic resin block was milled with a 12 degree total occlusal convergence (TOC) instrument producing a 12.83 degree TOC. For the other specimens, average TOC values ranged from 18 degrees to 52 degrees. The mean average margin width was 0.70 mm, and the mean average base dimension was 6.23 mm. The surface area/volume ratio, resistance length, and limiting taper were also calculated. The method described provides a basis for accurately evaluating preparation geometry without human input. Copyright © 2014 Editorial Council for the Journal of Prosthetic Dentistry. Published by Elsevier Inc. All rights reserved.
Osborne, I.; Brownson, E.; Eulisse, G.; Jones, C. D.; Lange, D. J.; Sexton-Kennedy, E.
2014-06-01
CMS faces real challenges with upgrade of the CMS detector through 2020 and beyond. One of the challenges, from the software point of view, is managing upgrade simulations with the same software release as the 2013 scenario. We present the CMS geometry description software model, its integration with the CMS event setup and core software. The CMS geometry configuration and selection is implemented in Python. The tools collect the Python configuration fragments into a script used in CMS workflow. This flexible and automated geometry configuration allows choosing either transient or persistent version of the same scenario and specific version of the same scenario. We describe how the geometries are integrated and validated, and how we define and handle different geometry scenarios in simulation and reconstruction. We discuss how to transparently manage multiple incompatible geometries in the same software release. Several examples are shown based on current implementation assuring consistent choice of scenario conditions. The consequences and implications for multiple/different code algorithms are discussed.
International Nuclear Information System (INIS)
Osborne, I; Brownson, E; Eulisse, G; Jones, C D; Sexton-Kennedy, E; Lange, D J
2014-01-01
CMS faces real challenges with upgrade of the CMS detector through 2020 and beyond. One of the challenges, from the software point of view, is managing upgrade simulations with the same software release as the 2013 scenario. We present the CMS geometry description software model, its integration with the CMS event setup and core software. The CMS geometry configuration and selection is implemented in Python. The tools collect the Python configuration fragments into a script used in CMS workflow. This flexible and automated geometry configuration allows choosing either transient or persistent version of the same scenario and specific version of the same scenario. We describe how the geometries are integrated and validated, and how we define and handle different geometry scenarios in simulation and reconstruction. We discuss how to transparently manage multiple incompatible geometries in the same software release. Several examples are shown based on current implementation assuring consistent choice of scenario conditions. The consequences and implications for multiple/different code algorithms are discussed.
Booth, Barbara J; Zwar, Nicholas; Harris, Mark F
2013-04-23
Interest in how to implement evidence-based practices into routine health care has never been greater. Primary care faces challenges in managing the increasing burden of chronic disease in an ageing population. Reliable prescriptions for translating knowledge into practice, however, remain elusive, despite intense research and publication activity. This study seeks to explore this dilemma in general practice by challenging the current way of thinking about healthcare improvement and asking what can be learned by looking at change through a complexity lens. This paper reports the local level of an embedded case study of organisational change for better chronic illness care over more than a decade. We used interviews, document review and direct observation to explore how improved chronic illness care developed in one practice. This formed a critical case to compare, using pattern matching logic, to the common prescription for local implementation of best evidence and a rival explanation drawn from complexity sciences interpreted through modern sociology and psychology. The practice changed continuously over more than a decade to deliver better chronic illness care in line with research findings and policy initiatives--re-designing care processes, developing community linkages, supporting patient self-management, using guidelines and clinical information systems, and integrating nurses into the practice team. None of these improvements was designed and implemented according to an explicit plan in response to a documented gap in chronic disease care. The process that led to high quality chronic illness care exhibited clear complexity elements of co-evolution, non-linearity, self-organisation, emergence and edge of chaos dynamics in a network of agents and relationships where a stable yet evolving way of organizing emerged from local level communicative interaction, power relating and values based choices. The current discourse of implementation science as planned
Monazzam, Mohammad Reza; Hosseini, Monireh; Matin, Laleh Farhang; Aghaei, Habib Allah; Khosroabadi, Hossein; Hesami, Ahmad
2014-01-01
Advances in science and technology of electrical equipment, despite increasing human welfare in everyday life, have increased the number of people exposed to Electro-Magnetic Fields (EMFs). Because of possible adverse effects on the health of exposed individuals, the EMFs have being the center of attention. This study was performed to determine possible correlation between Extremely Low Frequency Electro-Magnetic Fields (ELF EMFs) and sleep quality and public health of those working in substation units of a petrochemical complex in southern Iran. To begin with, magnetic flux density was measured at different parts of a Control Building and two substations in accordance with IEEE std 644-1994. Subsequently, the questionnaires "Pittsburgh Sleep Quality Index" (PSQI) and "General Health Quality (GHQ)" were used to investigate relationship between ELF exposure level and sleep quality and public health, respectively. Both questionnaires were placed at disposal of a total number of 40 workers at the complex. The filled out questionnaires were analyzed by T-test, Duncan and the Chi-square tests. The obtained results revealed that 28% of those in case group suffered from poor health status and 61% were diagnosed with a sleep disorder. However, all members in control group were in good health condition and only 4.5% of them had undesirable sleep quality. In spite of a significant difference between the case and control groups in terms of sleep quality and general health, no significant relationship was found between the exposure level and sleep quality and general health. It is worth noting that the measured EMF values were lower than the standard limits recommended by American Conference of Industrial Hygienists (ACGIH). However, given the uncertainties about the pathogenic effects caused by exposure to ELF EMFs, further epidemiological studies and periodic testing of personnel working in high voltage substations are of utmost importance.
Projective differential geometry of submanifolds
Akivis, M A
1993-01-01
In this book, the general theory of submanifolds in a multidimensional projective space is constructed. The topics dealt with include osculating spaces and fundamental forms of different orders, asymptotic and conjugate lines, submanifolds on the Grassmannians, different aspects of the normalization problems for submanifolds (with special emphasis given to a connection in the normal bundle) and the problem of algebraizability for different kinds of submanifolds, the geometry of hypersurfaces and hyperbands, etc. A series of special types of submanifolds with special projective structures are s
Tsallis Entropy for Geometry Simplification
Directory of Open Access Journals (Sweden)
Miguel Chover
2011-09-01
Full Text Available This paper presents a study and a comparison of the use of different information-theoretic measures for polygonal mesh simplification. Generalized measures from Information Theory such as Havrda–Charvát–Tsallis entropy and mutual information have been applied. These measures have been used in the error metric of a surfaces implification algorithm. We demonstrate that these measures are useful for simplifying three-dimensional polygonal meshes. We have also compared these metrics with the error metrics used in a geometry-based method and in an image-driven method. Quantitative results are presented in the comparison using the root-mean-square error (RMSE.
Projective geometry and projective metrics
Busemann, Herbert
2005-01-01
The basic results and methods of projective and non-Euclidean geometry are indispensable for the geometer, and this book--different in content, methods, and point of view from traditional texts--attempts to emphasize that fact. Results of special theorems are discussed in detail only when they are needed to develop a feeling for the subject or when they illustrate a general method. On the other hand, an unusual amount of space is devoted to the discussion of the fundamental concepts of distance, motion, area, and perpendicularity.Topics include the projective plane, polarities and conic sectio
Losa, Gabriele A
2009-01-01
The extension of the concepts of Fractal Geometry (Mandelbrot [1983]) toward the life sciences has led to significant progress in understanding complex functional properties and architectural / morphological / structural features characterising cells and tissues during ontogenesis and both normal and pathological development processes. It has even been argued that fractal geometry could provide a coherent description of the design principles underlying living organisms (Weibel [1991]). Fractals fulfil a certain number of theoretical and methodological criteria including a high level of organization, shape irregularity, functional and morphological self-similarity, scale invariance, iterative pathways and a peculiar non-integer fractal dimension [FD]. Whereas mathematical objects are deterministic invariant or self-similar over an unlimited range of scales, biological components are statistically self-similar only within a fractal domain defined by upper and lower limits, called scaling window, in which the relationship between the scale of observation and the measured size or length of the object can be established (Losa and Nonnenmacher [1996]). Selected examples will contribute to depict complex biological shapes and structures as fractal entities, and also to show why the application of the fractal principle is valuable for measuring dimensional, geometrical and functional parameters of cells, tissues and organs occurring within the vegetal and animal realms. If the criteria for a strict description of natural fractals are met, then it follows that a Fractal Geometry of Life may be envisaged and all natural objects and biological systems exhibiting self-similar patterns and scaling properties may be considered as belonging to the new subdiscipline of "fractalomics".
Sources of hyperbolic geometry
Stillwell, John
1996-01-01
This book presents, for the first time in English, the papers of Beltrami, Klein, and Poincaré that brought hyperbolic geometry into the mainstream of mathematics. A recognition of Beltrami comparable to that given the pioneering works of Bolyai and Lobachevsky seems long overdue-not only because Beltrami rescued hyperbolic geometry from oblivion by proving it to be logically consistent, but because he gave it a concrete meaning (a model) that made hyperbolic geometry part of ordinary mathematics. The models subsequently discovered by Klein and Poincaré brought hyperbolic geometry even further down to earth and paved the way for the current explosion of activity in low-dimensional geometry and topology. By placing the works of these three mathematicians side by side and providing commentaries, this book gives the student, historian, or professional geometer a bird's-eye view of one of the great episodes in mathematics. The unified setting and historical context reveal the insights of Beltrami, Klein, and Po...
Energy Technology Data Exchange (ETDEWEB)
Guedes, O
2005-04-15
With the difficulties encountered for the exploration of complex shape surfaces, particularly in nuclear industry, the ultrasonic conformable phased array transducer allows a non destructive evaluation of parts with 3D complex parts. For this, one can use the Smart Contact Transducer principle to generate an ultrasonic field by adaptive dynamic focalisation, with a matrix array composed of independent elements moulded in a soft resin. This work deals with the electro-acoustic conception, with the realization of such a prototype and with the study of it's mechanical and acoustic behaviour. The array design is defined using a radiation model adapted to the simulation of contact sources on a free surface. Once one have defined the shape of the radiating elements, a vibratory analysis using finite elements method allows the determination of the emitting structure with 1-3 piezocomposite, witch leads to the realization of emitting-receiving elements. With the measurement of the field transmitted by such elements, we deduced new hypothesis to change the model of radiation. Thus one can take into account normal and tangential stresses calculated with finite element modelling at the interface between the element and the propagation medium, to use it with the semi-analytical model. Some vibratory phenomena dealing with fluid coupling of contact transducers have been studied, and the prediction of the transverse wave radiation profile have been improved. The last part of this work deals with the realization of the first prototype of the conformable phased array transducer. For this a deformation measuring system have been developed, to determine the position of each element on real time with the displacement of the transducer on complex shape surfaces. With those positions, one can perform the calculation of the a delay law intended for the adaptive dynamic focusing of the desired ultrasonic field. The conformable phased array transducer have been characterized in
Vitório Pereira, Jorge
2015-01-01
This book takes an in-depth look at abelian relations of codimension one webs in the complex analytic setting. In its classical form, web geometry consists in the study of webs up to local diffeomorphisms. A significant part of the theory revolves around the concept of abelian relation, a particular kind of functional relation among the first integrals of the foliations of a web. Two main focuses of the book include how many abelian relations can a web carry and which webs are carrying the maximal possible number of abelian relations. The book offers complete proofs of both Chern’s bound and Trépreau’s algebraization theorem, including all the necessary prerequisites that go beyond elementary complex analysis or basic algebraic geometry. Most of the examples known up to date of non-algebraizable planar webs of maximal rank are discussed in detail. A historical account of the algebraization problem for maximal rank webs of codimension one is also presented.
Directory of Open Access Journals (Sweden)
Freiberger E
2013-08-01
Full Text Available Ellen Freiberger,1 Wolfgang A Blank,2 Johannes Salb,1 Barbara Geilhof,3 Christian Hentschke,1 Peter Landendoerfer,2 Martin Halle,3 Monika Siegrist31Institute of Sport Science and Sport Universität Erlangen-Nürnberg, Nuremberg, Germany; 2Institute of General Practice, Technische Universität München, Munich, Germany; 3Department of Prevention, Rehabilitation and Sports Medicine, Technische Universität München, Munich, GermanyPurpose: To study the feasibility of first, reaching functionally declined, but still independent older persons at risk of falls through their general practitioner (GP and second, to reduce their physiological and psychological fall risk factors with a complex exercise intervention. We investigated the effects of a 16-week exercise intervention on physiological (function, strength, and balance and psychological (fear of falling outcomes in community-dwelling older persons in comparison with usual care. In addition, we obtained data on adherence of the participants to the exercise program.Methods: Tests on physical and psychological fall risk were conducted at study inclusion, and after the 16-week intervention period in the GP office setting. The 16-week intervention included progressive and challenging balance, gait, and strength exercise as well as changes to behavioral aspects. To account for the hierarchical structure in the chosen study design, with patients nested in GPs and measurements nested in patients, a three-level linear mixed effects model was determined for analysis.Results: In total, 33 GPs recruited 378 participants (75.4% females. The mean age of the participants was 78.1 years (standard deviation 5.9 years. Patients in the intervention group showed an improvement in the Timed-Up-and-Go-test (TUG that was 1.5 seconds greater than that showed by the control group, equivalent to a small to moderate effect. For balance, a relative improvement of 0.8 seconds was accomplished, and anxiety about falls was
Students Discovering Spherical Geometry Using Dynamic Geometry Software
Guven, Bulent; Karatas, Ilhan
2009-01-01
Dynamic geometry software (DGS) such as Cabri and Geometers' Sketchpad has been regularly used worldwide for teaching and learning Euclidean geometry for a long time. The DGS with its inductive nature allows students to learn Euclidean geometry via explorations. However, with respect to non-Euclidean geometries, do we need to introduce them to…
Modeling of weld bead geometry for rapid manufacturing by robotic GMAW
Yang, Tao; Xiong, Jun; Chen, Hui; Chen, Yong
2015-03-01
Weld-based rapid prototyping (RP) has shown great promises for fabricating 3D complex parts. During the layered deposition of forming metallic parts with robotic gas metal arc welding, the geometry of a single weld bead has an important influence on surface finish quality, layer thickness and dimensional accuracy of the deposited layer. In order to obtain accurate, predictable and controllable bead geometry, it is essential to understand the relationships between the process variables with the bead geometry (bead width, bead height and ratio of bead width to bead height). This paper highlights an experimental study carried out to develop mathematical models to predict deposited bead geometry through the quadratic general rotary unitized design. The adequacy and significance of the models were verified via the analysis of variance. Complicated cause-effect relationships between the process parameters and the bead geometry were revealed. Results show that the developed models can be applied to predict the desired bead geometry with great accuracy in layered deposition with accordance to the slicing process of RP.
Ochiai, T.; Nacher, J. C.
2011-09-01
Recently, the application of geometry and conformal mappings to artificial materials (metamaterials) has attracted the attention in various research communities. These materials, characterized by a unique man-made structure, have unusual optical properties, which materials found in nature do not exhibit. By applying the geometry and conformal mappings theory to metamaterial science, it may be possible to realize so-called "Harry Potter cloaking device". Although such a device is still in the science fiction realm, several works have shown that by using such metamaterials it may be possible to control the direction of the electromagnetic field at will. We could then make an object hidden inside of a cloaking device. Here, we will explain how to design invisibility device using differential geometry and conformal mappings.
Yale, Paul B
2012-01-01
This book is an introduction to the geometry of Euclidean, affine, and projective spaces with special emphasis on the important groups of symmetries of these spaces. The two major objectives of the text are to introduce the main ideas of affine and projective spaces and to develop facility in handling transformations and groups of transformations. Since there are many good texts on affine and projective planes, the author has concentrated on the n-dimensional cases.Designed to be used in advanced undergraduate mathematics or physics courses, the book focuses on ""practical geometry,"" emphasi
Directory of Open Access Journals (Sweden)
Cámara Alicia
2003-01-01
Full Text Available This work presents the results of the detection of antibodies (immunoglobulin G for subtypes I and VI of VEE viruses complex (Togaviridae family in people from the General Belgrano island, Formosa province (Argentina. The prevalence of neutralizing (NT antibodies for subtype VI was from 30% to 70% and the prevalence of antibodies inhibitory of hemagglutination (HI was of 0% in the first and second inquiry respectively. For the subtype IAB the prevalence of NT antibodies was from 13% to 3.6%, similar to the prevalence total for both subtypes. HI antibodies were not detected in any inquiries for any subtype. It was observed that both subtypes circulate simultaneously, while subtype VI remains constant with some peaks, subtype I was found in low level.
Marmodoro, Alberto; Ernst, Arthur; Ostanin, Sergei; Staunton, Julie B.
2013-03-01
The coherent potential approximation has historically allowed the efficient study of disorder effects over a variety of solid state systems. Its original formulation is, however, limited to a single-site or uncorrelated model of local substitutions. This neglects the effects of correlation and short-range ordering, often found in real materials. Recent theoretical work has shown one possible way to systematically address such shortcomings for simple materials with only one element per unit cell. We briefly review the basic ideas of such development within the framework of multiple scattering theory and suggest its generalization to materials with complex lattices. We validate our extension through a systematic comparison with a classic Cu1-cZnc reference test case and propose, for further illustration of local environment effects, the example of the yttria-stabilized cubic phase of zirconia, re-examined through various techniques for the first-principles treatment of disorder.
DEFF Research Database (Denmark)
Milovanov, A.V.; Juul Rasmussen, J.
2005-01-01
Equations built on fractional derivatives prove to be a powerful tool in the description of complex systems when the effects of singularity, fractal supports, and long-range dependence play a role. In this Letter, we advocate an application of the fractional derivative formalism to a fairly general...... class of critical phenomena when the organization of the system near the phase transition point is influenced by a competing nonlocal ordering. Fractional modifications of the free energy functional at criticality and of the widely known Ginzburg-Landau equation central to the classical Landau theory...... of second-type phase transitions are discussed in some detail. An implication of the fractional Ginzburg-Landau equation is a renormalization of the transition temperature owing to the nonlocality present. (c) 2005 Elsevier B.V. All rights reserved....
VIII International Meeting on Lorentzian Geometry
Flores, José; Palomo, Francisco; GeLoMa 2016; Lorentzian geometry and related topics
2017-01-01
This volume contains a collection of research papers and useful surveys by experts in the field which provide a representative picture of the current status of this fascinating area. Based on contributions from the VIII International Meeting on Lorentzian Geometry, held at the University of Málaga, Spain, this volume covers topics such as distinguished (maximal, trapped, null, spacelike, constant mean curvature, umbilical...) submanifolds, causal completion of spacetimes, stationary regions and horizons in spacetimes, solitons in semi-Riemannian manifolds, relation between Lorentzian and Finslerian geometries and the oscillator spacetime. In the last decades Lorentzian geometry has experienced a significant impulse, which has transformed it from just a mathematical tool for general relativity to a consolidated branch of differential geometry, interesting in and of itself. Nowadays, this field provides a framework where many different mathematical techniques arise with applications to multiple parts of mathem...
Algebra, Geometry and Mathematical Physics Conference
Paal, Eugen; Silvestrov, Sergei; Stolin, Alexander
2014-01-01
This book collects the proceedings of the Algebra, Geometry and Mathematical Physics Conference, held at the University of Haute Alsace, France, October 2011. Organized in the four areas of algebra, geometry, dynamical symmetries and conservation laws and mathematical physics and applications, the book covers deformation theory and quantization; Hom-algebras and n-ary algebraic structures; Hopf algebra, integrable systems and related math structures; jet theory and Weil bundles; Lie theory and applications; non-commutative and Lie algebra and more. The papers explore the interplay between research in contemporary mathematics and physics concerned with generalizations of the main structures of Lie theory aimed at quantization, and discrete and non-commutative extensions of differential calculus and geometry, non-associative structures, actions of groups and semi-groups, non-commutative dynamics, non-commutative geometry and applications in physics and beyond. The book benefits a broad audience of researchers a...
Lee, David Y; Flaherty, Devin C; Lau, Briana J; Deutsch, Gary B; Kirchoff, Daniel D; Huynh, Kelly T; Lee, Ji-Hey; Faries, Mark B; Bilchik, Anton J
2015-11-01
With the first qualifying examination administered September 15, 2014, complex general surgical oncology (CGSO) is now a board-certified specialty. We aimed to assess the attitudes and perceptions of current and future surgical oncology fellows regarding the recently instituted Accreditation Council for Graduate Medical Education (ACGME) accreditation. A 29-question anonymous survey was distributed to fellows in surgical oncology fellowship programs and applicants interviewing at our fellowship program. There were 110 responses (79 fellows and 31 candidates). The response rate for the first- and second-year fellows was 66 %. Ninety-percent of the respondents were aware that completing an ACGME-accredited fellowship leads to board eligibility in CGSO. However, the majority (80 %) of the respondents stated that their decision to specialize in surgical oncology was not influenced by the ACGME accreditation. The fellows in training were concerned about the cost of the exam (90 %) and expressed anxiety in preparing for another board exam (83 %). However, the majority of the respondents believed that CGSO board certification will be helpful (79 %) in obtaining their future career goals. Interestingly, candidate fellows appeared more focused on a career in general complex surgical oncology (p = 0.004), highlighting the impact that fellowship training may have on organ-specific subspecialization. The majority of the surveyed surgical oncology fellows and candidates believe that obtaining board certification in CGSO is important and will help them pursue their career goals. However, the decision to specialize in surgical oncology does not appear to be motivated by ACGME accreditation or the new board certification.
Freiberger, Ellen; Blank, Wolfgang A; Salb, Johannes; Geilhof, Barbara; Hentschke, Christian; Landendoerfer, Peter; Halle, Martin; Siegrist, Monika
2013-01-01
To study the feasibility of first, reaching functionally declined, but still independent older persons at risk of falls through their general practitioner (GP) and second, to reduce their physiological and psychological fall risk factors with a complex exercise intervention. We investigated the effects of a 16-week exercise intervention on physiological (function, strength, and balance) and psychological (fear of falling) outcomes in community-dwelling older persons in comparison with usual care. In addition, we obtained data on adherence of the participants to the exercise program. Tests on physical and psychological fall risk were conducted at study inclusion, and after the 16-week intervention period in the GP office setting. The 16-week intervention included progressive and challenging balance, gait, and strength exercise as well as changes to behavioral aspects. To account for the hierarchical structure in the chosen study design, with patients nested in GPs and measurements nested in patients, a three-level linear mixed effects model was determined for analysis. In total, 33 GPs recruited 378 participants (75.4% females). The mean age of the participants was 78.1 years (standard deviation 5.9 years). Patients in the intervention group showed an improvement in the Timed-Up-and-Go-test (TUG) that was 1.5 seconds greater than that showed by the control group, equivalent to a small to moderate effect. For balance, a relative improvement of 0.8 seconds was accomplished, and anxiety about falls was reduced by 3.7 points in the Falls Efficacy Scale-International (FES-I), in the intervention group relative to control group. In total, 76.6% (N = 170) of the intervention group participated in more than 75% the supervised group sessions. The strategy to address older persons at high risk of falling in the GP setting with a complex exercise intervention was successful. In functionally declined, community-dwelling, older persons a complex intervention for reducing fall
MacKeown, P. K.
1984-01-01
Clarifies two concepts of gravity--those of a fictitious force and those of how space and time may have geometry. Reviews the position of Newton's theory of gravity in the context of special relativity and considers why gravity (as distinct from electromagnetics) lends itself to Einstein's revolutionary interpretation. (JN)
Implosions and hypertoric geometry
DEFF Research Database (Denmark)
Dancer, A.; Kirwan, F.; Swann, A.
2013-01-01
The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion....
Boyer, Carl B
2012-01-01
Designed as an integrated survey of the development of analytic geometry, this study presents the concepts and contributions from before the Alexandrian Age through the eras of the great French mathematicians Fermat and Descartes, and on through Newton and Euler to the "Golden Age," from 1789 to 1850.
Hartshorne, Robin
2000-01-01
In recent years, I have been teaching a junior-senior-level course on the classi cal geometries. This book has grown out of that teaching experience. I assume only high-school geometry and some abstract algebra. The course begins in Chapter 1 with a critical examination of Euclid's Elements. Students are expected to read concurrently Books I-IV of Euclid's text, which must be obtained sepa rately. The remainder of the book is an exploration of questions that arise natu rally from this reading, together with their modern answers. To shore up the foundations we use Hilbert's axioms. The Cartesian plane over a field provides an analytic model of the theory, and conversely, we see that one can introduce coordinates into an abstract geometry. The theory of area is analyzed by cutting figures into triangles. The algebra of field extensions provides a method for deciding which geometrical constructions are possible. The investigation of the parallel postulate leads to the various non-Euclidean geometries. And ...
Wares, Arsalan; Elstak, Iwan
2017-01-01
The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and algebra. The activity can be used as a context for illustrating how algebra…
DEFF Research Database (Denmark)
Frisvad, Jeppe Revall
2008-01-01
, whether the shape of the material should be coupled to the appearance model or not, etc. A generalised concept of shape and geometry is presented to provide a framework for handling these many degrees of freedom. Constraints between input and output parameters are modelled as multidimensional shapes...
Diophantine geometry an introduction
Hindry, Marc
2000-01-01
This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.
Metrics for Probabilistic Geometries
DEFF Research Database (Denmark)
Tosi, Alessandra; Hauberg, Søren; Vellido, Alfredo
2014-01-01
We investigate the geometrical structure of probabilistic generative dimensionality reduction models using the tools of Riemannian geometry. We explicitly define a distribution over the natural metric given by the models. We provide the necessary algorithms to compute expected metric tensors where...
Towards relativistic quantum geometry
Energy Technology Data Exchange (ETDEWEB)
Ridao, Luis Santiago [Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina); Bellini, Mauricio, E-mail: mbellini@mdp.edu.ar [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, C.P. 7600, Mar del Plata (Argentina); Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina)
2015-12-17
We obtain a gauge-invariant relativistic quantum geometry by using a Weylian-like manifold with a geometric scalar field which provides a gauge-invariant relativistic quantum theory in which the algebra of the Weylian-like field depends on observers. An example for a Reissner–Nordström black-hole is studied.
Coxeter, HSM
1965-01-01
This textbook introduces non-Euclidean geometry, and the third edition adds a new chapter, including a description of the two families of 'mid-lines' between two given lines and an elementary derivation of the basic formulae of spherical trigonometry and hyperbolic trigonometry, and other new material.
Hsü, K J; Hsü, A J
1990-01-01
Music critics have compared Bach's music to the precision of mathematics. What "mathematics" and what "precision" are the questions for a curious scientist. The purpose of this short note is to suggest that the mathematics is, at least in part, Mandelbrot's fractal geometry and the precision is the deviation from a log-log linear plot.
Cooper, Brett D.; Barger, Rita
2009-01-01
The many connections between music and mathematics are well known. The length of a plucked string determines its tone, the time signature of a piece of music is a ratio, and note durations are measured in fractions. One connection commonly overlooked is that between music and geometry--specifically, geometric transformations, including…
Martin, John
2010-01-01
The cycloid has been called the Helen of Geometry, not only because of its beautiful properties but also because of the quarrels it provoked between famous mathematicians of the 17th century. This article surveys the history of the cycloid and its importance in the development of the calculus.
Sliding vane geometry turbines
Sun, Harold Huimin; Zhang, Jizhong; Hu, Liangjun; Hanna, Dave R
2014-12-30
Various systems and methods are described for a variable geometry turbine. In one example, a turbine nozzle comprises a central axis and a nozzle vane. The nozzle vane includes a stationary vane and a sliding vane. The sliding vane is positioned to slide in a direction substantially tangent to an inner circumference of the turbine nozzle and in contact with the stationary vane.
DEFF Research Database (Denmark)
Booss-Bavnbek, Bernhelm
2011-01-01
This paper applies I.M. Gelfand's distinction between adequate and non-adequate use of mathematical language in different contexts to the newly opened window of model-based measurements of intracellular dynamics. The specifics of geometry and dynamics on the mesoscale of cell physiology are elabo...
Toric Geometry of the Regular Convex Polyhedra
Directory of Open Access Journals (Sweden)
Fiammetta Battaglia
2017-01-01
Full Text Available We describe symplectic and complex toric spaces associated with the five regular convex polyhedra. The regular tetrahedron and the cube are rational and simple, the regular octahedron is not simple, the regular dodecahedron is not rational, and the regular icosahedron is neither simple nor rational. We remark that the last two cases cannot be treated via standard toric geometry.
Interacting particle systems in time-dependent geometries
International Nuclear Information System (INIS)
Ali, A; Ball, R C; Grosskinsky, S; Somfai, E
2013-01-01
Many complex structures and stochastic patterns emerge from simple kinetic rules and local interactions, and are governed by scale invariance properties in combination with effects of the global geometry. We consider systems that can be described effectively by space–time trajectories of interacting particles, such as domain boundaries in two-dimensional growth or river networks. We study trajectories embedded in time-dependent geometries, and the main focus is on uniformly expanding or decreasing domains for which we obtain an exact mapping to simple fixed domain systems while preserving the local scale invariance properties. This approach was recently introduced in Ali et al (2013 Phys. Rev. E 87 020102(R)) and here we provide a detailed discussion on its applicability for self-affine Markovian models, and how it can be adapted to self-affine models with memory or explicit time dependence. The mapping corresponds to a nonlinear time transformation which converges to a finite value for a large class of trajectories, enabling an exact analysis of asymptotic properties in expanding domains. We further provide a detailed discussion of different particle interactions and generalized geometries. All our findings are based on exact computations and are illustrated numerically for various examples, including Lévy processes and fractional Brownian motion. (paper)
Path Toward a Unifid Geometry for Radiation Transport
Lee, Kerry; Barzilla, Janet; Davis, Andrew; Zachmann
2014-01-01
The Direct Accelerated Geometry for Radiation Analysis and Design (DAGRAD) element of the RadWorks Project under Advanced Exploration Systems (AES) within the Space Technology Mission Directorate (STMD) of NASA will enable new designs and concepts of operation for radiation risk assessment, mitigation and protection. This element is designed to produce a solution that will allow NASA to calculate the transport of space radiation through complex computer-aided design (CAD) models using the state-of-the-art analytic and Monte Carlo radiation transport codes. Due to the inherent hazard of astronaut and spacecraft exposure to ionizing radiation in low-Earth orbit (LEO) or in deep space, risk analyses must be performed for all crew vehicles and habitats. Incorporating these analyses into the design process can minimize the mass needed solely for radiation protection. Transport of the radiation fields as they pass through shielding and body materials can be simulated using Monte Carlo techniques or described by the Boltzmann equation, which is obtained by balancing changes in particle fluxes as they traverse a small volume of material with the gains and losses caused by atomic and nuclear collisions. Deterministic codes that solve the Boltzmann transport equation, such as HZETRN [high charge and energy transport code developed by NASA Langley Research Center (LaRC)], are generally computationally faster than Monte Carlo codes such as FLUKA, GEANT4, MCNP(X) or PHITS; however, they are currently limited to transport in one dimension, which poorly represents the secondary light ion and neutron radiation fields. NASA currently uses HZETRN space radiation transport software, both because it is computationally efficient and because proven methods have been developed for using this software to analyze complex geometries. Although Monte Carlo codes describe the relevant physics in a fully three-dimensional manner, their computational costs have thus far prevented their
International Nuclear Information System (INIS)
Taylor, R.P.; Horgan, C.; Hooper, M.; Burge, J.
1985-01-01
Soluble antibody/ 3 H-double-stranded PM2 DNA (dsDNA) immune complexes were briefly opsonized with complement and then allowed to bind to human erythrocytes (via complement receptors). The cells were washed and subsequently a volume of autologous blood in a variety of media was added, and the release of the bound immune complexes from the erythrocytes was studied as a function of temperature and time. After 1-2 h, the majority of the bound immune complexes were not released into the serum during blood clotting at either 37 degrees C or room temperature, but there was a considerably greater release of the immune complexes into the plasma of blood that was anticoagulated with EDTA. Similar results were obtained using various conditions of opsonization and also using complexes that contained lower molecular weight dsDNA. Thus, the kinetics of release of these antibody/dsDNA immune complexes differed substantially from the kinetics of release of antibody/bovine serum albumin complexes that was reported by others. Studies using the solution phase C1q immune complex binding assay confirmed that in approximately half of the SLE samples that were positive for immune complexes, there was a significantly higher level of detectable immune complexes in plasma vs. serum. Freshly drawn erythrocytes from some SLE patients exhibiting this plasma/serum discrepancy had IgG antigen on their surface that was released by incubation in EDTA plasma. Thus, the higher levels of immune complexes observed in EDTA plasma vs. serum using the C1q assay may often reflect the existence of immune complexes circulating in vivo bound to erythrocytes
International Nuclear Information System (INIS)
Gervais, J.L.
1993-01-01
By analyzing the extrinsic geometry of two dimensional surfaces chirally embedded in C P n (the C P n W-surface), we give exact treatments in various aspects of the classical W-geometry in the conformal gauge: First, the basis of tangent and normal vectors are defined at regular points of the surface, such that their infinitesimal displacements are given by connections which coincide with the vector potentials of the (conformal) A n -Toda Lax pair. Since the latter is known to be intrinsically related with the W symmetries, this gives the geometrical meaning of the A n W-Algebra. Second, W-surfaces are put in one-to-one correspondence with solutions of the conformally-reduced WZNW model, which is such that the Toda fields give the Cartan part in the Gauss decomposition of its solutions. Third, the additional variables of the Toda hierarchy are used as coordinates of C P n . This allows us to show that W-transformations may be extended as particular diffeomorphisms of this target-space. Higher-dimensional generalizations of the WZNW equations are derived and related with the Zakharov-Shabat equations of the Toda hierarchy. Fourth, singular points are studied from a global viewpoint, using our earlier observation that W-surfaces may be regarded as instantons. The global indices of the W-geometry, which are written in terms of the Toda fields, are shown to be the instanton numbers for associated mappings of W-surfaces into the Grassmannians. The relation with the singularities of W-surface is derived by combining the Toda equations with the Gauss-Bonnet theorem. (orig.)
Transformational plane geometry
Umble, Ronald N
2014-01-01
Axioms of Euclidean Plane Geometry The Existence and Incidence Postulates The Distance and Ruler Postulates The Plane Separation Postulate The Protractor Postulate The Side-Angle-Side Postulate and the Euclidean Parallel Postulate Theorems of Euclidean Plane Geometry The Exterior Angle Theorem Triangle Congruence Theorems The Alternate Interior Angles Theorem and the Angle Sum Theorem Similar Triangles Introduction to Transformations, Isometries, and Similarities Transformations Isometries and SimilaritiesAppendix: Proof of Surjectivity Translations, Rotations, and Reflections Translations Rotations Reflections Appendix: Geometer's Sketchpad Commands Required by Exploratory Activities Compositions of Translations, Rotations, and Reflections The Three Points Theorem Rotations as Compositions of Two Reflections Translations as Compositions of Two Halfturns or Two Reflections The Angle Addition Theorem Glide Reflections Classification of Isometries The Fundamental Theorem and Congruence Classification of Isometr...
Multivariate calculus and geometry
Dineen, Seán
2014-01-01
Multivariate calculus can be understood best by combining geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. This textbook has successfully followed this programme. It additionally provides a solid description of the basic concepts, via familiar examples, which are then tested in technically demanding situations. In this new edition the introductory chapter and two of the chapters on the geometry of surfaces have been revised. Some exercises have been replaced and others provided with expanded solutions. Familiarity with partial derivatives and a course in linear algebra are essential prerequisites for readers of this book. Multivariate Calculus and Geometry is aimed primarily at higher level undergraduates in the mathematical sciences. The inclusion of many practical examples involving problems of several variables will appeal to mathematics, science and engineering students.
Architectural Geometry and Fabrication-Aware Design
Pottmann, Helmut
2013-04-27
Freeform shapes and structures with a high geometric complexity play an increasingly important role in contemporary architecture. While digital models are easily created, the actual fabrication and construction remains a challenge. This is the source of numerous research problems many of which fall into the area of Geometric Computing and form part of a recently emerging research area, called "Architectural Geometry". The present paper provides a short survey of research in Architectural Geometry and shows how this field moves towards a new direction in Geometric Modeling which aims at combining shape design with important aspects of function and fabrication. © 2013 Kim Williams Books, Turin.
Algebra, Arithmetic, and Geometry
Tschinkel, Yuri
2009-01-01
The two volumes of "Algebra, Arithmetic, and Geometry: In Honor of Y.I. Manin" are composed of invited expository articles and extensions detailing Manin's contributions to the subjects, and are in celebration of his 70th birthday. The well-respected and distinguished contributors include: Behrend, Berkovich, Bost, Bressler, Calaque, Carlson, Chambert-Loir, Colombo, Connes, Consani, Dabrowski, Deninger, Dolgachev, Donaldson, Ekedahl, Elsenhans, Enriques, Etingof, Fock, Friedlander, Geemen, Getzler, Goncharov, Harris, Iskovskikh, Jahnel, Kaledin, Kapranov, Katz, Kaufmann, Kollar, Kont
Introducing geometry concept based on history of Islamic geometry
Maarif, S.; Wahyudin; Raditya, A.; Perbowo, K. S.
2018-01-01
Geometry is one of the areas of mathematics interesting to discuss. Geometry also has a long history in mathematical developments. Therefore, it is important integrated historical development of geometry in the classroom to increase’ knowledge of how mathematicians earlier finding and constructing a geometric concept. Introduction geometrical concept can be started by introducing the Muslim mathematician who invented these concepts so that students can understand in detail how a concept of geometry can be found. However, the history of mathematics development, especially history of Islamic geometry today is less popular in the world of education in Indonesia. There are several concepts discovered by Muslim mathematicians that should be appreciated by the students in learning geometry. Great ideas of mathematicians Muslim can be used as study materials to supplement religious character values taught by Muslim mathematicians. Additionally, by integrating the history of geometry in teaching geometry are expected to improve motivation and geometrical understanding concept.
Integral geometry and valuations
Solanes, Gil
2014-01-01
Valuations are finitely additive functionals on the space of convex bodies. Their study has become a central subject in convexity theory, with fundamental applications to integral geometry. In the last years there has been significant progress in the theory of valuations, which in turn has led to important achievements in integral geometry. This book originated from two courses delivered by the authors at the CRM and provides a self-contained introduction to these topics, covering most of the recent advances. The first part, by Semyon Alesker, is devoted to the theory of convex valuations, with emphasis on the latest developments. A special focus is put on the new fundamental structures of the space of valuations discovered after Alesker's irreducibility theorem. Moreover, the author describes the newly developed theory of valuations on manifolds. In the second part, Joseph H. G. Fu gives a modern introduction to integral geometry in the sense of Blaschke and Santaló, based on the notions and tools presented...
Integral geometry and holography
Energy Technology Data Exchange (ETDEWEB)
Czech, Bartłomiej; Lamprou, Lampros; McCandlish, Samuel [Stanford Institute for Theoretical Physics, Department of Physics, Stanford University,Stanford, CA 94305 (United States); Sully, James [Theory Group, SLAC National Accelerator Laboratory,Menlo Park, CA 94025 (United States)
2015-10-27
We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS{sub 3}/CFT{sub 2} correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length of any bulk curve. We explain how basic geometric concepts — points, distances and angles — are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we discuss in detail the static slice of AdS{sub 3} whose kinematic space is two-dimensional de Sitter space.
Foliations and the geometry of 3-manifolds
Calegari, Danny
2014-01-01
This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions.
Algebra and Geometry of Hamilton's Quaternions
Indian Academy of Sciences (India)
2016-08-26
Aug 26, 2016 ... ... Public Lectures · Lecture Workshops · Refresher Courses · Symposia. Home; Journals; Resonance – Journal of Science Education; Volume 21; Issue 6. Algebra and Geometry of Hamilton's Quaternions: 'Well, Papa, Can You Multiply Triplets?' General Article Volume 21 Issue 6 June 2016 pp 529-544 ...
Causal random geometry from stochastic quantization
DEFF Research Database (Denmark)
Ambjørn, Jan; Loll, R.; Westra, W.
2010-01-01
in this short note we review a recently found formulation of two-dimensional causal quantum gravity defined through Causal Dynamical Triangulations and stochastic quantization. This procedure enables one to extract the nonperturbative quantum Hamiltonian of the random surface model including the...... the sum over topologies. Interestingly, the generally fictitious stochastic time corresponds to proper time on the geometries...
Application of Analytical Geometry to the
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 18; Issue 9. Application of Analytical Geometry to the Form of Gear Teeth. V G A Goss. General Article Volume 18 Issue 9 September 2013 pp 817-831. Fulltext. Click here to view fulltext PDF. Permanent link:
The Geometry of the Universe: Part 1
Francis, Stephanie
2009-01-01
This article describes how the author carries out an investigation into the geometry of the three possible curvatures of the universe. The author begins the investigation by looking on the web and in books. She found that the general consensus was that there were three different possible curvatures of the universe, namely: (1) flat; (2) positive;…
Weyl gravity and Cartan geometry
Attard, J.; François, J.; Lazzarini, S.
2016-04-01
We point out that the Cartan geometry known as the second-order conformal structure provides a natural differential geometric framework underlying gauge theories of conformal gravity. We are concerned with two theories: the first one is the associated Yang-Mills-like Lagrangian, while the second, inspired by [1], is a slightly more general one that relaxes the conformal Cartan geometry. The corresponding gauge symmetry is treated within the Becchi-Rouet-Stora-Tyutin language. We show that the Weyl gauge potential is a spurious degree of freedom, analogous to a Stueckelberg field, that can be eliminated through the dressing field method. We derive sets of field equations for both the studied Lagrangians. For the second one, they constrain the gauge field to be the "normal conformal Cartan connection.''Finally, we provide in a Lagrangian framework a justification of the identification, in dimension 4, of the Bach tensor with the Yang-Mills current of the normal conformal Cartan connection, as proved in [2].
Generalized isothermic lattices
International Nuclear Information System (INIS)
Doliwa, Adam
2007-01-01
We study multi-dimensional quadrilateral lattices satisfying simultaneously two integrable constraints: a quadratic constraint and the projective Moutard constraint. When the lattice is two dimensional and the quadric under consideration is the Moebius sphere one obtains, after the stereographic projection, the discrete isothermic surfaces defined by Bobenko and Pinkall by an algebraic constraint imposed on the (complex) cross-ratio of the circular lattice. We derive the analogous condition for our generalized isothermic lattices using Steiner's projective structure of conics, and we present basic geometric constructions which encode integrability of the lattice. In particular, we introduce the Darboux transformation of the generalized isothermic lattice and we derive the corresponding Bianchi permutability principle. Finally, we study two-dimensional generalized isothermic lattices, in particular geometry of their initial boundary value problem
Geometry of curves and surfaces with Maple
Rovenski, Vladimir
2000-01-01
This concise text on geometry with computer modeling presents some elementary methods for analytical modeling and visualization of curves and surfaces. The author systematically examines such powerful tools as 2-D and 3-D animation of geometric images, transformations, shadows, and colors, and then further studies more complex problems in differential geometry. Well-illustrated with more than 350 figures---reproducible using Maple programs in the book---the work is devoted to three main areas: curves, surfaces, and polyhedra. Pedagogical benefits can be found in the large number of Maple programs, some of which are analogous to C++ programs, including those for splines and fractals. To avoid tedious typing, readers will be able to download many of the programs from the Birkhauser web site. Aimed at a broad audience of students, instructors of mathematics, computer scientists, and engineers who have knowledge of analytical geometry, i.e., method of coordinates, this text will be an excellent classroom resource...
Introductory non-Euclidean geometry
Manning, Henry Parker
1963-01-01
This fine and versatile introduction begins with the theorems common to Euclidean and non-Euclidean geometry, and then it addresses the specific differences that constitute elliptic and hyperbolic geometry. 1901 edition.
2010-12-02
will face in an uncertain future. Complexity Theory , History, Practice, Military Theory , Leadership 14. SUBJECT TERMS 70 15. NUMBER OF PAGES...complexity theory : scale, adaptive leadership , and bottom up feedback from the agents (the soldiers in the field). These are all key sub components of...Uhl-Bien, “Complexity v. Transformation: The New Leadership Revisited” (Ft. Meyers, Florida, Presented at Managing the Complex IV--Conference on
Magnetized target fusion in cylindrical geometry
Energy Technology Data Exchange (ETDEWEB)
Basko, M.M. E-mail: basko@vitep5.itep.ru; Churazov, M.D.; Kemp, A.; Meyer-ter-Vehn, J
2001-05-21
General ignition conditions for magnetized target fusion (MTF) in cylindrical geometry are formulated. To attain an MTF ignition state, the deuterium-tritium fuel must be compressed in the regime of self-sustained magnetized implosion (SSMI). We analyze the general conditions and optimal parameter values required for initiating such a regime, and demonstrate that the SSMI regime can already be realized in cylindrical implosions driven by {approx}100 kJ beams of fast ions.
Matter in toy dynamical geometries
International Nuclear Information System (INIS)
Konopka, Tomasz
2009-01-01
One of the objectives of theories describing quantum dynamical geometry is to compute expectation values of geometrical observables. The results of such computations can be affected by whether or not matter is taken into account. It is thus important to understand to what extent and to what effect matter can affect dynamical geometries. Using a simple model, it is shown that matter can effectively mold a geometry into an isotropic configuration. Implications for 'atomistic' models of quantum geometry are briefly discussed.
Recent topics in differential and analytic geometry
Ochiai, T
1990-01-01
Advanced Studies in Pure Mathematics, Volume 18-I: Recent Topics in Differential and Analytic Geometry presents the developments in the field of analytical and differential geometry. This book provides some generalities about bounded symmetric domains.Organized into two parts encompassing 12 chapters, this volume begins with an overview of harmonic mappings and holomorphic foliations. This text then discusses the global structures of a compact Kähler manifold that is locally decomposable as an isometric product of Ricci-positive, Ricci-negative, and Ricci-flat parts. Other chapters con
Third sound in a restricted geometry
International Nuclear Information System (INIS)
Brouwer, P.W.; Draisma, W.A.; Pinkse, P.W.H.; Beelen, H. van; Jochemsen, R.; Frossati, G.
1992-01-01
Bergman's general treatment of third sound waves has been extended to a (restricted) parallel plate geometry. In a parallel plate geometry two independent third sound modes can propagate: a symmetric and an antisymmetric one. Calculations show that at temperatures below 1 K the antisymmetric mode carries the most important part of the temperature amplitude. Because of the relatively strong substrate influence the temperature amplitude of the symmetric mode is suppressed. The ΔT/Δh versus T measurements by Laheurte et al. and of the ΔT/Δh versus ω measurements by Ellis et al. are explained. 7 refs., 2 figs
Introduction to global variational geometry
Krupka, Demeter
2015-01-01
The book is devoted to recent research in the global variational theory on smooth manifolds. Its main objective is an extension of the classical variational calculus on Euclidean spaces to (topologically nontrivial) finite-dimensional smooth manifolds; to this purpose the methods of global analysis of differential forms are used. Emphasis is placed on the foundations of the theory of variational functionals on fibered manifolds - relevant geometric structures for variational principles in geometry, physical field theory and higher-order fibered mechanics. The book chapters include: - foundations of jet bundles and analysis of differential forms and vector fields on jet bundles, - the theory of higher-order integral variational functionals for sections of a fibred space, the (global) first variational formula in infinitesimal and integral forms- extremal conditions and the discussion of Noether symmetries and generalizations,- the inverse problems of the calculus of variations of Helmholtz type- variational se...
Conformal geometry and quasiregular mappings
Vuorinen, Matti
1988-01-01
This book is an introduction to the theory of spatial quasiregular mappings intended for the uninitiated reader. At the same time the book also addresses specialists in classical analysis and, in particular, geometric function theory. The text leads the reader to the frontier of current research and covers some most recent developments in the subject, previously scatterd through the literature. A major role in this monograph is played by certain conformal invariants which are solutions of extremal problems related to extremal lengths of curve families. These invariants are then applied to prove sharp distortion theorems for quasiregular mappings. One of these extremal problems of conformal geometry generalizes a classical two-dimensional problem of O. Teichmüller. The novel feature of the exposition is the way in which conformal invariants are applied and the sharp results obtained should be of considerable interest even in the two-dimensional particular case. This book combines the features of a textbook an...
Teaching of Geometry in Bulgaria
Bankov, Kiril
2013-01-01
Geometry plays an important role in the school mathematics curriculum all around the world. Teaching of geometry varies a lot (Hoyls, Foxman, & Kuchemann, 2001). Many countries revise the objectives, the content, and the approaches to the geometry in school. Studies of the processes show that there are not common trends of these changes…
Graded geometry and Poisson reduction
Cattaneo, A S; Zambon, M
2009-01-01
The main result of [2] extends the Marsden-Ratiu reduction theorem [4] in Poisson geometry, and is proven by means of graded geometry. In this note we provide the background material about graded geometry necessary for the proof in [2]. Further, we provide an alternative algebraic proof for the main result. ©2009 American Institute of Physics
Secondary magnetic field harmonics dependence on vacuum beam chamber geometry
Directory of Open Access Journals (Sweden)
S. Y. Shim
2013-08-01
Full Text Available The harmonic magnetic field properties due to eddy currents have been studied with respect to the geometry of the vacuum beam chamber. We derived a generalized formula enabling the precise prediction of any field harmonics generated by eddy currents in beam tubes with different cross-sectional geometries. Applying our model to study the properties of field harmonics in beam tubes with linear dipole magnetic field ramping clearly proved that the circular cross section tube generates only a dipole field from eddy currents. The elliptic tube showed noticeable magnitudes of sextupole and dipole fields. We demonstrate theoretically that it is feasible to suppress the generation of the sextupole field component by appropriately varying the tube wall thickness as a function of angle around the tube circumference. This result indicates that it is possible to design an elliptical-shaped beam tube that generates a dipole field component with zero magnitude of sextupole. In a rectangular-shaped beam tube, one of the selected harmonic fields can be prevented if an appropriate wall thickness ratio between the horizontal and vertical tube walls is properly chosen. Our generalized formalism can be used for optimization of arbitrarily complex-shaped beam tubes, with respect to suppression of detrimental field harmonics.
Gillespie, Ronald J; Robinson, Edward A
2005-05-01
Although the structure of almost any molecule can now be obtained by ab initio calculations chemists still look for simple answers to the question "What determines the geometry of a given molecule?" For this purpose they make use of various models such as the VSEPR model and qualitative quantum mechanical models such as those based on the valence bond theory. The present state of such models, and the support for them provided by recently developed methods for analyzing calculated electron densities, are reviewed and discussed in this tutorial review.
2015-01-01
This stimulating volume offers a broad collection of the principles of geometry and trigonometry and contains colorful diagrams to bring mathematical principles to life. Subjects are enriched by references to famous mathematicians and their ideas, and the stories are presented in a very comprehensible way. Readers investigate the relationships of points, lines, surfaces, and solids. They study construction methods for drawing figures, a wealth of facts about these figures, and above all, methods to prove the facts. They learn about triangle measure for circular motion, sine and cosine, tangent