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Sample records for hexagonal geometry fast

  1. 2-DB, 2-D Multigroup Diffusion, X-Y, R-Theta, Hexagonal Geometry Fast Reactor, Criticality Search

    International Nuclear Information System (INIS)

    Little, W.W. Jr.; Hardie, R.W.; Hirons, T.J.; O'Dell, R.D.

    1969-01-01

    1 - Description of problem or function: 2DB is a flexible, two- dimensional (x-y, r-z, r-theta, hex geometry) diffusion code for use in fast reactor analyses. The code can be used to: (a) Compute fuel burnup using a flexible material shuffling scheme. (b) Perform criticality searches on time absorption (alpha), material concentrations, and region dimensions using a regular or adjoint model. Criticality searches can be performed during burnup to compensate for fuel depletion. (c) Compute flux distributions for an arbitrary extraneous source. 2 - Method of solution: Standard source-iteration techniques are used. Group re-balancing and successive over-relaxation with line inversion are used to accelerate convergence. Material burnup is by reactor zone. The burnup rate is determined by the zone and energy (group) averaged cross sections which are recomputed after each time-step. The isotopic chains, which can contain any number of isotopes, are formed by the user. The code does not contain built-in or internal chains. 3 - Restrictions on the complexity of the problem: Since variable dimensioning is employed, no simple bounds can be stated. The current 1108 version, however, is nominally restricted to 50 energy groups in a 65 K memory. In the 6600 version the power fraction, average burnup rate, and breeding ratio calculations are limited to reactors with a maximum of 50 zones

  2. Loading pattern optimization in hexagonal geometry using PANTHER

    International Nuclear Information System (INIS)

    Parks, G.T.; Knight, M.P.

    1996-01-01

    The extension of the loading pattern optimization capability of Nuclear Electric's reactor physics code PANTHER to hexagonal geometry cores is described. The variety of search methods available and the code's performance are illustrated by an example in which three search different methods are used in turn in order to find an optimal reload design for a sample hexagonal geometry problem. (author)

  3. Comparison of PANTHER nodal solutions in hexagonal-z geometry

    International Nuclear Information System (INIS)

    Knight, M.; Hutt, P.; Lewis, I.

    1995-01-01

    The reactor physics code PANTHER has been extended to hexagonal geometries. Steady-state, depletion, and transient calculations with feedback can all be performed. Two hexagonal nodal flux solutions have been developed. In the first method, transverse integration is performed exactly as in the rectangular case. The resulting transverse integrated equation has singular terms, which are simply ignored. The second approach applies a conformal mapping that transforms the hexagon onto a rectangle. Pin power reconstruction has also been developed with both methods. For a benchmark VVER-1000 reactor depletion problem, both methods give accurate results for standard depletion calculations. In the more extreme situation with all rods inserted, the simpler method breaks down. However, the accuracy of the conformal solution was found to be excellent in all cases studied

  4. Extension of the comet method to 2-D hexagonal geometry

    International Nuclear Information System (INIS)

    Connolly, Kevin John; Rahnema, Farzad; Zhang, Dingkang

    2011-01-01

    The capability of the heterogeneous coarse mesh radiation transport (COMET) method developed at Georgia Tech has been expanded. COMET is now able to treat hexagonal geometry in two dimensions, allowing reactor problems to be solved for those next-generation reactors which utilize prismatic block structure and hexagonal lattice geometry in their designs. The COMET method is used to solve whole core reactor analysis problems without resorting to homogenization or low-order transport approximations. The eigenvalue and fission density distribution of the reactor are determined iteratively using response functions. The method has previously proven accurate in solving PWR, BWR, and CANDU eigenvalue problems. In this paper, three simple test cases inspired by high temperature test reactor material cross sections and fuel block geometry are presented. These cases are given not in an attempt to model realistic nuclear power systems, but in order to test the ability of the improved method. Solutions determined by the new hexagonal version of COMET, COMET-Hex, are compared with solutions determined by MCNP5, and the results show the accuracy and efficiency of the improved COMET-Hex method in calculating the eigenvalue and fuel pin fission density in sample full-core problems. COMETHex determines the eigenvalues of these simple problems to an order of within 50 pcm of the reference solutions and all pin fission densities to an average error of 0.2%, and it requires fewer than three minutes to produce these results. (author)

  5. High-order discrete ordinate transport in hexagonal geometry: A new capability in ERANOS

    International Nuclear Information System (INIS)

    Le Tellier, R.; Suteau, C.; Fournier, D.; Ruggieri, J.M.

    2010-01-01

    This paper presents the implementation of an arbitrary order discontinuous Galerkin scheme within the framework of a discrete ordinate solver of the neutron transport equation for nuclear reactor calculations. More precisely, it deals with non-conforming spatial meshes for the 2 D and 3 D modeling of core geometries based on hexagonal assemblies. This work aims at improving the capabilities of the ERANOS code system dedicated to fast reactor analysis and design. Both the angular quadrature and spatial scheme peculiarities for hexagonal geometries are presented. A particular focus is set on the spatial non-conforming mesh and variable order capabilities of this scheme in anticipation to the development of spatial adaptiveness algorithms. These features are illustrated on a 3 D numerical benchmark with comparison to a Monte Carlo reference and a 2 D benchmark that shows the potential of this scheme for both h-and p-adaptation.

  6. Neutron noise calculations in a hexagonal geometry and comparison with analytical solutions

    International Nuclear Information System (INIS)

    Tran, H. N.; Demaziere, C.

    2012-01-01

    This paper presents the development of a neutronic and kinetic solver for hexagonal geometries. The tool is developed based on the diffusion theory with multi-energy groups and multi-groups of delayed neutron precursors allowing the solutions of forward and adjoint problems of static and dynamic states, and is applicable to both thermal and fast systems with hexagonal geometries. In the dynamic problems, the small stationary fluctuations of macroscopic cross sections are considered as noise sources, and then the induced first order noise is calculated fully in the frequency domain. Numerical algorithms for solving the static and noise equations are implemented with a spatial discretization based on finite differences and a power iterative solution. A coarse mesh finite difference method has been adopted for speeding up the convergence. Since no other numerical tool could calculate frequency-dependent noise in hexagonal geometry, validation calculations have been performed and benchmarked to analytical solutions based on a 2-D homogeneous system with two-energy groups and one-group of delayed neutron precursor, in which point-like perturbations of thermal absorption cross section at central and non-central positions are considered as noise sources. (authors)

  7. The COMET method in 3-D hexagonal geometry

    International Nuclear Information System (INIS)

    Connolly, K. J.; Rahnema, F.

    2012-01-01

    The hybrid stochastic-deterministic coarse mesh radiation transport (COMET) method developed at Georgia Tech now solves reactor core problems in 3-D hexagonal geometry. In this paper, the method is used to solve three preliminary test problems designed to challenge the method with steep flux gradients, high leakage, and strong asymmetry and heterogeneity in the core. The test problems are composed of blocks taken from a high temperature test reactor benchmark problem. As the method is still in development, these problems and their results are strictly preliminary. Results are compared to whole core Monte Carlo reference solutions in order to verify the method. Relative errors are on the order of 50 pcm in core eigenvalue, and mean relative error in pin fission density calculations is less than 1% in these difficult test cores. The method requires the one-time pre-computation of a response expansion coefficient library, which may be compiled in a comparable amount of time to a single whole core Monte Carlo calculation. After the library has been computed, COMET may solve any number of core configurations on the order of an hour, representing a significant gain in efficiency over other methods for whole core transport calculations. (authors)

  8. DUMA - a program to display distributions in hexagonal geometry

    International Nuclear Information System (INIS)

    Tran Quoc Dung; Makai, M.

    1987-09-01

    DUMA program displays hexagonal structures applied in WWER-440 reactors or one or two distributions in them. It helps users to display either integer, literal or real arrays in an arbitrary hexagonal structure. Possible applications: displaying reactor core layout, power distribution or activity measurements. (author)

  9. A nodal expansion method using conformal mapping for hexagonal geometry

    International Nuclear Information System (INIS)

    Chao, Y.A.; Shatilla, Y.A.

    1993-01-01

    Hexagonal nodal methods adopting the same transverse integration process used for square nodal methods face the subtle theoretical problem that this process leads to highly singular nonphysical terms in the diffusion equation. Lawrence, in developing the DIF3D-N code, tried to approximate the singular terms with relatively simple polynomials. In the HEX-NOD code, Wagner ignored the singularities to simplify the diffusion equation and introduced compensating terms in the nodal equations to restore the nodal balance relation. More recently developed hexagonal nodal codes, such as HEXPE-DITE and the hexagonal version of PANTHER, used methods similar to Wagner's. It will be shown that for light water reactor applications, these two different approximations significantly degraded the accuracy of the respective method as compared to the established square nodal methods. Alternatively, the method of conformal mapping was suggested to map a hexagon to a rectangle, with the unique feature of leaving the diffusion operator invariant, thereby fundamentally resolving the problems associated with transverse integration. This method is now implemented in the Westinghouse hexagonal nodal code ANC-H. In this paper we report on the results of comparing the three methods for a variety of problems via benchmarking against the fine-mesh finite difference code

  10. Extension of the analytic nodal diffusion solver ANDES to triangular-Z geometry and coupling with COBRA-IIIc for hexagonal core analysis

    International Nuclear Information System (INIS)

    Lozano, Juan-Andres; Jimenez, Javier; Garcia-Herranz, Nuria; Aragones, Jose-Maria

    2010-01-01

    In this paper the extension of the multigroup nodal diffusion code ANDES, based on the Analytic Coarse Mesh Finite Difference (ACMFD) method, from Cartesian to hexagonal geometry is presented, as well as its coupling with the thermal-hydraulic (TH) code COBRA-IIIc for hexagonal core analysis. In extending the ACMFD method to hexagonal assemblies, triangular-Z nodes are used. In the radial plane, a direct transverse integration procedure is applied along the three directions that are orthogonal to the triangle interfaces. The triangular nodalization avoids the singularities, that appear when applying transverse integration to hexagonal nodes, and allows the advantage of the mesh subdivision capabilities implicit within that geometry. As for the thermal-hydraulics, the extension of the coupling scheme to hexagonal geometry has been performed with the capability to model the core using either assembly-wise channels (hexagonal mesh) or a higher refinement with six channels per fuel assembly (triangular mesh). Achieving this level of TH mesh refinement with COBRA-IIIc code provides a better estimation of the in-core 3D flow distribution, improving the TH core modelling. The neutronics and thermal-hydraulics coupled code, ANDES/COBRA-IIIc, previously verified in Cartesian geometry core analysis, can also be applied now to full three-dimensional VVER core problems, as well as to other thermal and fast hexagonal core designs. Verification results are provided, corresponding to the different cases of the OECD/NEA-NSC VVER-1000 Coolant Transient Benchmarks.

  11. Hexagonal tube behaviour in fuel assemblies under neutron flux in a French fast neutron reactor core

    International Nuclear Information System (INIS)

    Bernard, A.; Ammann, P.

    This paper presents what is obtained in the field of the interpretation by calculation of the post irradiation examination of hexagonal tubes, and in the field of prevision by calculation of the behaviour of hexagonal tubes under fast flux [fr

  12. A co-ordinate system for reactor physics calculations in hexagonal geometry

    International Nuclear Information System (INIS)

    Burte, D.P.

    1990-01-01

    A method for generating all the geometric information concerning typical reactor physics calculations for a basically hexagonal reactor core or its sector involving any of the possible symmetries is presented. The geometrically allowed symmetries for regular hexagons are discussed. The approach is based on the choice of a suitable co-ordinate system, viz. one using three coplanar (including one redundant) axes, each at 120 0 with its cyclically preceding one. A code named KEKULE' is developed for a 2-D, finite difference, one-group diffusion analysis of a hexagonal core using the approach. It can cater to a full hexagonal core as well as to any symmetric sectorial part of it. The main feature of the code is that the input concerning geometry is a bare minimum. It is hoped that the approach presented will be useful even for the calculations for hexagonal fuel assemblies. (author)

  13. Finite element method for neutron diffusion problems in hexagonal geometry

    International Nuclear Information System (INIS)

    Wei, T.Y.C.; Hansen, K.F.

    1975-06-01

    The use of the finite element method for solving two-dimensional static neutron diffusion problems in hexagonal reactor configurations is considered. It is investigated as a possible alternative to the low-order finite difference method. Various piecewise polynomial spaces are examined for their use in hexagonal problems. The central questions which arise in the design of these spaces are the degree of incompleteness permissible and the advantages of using a low-order space fine-mesh approach over that of a high-order space coarse-mesh one. There is also the question of the degree of smoothness required. Two schemes for the construction of spaces are described and a number of specific spaces, constructed with the questions outlined above in mind, are presented. They range from a complete non-Lagrangian, non-Hermite quadratic space to an incomplete ninth order space. Results are presented for two-dimensional problems typical of a small high temperature gas-cooled reactor. From the results it is concluded that the space used should at least include the complete linear one. Complete spaces are to be preferred to totally incomplete ones. Once function continuity is imposed any additional degree of smoothness is of secondary importance. For flux shapes typical of the small high temperature gas-cooled reactor the linear space fine-mesh alternative is to be preferred to the perturbation quadratic space coarse-mesh one and the low-order finite difference method is to be preferred over both finite element schemes

  14. RTk/SN Solutions of the Two-Dimensional Multigroup Transport Equations in Hexagonal Geometry

    International Nuclear Information System (INIS)

    Valle, Edmundo del; Mund, Ernest H.

    2004-01-01

    This paper describes an extension to the hexagonal geometry of some weakly discontinuous nodal finite element schemes developed by Hennart and del Valle for the two-dimensional discrete ordinates transport equation in quadrangular geometry. The extension is carried out in a way similar to the extension to the hexagonal geometry of nodal element schemes for the diffusion equation using a composite mapping technique suggested by Hennart, Mund, and del Valle. The combination of the weakly discontinuous nodal transport scheme and the composite mapping is new and is detailed in the main section of the paper. The algorithm efficiency is shown numerically through some benchmark calculations on classical problems widely referred to in the literature

  15. Simulate-HEX - The multi-group diffusion equation in hexagonal-z geometry

    International Nuclear Information System (INIS)

    Lindahl, S. O.

    2013-01-01

    The multigroup diffusion equation is solved for the hexagonal-z geometry by dividing each hexagon into 6 triangles. In each triangle, the Fourier solution of the wave equation is approximated by 8 plane waves to describe the intra-nodal flux accurately. In the end an efficient Finite Difference like equation is obtained. The coefficients of this equation depend on the flux solution itself and they are updated once per power/void iteration. A numerical example demonstrates the high accuracy of the method. (authors)

  16. An incident flux expansion transport theory method suitable for coupling to diffusion theory methods in hexagonal geometry

    International Nuclear Information System (INIS)

    Hayward, Robert M.; Rahnema, Farzad; Zhang, Dingkang

    2013-01-01

    Highlights: ► A new hybrid stochastic–deterministic transport theory method to couple with diffusion theory. ► The method is implemented in 2D hexagonal geometry. ► The new method produces excellent results when compared with Monte Carlo reference solutions. ► The method is fast, solving all test cases in less than 12 s. - Abstract: A new hybrid stochastic–deterministic transport theory method, which is designed to couple with diffusion theory, is presented. The new method is an extension of the incident flux response expansion method, and it combines the speed of diffusion theory with the accuracy of transport theory. With ease of use in mind, the new method is derived in such a way that it can be implemented with only minimal modifications to an existing diffusion theory method. A new angular expansion, which is necessary for the diffusion theory coupling, is developed in 2D and 3D. The method is implemented in 2D hexagonal geometry, and an HTTR benchmark problem is used to test its accuracy in a standalone configuration. It is found that the new method produces excellent results (with average relative error in partial current less than 0.033%) when compared with Monte Carlo reference solutions. Furthermore, the method is fast, solving all test cases in less than 12 s

  17. Mixed dual finite element methods for the numerical treatment of the diffusion equation in hexagonal geometry

    International Nuclear Information System (INIS)

    Schneider, D.

    2001-01-01

    The nodal method Minos has been developed to offer a powerful method for the calculation of nuclear reactor cores in rectangular geometry. This method solves the mixed dual form of the diffusion equation and, also of the simplified P N approximation. The discretization is based on Raviart-Thomas' mixed dual finite elements and the iterative algorithm is an alternating direction method, which uses the current as unknown. The subject of this work is to adapt this method to hexagonal geometry. The guiding idea is to construct and test different methods based on the division of a hexagon into trapeze or rhombi with appropriate mapping of these quadrilaterals onto squares in order to take into advantage what is already available in the Minos solver. The document begins with a review of the neutron diffusion equation. Then we discuss its mixed dual variational formulation from a functional as well as from a numerical point of view. We study conformal and bilinear mappings for the two possible meshing of the hexagon. Thus, four different methods are proposed and are completely described in this work. Because of theoretical and numerical difficulties, a particular treatment has been necessary for methods based on the conformal mapping. Finally, numerical results are presented for a hexagonal benchmark to validate and compare the four methods with respect to pre-defined criteria. (authors)

  18. Solution of 2D and 3D hexagonal geometry benchmark problems by using the finite element diffusion code DIFGEN

    International Nuclear Information System (INIS)

    Gado, J.

    1986-02-01

    The four group, 2D and 3D hexagonal geometry HTGR benchmark problems and a 2D hexagonal geometry PWR (WWER) benchmark problem have been solved by using the finite element diffusion code DIFGEN. The hexagons (or hexagonal prisms) were subdivided into first order or second order triangles or quadrilaterals (or triangular or quadrilateral prisms). In the 2D HTGR case of the number of the inserted absorber rods was also varied (7, 6, 0 or 37 rods). The calculational results are in a good agreement with the results of other calculations. The larger systematic series of DIFGEN calculations have given a quantitative picture on the convergence properties of various finite element modellings of hexagonal grids in DIFGEN. (orig.)

  19. High Order Finite Element Method for the Lambda modes problem on hexagonal geometry

    International Nuclear Information System (INIS)

    Gonzalez-Pintor, S.; Ginestar, D.; Verdu, G.

    2009-01-01

    A High Order Finite Element Method to approximate the Lambda modes problem for reactors with hexagonal geometry has been developed. This method is based on the expansion of the neutron flux in terms of the modified Dubiner's polynomials on a triangular mesh. This mesh is fixed and the accuracy of the method is improved increasing the degree of the polynomial expansions without the necessity of remeshing. The performance of method has been tested obtaining the dominant Lambda modes of different 2D reactor benchmark problems.

  20. Solution of the Neutron transport equation in hexagonal geometry using strongly discontinuous nodal schemes

    International Nuclear Information System (INIS)

    Mugica R, C.A.; Valle G, E. del

    2005-01-01

    In 2002, E. del Valle and Ernest H. Mund developed a technique to solve numerically the Neutron transport equations in discrete ordinates and hexagonal geometry using two nodal schemes type finite element weakly discontinuous denominated WD 5,3 and WD 12,8 (of their initials in english Weakly Discontinuous). The technique consists on representing each hexagon in the union of three rhombuses each one of which it is transformed in a square in the one that the methods WD 5,3 and WD 12,8 were applied. In this work they are solved the mentioned equations of transport using the same discretization technique by hexagon but using two nodal schemes type finite element strongly discontinuous denominated SD 3 and SD 8 (of their initials in english Strongly Discontinuous). The application in each case as well as a reference problem for those that results are provided for the effective multiplication factor is described. It is carried out a comparison with the obtained results by del Valle and Mund for different discretization meshes so much angular as spatial. (Author)

  1. Improvements in practical applicability of NSHEX: nodal transport calculation code for three-dimensional hexagonal-Z geometry

    International Nuclear Information System (INIS)

    Sugino, Kazuteru

    1998-07-01

    As a tool to perform a fast reactor core calculations with high accuracy, NSHEX the nodal transport calculation code for three-dimensional hexagonal-Z geometry is under development. To improve the practical applicability of NSHEX, for instance, in its application to safety analysis and commercial reactor core design studies, we investigated the basic theory used in it, improved the program performance, and evaluated its applicability to the analysis of commercial reactor cores. The current studies show the following: (1) An improvement in the treatment of radial leakage in the radial nodal coupling equation bettered calculational convergence for safety analysis calculation, so the applicability of NSHEX to safety analysis was improved. (2) As a result of comparison of results from NSHEX and the standard core calculation code, it was confirmed that there was consistency between them. (3) According to the evaluation of the effect due to the difference of calculational condition, it was found that the calculation under appropriate nodal expansion orders and Sn orders correspond to the one under most detailed condition. However further investigation is required to reduce the uncertainty in calculational results due to the treatment of high order flux moments. (4) A whole core version of NSHEX enabling calculation for any FBR core geometry has been developed, this improved general applicability of NSHEX. (5) An investigation of the applicability of the rebalance method to acceleration clarified that this improved calculational convergence and it was effective. (J.P.N.)

  2. Reconstruction of pin burnup characteristics from nodal calculations in hexagonal geometry

    International Nuclear Information System (INIS)

    Yang, W.S.; Finck, P.J.; Khalil, H.S.

    1990-01-01

    A reconstruction method has been developed for recovering pin burnup characteristics from fuel cycle calculations performed in hexagonal-z geometry using the nodal diffusion option of the DIF3D/REBUS-3 code system. Intra-modal distributions of group fluxes, nuclide densities, power density, burnup, and fluence are efficiently computed using polynomial shapes constrained to satisfy nodal information. The accuracy of the method has been tested by performing several numerical benchmark calculations and by comparing predicted local burnups to values measured for experimental assemblies in EBR-11. The results indicate that the reconstruction methods are quite accurate, yielding maximum errors in power and nuclide densities that are less than 2% for driver assemblies and typically less than 5% for blanket assemblies. 14 refs., 2 figs., 5 tabs

  3. TRANSHEX, 2-D Thermal Neutron Flux Distribution from Epithermal Flux in Hexagonal Geometry

    International Nuclear Information System (INIS)

    Patrakka, E.

    1994-01-01

    1 - Description of program or function: TRANSHEX is a multigroup integral transport program that determines the thermal scalar flux distribution arising from a known epithermal flux in two- dimensional hexagonal geometry. 2 - Method of solution: The program solves the isotropic collision probability equations for a region-averaged scalar flux by an iterative method. Either a successive over-relaxation or an inner-outer iteration technique is applied. Flat flux collision probabilities between trigonal space regions with white boundary condition are utilized. The effect of epithermal flux is taken into consideration as a slowing-down source that is calculated for a given spatial distribution and 1/E energy dependence of the epithermal flux

  4. Towards Fast Tracking of the Keyhole Geometry

    Science.gov (United States)

    Brock, C.; Hohenstein, R.; Schmidt, M.

    We describe a sensor principle permitting the fast online measurement of the position of the optical process emissions in deep penetration laser welding. Experiments show a strong correlation between the position of the vapour plume and the keyhole geometry, demonstrated here by varying the penetration depth of the weld. In order to achieve an absolute position measurement, the sensor was calibrated using a light source with well defined characteristics. The setup for the calibration measurements and the corresponding data evaluation methods are discussed. The precision of the calibration with a green LED is 6 μm in lateral and 55 μm in axial direction, for a working distance of 200 mm.

  5. Simulation of a reactor FBR with hexagonal-Z geometry using the code PARCS 3.1

    International Nuclear Information System (INIS)

    Reyes F, M. C.; Del Valle G, E.; Filio L, C.

    2013-10-01

    The nuclear reactor core type FBR (Fast Breeder Reactor) was modeled in three dimensions of hexagonal-Z geometry using the code PARCS (Purdue Advanced Reactor Core Simulator) version 3.1 developed by Purdue University researchers. To carry out the modeling of the mentioned reactor was taken the corresponding information to one of the described benchmarks in the document NEACRP-L-330 (3-D Neutron Transport Benchmarks, 1991); fundamentally the corresponding to the geometric data and the cross sections. Being a quick reactor of breeding, known as the Knk-II, for which are considered 4 energy groups without dispersions up. The reactor core is formed by prismatic elements of hexagonal transversal cut where part of them only corresponds to nuclear fuel assemblies. This has four reflector rings and 6 identical control elements that together with the active part of the core is configured with 8 different types of elements.With the extracted information of the mentioned document the entrance file was prepared for PARCS 3.1 only considering a sixth part of the core due to the symmetry that presents their configuration. The NEACRP-L-330 shows a wide range of results reported by those who collaborated in its elaboration using different solution techniques that go from the Monte Carlo method to the approaches S 2 and P 1 . Of all the results were selected those obtained with the code HEXNOD, to which were carried out a comparison of the effective multiplication factor, being smaller differences to the 300 pcm, for three different scenarios: a) with the control bars extracted totally, b) with the semi-inserted control bars and c) with the control bars inserted completely and two different axial meshes, a thick mesh with 14 slices and another fine with 38, that which implies that the results can be considered very similar among if same. Radial maps and axial profiles are included, as much of the power as of the neutrons flow. (Author)

  6. Development of a perturbation code, PERT-K, for hexagonal core geometry

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Taek Kyum; Kim, Sang Ji; Song, Hoon; Kim, Young Il; Kim, Young Jin [Korea Atomic Energy Research Institute, Taejon (Korea)

    1999-01-01

    A perturbation code for hexagonal core geometry has been developed based on Nodal Expansion Method. By using relevant output files of DIF3D code, it can calculate the reactivity changes caused by perturbation in composition or/and neutron cross section libraries. The accuracy of PERT-K code has been validated by calculating the reactivity changes due to fuel composition change, the sodium void coefficients, and the sample reactivity worths of BFS-73-1 critical experiments. In the case of 10% reduction in all fuel isotopics at a assembly located in the outer core, PERT-K computation agrees with the direct computation by DIF3D within 60 pcm. The sample reactivity worths of BFS-73-1 critical experiments are predicted with PERT-K code within the experimental error bounds. For 100% sodium void occurrence at the inner core, the maximum difference of reactivity changes between PERT-K and direct DIF3D computations is less than 40 pcm. On the other hand, the same sodium void condition at the outer core leads to a difference of reactivity change greater than 400 pcm. However, as sodium voiding becomes near zero value, the difference becomes less and rapidly falls within the acceptable bound, i.e. 40 pcm. (author). 11 refs., 9 figs., 6 tabs.

  7. Fuel management optimization in pressure water reactors with hexagonal geometry using hill climbing method

    International Nuclear Information System (INIS)

    Andres Diaz, J.; Quintero, Ruben; Melian, Manuel; Rosete, Alejandro

    2000-01-01

    In this work the general-purpose optimization method, Hill Climbing, was applied to the Fuel Management Optimization problem in PWR reactors, WWER type. They were carried out a series of experiments in order to study the performance of Hill Climbing. It was proven two starting point for initialize the search: a reload configuration by project and a reload configuration generated with the application of a minimal knowledge of the problem. It was also studied the effect of imposing constraints based on the physics of the reactor in order to reduce the number of possible solutions to be generated. The operator used in Hill Climbing was defined as a binary exchange of fuel assemblies. For the simulation of each generated configuration, the tridimensional simulator program SPPS-1 was used. It was formulated an objective function with power peaking constraint to guide the search. As results, a methodology ws proposed for the In-core Fuel Management Optimization in hexagonal geometry, and the feasibility of the application of the Hill Climbing to this type of problem was demonstrated. (author)

  8. Fast rendering of scanned room geometries

    DEFF Research Database (Denmark)

    Olesen, Søren Krarup; Markovic, Milos; Hammershøi, Dorte

    2014-01-01

    Room acoustics are rendered in Virtual Realities based on models of the real world. These are typically rather coarse representations of the true geometry resulting in room impulse responses with a lack of natural detail. This problem can be overcome by using data scanned by sensors, such as e...

  9. Computer realization of an algorithm for determining the optimal arrangement of a fast power reactor core with hexagonal assemblies

    International Nuclear Information System (INIS)

    Karpov, V.A.; Rybnikov, A.F.

    1983-01-01

    An algorithm for solving the problems associated with fast nuclear reactor computer-aided design is suggested. Formulation of the discrete optimization problem dealing with chosing of the first loading arrangement, determination of the control element functional purpose and the order of their rearrangement during reactor operation as well as the choice of operations for core reloading is given. An algorithm for computerized solutions of the mentioned optimization problem based on variational methods relized in the form of the DESIGN program complex written in FORTRAN for the BEhSM-6 computer is proposed. A fast-response program for solving the diffusion equations of two-dimensional reactor permitting to obtain the optimization problem solution at reasonable period of time is developed to conduct necessary neutron-physical calculations for the reactor in hexagonal geometry. The DESIGN program can be included into a computer-aided design system for automation of the procedure of determining the fast power reactor core arrangement. Application of the DESIGN program permits to avoid the routine calculations on substantiation of neutron-physical and thermal-hydraulic characteristics of the reactor core that releases operators from essential waste of time and increases efficiency of their work

  10. A transmission probability method for calculation of neutron flux distributions in hexagonal geometry

    International Nuclear Information System (INIS)

    Wasastjerna, F.; Lux, I.

    1980-03-01

    A transmission probability method implemented in the program TPHEX is described. This program was developed for the calculation of neutron flux distributions in hexagonal light water reactor fuel assemblies. The accuracy appears to be superior to diffusion theory, and the computation time is shorter than that of the collision probability method. (author)

  11. Comparison of rod-ejection transient calculations in hexagonal-Z geometry

    International Nuclear Information System (INIS)

    Knight, M.P.; Brohan, P.; Finnemann, H.; Huesken, J.

    1995-01-01

    This paper proposes a set of 3-dimensional benchmark rod ejection problems for a VVER reactor, based on the well-known NEACRP PWR rod-ejection problems defined by Siemens/KWU. Predictions for these benchmarks derived using three hexagonal-z nodal transient codes, the PANTHER code of Nuclear Electric, the HEXTIME code of Siemens/KWU, and the DYN3D code of FZ-Rossendorf are presented and compared

  12. The response-matrix based AFEN method for the hexagonal geometry

    International Nuclear Information System (INIS)

    Noh, Jae Man; Kim, Keung Koo; Zee, Sung Quun; Joo, Hyung Kook; Cho, Byng Oh; Jeong, Hyung Guk; Cho, Jin Young

    1998-03-01

    The analytic function expansion nodal (AFEN) method, developed to overcome the limitations caused by the transverse integration, has been successfully to predict the neutron behavior in the hexagonal core as well as rectangular core. In the hexagonal node, the transverse leakage resulted from the transverse integration has some singular terms such as delta-function and step-functions near the node center line. In most nodal methods using the transverse integration, the accuracy of nodal method is degraded because the transverse leakage is approximated as a smooth function across the node center line by ignoring singular terms. However, the AFEN method in which there is no transverse leakage term in deriving nodal coupling equations keeps good accuracy for hexagonal node. In this study, the AFEN method which shows excellent accuracy in the hexagonal core analyses is reformulated as a response matrix form. This form of the AFEN method can be implemented easily to nodal codes based on the response matrix method. Therefore, the Coarse Mesh Rebalance (CMR) acceleration technique which is one of main advantages of the response matrix method can be utilized for the AFEN method. The response matrix based AFEN method has been successfully implemented into the MASTER code and its accuracy and computational efficiency were examined by analyzing the two- and three- dimensional benchmark problem of VVER-440. Based on the results, it can be concluded that the newly formulated AFEN method predicts accurately the assembly powers (within 0.2% average error) as well as the effective multiplication factor (within 0.2% average error) as well as the effective multiplication factor (within 20 pcm error). In addition, the CMR acceleration technique is quite efficient in reducing the computation time of the AFEN method by 8 to 10 times. (author). 22 refs., 1 tab., 4 figs

  13. DIF3D nodal neutronics option for two- and three-dimensional diffusion theory calculations in hexagonal geometry. [LMFBR

    Energy Technology Data Exchange (ETDEWEB)

    Lawrence, R.D.

    1983-03-01

    A nodal method is developed for the solution of the neutron-diffusion equation in two- and three-dimensional hexagonal geometries. The nodal scheme has been incorporated as an option in the finite-difference diffusion-theory code DIF3D, and is intended for use in the analysis of current LMFBR designs. The nodal equations are derived using higher-order polynomial approximations to the spatial dependence of the flux within the hexagonal-z node. The final equations, which are cast in the form of inhomogeneous response-matrix equations for each energy group, involved spatial moments of the node-interior flux distribution plus surface-averaged partial currents across the faces of the node. These equations are solved using a conventional fission-source iteration accelerated by coarse-mesh rebalance and asymptotic source extrapolation. This report describes the mathematical development and numerical solution of the nodal equations, as well as the use of the nodal option and details concerning its programming structure. This latter information is intended to supplement the information provided in the separate documentation of the DIF3D code.

  14. DIF3D nodal neutronics option for two- and three-dimensional diffusion theory calculations in hexagonal geometry

    International Nuclear Information System (INIS)

    Lawrence, R.D.

    1983-03-01

    A nodal method is developed for the solution of the neutron-diffusion equation in two- and three-dimensional hexagonal geometries. The nodal scheme has been incorporated as an option in the finite-difference diffusion-theory code DIF3D, and is intended for use in the analysis of current LMFBR designs. The nodal equations are derived using higher-order polynomial approximations to the spatial dependence of the flux within the hexagonal-z node. The final equations, which are cast in the form of inhomogeneous response-matrix equations for each energy group, involved spatial moments of the node-interior flux distribution plus surface-averaged partial currents across the faces of the node. These equations are solved using a conventional fission-source iteration accelerated by coarse-mesh rebalance and asymptotic source extrapolation. This report describes the mathematical development and numerical solution of the nodal equations, as well as the use of the nodal option and details concerning its programming structure. This latter information is intended to supplement the information provided in the separate documentation of the DIF3D code

  15. Neutron transport in hexagonal reactor cores modeled by trigonal-geometry diffusion and simplified P{sub 3} nodal methods

    Energy Technology Data Exchange (ETDEWEB)

    Duerigen, Susan

    2013-05-15

    The superior advantage of a nodal method for reactor cores with hexagonal fuel assemblies discretized as cells consisting of equilateral triangles is its mesh refinement capability. In this thesis, a diffusion and a simplified P{sub 3} (or SP{sub 3}) neutron transport nodal method are developed based on trigonal geometry. Both models are implemented in the reactor dynamics code DYN3D. As yet, no other well-established nodal core analysis code comprises an SP{sub 3} transport theory model based on trigonal meshes. The development of two methods based on different neutron transport approximations but using identical underlying spatial trigonal discretization allows a profound comparative analysis of both methods with regard to their mathematical derivations, nodal expansion approaches, solution procedures, and their physical performance. The developed nodal approaches can be regarded as a hybrid NEM/AFEN form. They are based on the transverse-integration procedure, which renders them computationally efficient, and they use a combination of polynomial and exponential functions to represent the neutron flux moments of the SP{sub 3} and diffusion equations, which guarantees high accuracy. The SP{sub 3} equations are derived in within-group form thus being of diffusion type. On this basis, the conventional diffusion solver structure can be retained also for the solution of the SP{sub 3} transport problem. The verification analysis provides proof of the methodological reliability of both trigonal DYN3D models. By means of diverse hexagonal academic benchmark and realistic detailed-geometry full-transport-theory problems, the superiority of the SP{sub 3} transport over the diffusion model is demonstrated in cases with pronounced anisotropy effects, which is, e.g., highly relevant to the modeling of fuel assemblies comprising absorber material.

  16. HEXAB-3D, 3-D Few-Group Diffusion for Hexagonal Core Geometry

    International Nuclear Information System (INIS)

    Apostolov, T.G.; Ivanov, K.N.; Manolova, M.A.

    2002-01-01

    1 - Description of program or function: A three-dimensional few-group calculational model based on diffusion theory has been developed for calculating the basic neutron physical characteristics of power reactors which have a hexagonal core configuration with a heterogeneous region structure in axial direction. There are two versions of the model: - HEXAB-III-30 - the solution range in horizontal plane is 30 - sector of reactor core - HEXAB-III-360 - the solution range in horizontal plane is full core. 2 - Method of solution: In the HEXAB-3D code the nine-point mesh-centered finite-difference approximation of neutron diffusion equation is applied. The standard inner-outer iterative strategy is used. Inner iterations are solved using two different incomplete factorization techniques: AGA two-sweep iterative method and modified AGA two-sweep iterative method both accelerated by the double successive over-relaxation procedure. The power method, combined with two- or three-term Chebishev polynomial acceleration for outer iterations is applied in the code. To improve the accuracy of the calculated integral and local reactor parameters without significantly increasing computer time and storage an effective approach has been developed. It decreases errors due to the use of coarse mesh by means of correcting the coefficients of finite- difference scheme. 3 - Restrictions on the complexity of the problem: Maximum of 10 energy groups, 30 horizontal layers and 100 material compositions

  17. Validation of new 3-D neutronics model in APROS for hexagonal geometry

    International Nuclear Information System (INIS)

    Rintala, J.

    2010-01-01

    APROS - Advanced PROcess Simulation environment-is a widely used simulation tool for nuclear power plant modelling. Earlier the three-dimensional neutronics calculation has been based on model using the difference method. The original three-dimensional core model is mainly used in power plant simulator applications, where it fits well because of its speed. For safety analysis purposes, however, a new model was considered to be an important improvement to meet the accuracy requirements. A sophisticated nodal model used already in HEXTRAN and TRAB-3D was decided to be implemented into APROS. The hexagonal part of the model has now been implemented and tested. For practical reasons, the model was programmed from scratch into APROS and also some small improvements were added and thus, an extensive validation program was necessary to prove the correct behaviour of the model. In this paper, the most important results from AER kinetic benchmarks 2 and 3 calculations are shown as well as the calculation results against data achieved LR-0 test reactor space-time kinetic experiments. Since the model is similar to the one in HEXTRAN, the results in benchmarks are compared to the results by it. In LR-0 calculations, results by both, original and new model are presented and compared to the measurements. The results shows that the implementation of the model has been successful and the new model improves the accuracy of three-dimensional neutronics calculation in APROS into the level required in safety analyses. (Author)

  18. Simulation of a reactor FBR with hexagonal-Z geometry using the code PARCS 3.1; Simulacion de un reactor FBR con geometria hexagonal-Z usando el codigo PARCS 3.1

    Energy Technology Data Exchange (ETDEWEB)

    Reyes F, M. C.; Del Valle G, E. [IPN, Escuela Superior de Fisica y Matematicas, Av. Instituto Politecnico Nacional s/n, U.P. Adolfo Lopez Mateos, Edificio 9, Col. San Pedro Zacatenco, 07738 Mexico D. F. (Mexico); Filio L, C., E-mail: rf.melisa@gmail.com [Comision Nacional de Seguridad Nuclear y Salvaguardias, Dr. Jose Ma. Barragan No. 779, Col. Narvarte, 03020 Mexico D. F. (Mexico)

    2013-10-15

    The nuclear reactor core type FBR (Fast Breeder Reactor) was modeled in three dimensions of hexagonal-Z geometry using the code PARCS (Purdue Advanced Reactor Core Simulator) version 3.1 developed by Purdue University researchers. To carry out the modeling of the mentioned reactor was taken the corresponding information to one of the described benchmarks in the document NEACRP-L-330 (3-D Neutron Transport Benchmarks, 1991); fundamentally the corresponding to the geometric data and the cross sections. Being a quick reactor of breeding, known as the Knk-II, for which are considered 4 energy groups without dispersions up. The reactor core is formed by prismatic elements of hexagonal transversal cut where part of them only corresponds to nuclear fuel assemblies. This has four reflector rings and 6 identical control elements that together with the active part of the core is configured with 8 different types of elements.With the extracted information of the mentioned document the entrance file was prepared for PARCS 3.1 only considering a sixth part of the core due to the symmetry that presents their configuration. The NEACRP-L-330 shows a wide range of results reported by those who collaborated in its elaboration using different solution techniques that go from the Monte Carlo method to the approaches S{sub 2} and P{sub 1}. Of all the results were selected those obtained with the code HEXNOD, to which were carried out a comparison of the effective multiplication factor, being smaller differences to the 300 pcm, for three different scenarios: a) with the control bars extracted totally, b) with the semi-inserted control bars and c) with the control bars inserted completely and two different axial meshes, a thick mesh with 14 slices and another fine with 38, that which implies that the results can be considered very similar among if same. Radial maps and axial profiles are included, as much of the power as of the neutrons flow. (Author)

  19. Neutronics code VALE for two-dimensional triagonal (hexagonal) and three-dimensional geometries

    International Nuclear Information System (INIS)

    Vondy, D.R.; Fowler, T.B.

    1981-08-01

    This report documents the computer code VALE designed to solve multigroup neutronics problems with the diffusion theory approximation to neutron transport for a triagonal arrangement of mesh points on planes in two- and three-dimensional geometry. This code parallels the VENTURE neutronics code in the local computation system, making exposure and fuel management capabilities available. It uses and generates interface data files adopted in the cooperative effort sponsored by Reactor Physics RRT Division of the US DOE. The programming in FORTRAN is straightforward, although data is transferred in blocks between auxiliary storage devices and main core, and direct access schemes are used. The size of problems which can be handled is essentially limited only by cost of calculation since the arrays are variably dimensioned. The memory requirement is held down while data transfer during iteration is increased only as necessary with problem size. There is provision for the more common boundary conditions including the repeating boundary, 180 0 rotational symmetry, and the rotational symmetry conditions for the 30 0 , 60 0 , and 120 0 triangular grids on planes. A variety of types of problems may be solved: the usual neutron flux eignevalue problem, or a direct criticality search on the buckling, on a reciprocal velocity absorber (prompt mode), or on nuclide concentrations. The adjoint problem and fixed source problem may be solved, as well as the dominating higher harmonic, or the importance problem for an arbitrary fixed source

  20. Geometry of fast magnetosonic rays, wavefronts and shock waves

    Energy Technology Data Exchange (ETDEWEB)

    Núñez, Manuel, E-mail: mnjmhd@am.uva.es

    2016-11-25

    Fast magnetosonic waves in a two-dimensional plasma are studied in the geometrical optics approximation. The geometry of rays and wavefronts influences decisively the formation and ulterior evolution of shock waves. It is shown that the curvature of the curve where rays start and the angle between rays and wavefronts are the main parameters governing a wide variety of possible outcomes. - Highlights: • Magnetosonic waves are studied in a genuinely multidimensional setting. • Curvature and the angle between rays and wavefronts are the main parameters. • Shock waves may exist or not, depending on initial conditions. • Both velocity and shape of those waves present a large variety of possible outcomes.

  1. Development of 3D multi-group neutron diffusion code for hexagonal geometry

    International Nuclear Information System (INIS)

    Sun Wei; Wang Kan; Ni Dongyang; Li Qing

    2013-01-01

    Based on the theory of new flux expansion nodal method to solve the neutron diffusion equations, the intra-nodal fluence rate distribution was expanded in a series of analytic basic functions for each group. In order to improve the accuracy of calculation result, continuities of neutron fluence rate and current were utilized across the nodal surfaces. According to the boundary conditions, the iteration method was adopted to solve the diffusion equation, where inner iteration speedup method is Gauss-Seidel method and outer is Lyusternik-Wagner. A new speedup method (one-outer-iteration and multi-inner-iteration method) was proposed according to the characteristic that the convergence speed of multiplication factor is faster than that of neutron fluence rate and the update of inner iteration matrix is slow. Based on the proposed model, the code HANDF-D was developed and tested by 3D two-group vver440 benchmark, experiment 2 of HFETR, 3D four-group thermal reactor benchmark, and 3D seven-group fast reactor benchmark. The numerical results show that HANDF-D can predict accurately the multiplication factor and nodal powers. (authors)

  2. Application of hexagonal element scheme in finite element method to three-dimensional diffusion problem of fast reactors

    International Nuclear Information System (INIS)

    Ishiguro, Misako; Higuchi, Kenji

    1983-01-01

    The finite element method is applied in Galerkin-type approximation to three-dimensional neutron diffusion equations of fast reactors. A hexagonal element scheme is adopted for treating the hexagonal lattice which is typical for fast reactors. The validity of the scheme is verified by applying the scheme as well as alternative schemes to the neutron diffusion calculation of a gas-cooled fast reactor of actual scale. The computed results are compared with corresponding values obtained using the currently applied triangular-element and also with conventional finite difference schemes. The hexagonal finite element scheme is found to yield a reasonable solution to the problem taken up here, with some merit in terms of saving in computing time, but the resulting multiplication factor differs by 1% and the flux by 9% compared with the triangular mesh finite difference scheme. The finite element method, even in triangular element scheme, would appear to incur error in inadmissible amount and which could not be easily eliminated by refining the nodes. (author)

  3. Solution of the Neutron transport equation in hexagonal geometry using strongly discontinuous nodal schemes; Solucion de la Ecuacion de transporte de neutrones en geometria hexagonal usando esquemas nodales fuertemente discontinuos

    Energy Technology Data Exchange (ETDEWEB)

    Mugica R, C.A.; Valle G, E. del [IPN, ESFM, Departamento de Ingenieria Nuclear, 07738 Mexico D.F. (Mexico)]. e-mail: cmugica@ipn.mx

    2005-07-01

    In 2002, E. del Valle and Ernest H. Mund developed a technique to solve numerically the Neutron transport equations in discrete ordinates and hexagonal geometry using two nodal schemes type finite element weakly discontinuous denominated WD{sub 5,3} and WD{sub 12,8} (of their initials in english Weakly Discontinuous). The technique consists on representing each hexagon in the union of three rhombuses each one of which it is transformed in a square in the one that the methods WD{sub 5,3} and WD{sub 12,8} were applied. In this work they are solved the mentioned equations of transport using the same discretization technique by hexagon but using two nodal schemes type finite element strongly discontinuous denominated SD{sub 3} and SD{sub 8} (of their initials in english Strongly Discontinuous). The application in each case as well as a reference problem for those that results are provided for the effective multiplication factor is described. It is carried out a comparison with the obtained results by del Valle and Mund for different discretization meshes so much angular as spatial. (Author)

  4. Mixed dual finite element methods for the numerical treatment of the diffusion equation in hexagonal geometry; Elements finis mixtes duaux pour la resolution numerique de l'equation de la diffusion neutronique en geometrie hexagonale

    Energy Technology Data Exchange (ETDEWEB)

    Schneider, D

    2001-07-01

    The nodal method Minos has been developed to offer a powerful method for the calculation of nuclear reactor cores in rectangular geometry. This method solves the mixed dual form of the diffusion equation and, also of the simplified P{sub N} approximation. The discretization is based on Raviart-Thomas' mixed dual finite elements and the iterative algorithm is an alternating direction method, which uses the current as unknown. The subject of this work is to adapt this method to hexagonal geometry. The guiding idea is to construct and test different methods based on the division of a hexagon into trapeze or rhombi with appropriate mapping of these quadrilaterals onto squares in order to take into advantage what is already available in the Minos solver. The document begins with a review of the neutron diffusion equation. Then we discuss its mixed dual variational formulation from a functional as well as from a numerical point of view. We study conformal and bilinear mappings for the two possible meshing of the hexagon. Thus, four different methods are proposed and are completely described in this work. Because of theoretical and numerical difficulties, a particular treatment has been necessary for methods based on the conformal mapping. Finally, numerical results are presented for a hexagonal benchmark to validate and compare the four methods with respect to pre-defined criteria. (authors)

  5. Mixed dual finite element methods for the numerical treatment of the diffusion equation in hexagonal geometry; Elements finis mixtes duaux pour la resolution numerique de l'equation de la diffusion neutronique en geometrie hexagonale

    Energy Technology Data Exchange (ETDEWEB)

    Schneider, D

    2001-07-01

    The nodal method Minos has been developed to offer a powerful method for the calculation of nuclear reactor cores in rectangular geometry. This method solves the mixed dual form of the diffusion equation and, also of the simplified P{sub N} approximation. The discretization is based on Raviart-Thomas' mixed dual finite elements and the iterative algorithm is an alternating direction method, which uses the current as unknown. The subject of this work is to adapt this method to hexagonal geometry. The guiding idea is to construct and test different methods based on the division of a hexagon into trapeze or rhombi with appropriate mapping of these quadrilaterals onto squares in order to take into advantage what is already available in the Minos solver. The document begins with a review of the neutron diffusion equation. Then we discuss its mixed dual variational formulation from a functional as well as from a numerical point of view. We study conformal and bilinear mappings for the two possible meshing of the hexagon. Thus, four different methods are proposed and are completely described in this work. Because of theoretical and numerical difficulties, a particular treatment has been necessary for methods based on the conformal mapping. Finally, numerical results are presented for a hexagonal benchmark to validate and compare the four methods with respect to pre-defined criteria. (authors)

  6. HEXNOD23, 2-D, 3-D Coarse Mesh Solution of Steady State Diffusion Equation in Hexagonal Geometry

    International Nuclear Information System (INIS)

    Grundmann, Ulrich

    1986-01-01

    1 - Description of program or function: Two- or three dimensional coarse mesh solution of steady state two group neutron diffusion equation in arrays of regular hexagons or hexagonal subassemblies. 2 - Method of solution: The neutron flux in a hexagonal node is expanded in a series of Bessel functions in the hexagonal plane. Polynomials up to the 4. order are used for the approximation of neutron flux in axial direction of three dimensional cases. Resulting relations between node averaged fluxes and mean partial currents of node faces in connection with the neutron balance of nodes are used to calculate the eigenvalue Keff, mean fluxes and mean powers of nodes. The iterations process is divided into inner and outer iterations. The iterations are accelerated by Ljusternik and Tschebyscheff extrapolation schemes. The power densities in the nodes and subassembly powers are computed for given reactor power in three dimensional cases. 30 degree reflectional, 60 and 120 degree rotational core symmetry and the whole core can be treated. 3 - Restrictions on the complexity of the problem: If the problem size designated by LIAR and LRAR exceeds 3000 and 50000 respectively, the lengths of the working array MIAR and MRAR in the main program can be increased. External sources are not permitted

  7. Application of the nodal method RTN-0 for the solution of the neutron diffusion equation dependent of time in hexagonal-Z geometry

    International Nuclear Information System (INIS)

    Esquivel E, J.; Alonso V, G.; Del Valle G, E.

    2015-09-01

    The solution of the neutron diffusion equation either for reactors in steady state or time dependent, is obtained through approximations generated by implementing of nodal methods such as RTN-0 (Raviart-Thomas-Nedelec of zero index), which is used in this study. Since the nodal methods are applied in quadrangular geometries, in this paper a technique in which the hexagonal geometry through the transfinite interpolation of Gordon-Hall becomes the appropriate geometry to make use of the nodal method RTN-0 is presented. As a result, a computer program was developed, whereby is possible to obtain among other results the neutron multiplication effective factor (k eff ), and the distribution of radial and/or axial power. To verify the operation of the code, was applied to three benchmark problems: in the first two reactors VVER and FBR, results k eff and power distribution are obtained, considering the steady state case of reactor; while the third problem a type VVER is analyzed, in its case dependent of time, which qualitative results are presented on the behavior of the reactor power. (Author)

  8. A fast direct solver for boundary value problems on locally perturbed geometries

    Science.gov (United States)

    Zhang, Yabin; Gillman, Adrianna

    2018-03-01

    Many applications including optimal design and adaptive discretization techniques involve solving several boundary value problems on geometries that are local perturbations of an original geometry. This manuscript presents a fast direct solver for boundary value problems that are recast as boundary integral equations. The idea is to write the discretized boundary integral equation on a new geometry as a low rank update to the discretized problem on the original geometry. Using the Sherman-Morrison formula, the inverse can be expressed in terms of the inverse of the original system applied to the low rank factors and the right hand side. Numerical results illustrate for problems where perturbation is localized the fast direct solver is three times faster than building a new solver from scratch.

  9. Geometries

    CERN Document Server

    Sossinsky, A B

    2012-01-01

    The book is an innovative modern exposition of geometry, or rather, of geometries; it is the first textbook in which Felix Klein's Erlangen Program (the action of transformation groups) is systematically used as the basis for defining various geometries. The course of study presented is dedicated to the proposition that all geometries are created equal--although some, of course, remain more equal than others. The author concentrates on several of the more distinguished and beautiful ones, which include what he terms "toy geometries", the geometries of Platonic bodies, discrete geometries, and classical continuous geometries. The text is based on first-year semester course lectures delivered at the Independent University of Moscow in 2003 and 2006. It is by no means a formal algebraic or analytic treatment of geometric topics, but rather, a highly visual exposition containing upwards of 200 illustrations. The reader is expected to possess a familiarity with elementary Euclidean geometry, albeit those lacking t...

  10. Geometry

    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 ...

  11. Geometry

    CERN Document Server

    Prasolov, V V

    2015-01-01

    This book provides a systematic introduction to various geometries, including Euclidean, affine, projective, spherical, and hyperbolic geometries. Also included is a chapter on infinite-dimensional generalizations of Euclidean and affine geometries. A uniform approach to different geometries, based on Klein's Erlangen Program is suggested, and similarities of various phenomena in all geometries are traced. An important notion of duality of geometric objects is highlighted throughout the book. The authors also include a detailed presentation of the theory of conics and quadrics, including the theory of conics for non-Euclidean geometries. The book contains many beautiful geometric facts and has plenty of problems, most of them with solutions, which nicely supplement the main text. With more than 150 figures illustrating the arguments, the book can be recommended as a textbook for undergraduate and graduate-level courses in geometry.

  12. Study on beam geometry and image reconstruction algorithm in fast neutron computerized tomography at NECTAR facility

    Science.gov (United States)

    Guo, J.; Bücherl, T.; Zou, Y.; Guo, Z.

    2011-09-01

    Investigations on the fast neutron beam geometry for the NECTAR facility are presented. The results of MCNP simulations and experimental measurements of the beam distributions at NECTAR are compared. Boltzmann functions are used to describe the beam profile in the detection plane assuming the area source to be set up of large number of single neutron point sources. An iterative algebraic reconstruction algorithm is developed, realized and verified by both simulated and measured projection data. The feasibility for improved reconstruction in fast neutron computerized tomography at the NECTAR facility is demonstrated.

  13. Study on beam geometry and image reconstruction algorithm in fast neutron computerized tomography at NECTAR facility

    International Nuclear Information System (INIS)

    Guo, J.; Buecherl, T.; Zou, Y.; Guo, Z.

    2011-01-01

    Investigations on the fast neutron beam geometry for the NECTAR facility are presented. The results of MCNP simulations and experimental measurements of the beam distributions at NECTAR are compared. Boltzmann functions are used to describe the beam profile in the detection plane assuming the area source to be set up of large number of single neutron point sources. An iterative algebraic reconstruction algorithm is developed, realized and verified by both simulated and measured projection data. The feasibility for improved reconstruction in fast neutron computerized tomography at the NECTAR facility is demonstrated.

  14. Study on beam geometry and image reconstruction algorithm in fast neutron computerized tomography at NECTAR facility

    Energy Technology Data Exchange (ETDEWEB)

    Guo, J. [State Key Laboratory of Nuclear Physics and Technology and School of Physics, Peking University, 5 Yiheyuan Lu, Beijing 100871 (China); Lehrstuhl fuer Radiochemie, Technische Universitaet Muenchen, Garching 80748 (Germany); Buecherl, T. [Lehrstuhl fuer Radiochemie, Technische Universitaet Muenchen, Garching 80748 (Germany); Zou, Y., E-mail: zouyubin@pku.edu.cn [State Key Laboratory of Nuclear Physics and Technology and School of Physics, Peking University, 5 Yiheyuan Lu, Beijing 100871 (China); Guo, Z. [State Key Laboratory of Nuclear Physics and Technology and School of Physics, Peking University, 5 Yiheyuan Lu, Beijing 100871 (China)

    2011-09-21

    Investigations on the fast neutron beam geometry for the NECTAR facility are presented. The results of MCNP simulations and experimental measurements of the beam distributions at NECTAR are compared. Boltzmann functions are used to describe the beam profile in the detection plane assuming the area source to be set up of large number of single neutron point sources. An iterative algebraic reconstruction algorithm is developed, realized and verified by both simulated and measured projection data. The feasibility for improved reconstruction in fast neutron computerized tomography at the NECTAR facility is demonstrated.

  15. Hyper-fast interstellar travel via a modification of spacetime geometry

    Energy Technology Data Exchange (ETDEWEB)

    Kheyfets, A. [Department of Mathematics, North Carolina State University, Raleigh, NC (United States); Miller, W.A. [Los Alamos National Lab., NM (United States)

    1997-08-01

    We analyze difficulties with proposals for hyper-fast interstellar travel via modifying the spacetime geometry, using as illustrations the Alcubierre warp drive and the Krasnikov tube. As it is easy to see, no violations of local causality or any other known physical principles are involved as far as motion of spacecrafts is concerned. However, the generation and support of the appropriate spacetime geometry configurations does create problems, the most significant of which are a violation of the weak energy condition, a violation of local causality, and a violation of the global causality protection. The violation of the chronology protection is the most serious of them as it opens a possibility of time travel. We trace the origin of the difficulties to the classical nature of the gravity field. This strongly indicates that hyper-fast interstellar travel should be transferred to the realm of a fully quantized gravitational theory. We outline an approach to further the research in this direction.

  16. Simple spectral method for solving propagation problems in cylindrical geometry with fast Fourier transforms

    International Nuclear Information System (INIS)

    Feit, M.D.; Fleck, J.A. Jr.

    1989-01-01

    We describe a spectral method for solving the paraxial wave equation in cylindrical geometry that is based on expansion of the exponential evolution operator in a Taylor series and use of fast Fourier transforms to evaluate derivatives. A fourth-order expansion gives excellent agreement with a two-transverse-dimensional split-operator calculation at a fraction of the cost in computation time per z step and at a considerable savings in storage

  17. Performance evaluation of novel LaBr3(Ce) scintillator geometries for fast-timing applications

    International Nuclear Information System (INIS)

    Vedia, V.; Carmona-Gallardo, M.; Fraile, L.M.; Mach, H.; Udías, J.M.

    2017-01-01

    We evaluate the performance of two LaBr 3 (Ce) crystals that were produced with special geometries, aimed at enhancing the scintillation light collection and thus the time resolution. Their design was motivated by the construction of high-performance fast-timing arrays like the FAst TIMing array for DESPEC (FATIMA), which demands a high packing factor in addition to good time and energy resolutions. Energy resolution and efficiency were measured using standard calibration sources. Timing measurements were performed at 60 Co and 22 Na γ-energies against a fast BaF 2 reference detector. The time resolution was optimized by the choice of the photomultiplier bias voltage and the fine tuning of the constant fraction discriminator parameters. Monte Carlo simulations using the Geant4 toolkit were performed in order to achieve a better understanding of how the new geometries affect the light transport and thus the performance of the crystals. It is found that the conical-shaped LaBr 3 (Ce) crystals are optimal for fast-timing applications and for the construction of arrays such as FATIMA.

  18. Geometry

    CERN Document Server

    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

  19. Transient analyses for a molten salt fast reactor with optimized core geometry

    Energy Technology Data Exchange (ETDEWEB)

    Li, R., E-mail: rui.li@kit.edu [Institute for Nuclear and Energy Technologies (IKET), Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen (Germany); Wang, S.; Rineiski, A.; Zhang, D. [Institute for Nuclear and Energy Technologies (IKET), Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen (Germany); Merle-Lucotte, E. [Laboratoire de Physique Subatomique et de Cosmologie – IN2P3 – CNRS/Grenoble INP/UJF, 53, rue des Martyrs, 38026 Grenoble (France)

    2015-10-15

    Highlights: • MSFR core is analyzed by fully coupling neutronics and thermal-hydraulics codes. • We investigated four types of transients intensively with the optimized core geometry. • It demonstrates MSFR has a high safety potential. - Abstract: Molten salt reactors (MSRs) have encountered a marked resurgence of interest over the past decades, highlighted by their inclusion as one of the six candidate reactors of the Generation IV advanced nuclear power systems. The present work is carried out in the framework of the European FP-7 project EVOL (Evaluation and Viability Of Liquid fuel fast reactor system). One of the project tasks is to report on safety analyses: calculations of reactor transients using various numerical codes for the molten salt fast reactor (MSFR) under different boundary conditions, assumptions, and for different selected scenarios. Based on the original reference core geometry, an optimized geometry was proposed by Rouch et al. (2014. Ann. Nucl. Energy 64, 449) on thermal-hydraulic design aspects to avoid a recirculation zone near the blanket which accumulates heat and very high temperature exceeding the salt boiling point. Using both fully neutronics thermal-hydraulic coupled codes (SIMMER and COUPLE), we also re-confirm the efforts step by step toward a core geometry without the recirculation zone in particular as concerns the modifications of the core geometrical shape. Different transients namely Unprotected Loss of Heat Sink (ULOHS), Unprotected Loss of Flow (ULOF), Unprotected Transient Over Power (UTOP), Fuel Salt Over Cooling (FSOC) are intensively investigated and discussed with the optimized core geometry. It is demonstrated that due to inherent negative feedbacks, an MSFR plant has a high safety potential.

  20. A model of gas cavity breakup behind a blockage in fast breeder reactor subassembly geometry

    International Nuclear Information System (INIS)

    Fukuzawa, Y.

    1980-05-01

    A semi-empirical model has been developed to describe the transient behaviour of a gas cavity due to breakup behind a blockage in Liquid Metal Fast Breeder Reactor subassembly geometry. The main mechanisms assumed for gas cavity breakup in the present model are as follows: The gas cavity is broken up by the pressure fluctuation at the interface due to turbulence in the liquid. The centrifugal force on the liquid opposes breakup. The model is able to describe experimental results on the transient behaviour of a gas cavity due to breakup after the termination of gas injection. On the basis of the present model the residence time of a gas cavity behind a blockage in sodium is predicted and the dependence of the residence time on blockage size is discussed. (orig.) [de

  1. Hexagonal graphene quantum dots

    KAUST Repository

    Ghosh, Sumit; Schwingenschlö gl, Udo

    2016-01-01

    We study hexagonal graphene quantum dots, using density functional theory, to obtain a quantitative description of the electronic properties and their size dependence, considering disk and ring geometries with both armchair and zigzag edges. We show that the electronic properties of quantum dots with armchair edges are more sensitive to structural details than those with zigzag edges. As functions of the inner and outer radii, we find in the case of armchair edges that the size of the band gap follows distinct branches, while in the case of zigzag edges it changes monotonically. This behaviour is further analyzed by studying the ground state wave function and explained in terms of its localisation.

  2. Hexagonal graphene quantum dots

    KAUST Repository

    Ghosh, Sumit

    2016-12-05

    We study hexagonal graphene quantum dots, using density functional theory, to obtain a quantitative description of the electronic properties and their size dependence, considering disk and ring geometries with both armchair and zigzag edges. We show that the electronic properties of quantum dots with armchair edges are more sensitive to structural details than those with zigzag edges. As functions of the inner and outer radii, we find in the case of armchair edges that the size of the band gap follows distinct branches, while in the case of zigzag edges it changes monotonically. This behaviour is further analyzed by studying the ground state wave function and explained in terms of its localisation.

  3. Effects of gas chamber geometry and gas flow on the neutron production in a fast plasma focus neutron source

    International Nuclear Information System (INIS)

    Tarifeño-Saldivia, Ariel; Soto, Leopoldo

    2014-01-01

    This work reports that gas chamber geometry and gas flow management substantially affect the neutron production of a repetitive fast plasma focus. The gas flow rate is the most sensitive parameter. An appropriate design of the gas chamber combined with a suitable flow-rate management can lead to improvements in the neutron production of one order of magnitude working in a fast repetitive mode. (paper)

  4. Application of the nodal method RTN-0 for the solution of the neutron diffusion equation dependent of time in hexagonal-Z geometry; Aplicacion del metodo nodal RTN-0 para la solucion de la ecuacion de difusion de neutrones dependiente del tiempo en geometria hexagonal-Z

    Energy Technology Data Exchange (ETDEWEB)

    Esquivel E, J.; Alonso V, G. [ININ, Carretera Mexico-Toluca s/n, 52750 Ocoyoacac, Estado de Mexico (Mexico); Del Valle G, E., E-mail: jaime.esquivel@inin.gob.mx [IPN, Escuela Superior de Fisica y Matematicas, Av. IPN s/n, Col. Lindavista, 07738 Ciudad de Mexico (Mexico)

    2015-09-15

    The solution of the neutron diffusion equation either for reactors in steady state or time dependent, is obtained through approximations generated by implementing of nodal methods such as RTN-0 (Raviart-Thomas-Nedelec of zero index), which is used in this study. Since the nodal methods are applied in quadrangular geometries, in this paper a technique in which the hexagonal geometry through the transfinite interpolation of Gordon-Hall becomes the appropriate geometry to make use of the nodal method RTN-0 is presented. As a result, a computer program was developed, whereby is possible to obtain among other results the neutron multiplication effective factor (k{sub eff}), and the distribution of radial and/or axial power. To verify the operation of the code, was applied to three benchmark problems: in the first two reactors VVER and FBR, results k{sub eff} and power distribution are obtained, considering the steady state case of reactor; while the third problem a type VVER is analyzed, in its case dependent of time, which qualitative results are presented on the behavior of the reactor power. (Author)

  5. Experimental and modeling analysis of fast ionization wave discharge propagation in a rectangular geometry

    International Nuclear Information System (INIS)

    Takashima, Keisuke; Adamovich, Igor V.; Xiong Zhongmin; Kushner, Mark J.; Starikovskaia, Svetlana; Czarnetzki, Uwe; Luggenhoelscher, Dirk

    2011-01-01

    Fast ionization wave (FIW), nanosecond pulse discharge propagation in nitrogen and helium in a rectangular geometry channel/waveguide is studied experimentally using calibrated capacitive probe measurements. The repetitive nanosecond pulse discharge in the channel was generated using a custom designed pulsed plasma generator (peak voltage 10-40 kV, pulse duration 30-100 ns, and voltage rise time ∼1 kV/ns), generating a sequence of alternating polarity high-voltage pulses at a pulse repetition rate of 20 Hz. Both negative polarity and positive polarity ionization waves have been studied. Ionization wave speed, as well as time-resolved potential distributions and axial electric field distributions in the propagating discharge are inferred from the capacitive probe data. ICCD images show that at the present conditions the FIW discharge in helium is diffuse and volume-filling, while in nitrogen the discharge propagates along the walls of the channel. FIW discharge propagation has been analyzed numerically using quasi-one-dimensional and two-dimensional kinetic models in a hydrodynamic (drift-diffusion), local ionization approximation. The wave speed and the electric field distribution in the wave front predicted by the model are in good agreement with the experimental results. A self-similar analytic solution of the fast ionization wave propagation equations has also been obtained. The analytic model of the FIW discharge predicts key ionization wave parameters, such as wave speed, peak electric field in the front, potential difference across the wave, and electron density as functions of the waveform on the high voltage electrode, in good agreement with the numerical calculations and the experimental results.

  6. Air core notch-coil magnet with variable geometry for fast-field-cycling NMR.

    Science.gov (United States)

    Kruber, S; Farrher, G D; Anoardo, E

    2015-10-01

    In this manuscript we present details on the optimization, construction and performance of a wide-bore (71 mm) α-helical-cut notch-coil magnet with variable geometry for fast-field-cycling NMR. In addition to the usual requirements for this kind of magnets (high field-to-power ratio, good magnetic field homogeneity, low inductance and resistance values) a tunable homogeneity and a more uniform heat dissipation along the magnet body are considered. The presented magnet consists of only one machined metallic cylinder combined with two external movable pieces. The optimal configuration is calculated through an evaluation of the magnetic flux density within the entire volume of interest. The magnet has a field-to-current constant of 0.728 mT/A, allowing to switch from zero to 0.125 T in less than 3 ms without energy storage assistance. For a cylindrical sample volume of 35 cm(3) the effective magnet homogeneity is lower than 130 ppm. Copyright © 2015 Elsevier Inc. All rights reserved.

  7. NodHex3D: An application for solving the neutron diffusion equations in hexagonal-Z geometry and steady state

    International Nuclear Information System (INIS)

    Esquivel E, J.; Del Valle G, E.

    2014-10-01

    The system called NodHex3D is a graphical application that allows the solution of the neutron diffusion equation. The system considers fuel assemblies of hexagonal cross section. This application arose from the idea of expanding the development of neutron own codes, used primarily for academic purposes. The advantage associated with the use of NodHex3D, is that the kernel configuration and fuel batches is dynamically without affecting directly the base source code of the solution of the neutron diffusion equation. In addition to the kernel configuration to use, specify the values for the cross sections for each batch of fuel used, these values are: diffusion coefficient, removal cross section, absorption cross section, fission cross section and dispersion cross section. Important also, considering that the system is able to perform calculations for various energy groups. As evidence of the operation of NodHex3D, was proposed to model three-dimensional core of a nuclear reactor VVER-1000, based on the reference problem AER-FCM-101. The configuration of the reactor core consists of fuel assemblies (25 batches), composed of seven distinct materials, one of which reflector material, vacuum boundary conditions on the surface delimiting the reactor core. The diffusion equation for two energy groups solves, obtaining the value of the effective neutron multiplication factor. The obtained results are compared to those documented in the reference problem and by 3-DNT codes. (Author)

  8. ARGO, 1-D Neutron Diffusion in Slab, Cylindrical, Spherical Geometry from JAERI Fast-Set, ABBN, RCBN

    International Nuclear Information System (INIS)

    Ikawa, Koji

    1971-01-01

    1 - Nature of physical problem solved: ARGO is a one-dimensional (slab, cylinder or sphere), multigroup diffusion code for use in fast reactor criticality and kinetic parameter analysis. Three cross section sets, i.e., JAERI-Fast-Set, ABBN-Set and RCBN-Set, of 25 groups are prepared for the code as its library tapes. 2 - Method of solution: Eigenvalues are computed by ordinary source-iteration techniques with ordinary acceleration methods for convergence. 3 - Restrictions on the complexity of the problem: Sphere geometry

  9. Performance evaluation of novel LaBr{sub 3}(Ce) scintillator geometries for fast-timing applications

    Energy Technology Data Exchange (ETDEWEB)

    Vedia, V., E-mail: mv.vedia@ucm.es [Grupo de Física Nuclear, Facultad de CC. Físicas, Universidad Complutense, CEI Moncloa, 28040 Madrid (Spain); Carmona-Gallardo, M.; Fraile, L.M. [Grupo de Física Nuclear, Facultad de CC. Físicas, Universidad Complutense, CEI Moncloa, 28040 Madrid (Spain); Mach, H. [Grupo de Física Nuclear, Facultad de CC. Físicas, Universidad Complutense, CEI Moncloa, 28040 Madrid (Spain); National Centre for Nuclear Research, Division for Nuclear Physics, BP1, Warsaw (Poland); Udías, J.M. [Grupo de Física Nuclear, Facultad de CC. Físicas, Universidad Complutense, CEI Moncloa, 28040 Madrid (Spain)

    2017-06-11

    We evaluate the performance of two LaBr{sub 3}(Ce) crystals that were produced with special geometries, aimed at enhancing the scintillation light collection and thus the time resolution. Their design was motivated by the construction of high-performance fast-timing arrays like the FAst TIMing array for DESPEC (FATIMA), which demands a high packing factor in addition to good time and energy resolutions. Energy resolution and efficiency were measured using standard calibration sources. Timing measurements were performed at {sup 60}Co and {sup 22}Na γ-energies against a fast BaF{sub 2} reference detector. The time resolution was optimized by the choice of the photomultiplier bias voltage and the fine tuning of the constant fraction discriminator parameters. Monte Carlo simulations using the Geant4 toolkit were performed in order to achieve a better understanding of how the new geometries affect the light transport and thus the performance of the crystals. It is found that the conical-shaped LaBr{sub 3}(Ce) crystals are optimal for fast-timing applications and for the construction of arrays such as FATIMA.

  10. First-principles calculations of 5d atoms doped hexagonal-AlN sheets: Geometry, magnetic property and the influence of symmetry and symmetry-breaking on the electronic structure

    International Nuclear Information System (INIS)

    Zhang Zhao-Fu; Zhou Tie-Ge; Zhao Hai-Yang; Wei Xiang-Lei

    2014-01-01

    The geometry, electronic structure and magnetic property of the hexagonal AlN (h-AlN) sheet doped by 5d atoms (Lu, Hf, Ta, W, Re, Os, Ir, Pt, Au and Hg) are investigated by first-principles calculations based on the density functional theory. The influence of symmetry and symmetry-breaking is also studied. There are two types of local symmetries of the doped systems: C 3v and D 3h . The symmetry will deviate from exact C 3v and D 3h for some particular dopants after optimization. The total magnetic moments of the doped systems are 0μ B for Lu, Ta and Ir; 1μ B for Hf, W, Pt and Hg; 2μ B for Re and Au; and 3μ B for Os and Al-vacancy. The total densities of state are presented, where impurity energy levels exist. The impurity energy levels and total magnetic moments can be explained by the splitting of 5d orbitals or molecular orbitals under different symmetries. (condensed matter: structural, mechanical, and thermal properties)

  11. Fast Erasure and Error decoding of Algebraic Geometry Codes up to the Feng-Rao Bound

    DEFF Research Database (Denmark)

    Jensen, Helge Elbrønd; Sakata, S.; Leonard, D.

    1996-01-01

    This paper gives an errata(that is erasure-and error-) decoding algorithm of one-point algebraic geometry codes up to the Feng-Rao designed minimum distance using Sakata's multidimensional generalization of the Berlekamp-massey algorithm and the votin procedure of Feng and Rao.......This paper gives an errata(that is erasure-and error-) decoding algorithm of one-point algebraic geometry codes up to the Feng-Rao designed minimum distance using Sakata's multidimensional generalization of the Berlekamp-massey algorithm and the votin procedure of Feng and Rao....

  12. Fast multifrequency focal beam analysis for 3D seismic acquisition geometry

    NARCIS (Netherlands)

    Wei, W.; Fu, L.; Blacquiere, G.

    2012-01-01

    A method for the efficient computation of multifrequency focal beams for 3D seismic acquisition geometry analysis has been developed. By computing them for all the frequency components of seismic data, single-frequency focal beams can be extended to multifrequency focal beams. However, this

  13. A fast implementation of the incremental backprojection algorithms for parallel beam geometries

    International Nuclear Information System (INIS)

    Chen, C.M.; Wang, C.Y.; Cho, Z.H.

    1996-01-01

    Filtered-backprojection algorithms are the most widely used approaches for reconstruction of computed tomographic (CT) images, such as X-ray CT and positron emission tomographic (PET) images. The Incremental backprojection algorithm is a fast backprojection approach based on restructuring the Shepp and Logan algorithm. By exploiting interdependency (position and values) of adjacent pixels, the Incremental algorithm requires only O(N) and O(N 2 ) multiplications in contrast to O(N 2 ) and O(N 3 ) multiplications for the Shepp and Logan algorithm in two-dimensional (2-D) and three-dimensional (3-D) backprojections, respectively, for each view, where N is the size of the image in each dimension. In addition, it may reduce the number of additions for each pixel computation. The improvement achieved by the Incremental algorithm in practice was not, however, as significant as expected. One of the main reasons is due to inevitably visiting pixels outside the beam in the searching flow scheme originally developed for the Incremental algorithm. To optimize implementation of the Incremental algorithm, an efficient scheme, namely, coded searching flow scheme, is proposed in this paper to minimize the overhead caused by searching for all pixels in a beam. The key idea of this scheme is to encode the searching flow for all pixels inside each beam. While backprojecting, all pixels may be visited without any overhead due to using the coded searching flow as the a priori information. The proposed coded searching flow scheme has been implemented on a Sun Sparc 10 and a Sun Sparc 20 workstations. The implementation results show that the proposed scheme is 1.45--2.0 times faster than the original searching flow scheme for most cases tested

  14. Structural Characterization of Hexagonal Braiding Architecture Aided by 3D Printing

    Directory of Open Access Journals (Sweden)

    Li Zhengning

    2018-01-01

    Full Text Available Hexagonal braiding method has the advantages of high shape compatibility, interlacing density and high volume fraction. Based on hexagonal braiding method, a hexagonal preform was braided. Then, by following the characteristics of repeatability and concentricity of hexagonal braided preform, the printed geometry structure was got in order to understand and optimize geometric structure to make it more compact like the braided geometric structure. Finally, the unit cells were defined with hexagonal prism to analyze the micro-geometric structure of hexagonal braided preform.

  15. Observations of the behaviour of gas in the wake behind a corner blockage in fast breeder reactor subassembly geometry

    International Nuclear Information System (INIS)

    Fukuzawa, Y.

    1979-07-01

    Observations were made of gas behaviour in the wake behind a 21% corner blockage in the subassembly geometry of a liquid metal fast breeder reactor. The test section used represented one half of the reactor fuel subassembly, divided along the vertical plane of symmetry through the blockage. A glass wall occupied the position of this plane. Water was allowed to flow between glass rods simulating fuel pins, the velocity being changed from 1.2 to 4.5 m/s. Argon was injected into the wake or into the flow upstream of the blockage, the injection rate being changed from 1 to 230 Ncm 3 /s (standard temperature and pressure). From the present experiment, the following is evident: The gas is accumulated in the wake behind the blockage, forming a gas cavity. The flow patterns of the two-phase mixture in the wake are classified into three types, depending on the liquid velocity. In the lower velocity range, a gas cavity cannot be present at rest, rising up through the wake as a single bubble due to buoyancy. In the higher velocity range, the gas cavity is broken up by the liquid flow forces, only small gas bubbles circulating in the wake. In the velocity range in between, the gas cavity is present in the wake. The cavity size depends on the gas injection rate and on the liquid velocity. From the results, the possibility of fuel failure caused by fission gas release at a blockage in the fast breeder reactor can be considered to depend on the operating conditions of the reactor, specially on the coolant velocity. (orig.) [de

  16. Hexagon solar power panel

    Science.gov (United States)

    Rubin, I. (Inventor)

    1978-01-01

    A solar energy panel support is described upon which silicon cells are arrayed. The cells are wafer thin and of two geometrical types, both of the same area and electrical rating, namely hexagon cells and hourglass cells. The hourglass cells are composites of half hexagons. A near perfect nesting relationship of the cells achieves a high density packing whereby optimum energy production per panel area is achieved.

  17. Hexagonalization of correlation functions

    Energy Technology Data Exchange (ETDEWEB)

    Fleury, Thiago [Instituto de Física Teórica, UNESP - University Estadual Paulista,ICTP South American Institute for Fundamental Research,Rua Dr. Bento Teobaldo Ferraz 271, 01140-070, São Paulo, SP (Brazil); Komatsu, Shota [Perimeter Institute for Theoretical Physics,31 Caroline St N Waterloo, Ontario N2L 2Y5 (Canada)

    2017-01-30

    We propose a nonperturbative framework to study general correlation functions of single-trace operators in N=4 supersymmetric Yang-Mills theory at large N. The basic strategy is to decompose them into fundamental building blocks called the hexagon form factors, which were introduced earlier to study structure constants using integrability. The decomposition is akin to a triangulation of a Riemann surface, and we thus call it hexagonalization. We propose a set of rules to glue the hexagons together based on symmetry, which naturally incorporate the dependence on the conformal and the R-symmetry cross ratios. Our method is conceptually different from the conventional operator product expansion and automatically takes into account multi-trace operators exchanged in OPE channels. To illustrate the idea in simple set-ups, we compute four-point functions of BPS operators of arbitrary lengths and correlation functions of one Konishi operator and three short BPS operators, all at one loop. In all cases, the results are in perfect agreement with the perturbative data. We also suggest that our method can be a useful tool to study conformal integrals, and show it explicitly for the case of ladder integrals.

  18. CALIPSO - a computer code for the calculation of fluiddynamics, thermohydraulics and changes of geometry in failing fuel elements of a fast breeder reactor

    International Nuclear Information System (INIS)

    Kedziur, F.

    1982-07-01

    The computer code CALIPSO was developed for the calculation of a hypothetical accident in an LMFBR (Liquid Metal Fast Breeder Reactor), where the failure of fuel pins is assumed. It calculates two-dimensionally the thermodynamics, fluiddynamics and changes in geometry of a single fuel pin and its coolant channel in a time period between failure of the pin and a state, at which the geometry is nearly destroyed. The determination of temperature profiles in the fuel pin cladding and the channel wall make it possible to take melting and freezing processes into account. Further features of CALIPSO are the variable channel cross section in order to model disturbances of the channel geometry as well as the calculation of two velocity fields including the consideration of virtual mass effects. The documented version of CALIPSO is especially suited for the calculation of the SIMBATH experiments carried out at the Kernforschungszentrum Karlsruhe, which simulate the above-mentioned accident. The report contains the complete documentation of the CALIPSO code: the modeling of the geometry, the equations used, the structure of the code and the solution procedure as well as the instructions for use with an application example. (orig.) [de

  19. Fast Erasure-and error decoding of algebraic geometry codes up to the Feng-Rao bound

    DEFF Research Database (Denmark)

    Høholdt, Tom; Jensen, Helge Elbrønd; Sakata, Shojiro

    1998-01-01

    This correspondence gives an errata (that is erasure-and error-) decoding algorithm of one-point algebraic-geometry codes up to the Feng-Rao designed minimum distance using Sakata's multidimensional generalization of the Berlekamp-Massey algorithm and the voting procedure of Feng and Rao....

  20. NodHex3D: An application for solving the neutron diffusion equations in hexagonal-Z geometry and steady state; NodHex3D: Una aplicacion para solucionar las ecuaciones de difusion de neutrones en geometria hexagonal-Z y estado estacionario

    Energy Technology Data Exchange (ETDEWEB)

    Esquivel E, J. [ININ, Carretera Mexico-Toluca s/n, 52750 Ocoyoacac, Estado de Mexico (Mexico); Del Valle G, E., E-mail: jaime.esquivel@inin.gob.mx [IPN, Escuela Superior de Fisica y Matematicas, Av. IPN s/n, Edificio 9, Col. San Pedro Zacatenco, 07738 Mexico D. F. (Mexico)

    2014-10-15

    The system called NodHex3D is a graphical application that allows the solution of the neutron diffusion equation. The system considers fuel assemblies of hexagonal cross section. This application arose from the idea of expanding the development of neutron own codes, used primarily for academic purposes. The advantage associated with the use of NodHex3D, is that the kernel configuration and fuel batches is dynamically without affecting directly the base source code of the solution of the neutron diffusion equation. In addition to the kernel configuration to use, specify the values for the cross sections for each batch of fuel used, these values are: diffusion coefficient, removal cross section, absorption cross section, fission cross section and dispersion cross section. Important also, considering that the system is able to perform calculations for various energy groups. As evidence of the operation of NodHex3D, was proposed to model three-dimensional core of a nuclear reactor VVER-1000, based on the reference problem AER-FCM-101. The configuration of the reactor core consists of fuel assemblies (25 batches), composed of seven distinct materials, one of which reflector material, vacuum boundary conditions on the surface delimiting the reactor core. The diffusion equation for two energy groups solves, obtaining the value of the effective neutron multiplication factor. The obtained results are compared to those documented in the reference problem and by 3-DNT codes. (Author)

  1. Bronze-mean hexagonal quasicrystal

    Science.gov (United States)

    Dotera, Tomonari; Bekku, Shinichi; Ziherl, Primož

    2017-10-01

    The most striking feature of conventional quasicrystals is their non-traditional symmetry characterized by icosahedral, dodecagonal, decagonal or octagonal axes. The symmetry and the aperiodicity of these materials stem from an irrational ratio of two or more length scales controlling their structure, the best-known examples being the Penrose and the Ammann-Beenker tiling as two-dimensional models related to the golden and the silver mean, respectively. Surprisingly, no other metallic-mean tilings have been discovered so far. Here we propose a self-similar bronze-mean hexagonal pattern, which may be viewed as a projection of a higher-dimensional periodic lattice with a Koch-like snowflake projection window. We use numerical simulations to demonstrate that a disordered variant of this quasicrystal can be materialized in soft polymeric colloidal particles with a core-shell architecture. Moreover, by varying the geometry of the pattern we generate a continuous sequence of structures, which provide an alternative interpretation of quasicrystalline approximants observed in several metal-silicon alloys.

  2. Multilayer DNA Origami Packed on Hexagonal and Hybrid Lattices

    DEFF Research Database (Denmark)

    Ke, Yonggang; Voigt, Niels Vinther; Shih, William M.

    2012-01-01

    “Scaffolded DNA origami” has been proven to be a powerful and efficient approach to construct two-dimensional or three-dimensional objects with great complexity. Multilayer DNA origami has been demonstrated with helices packing along either honeycomb-lattice geometry or square-lattice geometry....... Here we report successful folding of multilayer DNA origami with helices arranged on a close-packed hexagonal lattice. This arrangement yields a higher density of helical packing and therefore higher resolution of spatial addressing than has been shown previously. We also demonstrate hybrid multilayer...... DNA origami with honeycomb-lattice, square-lattice, and hexagonal-lattice packing of helices all in one design. The availability of hexagonal close-packing of helices extends our ability to build complex structures using DNA nanotechnology....

  3. Multilayer DNA origami packed on hexagonal and hybrid lattices.

    Science.gov (United States)

    Ke, Yonggang; Voigt, Niels V; Gothelf, Kurt V; Shih, William M

    2012-01-25

    "Scaffolded DNA origami" has been proven to be a powerful and efficient approach to construct two-dimensional or three-dimensional objects with great complexity. Multilayer DNA origami has been demonstrated with helices packing along either honeycomb-lattice geometry or square-lattice geometry. Here we report successful folding of multilayer DNA origami with helices arranged on a close-packed hexagonal lattice. This arrangement yields a higher density of helical packing and therefore higher resolution of spatial addressing than has been shown previously. We also demonstrate hybrid multilayer DNA origami with honeycomb-lattice, square-lattice, and hexagonal-lattice packing of helices all in one design. The availability of hexagonal close-packing of helices extends our ability to build complex structures using DNA nanotechnology. © 2011 American Chemical Society

  4. An inexpensive and fast method for infiltration coating of complex geometry matrices for ISOL production target applications

    International Nuclear Information System (INIS)

    Kawai, Y.; Alton, G.D.; Bilheux, J.-C.

    2005-01-01

    An inexpensive, fast, and close to universal infiltration coating technique has been developed for fabricating fast diffusion-release ISOL targets. Targets are fabricated by deposition of finely divided (∼1μm) compound materials in a paint-slurry onto highly permeable, complex structure reticulated-vitreous-carbon-foam (RVCF) matrices, followed by thermal heat treatment. In this article, we describe the coating method and present information on the physical integrity, uniformity of deposition, and matrix adherence of SiC, HfC and UC 2 targets, destined for on-line use as targets at the Holifield Radioactive Ion Beam Facility (HRIBF)

  5. Multilayer DNA Origami Packed on Hexagonal and Hybrid Lattices

    OpenAIRE

    Ke, Yonggang; Voigt, Niels V.; Gothelf, Kurt V.; Shih, William M.

    2012-01-01

    “Scaffolded DNA origami” has been proven to be a powerful and efficient approach to construct two-dimensional or three-dimensional objects with great complexity. Multilayer DNA origami has been demonstrated with helices packing along either honeycomb-lattice geometry or square-lattice geometry. Here we report successful folding of multilayer DNA origami with helices arranged on a close-packed hexagonal lattice. This arrangement yields a higher density of helical packing and therefore higher r...

  6. Non-linear triangle-based polynomial expansion nodal method for hexagonal core analysis

    International Nuclear Information System (INIS)

    Cho, Jin Young; Cho, Byung Oh; Joo, Han Gyu; Zee, Sung Qunn; Park, Sang Yong

    2000-09-01

    This report is for the implementation of triangle-based polynomial expansion nodal (TPEN) method to MASTER code in conjunction with the coarse mesh finite difference(CMFD) framework for hexagonal core design and analysis. The TPEN method is a variation of the higher order polynomial expansion nodal (HOPEN) method that solves the multi-group neutron diffusion equation in the hexagonal-z geometry. In contrast with the HOPEN method, only two-dimensional intranodal expansion is considered in the TPEN method for a triangular domain. The axial dependence of the intranodal flux is incorporated separately here and it is determined by the nodal expansion method (NEM) for a hexagonal node. For the consistency of node geometry of the MASTER code which is based on hexagon, TPEN solver is coded to solve one hexagonal node which is composed of 6 triangular nodes directly with Gauss elimination scheme. To solve the CMFD linear system efficiently, stabilized bi-conjugate gradient(BiCG) algorithm and Wielandt eigenvalue shift method are adopted. And for the construction of the efficient preconditioner of BiCG algorithm, the incomplete LU(ILU) factorization scheme which has been widely used in two-dimensional problems is used. To apply the ILU factorization scheme to three-dimensional problem, a symmetric Gauss-Seidel Factorization scheme is used. In order to examine the accuracy of the TPEN solution, several eigenvalue benchmark problems and two transient problems, i.e., a realistic VVER1000 and VVER440 rod ejection benchmark problems, were solved and compared with respective references. The results of eigenvalue benchmark problems indicate that non-linear TPEN method is very accurate showing less than 15 pcm of eigenvalue errors and 1% of maximum power errors, and fast enough to solve the three-dimensional VVER-440 problem within 5 seconds on 733MHz PENTIUM-III. In the case of the transient problems, the non-linear TPEN method also shows good results within a few minute of

  7. MORET: a Monte Carlo program for fast computation of the effective multiplying factors of fissile media within complex geometries

    International Nuclear Information System (INIS)

    Caizergues, Robert; Poullot, Gilles; Teillet, J.-R.

    1976-06-01

    The MORET code determines effective multiplying factors. It uses the Monte Carlo technique and the multigroup theory; a collision is taken as isotropic, but anisotropy is taken into account by means of the transport correction. Complex geometries can be rapidly treated: the array to be studied is divided in simple elementary volumes (spheres, cylinders, boxes, cones, half space planes...) to which are applied operators of the theory of sets. Some constant or differential (albedos) reflection coefficients simulate neighboring reflections on the outer volume [fr

  8. 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)

  9. FAST

    DEFF Research Database (Denmark)

    Zuidmeer-Jongejan, Laurian; Fernandez-Rivas, Montserrat; Poulsen, Lars K.

    2012-01-01

    ABSTRACT: The FAST project (Food Allergy Specific Immunotherapy) aims at the development of safe and effective treatment of food allergies, targeting prevalent, persistent and severe allergy to fish and peach. Classical allergen-specific immunotherapy (SIT), using subcutaneous injections with aqu...

  10. HEXBU-3D, a three-dimensional PWR-simulator program for hexagonal fuel assemblies

    International Nuclear Information System (INIS)

    Karvinen, E.

    1981-06-01

    HEXBU-3D is a three-dimensional nodal simulator program for PWR reactors. It is designed for a reactor core that consists of hexagonal fuel assemblies and of big follower-type control assemblies. The program solves two-group diffusion equations in homogenized fuel assembly geometry by a sophisticated nodal method. The treatment of feedback effects from xenon-poisoning, fuel temperature, moderator temperature and density and soluble boron concentration are included in the program. The nodal equations are solved by a fast two-level iteration technique and the eigenvalue can be either the effective multiplication factor or the boron concentration of the moderator. Burnup calculations are performed by tabulated sets of burnup-dependent cross sections evaluated by a cell burnup program. HEXBY-3D has been originally programmed in FORTRAN V for the UNIVAC 1108 computer, but there is also another version which is operable on the CDC CYBER 170 computer. (author)

  11. An efficient fast response and high-gain solar-blind flexible ultraviolet photodetector employing hybrid geometry

    Science.gov (United States)

    Hussain, Amreen A.; Pal, Arup R.; Patil, Dinkar S.

    2014-05-01

    We report high performance flexible hybrid ultraviolet photodetector with solar-blind sensitivity using nanocomposite film of plasma polymerized aniline-titanium dioxide. A facile solvent-free plasma technique is used to synthesize superior quality hybrid material with high yield. The hybrid photodetector exhibited high photoconductive gain of the order of ˜105 and fast speed with response and recovery time of 22.87 ms and 34.23 ms. This is an excellent result towards getting a balance in the response speed and photoconductive gain trade-off of the photodetectors reported so far. In addition, the device has the advantages of enhanced photosensitivity ((Ilight - Idark)/Idark) of the order of ˜102 and high responsivity of ˜104 AW-1. All the merits substantiates that, to prepare hybrid material, plasma based method holds potential to be an easy way for realizing large scale nanostructured photodetectors for practical applications.

  12. Extension of the mixed dual finite element method to the solution of the SPN transport equation in 2D unstructured geometries composed by arbitrary quadrilaterals

    International Nuclear Information System (INIS)

    Lautard, J.J.; Flumiani, T.

    2003-01-01

    The mixed dual finite element method is usually used for the resolution of the SPN transport equations (simplified PN equations) in 3D homogenized geometries (composed by homogenized rectangles or hexagons). This method produces fast results with little memory requirements. We have extended the previous method to the treatment of unstructured geometries composed by quadrilaterals (for the moment limited to 2D), allowing us to treat geometries where fuel pins are exactly represented. The iterative resolution of the resulting matrix system is a generalization of the one already developed for the cartesian and the hexagonal geometries. In order to illustrate and to show the efficiency of this method, results on the NEA-C5G7-MOX benchmark are given. The previous benchmark has been extended for the hexagonal geometry and we provide here some results. This method is a first step towards the treatment of pin by pin core calculations without homogenization. The present solver is a prototype. It shows the efficiency of the method and it has to be extended to 3D calculations as well as to exact transport calculations. We also intend to extend the method to the treatment of unstructured geometries composed by quadrilaterals with curved edges (sectors of a circle).The iterative algorithm has yet to be accelerated using multigrid techniques through a coupling with the present homogenized solver (MINOS). In the future, it will be included in the next generation neutronic toolbox DESCARTES currently under development

  13. Experimental and Numerical Studies on Fiber Deformation and Formability in Thermoforming Process Using a Fast-Cure Carbon Prepreg: Effect of Stacking Sequence and Mold Geometry

    Science.gov (United States)

    Bae, Daeryeong; Kim, Shino; Lee, Wonoh; Yi, Jin Woo; Um, Moon Kwang; Seong, Dong Gi

    2018-01-01

    A fast-cure carbon fiber/epoxy prepreg was thermoformed against a replicated automotive roof panel mold (square-cup) to investigate the effect of the stacking sequence of prepreg layers with unidirectional and plane woven fabrics and mold geometry with different drawing angles and depths on the fiber deformation and formability of the prepreg. The optimum forming condition was determined via analysis of the material properties of epoxy resin. The non-linear mechanical properties of prepreg at the deformation modes of inter- and intra-ply shear, tensile and bending were measured to be used as input data for the commercial virtual forming simulation software. The prepreg with a stacking sequence containing the plain-woven carbon prepreg on the outer layer of the laminate was successfully thermoformed against a mold with a depth of 20 mm and a tilting angle of 110°. Experimental results for the shear deformations at each corner of the thermoformed square-cup product were compared with the simulation and a similarity in the overall tendency of the shear angle in the path at each corner was observed. The results are expected to contribute to the optimization of parameters on materials, mold design and processing in the thermoforming mass-production process for manufacturing high quality automotive parts with a square-cup geometry. PMID:29883413

  14. Experimental and Numerical Studies on Fiber Deformation and Formability in Thermoforming Process Using a Fast-Cure Carbon Prepreg: Effect of Stacking Sequence and Mold Geometry

    Directory of Open Access Journals (Sweden)

    Daeryeong Bae

    2018-05-01

    Full Text Available A fast-cure carbon fiber/epoxy prepreg was thermoformed against a replicated automotive roof panel mold (square-cup to investigate the effect of the stacking sequence of prepreg layers with unidirectional and plane woven fabrics and mold geometry with different drawing angles and depths on the fiber deformation and formability of the prepreg. The optimum forming condition was determined via analysis of the material properties of epoxy resin. The non-linear mechanical properties of prepreg at the deformation modes of inter- and intra-ply shear, tensile and bending were measured to be used as input data for the commercial virtual forming simulation software. The prepreg with a stacking sequence containing the plain-woven carbon prepreg on the outer layer of the laminate was successfully thermoformed against a mold with a depth of 20 mm and a tilting angle of 110°. Experimental results for the shear deformations at each corner of the thermoformed square-cup product were compared with the simulation and a similarity in the overall tendency of the shear angle in the path at each corner was observed. The results are expected to contribute to the optimization of parameters on materials, mold design and processing in the thermoforming mass-production process for manufacturing high quality automotive parts with a square-cup geometry.

  15. Finite-Geometry and Polarized Multiple-Scattering Corrections of Experimental Fast- Neutron Polarization Data by Means of Monte Carlo Methods

    Energy Technology Data Exchange (ETDEWEB)

    Aspelund, O; Gustafsson, B

    1967-05-15

    After an introductory discussion of various methods for correction of experimental left-right ratios for polarized multiple-scattering and finite-geometry effects necessary and sufficient formulas for consistent tracking of polarization effects in successive scattering orders are derived. The simplifying assumptions are then made that the scattering is purely elastic and nuclear, and that in the description of the kinematics of the arbitrary Scattering {mu}, only one triple-parameter - the so-called spin rotation parameter {beta}{sup ({mu})} - is required. Based upon these formulas a general discussion of the importance of the correct inclusion of polarization effects in any scattering order is presented. Special attention is then paid to the question of depolarization of an already polarized beam. Subsequently, the afore-mentioned formulas are incorporated in the comprehensive Monte Carlo program MULTPOL, which has been designed so as to correctly account for finite-geometry effects in the sense that both the scattering sample and the detectors (both having cylindrical shapes) are objects of finite dimensions located at finite distances from each other and from the source of polarized fast-neutrons. A special feature of MULTPOL is the application of the method of correlated sampling for reduction of the standard deviations .of the results of the simulated experiment. Typical data of performance of MULTPOL have been obtained by the application of this program to the correction of experimental polarization data observed in n + '{sup 12}C elastic scattering between 1 and 2 MeV. Finally, in the concluding remarks the possible modification of MULTPOL to other experimental geometries is briefly discussed.

  16. Novel high pressure hexagonal OsB2 by mechanochemistry

    Science.gov (United States)

    Xie, Zhilin; Graule, Moritz; Orlovskaya, Nina; Andrew Payzant, E.; Cullen, David A.; Blair, Richard G.

    2014-07-01

    Hexagonal OsB2, a theoretically predicted high-pressure phase, has been synthesized for the first time by a mechanochemical method, i.e., high energy ball milling. X-ray diffraction indicated that formation of hexagonal OsB2 begins after 2.5 h of milling, and the reaction reaches equilibrium after 18 h of milling. Rietveld refinement of the powder data indicated that hexagonal OsB2 crystallizes in the P63/mmc space group (No. 194) with lattice parameters of a=2.916 Å and c=7.376 Å. Transmission electron microscopy confirmed the appearance of the hexagonal OsB2 phase after high energy ball milling. in situ X-ray diffraction experiments showed that the phase is stable from -225 °C to 1050 °C. The hexagonal OsB2 powder was annealed at 1050 °C for 6 days in vacuo to improve crystallinity and remove strain induced during the mechanochemical synthesis. The structure partially converted to the orthorhombic phase (20 wt%) after fast current assisted sintering of hexagonal OsB2 at 1500 °C for 5 min. Mechanochemical approaches to the synthesis of hard boride materials allow new phases to be produced that cannot be prepared using conventional methods.

  17. Novel high pressure hexagonal OsB2 by mechanochemistry

    International Nuclear Information System (INIS)

    Xie, Zhilin; Graule, Moritz; Orlovskaya, Nina; Andrew Payzant, E.; Cullen, David A.; Blair, Richard G.

    2014-01-01

    Hexagonal OsB 2 , a theoretically predicted high-pressure phase, has been synthesized for the first time by a mechanochemical method, i.e., high energy ball milling. X-ray diffraction indicated that formation of hexagonal OsB 2 begins after 2.5 h of milling, and the reaction reaches equilibrium after 18 h of milling. Rietveld refinement of the powder data indicated that hexagonal OsB 2 crystallizes in the P63/mmc space group (No. 194) with lattice parameters of a=2.916 Å and c=7.376 Å. Transmission electron microscopy confirmed the appearance of the hexagonal OsB 2 phase after high energy ball milling. in situ X-ray diffraction experiments showed that the phase is stable from −225 °C to 1050 °C. The hexagonal OsB 2 powder was annealed at 1050 °C for 6 days in vacuo to improve crystallinity and remove strain induced during the mechanochemical synthesis. The structure partially converted to the orthorhombic phase (20 wt%) after fast current assisted sintering of hexagonal OsB 2 at 1500 °C for 5 min. Mechanochemical approaches to the synthesis of hard boride materials allow new phases to be produced that cannot be prepared using conventional methods. - Graphical abstract: High resolution transmission electron micrograph of hexagonal OsB 2 nanocrystallite with corresponding fast Fourier transform and simulated diffraction pattern. - Highlights: • Hexagonal OsB 2 has been synthesized for the first time by mechanochemical method. • Hexagonal OsB 2 crystallizes in P63/mmc space group (No. 194), a=2.916 Å and c=7.376 Å. • The hexagonal structure was confirmed by a transmission electron microscope. • No phase transformation was observed after being annealed at 1050 °C for 6 days. • 20 wt% of h-OsB 2 was transformed to o-OsB 2 after being sintered at 1500 °C for 5 min

  18. Scattering phase functions of horizontally oriented hexagonal ice crystals

    International Nuclear Information System (INIS)

    Chen Guang; Yang Ping; Kattawar, George W.; Mishchenko, Michael I.

    2006-01-01

    Finite-difference time domain (FDTD) solutions are first compared with the corresponding T-matrix results for light scattering by circular cylinders with specific orientations. The FDTD method is then utilized to study the scattering properties of horizontally oriented hexagonal ice plates at two wavelengths, 0.55 and 12 μm. The phase functions of horizontally oriented ice plates deviate substantially from their counterparts obtained for randomly oriented particles. Furthermore, we compute the phase functions of horizontally oriented ice crystal columns by using the FDTD method along with two schemes for averaging over the particle orientations. It is shown that the phase functions of hexagonal ice columns with horizontal orientations are not sensitive to the rotation about the principal axes of the particles. Moreover, hexagonal ice crystals and circular cylindrical ice particles have similar optical properties, particularly, at a strongly absorbing wavelength, if the two particle geometries have the same length and aspect ratio defined as the ratio of the radius or semi-width of the cross section of a particle to its length. The phase functions for the two particle geometries are slightly different in the case of weakly absorbing plates with large aspect ratios. However, the solutions for circular cylinders agree well with their counterparts for hexagonal columns

  19. Dancoff Correction in Square and Hexagonal Lattices

    Energy Technology Data Exchange (ETDEWEB)

    Carlvik, I

    1966-11-15

    This report presents the results of a series of calculations of Dancoff corrections for square and hexagonal rod lattices. The tables cover a wide range of volume ratios and moderator cross sections. The results were utilized for checking the approximative formula of Sauer and also the modification of Bonalumi to Sauer's formula. The modified formula calculates the Dancoff correction with an accuracy of 0.01 - 0.02 in cases of practical interest. Calculations have also been performed on square lattices with an empty gap surrounding the rods. The results demonstrate the error involved in treating this kind of geometry by means of homogenizing the gap and the moderator. The calculations were made on the Ferranti Mercury computer of AB Atomenergi before it was closed down. Since then FORTRAN routines for Dancoff corrections have been written, and a subroutine DASQHE is included in the report.

  20. HEXAN - a hexagonal nodal code for solving the diffusion equation

    International Nuclear Information System (INIS)

    Makai, M.

    1982-07-01

    This report describes the theory of and provides a user's manual for the HEXAN program, which is a nodal program for the solution of the few-group diffusion equation in hexagonal geometry. Based upon symmetry considerations, the theory provides an analytical solution in a homogeneous node. WWER and HTGR test problem solutions are presented. The equivalence of the finite-difference scheme and the response matrix method is proven. The properties of a symmetric node's response matrix are investigated. (author)

  1. Hexagonal response matrix using symmetries

    International Nuclear Information System (INIS)

    Gotoh, Y.

    1991-01-01

    A response matrix for use in core calculations for nuclear reactors with hexagonal fuel assemblies is presented. It is based on the incoming currents averaged over the half-surface of a hexagonal node by applying symmetry theory. The boundary conditions of the incoming currents on the half-surface of the node are expressed by a complete set of orthogonal vectors which are constructed from symmetrized functions. The expansion coefficients of the functions are determined by the boundary conditions of incoming currents. (author)

  2. Thermal performance analysis of optimized hexagonal finned heat sinks in impinging air jet

    Energy Technology Data Exchange (ETDEWEB)

    Yakut, Kenan, E-mail: kyakut@atauni.edu.tr [Department of Mechanical Engineering, Faculty of Engineering, Atatürk University, 25100, Erzurum (Turkey); Yeşildal, Faruk, E-mail: fayesildal@agri.edu.tr [Department of Mechanical Engineering, Faculty of Patnos Sultan Alparslan Natural Sciences and Engineering, Ağrı İbrahim Çeçen University, 04100, Ağrı (Turkey); Karabey, Altuğ, E-mail: akarabey@yyu.edu.tr [Department of Machinery and Metal Technology, Erciş Vocational High School, Yüzüncü Yıl University, 65400, Van (Turkey); Yakut, Rıdvan, E-mail: ryakut@kafkas.edu.tr [Department of Mechanical Engineering, Faculty of Engineering and Architecture, Kafkas University, 36100, Kars (Turkey)

    2016-04-18

    In this study, thermal performance analysis of hexagonal finned heat sinks which optimized according to the experimental design and optimization method of Taguchi were investigated. Experiments of air jet impingement on heated hexagonal finned heat sinks were carried out adhering to the L{sub 18}(2{sup 1*}3{sup 6}) orthogonal array test plan. Optimum geometries were determined and named OH-1, OH-2. Enhancement efficiency with the first law of thermodynamics was analyzed for optimized heat sinks with 100, 150, 200 mm heights of hexagonal fin. Nusselt correlations were found out and variations of enhancement efficiency with Reynolds number presented in η–Re graphics.

  3. Dynamic response of cracked hexagonal subassembly ducts

    International Nuclear Information System (INIS)

    Glazik, J.L.; Petroski, H.J.

    1979-01-01

    The hexagonal subassembly ducts (hexcans) of current Liquid Metal Fast Breeder Reactor (LMFBR) designs are typically made of 20% coldworked Type 316 stainless steel. Prolonged exposure of this initially tough and ductile material to a fast neutron flux at high temperatures can result in severe embrittlement. Under these conditions, the unstable crack propagation of flaws, which may have been introduced during fabrication or transportation of the hexcans, is a problem of interest in LMFBR safety analysis. The abnormal overpressurization resulting from certain interactions within a subassembly, or the rupture of one or more fuel pins, may be sufficient to overload an otherwise subcritical crack in an embrittled hexcan. This paper examines the dynamic elastic response of flawed and unflawed fast reactor subassembly ducts. A plane-strain finite element analysis was performed for ducts containing internal corner cracks, as well as external midflat cracks. Two worst case loading situations were considered: rapid uniform internal pressurization and suddenly applied point loads at opposite midflats. The finite-element code CHILES, which can accomodate the stress singularities that occur at crack tips, was given dynamic capabilities through the inclusion of a consistent mass matrix and step-by-step time integration scheme. The SAP IV code was also employed for eigenvalue analysis and modal response. Although this code does not contain singular elements in its element library, dynamic stress intensity factors were calculated by a technique requiring only ordinary isoparametric quadrilaterals

  4. Crystallization of -type hexagonal ferrites from mechanically

    Indian Academy of Sciences (India)

    Crystallization of -type hexagonal ferrites from mechanically activated mixtures of barium carbonate and goethite ... Abstract. -type hexagonal ferrite precursor was prepared by a soft mechanochemical ... Bulletin of Materials Science | News.

  5. Fast determination of Ziziphora tenuior L. essential oil by inorganic-organic hybrid material based on ZnO nanoparticles anchored to a composite made from polythiophene and hexagonally ordered silica.

    Science.gov (United States)

    Piryaei, Marzieh; Abolghasemi, Mir Mahdi; Nazemiyeh, Hossein

    2015-01-01

    In this paper, for the first time, an inorganic-organic hybrid material based on ZnO nanoparticles was anchored to a composite made from polythiophene and hexagonally ordered silica (ZnO/PT/SBA-15) for use in solid-phase fibre microextraction (SPME) of medicinal plants. A homemade SPME apparatus was used for the extraction of volatile components of Ziziphora tenuior L. A simplex method was used for optimisation of five different parameters affecting the efficiency of the extraction. The main constituents extracted by ZnO/PT/SBA-15 and PDMS fibres and hydrodistillation (HD) methods, respectively, included pulegone (51.25%, 53.64% and 56.68%), limonene (6.73%, 6.58% and 8.3%), caryophyllene oxide (5.33%, 4.31% and 4.53%) and 1,8-cineole (4.21%, 3.31% and 3.18%). In comparison with the HD method, the proposed technique could equally monitor almost all the components of the sample, in an easier way, in a shorter time and requiring a much lower amount of the sample.

  6. Epitaxial Garnets and Hexagonal Ferrites.

    Science.gov (United States)

    1982-04-20

    guide growth of the epitaxial YIG films. Aluminum or gallium substitu- tions for iron were used in combination with lanthanum substitutions for yttrium... gallate spinel sub- strates. There was no difficulty with nucleation in the melt and film quality appeared to be similar to that observed previously...hexagonal ferrites. We succeeded in growing the M-type lead hexaferrite (magnetoplumbite) on gallate spinel substrates. We found that the PbO-based

  7. Hyperbolic geometry

    CERN Document Server

    Iversen, Birger

    1992-01-01

    Although it arose from purely theoretical considerations of the underlying axioms of geometry, the work of Einstein and Dirac has demonstrated that hyperbolic geometry is a fundamental aspect of modern physics

  8. Twistor geometry

    NARCIS (Netherlands)

    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.

  9. Lectures on Symplectic Geometry

    CERN Document Server

    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...

  10. Development of a code in three-dimensional cylindrical geometry based on analytic function expansion nodal (AFEN) method

    International Nuclear Information System (INIS)

    Lee, Joo Hee

    2006-02-01

    There is growing interest in developing pebble bed reactors (PBRs) as a candidate of very high temperature gas-cooled reactors (VHTRs). Until now, most existing methods of nuclear design analysis for this type of reactors are base on old finite-difference solvers or on statistical methods. But for realistic analysis of PBRs, there is strong desire of making available high fidelity nodal codes in three-dimensional (r,θ,z) cylindrical geometry. Recently, the Analytic Function Expansion Nodal (AFEN) method developed quite extensively in Cartesian (x,y,z) geometry and in hexagonal-z geometry was extended to two-group (r,z) cylindrical geometry, and gave very accurate results. In this thesis, we develop a method for the full three-dimensional cylindrical (r,θ,z) geometry and implement the method into a code named TOPS. The AFEN methodology in this geometry as in hexagonal geometry is 'robus' (e.g., no occurrence of singularity), due to the unique feature of the AFEN method that it does not use the transverse integration. The transverse integration in the usual nodal methods, however, leads to an impasse, that is, failure of the azimuthal term to be transverse-integrated over r-z surface. We use 13 nodal unknowns in an outer node and 7 nodal unknowns in an innermost node. The general solution of the node can be expressed in terms of that nodal unknowns, and can be updated using the nodal balance equation and the current continuity condition. For more realistic analysis of PBRs, we implemented em Marshak boundary condition to treat the incoming current zero boundary condition and the partial current translation (PCT) method to treat voids in the core. The TOPS code was verified in the various numerical tests derived from Dodds problem and PBMR-400 benchmark problem. The results of the TOPS code show high accuracy and fast computing time than the VENTURE code that is based on finite difference method (FDM)

  11. Molecular geometry

    CERN Document Server

    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

  12. Bandgap engineered graphene and hexagonal boron nitride

    Indian Academy of Sciences (India)

    In this article a double-barrier resonant tunnelling diode (DBRTD) has been modelled by taking advantage of single-layer hexagonal lattice of graphene and hexagonal boron nitride (h-BN). The DBRTD performance and operation are explored by means of a self-consistent solution inside the non-equilibrium Green's ...

  13. Optical geometry

    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

  14. Electrodeposited Silver Nanoparticles Patterned Hexagonally for SERS

    International Nuclear Information System (INIS)

    Gu, Geun Hoi; Lee, Sue Yeone; Suh, Jung Sang

    2010-01-01

    We have fabricated hexagonally patterned silver nanoparticles for surface-enhanced Raman scattering (SERS) by electrodepositing silver on the surface of an aluminum plate prepared by completely removing the oxide from anodic aluminum oxide (AAO) templates. Even after completely removing the oxide, well-ordered hexagonal patterns, similar to the shape of graphene, remained on the surface of the aluminum plate. The borders of the hexagonal pattern protruded up to form sorts of nano-mountains at both the sides and apexes of the hexagon, with the apexes protruding even more significantly than the sides. The aluminum plate prepared by completely removing the oxide has been used in the preparation of SERS substrates by sputter-coating of gold or silver on it. Instead of sputter-coating, here we have electro-deposited silver on the aluminum plate. When silver was electro-deposited on the plate, silver nanoparticles were made along the hexagonal margins.

  15. Architectural geometry

    KAUST Repository

    Pottmann, Helmut; Eigensatz, Michael; Vaxman, Amir; Wallner, Johannes

    2014-01-01

    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.

  16. Architectural geometry

    KAUST Repository

    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.

  17. Solution of two-dimensional diffusion equation for hexagonal cells by the finite Fourier transformation

    International Nuclear Information System (INIS)

    Kobayashi, Keisuke

    1975-01-01

    A method of solution is presented for a monoenergetic diffusion equation in two-dimensional hexagonal cells by a finite Fourier transformation. Up to the present, the solution by the finite Fourier transformation has been developed for x-y, r-z and x-y-z geometries, and the flux and current at the boundary are obtained in terms of Fourier series. It is shown here that the method can be applied to hexagonal cells and the expansion of boundary values in a Legendre polynomials gives numerically a higher accuracy than is obtained by a Fourier series. (orig.) [de

  18. Development of a computer code for neutronic calculations of a hexagonal lattice of nuclear reactor using the flux expansion nodal method

    Directory of Open Access Journals (Sweden)

    Mohammadnia Meysam

    2013-01-01

    Full Text Available The flux expansion nodal method is a suitable method for considering nodalization effects in node corners. In this paper we used this method to solve the intra-nodal flux analytically. Then, a computer code, named MA.CODE, was developed using the C# programming language. The code is capable of reactor core calculations for hexagonal geometries in two energy groups and three dimensions. The MA.CODE imports two group constants from the WIMS code and calculates the effective multiplication factor, thermal and fast neutron flux in three dimensions, power density, reactivity, and the power peaking factor of each fuel assembly. Some of the code's merits are low calculation time and a user friendly interface. MA.CODE results showed good agreement with IAEA benchmarks, i. e. AER-FCM-101 and AER-FCM-001.

  19. Beautiful geometry

    CERN Document Server

    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

  20. Comparison of diffusion and transport theory analysis with experimental results in fast breeder test reactor

    International Nuclear Information System (INIS)

    Sathyabama, N.; Mohanakrishnan, P.; Lee, S.M.

    1994-01-01

    A systematic analysis has been performed by 3 dimensional diffusion and transport methods to calculate the measured control rod worths and subassembly wise power distribution in fast breeder test reactor. Geometry corrections (rectangular to hexagonal and diffusion to transport corrections are estimated for multiplication factors and control rod worths. Calculated control rod worths by diffusion and transport theory are nearly the same and 10% above measured values. Power distribution in the core periphery is over predicted (15%) by diffusion theory. But, this over prediction reduces to 8% by use of the S N method. (authors). 9 refs., 4 tabs., 3 fig

  1. Analytische Geometrie

    Science.gov (United States)

    Kemnitz, Arnfried

    Der Grundgedanke der Analytischen Geometrie besteht darin, dass geometrische Untersuchungen mit rechnerischen Mitteln geführt werden. Geometrische Objekte werden dabei durch Gleichungen beschrieben und mit algebraischen Methoden untersucht.

  2. Algebraic geometry

    CERN Document Server

    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.

  3. Information geometry

    CERN Document Server

    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...

  4. Fermionic pentagons and NMHV hexagon

    Directory of Open Access Journals (Sweden)

    A.V. Belitsky

    2015-05-01

    Full Text Available We analyze the near-collinear limit of the null polygonal hexagon super Wilson loop in the planar N=4 super-Yang–Mills theory. We focus on its Grassmann components which are dual to next-to-maximal helicity-violating (NMHV scattering amplitudes. The kinematics in question is studied within a framework of the operator product expansion that encodes propagation of excitations on the background of the color flux tube stretched between the sides of Wilson loop contour. While their dispersion relation is known to all orders in 't Hooft coupling from previous studies, we find their form factor couplings to the Wilson loop. This is done making use of a particular tessellation of the loop where pentagon transitions play a fundamental role. Being interested in NMHV amplitudes, the corresponding building blocks carry a nontrivial charge under the SU(4 R-symmetry group. Restricting the current consideration to twist-two accuracy, we analyze two-particle contributions with a fermion as one of the constituents in the pair. We demonstrate that these nonsinglet pentagons obey bootstrap equations that possess consistent solutions for any value of the coupling constant. To confirm the correctness of these predictions, we calculate their contribution to the super Wilson loop demonstrating agreement with recent results to four-loop order in 't Hooft coupling.

  5. Quasi-dimensional modeling of a fast-burn combustion dual-plug spark-ignition engine with complex combustion chamber geometries

    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

  6. Novel high pressure hexagonal OsB{sub 2} by mechanochemistry

    Energy Technology Data Exchange (ETDEWEB)

    Xie, Zhilin; Graule, Moritz [Department of Mechanical and Aerospace Engineering, University of Central Florida, Orlando, FL 32816 (United States); Orlovskaya, Nina, E-mail: Nina.Orlovskaya@ucf.edu [Department of Mechanical and Aerospace Engineering, University of Central Florida, Orlando, FL 32816 (United States); Andrew Payzant, E. [Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, 1 Bethel Valley Road, Oak Ridge, TN 37831 (United States); Cullen, David A. [Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831 (United States); Blair, Richard G. [Department of Chemistry, University of Central Florida, Orlando, FL 32816 (United States)

    2014-07-01

    Hexagonal OsB{sub 2}, a theoretically predicted high-pressure phase, has been synthesized for the first time by a mechanochemical method, i.e., high energy ball milling. X-ray diffraction indicated that formation of hexagonal OsB{sub 2} begins after 2.5 h of milling, and the reaction reaches equilibrium after 18 h of milling. Rietveld refinement of the powder data indicated that hexagonal OsB{sub 2} crystallizes in the P63/mmc space group (No. 194) with lattice parameters of a=2.916 Å and c=7.376 Å. Transmission electron microscopy confirmed the appearance of the hexagonal OsB{sub 2} phase after high energy ball milling. in situ X-ray diffraction experiments showed that the phase is stable from −225 °C to 1050 °C. The hexagonal OsB{sub 2} powder was annealed at 1050 °C for 6 days in vacuo to improve crystallinity and remove strain induced during the mechanochemical synthesis. The structure partially converted to the orthorhombic phase (20 wt%) after fast current assisted sintering of hexagonal OsB{sub 2} at 1500 °C for 5 min. Mechanochemical approaches to the synthesis of hard boride materials allow new phases to be produced that cannot be prepared using conventional methods. - Graphical abstract: High resolution transmission electron micrograph of hexagonal OsB{sub 2} nanocrystallite with corresponding fast Fourier transform and simulated diffraction pattern. - Highlights: • Hexagonal OsB{sub 2} has been synthesized for the first time by mechanochemical method. • Hexagonal OsB{sub 2} crystallizes in P63/mmc space group (No. 194), a=2.916 Å and c=7.376 Å. • The hexagonal structure was confirmed by a transmission electron microscope. • No phase transformation was observed after being annealed at 1050 °C for 6 days. • 20 wt% of h-OsB{sub 2} was transformed to o-OsB{sub 2} after being sintered at 1500 °C for 5 min.

  7. Analytic geometry

    CERN Document Server

    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

  8. Geometry Revealed

    CERN Document Server

    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,

  9. Vector geometry

    CERN Document Server

    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

  10. Noncommutative geometry

    CERN Document Server

    Connes, Alain

    1994-01-01

    This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields.Key Features* First full treatment of the subject and its applications* Written by the pioneer of this field* Broad applications in mathemat

  11. Group of Hexagonal Search Patterns for Motion Estimation and Object Tracking

    International Nuclear Information System (INIS)

    Elazm, A.A.; Mahmoud, I.I; Hashima, S.M.

    2010-01-01

    This paper presents a group of fast block matching algorithms based on the hexagon pattern search .A new predicted one point hexagon (POPHEX) algorithm is proposed and compared with other well known algorithms. The comparison of these algorithms and our proposed one is performed for both motion estimation and object tracking. Test video sequences are used to demonstrate the behavior of studied algorithms. All algorithms are implemented in MATLAB environment .Experimental results showed that the proposed algorithm posses less number of search points however its computational overhead is little increased due to prediction procedure.

  12. Van der Waals epitaxy and photoresponse of hexagonal tellurium nanoplates on flexible mica sheets.

    Science.gov (United States)

    Wang, Qisheng; Safdar, Muhammad; Xu, Kai; Mirza, Misbah; Wang, Zhenxing; He, Jun

    2014-07-22

    Van der Waals epitaxy (vdWE) is of great interest due to its extensive applications in the synthesis of ultrathin two-dimensional (2D) layered materials. However, vdWE of nonlayered functional materials is still not very well documented. Here, although tellurium has a strong tendency to grow into one-dimensional nanoarchitecture due to its chain-like structure, we successfully realize 2D hexagonal tellurium nanoplates on flexible mica sheets via vdWE. Chemically inert mica surface is found to be crucial for the lateral growth of hexagonal tellurium nanoplates since it (1) facilitates the migration of tellurium adatoms along mica surface and (2) allows a large lattice mismatch. Furthermore, 2D tellurium hexagonal nanoplates-based photodetectors are in situ fabricated on flexible mica sheets. Efficient photoresponse is obtained even after bending the device for 100 times, indicating 2D tellurium hexagonal nanoplates-based photodetectors on mica sheets have a great application potential in flexible and wearable optoelectronic devices. We believe the fundamental understanding of vdWE effect on the growth of 2D tellurium hexagonal nanoplate can pave the way toward leveraging vdWE as a useful channel to realize the 2D geometry of other nonlayered materials.

  13. S/sub N/ computational benchmark solutions for slab geometry models of a gas-cooled fast reactor (GCFR) lattice cell

    International Nuclear Information System (INIS)

    McCoy, D.R.

    1981-01-01

    S/sub N/ computational benchmark solutions are generated for a onegroup and multigroup fuel-void slab lattice cell which is a rough model of a gas-cooled fast reactor (GCFR) lattice cell. The reactivity induced by the extrusion of the fuel material into the voided region is determined for a series of partially extruded lattice cell configurations. A special modified Gauss S/sub N/ ordinate array design is developed in order to obtain eigenvalues with errors less than 0.03% in all of the configurations that are considered. The modified Gauss S/sub N/ ordinate array design has a substantially improved eigenvalue angular convergence behavior when compared to existing S/sub N/ ordinate array designs used in neutron streaming applications. The angular refinement computations are performed in some cases by using a perturbation theory method which enables one to obtain high order S/sub N/ eigenvalue estimates for greatly reduced computational costs

  14. Projective Geometry

    Indian Academy of Sciences (India)

    mathematicians are trained to use very precise language, and so find it hard to simplify and state .... thing. If you take a plane on which there are two such triangles which enjoy the above ... within this geometry to simplify things if needed.

  15. Geometry -----------~--------------RESONANCE

    Indian Academy of Sciences (India)

    Parallel: A pair of lines in a plane is said to be parallel if they do not meet. Mathematicians were at war ... Subsequently, Poincare, Klein, Beltrami and others refined non-. Euclidean geometry. ... plane divides the plane into two half planes and.

  16. Experimental investigation of the coolability of blocked hexagonal bundles

    Energy Technology Data Exchange (ETDEWEB)

    Hózer, Zoltán, E-mail: zoltan.hozer@energia.mta.hu; Nagy, Imre; Kunstár, Mihály; Szabó, Péter; Vér, Nóra; Farkas, Róbert; Trosztel, István; Vimi, András

    2017-06-15

    Highlights: • Experiments were performed with electrically heated hexagonal fuel bundles. • Coolability of ballooned VVER-440 type bundle was confirmed up to high blockage rate. • Pellet relocation effect causes delay in the cool-down of the bundle. • The bypass line does not prevent the reflood of ballooned fuel rods. - Abstract: The CODEX-COOL experimental series was carried out in order to evaluate the effect of ballooning and pellet relocation in hexagonal bundles on the coolability of fuel rods after a LOCA event. The effects of blockage geometry, coolant flowrate, initial temperature and axial profile were investigated. The experimental results confirmed that a VVER bundle up to 80% blockage rate remains coolable after a LOCA event under design basis conditions. The ballooned section creates some obstacles for the cooling water during reflood of the bundle, but this effect causes only a short delay in the cooling down of the hot fuel rods. The accumulation of fuel pellet debris in the ballooned volume results in a local power peak, which leads to further slowing down of quench front.

  17. Hydrothermal synthesis of hexagonal magnesium hydroxide nanoflakes

    International Nuclear Information System (INIS)

    Wang, Qiang; Li, Chunhong; Guo, Ming; Sun, Lingna; Hu, Changwen

    2014-01-01

    Graphical abstract: Hexagonal Mg(OH) 2 nanoflakes were synthesized via hydrothermal method in the presence of PEG-20,000. Results show that PEG-20,000 plays an important role in the formation of this kind of nanostructure. The SAED patterns taken from the different positions on a single hexagonal Mg(OH) 2 nanoflake yielded different crystalline structures. The structure of the nanoflakes are polycrystalline and the probable formation mechanism of Mg(OH) 2 nanoflakes is discussed. - Highlights: • Hexagonal Mg(OH) 2 nanoflakes were synthesized via hydrothermal method. • PEG-20,000 plays an important role in the formation of hexagonal nanostructure. • Mg(OH) 2 nanoflakes show different crystalline structures at different positions. • The probable formation mechanism of hexagonal Mg(OH) 2 nanoflakes was reported. - Abstract: Hexagonal magnesium hydroxide (Mg(OH) 2 ) nanoflakes were successfully synthesized via hydrothermal method in the presence of the surfactant polyethylene glycol 20,000 (PEG-20,000). Results show that PEG-20,000 plays an important role in the formation of this kind of nanostructure. The composition, morphologies and structure of the Mg(OH) 2 nanoflakes were characterized by X-ray diffraction (XRD), field-emission scanning electron microscopy (FE-SEM), high-resolution transmission electron microscopy (HRTEM), and selected area electron diffraction (SAED). The SAED patterns taken from the different positions on a single hexagonal Mg(OH) 2 nanoflake show different crystalline structures. The structure of the nanoflakes are polycrystalline and the probable formation mechanism of Mg(OH) 2 nanoflakes is discussed. Brunauer–Emmett–Teller (BET) analysis were performed to investigate the porous structure and surface area of the as-obtained nanoflakes

  18. 3-DB, 3-D Multigroup Diffusion, X-Y-Z, R-Theta-Z, Triangular-Z Geometry, Fast Reactor Burnup

    International Nuclear Information System (INIS)

    Hardie, R.W.; Little, W.W. Jr.; Mroz, W.

    1974-01-01

    1 - Description of problem or function: 3DB is a three-dimensional (x-y-z, r-theta-z, triangular-z) multigroup diffusion code for use in detailed fast-reactor criticality and burnup analysis. The code can be used to - (a) compute k eff and perform criticality searches on time absorption, reactor composition, and reactor dimensions by means of either a flux or an adjoint model, (b) compute material burnup using a flexible material shuffling scheme, and (c) compute flux distributions for an arbitrary extraneous source. 2 - Method of solution: Eigenvalues are computed by standard source- iteration techniques. Group re-balancing and successive over-relaxation with line inversion are used to accelerate convergence. Adjoint solutions are obtained by inverting the input data and redefining the source terms. Material burnup is by reactor zone. The burnup rate is determined by the zone and energy-averaged cross sections which are recomputed after each time-step. The isotopic chains, which can contain any number of isotopes are formed by the user. The code does not contain built- in or internal chains. 3 - Restrictions on the complexity of the problem: Since variable dimensioning is employed, no simple bounds can be stated

  19. Riemannian geometry

    CERN Document Server

    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...

  20. Special geometry

    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.)

  1. Response of hexagonal fuel assembly coupled with internal hydrodynamics

    International Nuclear Information System (INIS)

    Marchertas, A.H.; Julke, R.T.

    1975-01-01

    For safety considerations of sodium cooled fast breeder reactors the mechanistic accident-initiating conditions must be studied. In previous investigations of such initiating accidents the models assumed axisymmetric configurations and in general neglected the coupling effects with the subassembly boundary. This paper presents a more precise treatment of the subassembly boundary and also provides feedback of the boundary response to the pressure source. This is accomplished by marking use of two computer codes: REXCO-HT and SADCAT. The internal hydrodynamics of the fuel subassembly is simulated by the REXCO-HT code which possesses certain models of fuel-coolant interactions (MFCI) to be used as a pressure source. The hexagonal boundary of the fuel subassembly is modeled by the SADCAT code. Since both codes involve explicit time integration, coupling between the two is effected at each time step. The pressure at the outside boundary of the REXCO-HT model provides the loading on the SADCAT model. Given the load, the SADCAT model yields the three-dimensional deformation of the hexagonal boundary. With the deformation known, the outside REXCO-HT model boundary is adjusted and the computation cycle of the coupling is completed. In effect, the coupling of the two codes substitutes a cylindrical vessel of the REXCO-HT code by a hexagonal duct. It is shown by the use of this procedure that the assumption of a cylindrical vessel of the same thickness as that of the hexcan is quite erroneous. The maximum deformation of the flat of the hexcan in the illustrative examples is larger by as much as one order of magnitude. The maximum strains at the inside CORNER of the hexcan are also underestimated by a similar amount

  2. General Geometry and Geometry of Electromagnetism

    OpenAIRE

    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...

  3. The simplified P3 approach on a trigonal geometry in the nodal reactor code DYN3D

    International Nuclear Information System (INIS)

    Duerigen, S.; Fridman, E.

    2011-01-01

    DYN3D is a three-dimensional nodal diffusion code for steady-state and transient analyses of Light-Water Reactors with square and hexagonal fuel assembly geometries. Currently, several versions of the DYN3D code are available including a multi-group diffusion and a simplified P 3 (SP 3 ) neutron transport option. In this work, the multi-group SP 3 method based on trigonal-z geometry was developed. The method is applicable to the analysis of reactor cores with hexagonal fuel assemblies and allows flexible mesh refinement, which is of particular importance for WWER-type Pressurized Water Reactors as well as for innovative reactor concepts including block type High-Temperature Reactors and Sodium Fast Reactors. In this paper, the theoretical background for the trigonal SP 3 methodology is outlined and the results of a preliminary verification analysis are presented by means of a simplified WWER-440 core test example. The accordant cross sections and reference solutions were produced by the Monte Carlo code SERPENT. The DYN3D results are in good agreement with the reference solutions. The average deviation in the nodal power distribution is about 1%. (Authors)

  4. Differential geometry

    CERN Document Server

    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

  5. Intrinsic ferromagnetism in hexagonal boron nitride nanosheets

    Energy Technology Data Exchange (ETDEWEB)

    Si, M. S.; Gao, Daqiang, E-mail: gaodq@lzu.edu.cn, E-mail: xueds@lzu.edu.cn; Yang, Dezheng; Peng, Yong; Zhang, Z. Y.; Xue, Desheng, E-mail: gaodq@lzu.edu.cn, E-mail: xueds@lzu.edu.cn [Key Laboratory for Magnetism and Magnetic Materials of the Ministry of Education, Lanzhou University, Lanzhou 730000 (China); Liu, Yushen [Jiangsu Laboratory of Advanced Functional Materials and College of Physics and Engineering, Changshu Institute of Technology, Changshu 215500 (China); Deng, Xiaohui [Department of Physics and Electronic Information Science, Hengyang Normal University, Hengyang 421008 (China); Zhang, G. P. [Department of Physics, Indiana State University, Terre Haute, Indiana 47809 (United States)

    2014-05-28

    Understanding the mechanism of ferromagnetism in hexagonal boron nitride nanosheets, which possess only s and p electrons in comparison with normal ferromagnets based on localized d or f electrons, is a current challenge. In this work, we report an experimental finding that the ferromagnetic coupling is an intrinsic property of hexagonal boron nitride nanosheets, which has never been reported before. Moreover, we further confirm it from ab initio calculations. We show that the measured ferromagnetism should be attributed to the localized π states at edges, where the electron-electron interaction plays the role in this ferromagnetic ordering. More importantly, we demonstrate such edge-induced ferromagnetism causes a high Curie temperature well above room temperature. Our systematical work, including experimental measurements and theoretical confirmation, proves that such unusual room temperature ferromagnetism in hexagonal boron nitride nanosheets is edge-dependent, similar to widely reported graphene-based materials. It is believed that this work will open new perspectives for hexagonal boron nitride spintronic devices.

  6. Coincidence orientations of grains in hexagonal materials

    International Nuclear Information System (INIS)

    Grimmer, H.; Warrington, D.H.

    1986-06-01

    The connection between the rotation matrix in hexagonal lattice coordinates and an angle-axis quadruple is given. The multiplication law of quadruples is derived. It corresponds to multiplying two matrices and gives the effect of two successive rotations. The relation is given between two quadruples that describe the same relative orientation of two lattices due to their hexagonal symmetry; a unique standard description of the relative orientation is proposed. The restrictions satisfied by rotations generating coincidence site lattices (CSLs) are derived for any value of the axial ratio rho = c/a. It is shown that the law for cubic lattices, where the multiplicity SIGMA of the CSL was equal to the least common denominator of the elements of the rotation matrix, does not always hold for hexagonal lattices. A generalisation of this law to lattices of arbitrary symmetry is given and another, quicker method to determine SIGMA for hexagonal lattices is derived. Finally, convenient algorithms are described for determining bases of the CSL and the DSC lattice. (author)

  7. Numerically robust geometry engine for compound solid geometries

    International Nuclear Information System (INIS)

    Vlachoudis, V.; Sinuela-Pastor, D.

    2013-01-01

    Monte Carlo programs heavily rely on a fast and numerically robust solid geometry engines. However the success of solid modeling, depends on facilities for specifying and editing parameterized models through a user-friendly graphical front-end. Such a user interface has to be fast enough in order to be interactive for 2D and/or 3D displays, but at the same time numerically robust in order to display possible modeling errors at real time that could be critical for the simulation. The graphical user interface Flair for FLUKA currently employs such an engine where special emphasis has been given on being fast and numerically robust. The numerically robustness is achieved by a novel method of estimating the floating precision of the operations, which dynamically adapts all the decision operations accordingly. Moreover a predictive caching mechanism is ensuring that logical errors in the geometry description are found online, without compromising the processing time by checking all regions. (authors)

  8. Finite element method solution of simplified P3 equation for flexible geometry handling

    International Nuclear Information System (INIS)

    Ryu, Eun Hyun; Joo, Han Gyu

    2011-01-01

    In order to obtain efficiently core flux solutions which would be much closer to the transport solution than the diffusion solution is, not being limited by the geometry of the core, the simplified P 3 (SP 3 ) equation is solved with the finite element method (FEM). A generic mesh generator, GMSH, is used to generate linear and quadratic mesh data. The linear system resulting from the SP 3 FEM discretization is solved by Krylov subspace methods (KSM). A symmetric form of the SP 3 equation is derived to apply the conjugate gradient method rather than the KSMs for nonsymmetric linear systems. An optional iso-parametric quadratic mapping scheme, which is to selectively model nonlinear shapes with a quadratic mapping to prevent significant mismatch in local domain volume, is also implemented for efficient application of arbitrary geometry handling. The gain in the accuracy attainable by the SP 3 solution over the diffusion solution is assessed by solving numerous benchmark problems having various core geometries including the IAEA PWR problems involving rectangular fuels and the Takeda fast reactor problems involving hexagonal fuels. The reference transport solution is produced by the McCARD Monte Carlo code and the multiplication factor and power distribution errors are assessed. In addition, the effect of quadratic mapping is examined for circular cell problems. It is shown that significant accuracy gain is possible with the SP 3 solution for the fast reactor problems whereas only marginal improvement is noted for thermal reactor problems. The quadratic mapping is also quite effective handling geometries with curvature. (author)

  9. Whole core transport calculation for the VHTR hexagonal core

    International Nuclear Information System (INIS)

    Cho, J. Y.; Kim, K. S.; Lee, C. C.; Joo, H. G.

    2007-01-01

    Recently, the DeCART code which performs the whole core calculation by coupling the radial MOC transport kernel with the axial nodal kernel has equipped a kernel to deal with the hexagonal geometry and applied to the VHTR hexagonal core to examine the accuracy and the computational efficiency of the implemented kernel. The implementation includes a modular ray tracing module based on the hexagonal assembly and a multi-group CMFD module to perform an efficient transport calculation. The requirements for the modular ray are: (1) the assembly based path linking and (2) the complete reflection capabilities. The first requirement is met by adjusting the azimuthal angle and the ray spacing for the modular ray to construct a core ray by the path linking. The second requirement is met by expanding the constructed azimuthal angle in the range of [0,30 degree] to the remained range to reflect completely at the core boundaries. The considered reflecting surface angles for the complete reflection are 30n's (n=1,2,1,12). The CMFD module performs the equivalent diffusion calculation to the radial MOC transport calculation based on the homogenized structure units. The structure units include the hexagonal pin cells and gap cells appearing at the assembly boundary. Therefore, the CMFD module is programmed to deal with the unstructured cells such as the gap cells. The CMFD equation consists of the two parts of (1) the conventional FDM and (2) the current corrective parts. Since the second part of the CMFD equation guarantees the reproducibility of the radial MOC transport solutions for the cell averaged reaction rate and the net current at the cell surfaces, how to build the first part of the CMFD equation is not important. Therefore, the first part of the CMFD equation is roughly built by using the normal distance from the gravity center to the surface. The VHTR core uses helium as a coolant which is realized as a void hole in a neutronics calculation. This void hole which

  10. Chain hexagonal cacti with the extremal eccentric distance sum.

    Science.gov (United States)

    Qu, Hui; Yu, Guihai

    2014-01-01

    Eccentric distance sum (EDS), which can predict biological and physical properties, is a topological index based on the eccentricity of a graph. In this paper we characterize the chain hexagonal cactus with the minimal and the maximal eccentric distance sum among all chain hexagonal cacti of length n, respectively. Moreover, we present exact formulas for EDS of two types of hexagonal cacti.

  11. Development of an advanced code system for fast-reactor transient analysis

    International Nuclear Information System (INIS)

    Konstantin Mikityuk; Sandro Pelloni; Paul Coddington

    2005-01-01

    FAST (Fast-spectrum Advanced Systems for power production and resource management) is a recently approved PSI activity in the area of fast spectrum core and safety analysis with emphasis on generic developments and Generation IV systems. In frames of the FAST project we will study both statics and transients core physics, reactor system behaviour and safety; related international experiments. The main current goal of the project is to develop unique analytical and code capability for core and safety analysis of critical (and sub-critical) fast spectrum systems with an initial emphasis on a gas cooled fast reactors. A structure of the code system is shown on Fig. 1. The main components of the FAST code system are 1) ERANOS code for preparation of basic x-sections and their partial derivatives; 2) PARCS transient nodal-method multi-group neutron diffusion code for simulation of spatial (3D) neutron kinetics in hexagonal and square geometries; 3) TRAC/AAA code for system thermal hydraulics; 4) FRED transient model for fuel thermal-mechanical behaviour; 5) PVM system as an interface between separate parts of the code system. The paper presents a structure of the code system (Fig. 1), organization of interfaces and data exchanges between main parts of the code system, examples of verification and application of separate codes and the system as a whole. (authors)

  12. MOCA, Criticality of VVER Reactor Hexagonal Fuel Assemblies

    International Nuclear Information System (INIS)

    KYNCL, Jan

    1994-01-01

    1 - Description of program or function: Criticality problem in neutron transport for hexagonal fuel assembly in VVER nuclear reactor. The assembly is assumed to be either arranged in an infinite hexagonal array or placed in vacuum. The problem is solved in three- dimensional geometry, using standard energy group formalism and assuming that effective scattering cross sections are presented as Legendre polynomial expansions. The code evaluates ten different physical quantities, e.g. multiplication factor, neutron flux per energy group and spatial zone, integrated over angle and power in any zone of the assembly. 2 - Method of solution: Monte Carlo method of successive generations is applied. Computation proceeds according to an analog random process. The code is organized into three blocks: In the first block, the input data are converted to quantities for use in the Monte Carlo calculation. An initial neutron distribution is calculated, which corresponds to a fission spectrum uniform in spatial and angular variables. The main calculations are carried out in the second block (subroutine PROC2). This block is subdivided into geometrical and physical parts. Neutron tracks in individual zones and groups as well as probabilities for the formation of secondary neutrons are calculated. In the third block (subroutine PROC3), the results are evaluated statistically. Effective multiplication coefficients, the neutron flux per group and zone, and respective errors are computed. These quantities serve as a basis for the evaluation of other quantities. The results are either printed or stored for future evaluations. 3 - Restrictions on the complexity of the problem: In the PC version of the program, the maximum number of neutrons is 1000, the maximum number of energy groups is 4, and the maximum number of material compositions is 15. Angular expansion of scattering cross sections is allowed up to P10. These restrictions can easily be removed by increasing input parameters and

  13. Diamagnetic response in zigzag hexagonal silicene rings

    International Nuclear Information System (INIS)

    Xu, Ning; Chen, Qiao; Tian, Hongyu; Ding, Jianwen; Liu, Junfeng

    2016-01-01

    Highlights: • Hexagonal silicene rings possess unusually large diamagnetic moments. • The magnetic-field-driven spin-up electrons flow anticlockwise and spin-down electrons flow clockwise along the rings. • The large diamagnetic moment is the result of competition of spin-up and spin-down electrons. - Abstract: Hexagonal silicene rings with unusually large diamagnetic moments have been found in a theoretical study of the electronic and magnetic properties. In the presence of effective spin–orbit coupling, the magnetic-field-driven spin-up electrons flow anticlockwise exhibiting colossal diamagnetic moments, while the spin-down electrons flow clockwise exhibiting colossal paramagnetic moments along the rings. The large diamagnetic moment is thus the result of competition of spin-up and spin-down electrons, which can be modulated by spin–orbit coupling strength and exchange field.

  14. Diamagnetic response in zigzag hexagonal silicene rings

    Energy Technology Data Exchange (ETDEWEB)

    Xu, Ning, E-mail: nxu@ycit.cn [Department of Physics, Yancheng Institute of Technology, Yancheng 224051 (China); Chen, Qiao [Department of Physics, Hunan Institute of Engineering, Xiangtan 411104 (China); Tian, Hongyu [Department of Physics, Yancheng Institute of Technology, Yancheng 224051 (China); Ding, Jianwen [Department of Physics, Xiangtan University, Xiangtan 411105 (China); Liu, Junfeng, E-mail: liu.jf@sustc.edu.cn [Department of Physics, South University of Science and Technology of China, Shenzhen 518055 (China)

    2016-09-16

    Highlights: • Hexagonal silicene rings possess unusually large diamagnetic moments. • The magnetic-field-driven spin-up electrons flow anticlockwise and spin-down electrons flow clockwise along the rings. • The large diamagnetic moment is the result of competition of spin-up and spin-down electrons. - Abstract: Hexagonal silicene rings with unusually large diamagnetic moments have been found in a theoretical study of the electronic and magnetic properties. In the presence of effective spin–orbit coupling, the magnetic-field-driven spin-up electrons flow anticlockwise exhibiting colossal diamagnetic moments, while the spin-down electrons flow clockwise exhibiting colossal paramagnetic moments along the rings. The large diamagnetic moment is thus the result of competition of spin-up and spin-down electrons, which can be modulated by spin–orbit coupling strength and exchange field.

  15. Higher order polynomial expansion nodal method for hexagonal core neutronics analysis

    International Nuclear Information System (INIS)

    Jin, Young Cho; Chang, Hyo Kim

    1998-01-01

    A higher-order polynomial expansion nodal(PEN) method is newly formulated as a means to improve the accuracy of the conventional PEN method solutions to multi-group diffusion equations in hexagonal core geometry. The new method is applied to solving various hexagonal core neutronics benchmark problems. The computational accuracy of the higher order PEN method is then compared with that of the conventional PEN method, the analytic function expansion nodal (AFEN) method, and the ANC-H method. It is demonstrated that the higher order PEN method improves the accuracy of the conventional PEN method and that it compares very well with the other nodal methods like the AFEN and ANC-H methods in accuracy

  16. Determination of temperature distributions in fast reactor core coolants

    International Nuclear Information System (INIS)

    Tillman, M.

    1975-04-01

    An analytical method of determination of a temperature distribution in the coolant medium in a fuel assembly of a liquid-metal-fast-breeder-reactor (LMFBR) is presented. The temperature field obtained is applied for a constant velocity (slug flow) fluid flowing, parallel to the fuel pins of a square and hexagonal array assembly. The coolant subchannels contain irregular boundaries. The geometry of the channel due to the rod adjacent to the wall (edge rod) differs from the geometry of the other channels. The governing energy equation is solved analytically, assuming series solutions for the Poisson and diffusion equations, and the total solution is superposed by the two. The boundary conditions are specified by symmetry considerations, assembly wall insulation and a continuity of the temperature field and heat fluxes. The initial condition is arbitrary. The method satisfies the boundary conditions on the irregular boundaries and the initial condition by a least squares technique. Computed results are presented for various geometrical forms, with ratio of rod pitch-to-diameter typical for LMFBR cores. These results are applicable for various fast-reactors, and thus the influence of the transient solution (which solves the diffusion equation) on the total depends on the core parameters. (author)

  17. Thermal conductivity of hexagonal Si and hexagonal Si nanowires from first-principles

    Science.gov (United States)

    Raya-Moreno, Martí; Aramberri, Hugo; Seijas-Bellido, Juan Antonio; Cartoixà, Xavier; Rurali, Riccardo

    2017-07-01

    We calculate the thermal conductivity, κ, of the recently synthesized hexagonal diamond (lonsdaleite) Si using first-principles calculations and solving the Boltzmann Transport Equation. We find values of κ which are around 40% lower than in the common cubic diamond polytype of Si. The trend is similar for [111] Si nanowires, with reductions of the thermal conductivity that are even larger than in the bulk in some diameter range. The Raman active modes are identified, and the role of mid-frequency optical phonons that arise as a consequence of the reduced symmetry of the hexagonal lattice is discussed. We also show briefly that popular classic potentials used in molecular dynamics might not be suited to describe hexagonal polytypes, discussing the case of the Tersoff potential.

  18. Computational study of packing a collagen-like molecule: quasi-hexagonal vs "Smith" collagen microfibril model.

    Science.gov (United States)

    Lee, J; Scheraga, H A; Rackovsky, S

    1996-01-01

    The lateral packing of a collagen-like molecule, CH3CO-(Gly-L-Pro-L-Pro)4-NHCH3, has been examined by energy minimization with the ECEPP/3 force field. Two current packing models, the Smith collagen microfibril twisted equilateral pentagonal model and the quasi-hexagonal packing model, have been extensively investigated. In treating the Smith microfibril model, energy minimization was carried out on various conformations including those with the symmetry of equivalent packing, i.e., in which the triple helices were arranged equivalently with respect to each other. Both models are based on the experimental observation of the characteristic axial periodicity, D = 67 nm, of light and dark bands, indicating that, if any superstructure exists, it should consist of five triple helices. The quasi-hexagonal packing structure is found to be energetically more favorable than the Smith microfibril model by as much as 31.2 kcal/mol of five triple helices. This is because the quasi-hexagonal packing geometry provides more nonbonded interaction possibilities between triple helices than does the Smith microfibril geometry. Our results are consistent with recent x-ray studies with synthetic collagen-like molecules and rat tail tendon, in which the data were interpreted as being consistent with either a quasi-hexagonal or a square-triangular structure.

  19. On the perfect hexagonal packing of rods

    International Nuclear Information System (INIS)

    Starostin, E L

    2006-01-01

    In most cases the hexagonal packing of fibrous structures or rods extremizes the energy of interaction between strands. If the strands are not straight, then it is still possible to form a perfect hexatic bundle. Conditions under which the perfect hexagonal packing of curved tubular structures may exist are formulated. Particular attention is given to closed or cycled arrangements of the rods like in the DNA toroids and spools. The closure or return constraints of the bundle result in an allowable group of automorphisms of the cross-sectional hexagonal lattice. The structure of this group is explored. Examples of open helical-like and closed toroidal-like bundles are presented. An expression for the elastic energy of a perfectly packed bundle of thin elastic rods is derived. The energy accounts for both the bending and torsional stiffnesses of the rods. It is shown that equilibria of the bundle correspond to solutions of a variational problem formulated for the curve representing the axis of the bundle. The functional involves a function of the squared curvature under the constraints on the total torsion and the length. The Euler-Lagrange equations are obtained in terms of curvature and torsion and due to the existence of the first integrals the problem is reduced to the quadrature. The three-dimensional shape of the bundle may be readily reconstructed by integration of the Ilyukhin-type equations in special cylindrical coordinates. The results are of universal nature and are applicable to various fibrous structures, in particular, to intramolecular liquid crystals formed by DNA condensed in toroids or packed inside the viral capsids

  20. Facile synthesis and structure characterization of hexagonal tungsten bronzes crystals

    Science.gov (United States)

    Lee, Jiann-Shing; Liu, Hao-Chuan; Peng, Gao-De; Tseng, Yawteng

    2017-05-01

    A facile molten-salt route was used to synthesize hexagonal Cs0.33WO3, Rb0.33WO3 and K0.30WO3 crystals. The three isostructural compounds were successfully prepared from the reaction of MxWO3 powders (M = Cs, Rb, K) in the CsCl/NaCl, RbCl/NaCl and KCl/NaCl fluxes, respectively. The structure determination and refinement, based on single-crystal X-ray diffraction data, are in agreement with previous works, possessing space group P63/mcm. The a and c parameters vary non-linearly with increasing radii of the M+ cations (rM) that is coordinated to twelve oxygen atoms. Both the volumes of unit-cell and WO6 octahedra vary linearly with rM, which become smaller from Cs0.33WO3 to K0.30WO3. The distortion of WO6 octahedra as well as isotropic displacement parameters increases from Cs0.33WO3 to K0.30WO3. The geometry of the WO6 octahedron becomes more regular with increasing rM. These structural trends arise from the effective size of the M+ cation.

  1. Diagonal form factors and hexagon form factors

    International Nuclear Information System (INIS)

    Jiang, Yunfeng; Petrovskii, Andrei

    2016-01-01

    We study the heavy-heavy-light (HHL) three-point functions in the planar N=4 super-Yang-Mills theory using the recently proposed hexagon bootstrap program http://arxiv.org/abs/1505.06745. We prove the conjecture of Bajnok, Janik and Wereszczynski http://dx.doi.org/10.1007/JHEP09(2014)050 on the polynomial L-dependence of HHL structure constant up to the leading finite-size corrections, where L is the length of the heavy operators. The proof is presented for a specific set-up but the method can be applied to more general situations.

  2. Diagonal form factors and hexagon form factors

    Energy Technology Data Exchange (ETDEWEB)

    Jiang, Yunfeng [Institute for Theoretical Physics, ETH Zürich,Honggerberg, Zürich, 8093 (Switzerland); Petrovskii, Andrei [Institut de Physique Théorique, CEA, URA 2306 CNRS Saclay,Gif-sur-Yvette, F91191 (France)

    2016-07-25

    We study the heavy-heavy-light (HHL) three-point functions in the planar N=4 super-Yang-Mills theory using the recently proposed hexagon bootstrap program http://arxiv.org/abs/1505.06745. We prove the conjecture of Bajnok, Janik and Wereszczynski http://dx.doi.org/10.1007/JHEP09(2014)050 on the polynomial L-dependence of HHL structure constant up to the leading finite-size corrections, where L is the length of the heavy operators. The proof is presented for a specific set-up but the method can be applied to more general situations.

  3. Complex analysis and geometry

    CERN Document Server

    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.

  4. Non-Riemannian geometry

    CERN Document Server

    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.

  5. Growth of InAs Wurtzite Nanocrosses from Hexagonal and Cubic Basis

    DEFF Research Database (Denmark)

    Krizek, Filip; Kanne, Thomas; Razmadze, Davydas

    2017-01-01

    . Two methods use conventional wurtzite nanowire arrays as a 6-fold hexagonal basis for growing single crystal wurtzite nanocrosses. A third method uses the 2-fold cubic symmetry of (100) substrates to form well-defined coherent inclusions of zinc blende in the center of the nanocrosses. We show......Epitaxially connected nanowires allow for the design of electron transport experiments and applications beyond the standard two terminal device geometries. In this Letter, we present growth methods of three distinct types of wurtzite structured InAs nanocrosses via the vapor-liquid-solid mechanism...

  6. Geometry of the Universe

    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

  7. Dirac cones in isogonal hexagonal metallic structures

    Science.gov (United States)

    Wang, Kang

    2018-03-01

    A honeycomb hexagonal metallic lattice is equivalent to a triangular atomic one and cannot create Dirac cones in its electromagnetic wave spectrum. We study in this work the low-frequency electromagnetic band structures in isogonal hexagonal metallic lattices that are directly related to the honeycomb one and show that such structures can create Dirac cones. The band formation can be described by a tight-binding model that allows investigating, in terms of correlations between local resonance modes, the condition for the Dirac cones and the consequence of the third structure tile sustaining an extra resonance mode in the unit cell that induces band shifts and thus nonlinear deformation of the Dirac cones following the wave vectors departing from the Dirac points. We show further that, under structure deformation, the deformations of the Dirac cones result from two different correlation mechanisms, both reinforced by the lattice's metallic nature, which directly affects the resonance mode correlations. The isogonal structures provide new degrees of freedom for tuning the Dirac cones, allowing adjustment of the cone shape by modulating the structure tiles at the local scale without modifying the lattice periodicity and symmetry.

  8. Axial magnetic field and toroidally streaming fast ions in the dense plasma focus are natural consequences of conservation laws in the curved axisymmetric geometry of the current sheath. II. Towards a first principles theory

    Science.gov (United States)

    Auluck, S. K. H.

    2017-11-01

    This paper continues earlier discussion [S. K. H. Auluck, Phys. Plasmas 21, 102515 (2014)] concerning the formulation of conservation laws of mass, momentum, and energy in a local curvilinear coordinate system in the dense plasma focus. This formulation makes use of the revised Gratton-Vargas snowplow model [S. K. H. Auluck, Phys. Plasmas 20, 112501 (2013)], which provides an analytically defined imaginary surface in three dimensions which resembles the experimentally determined shape of the plasma. Unit vectors along the local tangent to this surface, along the azimuth, and along the local normal define a right-handed orthogonal local curvilinear coordinate system. The simplifying assumption that physical quantities have significant variation only along the normal enables writing laws of conservation of mass, momentum, and energy in the form of effectively one-dimensional hyperbolic conservation law equations using expressions for various differential operators derived for this coordinate system. This formulation demonstrates the highly non-trivial result that the axial magnetic field and toroidally streaming fast ions, experimentally observed by multiple prestigious laboratories, are natural consequences of conservation of mass, momentum, and energy in the curved geometry of the dense plasma focus current sheath. The present paper continues the discussion in the context of a 3-region shock structure similar to the one experimentally observed: an unperturbed region followed by a hydrodynamic shock containing some current followed by a magnetic piston. Rankine-Hugoniot conditions are derived, and expressions are obtained for the specific volumes and pressures using the mass-flux between the hydrodynamic shock and the magnetic piston and current fraction in the hydrodynamic shock as unknown parameters. For the special case of a magnetic piston that remains continuously in contact with the fluid being pushed, the theory gives closed form algebraic results for the

  9. Tracking algorithms for multi-hexagonal assemblies (2D and 3D)

    International Nuclear Information System (INIS)

    Prabha, Hem; Marleau, Guy; Hébert, Alain

    2014-01-01

    Highlights: • We present the method of computations of 2D and 3D fluxes in hexagonal assemblies. • Computation of fluxes requires computation of track lengths. • Equations are developed (in 2D and 3D) and are implemented in a program HX7. • The program HX7 is implemented in the NXT module of the code DRAGON. • The tracks are plotted and fluxes are compared with the EXCELT module of DRAGON. - Abstract: Background: There has been a continuous effort to design new reactors and study these reactors under different conditions. Some of these reactors have fuel pins arranged in hexagonal pitch. To study these reactors, development of computational methods and computer codes is required. For this purpose, we have developed algorithms to track two dimensional and three dimensional cluster geometries. These algorithms have been implemented in a subprogram HX7, that is implemented in the code DRAGON (Version 3.06F) to compute neutron flux distributions in these systems. Methods: Computation of the neutron flux distribution requires solution of neutron transport equation. While solving this equation, by using Carlvik’s method of collision probabilities, computation of tracks in the hexagonal geometries is required. In this paper we present equations that we have developed for the computation of tracks in two dimensional (2D) and three dimensional (3D) multi-hexagonal assemblies (with two rotational orientations). These equations have been implemented in a subprogram HX7, to compute tracks in seven hexagonal assemblies. The subprogram HX7 has been implemented in the NXT module of the DRAGON code, where tracks in the pins are computed. Results: The results of our algorithms NXT(+HX7) have been compared with the results obtained by the EXCELT module of DRAGON (Version 3.06F). Conclusions: We find that all the fluxes in 2D and fluxes in the outer pin (3D) are converging to their 3rd decimal places, in both the modules EXCELT and NXT(+HX7). For other regions 3D fluxes

  10. Development of square and hexagonal lattice analysis capability in WIMS-AECL

    International Nuclear Information System (INIS)

    Donnelly, J.V.

    1990-11-01

    WIMS, originally developed by the UKAEA (Winfrith), is a widely used computer code for reactor physics analysis of lattice cells. WIMS-AECL (Atomic Energy of Canada Limited) has been developed from a version of the code received from Winfrith in the early 1970s and is generally used within AECL. The facilities existing in the original version of WIMS were very capable for the analysis of reactor designs normally encountered within AECL at that time, such as CANDU fuel lattices, but had limitations in the analysis of more general reactor geometries, such as square light-reactor assemblies. This paper discusses the development and testing of modifications to the two-dimensional collision-probability calculation module in WIMS-AECL to enable more rigorous analysis of lattice geometries based on square or hexagonal cells

  11. Permeation of Light Gases through Hexagonal Ice

    Directory of Open Access Journals (Sweden)

    Luis Gales

    2012-09-01

    Full Text Available Gas separation using porous solids have attracted great attention due to their energetic applications. There is an enormous economic and environmental interest in the development of improved technologies for relevant processes, such as H2 production, CO2 separation or O2 and N2 purification from air. New materials are needed for achieving major improvements. Crystalline materials, displaying unidirectional and single-sized pores, preferentially with low pore tortuosity and high pore density, are promising candidates for membrane synthesis. Herein, we study hexagonal ice crystals as an example of this class of materials. By slowly growing ice crystals inside capillary tubes we were able to measure the permeation of several gas species through ice crystals and investigate its relation with both the size of the guest molecules and temperature of the crystal.

  12. Hexagonal boron nitride and water interaction parameters

    Energy Technology Data Exchange (ETDEWEB)

    Wu, Yanbin; Aluru, Narayana R., E-mail: aluru@illinois.edu [Department of Mechanical Science and Engineering, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 (United States); Wagner, Lucas K. [Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-3080 (United States)

    2016-04-28

    The study of hexagonal boron nitride (hBN) in microfluidic and nanofluidic applications at the atomic level requires accurate force field parameters to describe the water-hBN interaction. In this work, we begin with benchmark quality first principles quantum Monte Carlo calculations on the interaction energy between water and hBN, which are used to validate random phase approximation (RPA) calculations. We then proceed with RPA to derive force field parameters, which are used to simulate water contact angle on bulk hBN, attaining a value within the experimental uncertainties. This paper demonstrates that end-to-end multiscale modeling, starting at detailed many-body quantum mechanics and ending with macroscopic properties, with the approximations controlled along the way, is feasible for these systems.

  13. Hexagonal wavelet processing of digital mammography

    Science.gov (United States)

    Laine, Andrew F.; Schuler, Sergio; Huda, Walter; Honeyman-Buck, Janice C.; Steinbach, Barbara G.

    1993-09-01

    This paper introduces a novel approach for accomplishing mammographic feature analysis through overcomplete multiresolution representations. We show that efficient representations may be identified from digital mammograms and used to enhance features of importance to mammography within a continuum of scale-space. We present a method of contrast enhancement based on an overcomplete, non-separable multiscale representation: the hexagonal wavelet transform. Mammograms are reconstructed from transform coefficients modified at one or more levels by local and global non-linear operators. Multiscale edges identified within distinct levels of transform space provide local support for enhancement. We demonstrate that features extracted from multiresolution representations can provide an adaptive mechanism for accomplishing local contrast enhancement. We suggest that multiscale detection and local enhancement of singularities may be effectively employed for the visualization of breast pathology without excessive noise amplification.

  14. The hexagon hypothesis: Six disruptive scenarios.

    Science.gov (United States)

    Burtles, Jim

    2015-01-01

    This paper aims to bring a simple but effective and comprehensive approach to the development, delivery and monitoring of business continuity solutions. To ensure that the arguments and principles apply across the board, the paper sticks to basic underlying concepts rather than sophisticated interpretations. First, the paper explores what exactly people are defending themselves against. Secondly, the paper looks at how defences should be set up. Disruptive events tend to unfold in phases, each of which invites a particular style of protection, ranging from risk management through to business continuity to insurance cover. Their impact upon any business operation will fall into one of six basic scenarios. The hexagon hypothesis suggests that everyone should be prepared to deal with each of these six disruptive scenarios and it provides them with a useful benchmark for business continuity.

  15. Structural domain walls in polar hexagonal manganites

    Science.gov (United States)

    Kumagai, Yu

    2014-03-01

    The domain structure in the multiferroic hexagonal manganites is currently intensely investigated, motivated by the observation of intriguing sixfold topological defects at their meeting points [Choi, T. et al,. Nature Mater. 9, 253 (2010).] and nanoscale electrical conductivity at the domain walls [Wu, W. et al., Phys. Rev. Lett. 108, 077203 (2012).; Meier, D. et al., Nature Mater. 11, 284 (2012).], as well as reports of coupling between ferroelectricity, magnetism and structural antiphase domains [Geng, Y. et al., Nano Lett. 12, 6055 (2012).]. The detailed structure of the domain walls, as well as the origin of such couplings, however, was previously not fully understood. In the present study, we have used first-principles density functional theory to calculate the structure and properties of the low-energy structural domain walls in the hexagonal manganites [Kumagai, Y. and Spaldin, N. A., Nature Commun. 4, 1540 (2013).]. We find that the lowest energy domain walls are atomically sharp, with {210}orientation, explaining the orientation of recently observed stripe domains and suggesting their topological protection [Chae, S. C. et al., Phys. Rev. Lett. 108, 167603 (2012).]. We also explain why ferroelectric domain walls are always simultaneously antiphase walls, propose a mechanism for ferroelectric switching through domain-wall motion, and suggest an atomistic structure for the cores of the sixfold topological defects. This work was supported by ETH Zurich, the European Research Council FP7 Advanced Grants program me (grant number 291151), the JSPS Postdoctoral Fellowships for Research Abroad, and the MEXT Elements Strategy Initiative to Form Core Research Center TIES.

  16. Geometric triangular chiral hexagon crystal-like complexes organization in pathological tissues biological collision order.

    Directory of Open Access Journals (Sweden)

    Jairo A Díaz

    Full Text Available The present study describes and documents self-assembly of geometric triangular chiral hexagon crystal like complex organizations (GTCHC in human pathological tissues. The authors have found this architectural geometric expression at macroscopic and microscopic levels mainly in cancer processes. This study is based essentially on macroscopic and histopathologic analyses of 3000 surgical specimens: 2600 inflammatory lesions and 400 malignant tumours. Geometric complexes identified photographically at macroscopic level were located in the gross surgical specimen, and these areas were carefully dissected. Samples were taken to carry out histologic analysis. Based on the hypothesis of a collision genesis mechanism and because it is difficult to carry out an appropriate methodological observation in biological systems, the authors designed a model base on other dynamic systems to obtain indirect information in which a strong white flash wave light discharge, generated by an electronic device, hits over the lines of electrical conductance structured in helicoidal pattern. In their experimental model, the authors were able to reproduce and to predict polarity, chirality, helicoid geometry, triangular and hexagonal clusters through electromagnetic sequential collisions. They determined that similar events among constituents of extracelular matrix which drive and produce piezoelectric activity are responsible for the genesis of GTCHC complexes in pathological tissues. This research suggests that molecular crystals represented by triangular chiral hexagons derived from a collision-attraction event against collagen type I fibrils emerge at microscopic and macroscopic scales presenting a lateral assembly of each side of hypertrophy helicoid fibers, that represent energy flow in cooperative hierarchically chiral electromagnetic interaction in pathological tissues and arises as a geometry of the equilibrium in perturbed biological systems. Further

  17. Geometric triangular chiral hexagon crystal-like complexes organization in pathological tissues biological collision order.

    Science.gov (United States)

    Díaz, Jairo A; Jaramillo, Natalia A; Murillo, Mauricio F

    2007-12-12

    The present study describes and documents self-assembly of geometric triangular chiral hexagon crystal like complex organizations (GTCHC) in human pathological tissues. The authors have found this architectural geometric expression at macroscopic and microscopic levels mainly in cancer processes. This study is based essentially on macroscopic and histopathologic analyses of 3000 surgical specimens: 2600 inflammatory lesions and 400 malignant tumours. Geometric complexes identified photographically at macroscopic level were located in the gross surgical specimen, and these areas were carefully dissected. Samples were taken to carry out histologic analysis. Based on the hypothesis of a collision genesis mechanism and because it is difficult to carry out an appropriate methodological observation in biological systems, the authors designed a model base on other dynamic systems to obtain indirect information in which a strong white flash wave light discharge, generated by an electronic device, hits over the lines of electrical conductance structured in helicoidal pattern. In their experimental model, the authors were able to reproduce and to predict polarity, chirality, helicoid geometry, triangular and hexagonal clusters through electromagnetic sequential collisions. They determined that similar events among constituents of extracelular matrix which drive and produce piezoelectric activity are responsible for the genesis of GTCHC complexes in pathological tissues. This research suggests that molecular crystals represented by triangular chiral hexagons derived from a collision-attraction event against collagen type I fibrils emerge at microscopic and macroscopic scales presenting a lateral assembly of each side of hypertrophy helicoid fibers, that represent energy flow in cooperative hierarchically chiral electromagnetic interaction in pathological tissues and arises as a geometry of the equilibrium in perturbed biological systems. Further interdisciplinary studies must

  18. Dependence of displacement fields on the damage cluster nucleus geometry

    International Nuclear Information System (INIS)

    Grigor'ev, A.N.; Zabela, A.G.; Nikolajchuk, L.I.; Prokhorenko, E.M.; Khizhnyak, N.A.

    1988-01-01

    Displacement fields in doped crystals of cubic and hexagonal structures containing extended defects are studied. The numerical results are presented depending on the damage cluster nucleus geometry. All calculations are based on analytical representations of displacement fields in an integral form using elasticity theory equations. The investigation results are vital for radiation physics as they permit to predict and calculate both the character and geometry of distortions near damaged region cluster and determine cluster parameters on the basis of the known structure of distortions. Dependences are obtained for the following monocrystals: Mg, ZnO, CdS, W, Au. 6 refs.; 3 figs

  19. Calculation of the mechanical equilibrium in a lattice of deformed hexagonal subassemblies

    International Nuclear Information System (INIS)

    Bernard, A.

    1979-01-01

    Stainless steel swelling and irradiation creep in the hexagonal wrappers of fast breeder cores induce deformations (mostly bowing), hence mutual interaction (displacements, forces and stresses, which must be calculated). The HARMONIE code was developed to meet these requirements. In this three dimensional code, one minimizes the elastic potential bending energy (quadratic form), with given linear conditions (no overlapping between adjacent subassemblies). The convergence of this function is obtained through a numerical method (parallel gradient). The free bowing of the subassemblies are given as input datas; the output gives the equilibrium displacements and forces while stresses are calculated in a classical manner

  20. Comparison of square and hexagonal fuel lattices for high conversion PWRs

    International Nuclear Information System (INIS)

    Kotlyar, D.; Shwageraus, E.

    2011-01-01

    This paper reports on an investigation into fuel design choices of a PWR operating in a self sustainable Th- 233 U fuel cycle. Achieving such self-sustainable with respect to fissile material fuel cycle would practically eliminate concerns over nuclear fuel supply hundreds of years into the future. Moreover, utilization of light water reactor technology and its associated vast experience would allow faster deployment of such fuel cycle without immediate need for development of fast reactor technology, which tends to be more complex and costly. In order to evaluate feasibility of this concept, two types of fuel assembly lattices were considered: square and hexagonal. The hexagonal lattice may offer some advantages over the square one. For example, the fertile blanket fuel can be packed more tightly reducing the blanket volume fraction in the core and potentially allowing to achieve higher core average power density. Furthermore, hexagonal lattice may allow more uniform leakage of neutrons from fissile to fertile regions and therefore more uniform neutron captures in thorium blanket. The calculations were carried out with Monte-Carlo based BGCore system, which includes neutronic, fuel depletion and thermo-hydraulic modules. The results were compared to those obtained from Serpent Monte-Carlo code and deterministic fuel assembly transport code BOXER. One of the major design challenges associated with the square seed-blanket concept is high power peaking due to the high concentration of fissile material in the seed region. In order to explore feasibility of the studied designs, the calculations were extended to include 3D fuel assembly analysis with thermal-hydraulic feedback. The coupled neutronic - thermal-hydraulic calculations were performed with BGCore code system. The analysis showed that both hexagonal and square seed-blanket fuel assembly designs have a potential of achieving net breeding. While no major neutronic advantages were observed for either fuel

  1. Simulation software of 3-D two-neutron energy groups for ship reactor with hexagonal fuel subassembly

    International Nuclear Information System (INIS)

    Zhang Fan; Cai Zhangsheng; Yu Lei; Gui Xuewen

    2005-01-01

    Core simulation software for 3-D two-neutron energy groups is developed. This software is used to simulate the ship reactor with hexagonal fuel subassembly after 10, 150 and 200 burnup days, considering the hydraulic and thermal feedback. It accurately simulates the characteristics of the fast and thermal neutrons and the detailed power distribution in a reactor under normal and abnormal operation condition. (authors)

  2. Multilinear Computing and Multilinear Algebraic Geometry

    Science.gov (United States)

    2016-08-10

    Laplacians on graphs,” S. Mukherjee (Ed.), Geometry and Topology in Statistical Inference, Proc. Sympos. Appl. Math ., 73, AMS, Providence, RI, 2015...8–12, 2015. • “Fast(est) algorithms for structured matrices via tensor decompositions,” Applied Mathe - matics and Analysis Seminar, Duke University...Durham, NC, April 13, 2015. • “Fast(est) algorithms for structured matrices via tensor decompositions,” Applied Mathe - matics Seminar, Stanford

  3. Geometry and its applications

    CERN Document Server

    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...

  4. Algebraic geometry in India

    Indian Academy of Sciences (India)

    algebraic geometry but also in related fields like number theory. ... every vector bundle on the affine space is trivial. (equivalently ... les on a compact Riemann surface to unitary rep- ... tial geometry and topology and was generalised in.

  5. Spinorial Geometry and Branes

    International Nuclear Information System (INIS)

    Sloane, Peter

    2007-01-01

    We adapt the spinorial geometry method introduced in [J. Gillard, U. Gran and G. Papadopoulos, 'The spinorial geometry of supersymmetric backgrounds,' Class. Quant. Grav. 22 (2005) 1033 [ (arXiv:hep-th/0410155)

  6. Spinorial Geometry and Branes

    Energy Technology Data Exchange (ETDEWEB)

    Sloane, Peter [Department of Mathematics, King' s College, University of London, Strand, London WC2R 2LS (United Kingdom)

    2007-09-15

    We adapt the spinorial geometry method introduced in [J. Gillard, U. Gran and G. Papadopoulos, 'The spinorial geometry of supersymmetric backgrounds,' Class. Quant. Grav. 22 (2005) 1033 [ (arXiv:hep-th/0410155)

  7. Study the Postbuckling of Hexagonal Piezoelectric Nanowires with Surface Effect

    Directory of Open Access Journals (Sweden)

    O. Rahmani

    2014-04-01

    Full Text Available Piezoelectric nanobeams having circular, rectangular and hexagonal cross-sections are synthesized and used in various Nano structures; however, piezoelectric nanobeams with hexagonal cross-sections have not been studied in detail. In particular, the physical mechanisms of the surface effect and the role of surface stress, surface elasticity and surface piezoelectricity have not been discussed thoroughly. The present study investigated post-buckling behavior of piezoelectric nanobeams by examining surface effects. The energy method was applied to post-buckling of hexagonal nanobeams and the critical buckling voltage and amplitude are derived analytically from bulk and surface material properties and geometric factors.

  8. Theoretical Investigations of the Hexagonal Germanium Carbonitride

    Directory of Open Access Journals (Sweden)

    Xinhai Yu

    2018-04-01

    Full Text Available The structural, mechanical, elastic anisotropic, and electronic properties of hexagonal germanium carbonitride (h-GeCN are systematically investigated using the first-principle calculations method with the ultrasoft pseudopotential scheme in the frame of generalized gradient approximation in the present work. The h-GeCN are mechanically and dynamically stable, as proved by the elastic constants and phonon spectra, respectively. The h-GeCN is brittle because the ratio B/G and Poisson’s ratio v of the h-GeCN are less than 1.75 and 0.26, respectively. For h-GeCN, from brittleness to ductility, the transformation pressures are 5.56 GPa and 5.63 GPa for B/G and Poisson’s ratio v, respectively. The h-GeCN exhibits the greater elastic anisotropy in Young’s modulus and the sound velocities. In addition, the calculated band structure of h-GeCN reveals that there is no band gap for h-GeCN with the HSE06 hybrid functional, so the h-GeCN is metallic.

  9. Mathematical Foundation for Plane Covering Using Hexagons

    Science.gov (United States)

    Johnson, Gordon G.

    1999-01-01

    This work is to indicate the development and mathematical underpinnings of the algorithms previously developed for covering the plane and the addressing of the elements of the covering. The algorithms are of interest in that they provides a simple systematic way of increasing or decreasing resolution, in the sense that if we have the covering in place and there is an image superimposed upon the covering, then we may view the image in a rough form or in a very detailed form with minimal effort. Such ability allows for quick searches of crude forms to determine a class in which to make a detailed search. In addition, the addressing algorithms provide an efficient way to process large data sets that have related subsets. The algorithms produced were based in part upon the work of D. Lucas "A Multiplication in N Space" which suggested a set of three vectors, any two of which would serve as a bases for the plane and also that the hexagon is the natural geometric object to be used in a covering with a suggested bases. The second portion is a refinement of the eyeball vision system, the globular viewer.

  10. Bootstrapping the Three-Loop Hexagon

    Energy Technology Data Exchange (ETDEWEB)

    Dixon, Lance J.; /CERN /SLAC; Drummond, James M.; /CERN /Annecy, LAPTH; Henn, Johannes M.; /Humboldt U., Berlin /Santa Barbara, KITP

    2011-11-08

    We consider the hexagonal Wilson loop dual to the six-point MHV amplitude in planar N = 4 super Yang-Mills theory. We apply constraints from the operator product expansion in the near-collinear limit to the symbol of the remainder function at three loops. Using these constraints, and assuming a natural ansatz for the symbol's entries, we determine the symbol up to just two undetermined constants. In the multi-Regge limit, both constants drop out from the symbol, enabling us to make a non-trivial confirmation of the BFKL prediction for the leading-log approximation. This result provides a strong consistency check of both our ansatz for the symbol and the duality between Wilson loops and MHV amplitudes. Furthermore, we predict the form of the full three-loop remainder function in the multi-Regge limit, beyond the leading-log approximation, up to a few constants representing terms not detected by the symbol. Our results confirm an all-loop prediction for the real part of the remainder function in multi-Regge 3 {yields} 3 scattering. In the multi-Regge limit, our result for the remainder function can be expressed entirely in terms of classical polylogarithms. For generic six-point kinematics other functions are required.

  11. Structure of grain boundaries in hexagonal materials

    International Nuclear Information System (INIS)

    Sarrazit, F.

    1998-05-01

    The work presented in this thesis describes experimental and theoretical aspects associated with the structure of grain boundaries in hexagonal materials. It has been found useful to classify grain boundaries as low-angle, special or general on the basis of their structure. High-angle grain boundaries were investigated in tungsten carbide (WC) using conventional electron microscopy techniques, and three examples characteristic of the interfaces observed in this material were studied extensively. Three-dimensionally periodic patterns are proposed as plausible reference configurations, and the Burgers vectors of observed interfacial dislocations were predicted using a theory developed recently. The comparison of experimental observations with theoretical predictions proved to be difficult as contrast simulation techniques require further development for analysis to be completed confidently. Another part of this work involves the characterisation of high-angle grain boundaries in zinc oxide (ZnO) using circuit mapping. Two boundaries displayed structural features characteristic of the 'special' category, however, one boundary presented features which did not conform to this model. It is proposed that the latter observation shows a structural transition from the special to a more general type. Material fluxes involved in defect interactions were considered using the topological framework described in this work. A genera) expression was derived for the total flux arising which allows the behaviour of line-defects to be studied in complex interfacial processes. (author)

  12. An invitation to noncommutative geometry

    CERN Document Server

    Marcolli, Matilde

    2008-01-01

    This is the first existing volume that collects lectures on this important and fast developing subject in mathematics. The lectures are given by leading experts in the field and the range of topics is kept as broad as possible by including both the algebraic and the differential aspects of noncommutative geometry as well as recent applications to theoretical physics and number theory. Sample Chapter(s). A Walk in the Noncommutative Garden (1,639 KB). Contents: A Walk in the Noncommutative Garden (A Connes & M Marcolli); Renormalization of Noncommutative Quantum Field Theory (H Grosse & R Wulke

  13. Computation of 3D neutron fluxes in one pin hexagonal cell

    International Nuclear Information System (INIS)

    Prabha, Hem; Marleau, Guy

    2013-01-01

    Highlights: ► Computations of 3D neutron fluxes in one pin hexagonal cell is performed by Carlvik’s method of collision probability. ► Carlvik’s method requires computation of track lengths in the geometry. ► Equations are developed to compute tracks, in 2D and 3D, in hexagons and are implemented in a program HX7. ► The program HX7 is implemented in NXT module of the code DRAGON, where tracks in pins are computed. ► The tracks are plotted and fluxes are compared with the EXCELT module of the code DRAGON. - Abstract: In this paper we are presenting the method of computation of three dimensional (3D) neutron fluxes in one pin hexagonal cell. Carlvik’s collision probability method of solving neutron transport equation for computing fluxes has been used here. This method can consider exact geometrical details of the given geometry. While using this method, track length computations are required to be done. We have described here the method of computing tracks in one 3D hexagon. A program HX7 has been developed for this purpose. This program has been implemented in the NXT module of the code DRAGON, where tracks in the pins are computed. For computing tracks in 3D, first we use the tracks computed in the two dimensions (2D) and then we project them in the third dimension. We have developed equations for this purpose. In both the regions, fuel pin as well as in the moderator surrounding the pin the fluxes are assumed to be uniform. A uniform source is assumed in the moderator region. Reflecting boundary conditions are applied on all the sides as well as on the top and bottom surfaces. One group 2D and 3D fluxes are compared with the respective results obtained by the EXCELT module of DRAGON. To check the computations, tracks are plotted and errors in the computations are obtained. It is observed by using both the modules EXCELT and NXT that the fluxes in the pins converge faster and in the moderator region fluxes converge very slowly

  14. Geometry essentials for dummies

    CERN Document Server

    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

  15. Low Complexity Connectivity Driven Dynamic Geometry Compression for 3D Tele-Immersion

    NARCIS (Netherlands)

    R.N. Mekuria (Rufael); D.C.A. Bulterman (Dick); P.S. Cesar Garcia (Pablo Santiago)

    2014-01-01

    htmlabstractGeometry based 3D Tele-Immersion is a novel emerging media application that involves on the fly reconstructed 3D mesh geometry. To enable real-time communication of such live reconstructed mesh geometry over a bandwidth limited link, fast dynamic geometry compression is needed. However,

  16. Transition behavior of asymmetric polystyrene-b-poly(2-vinylpyridine) films: A stable hexagonally modulated layer structure

    Energy Technology Data Exchange (ETDEWEB)

    Park, Sungmin; Koo, Kyosung; Kim, Kyunginn; Ahn, Hyungju; Lee, Byeongdu; Park, Cheolmin; Ryu, Du Yeol

    2015-03-09

    The phase transitions in the films of an asymmetric polystyrene-b-poly(2-vinylpyridine) (PS-b-P2VP) were investigated by grazing incidence small-angle X-ray scattering (GISAXS) and transmission electron microscopy (TEM). Compared with the sequential transitions in the bulk, hexagonally perforated layer (HPL) – gyroid (GYR) – disorder (DIS) upon heating, the transitions in film geometry were dramatically changed with decreasing thickness due to the growing preferential interactions from substrate, resulting in a thickness-dependent transition diagram including four different morphologies of hexagonally modulated layer (HML), coexisting (HML and GYR), GYR, and DIS. Particularly in the films ≤10Lo, where Lo is d-spacing at 150 °C, a stable HML structure was identified even above the order-to-disorder transition (ODT) temperature of the bulk, which was attributed to the suppressed compositional fluctuations by the enhanced substrate interactions.

  17. Arithmetic noncommutative geometry

    CERN Document Server

    Marcolli, Matilde

    2005-01-01

    Arithmetic noncommutative geometry denotes the use of ideas and tools from the field of noncommutative geometry, to address questions and reinterpret in a new perspective results and constructions from number theory and arithmetic algebraic geometry. This general philosophy is applied to the geometry and arithmetic of modular curves and to the fibers at archimedean places of arithmetic surfaces and varieties. The main reason why noncommutative geometry can be expected to say something about topics of arithmetic interest lies in the fact that it provides the right framework in which the tools of geometry continue to make sense on spaces that are very singular and apparently very far from the world of algebraic varieties. This provides a way of refining the boundary structure of certain classes of spaces that arise in the context of arithmetic geometry, such as moduli spaces (of which modular curves are the simplest case) or arithmetic varieties (completed by suitable "fibers at infinity"), by adding boundaries...

  18. Bifurcation theory for hexagonal agglomeration in economic geography

    CERN Document Server

    Ikeda, Kiyohiro

    2014-01-01

    This book contributes to an understanding of how bifurcation theory adapts to the analysis of economic geography. It is easily accessible not only to mathematicians and economists, but also to upper-level undergraduate and graduate students who are interested in nonlinear mathematics. The self-organization of hexagonal agglomeration patterns of industrial regions was first predicted by the central place theory in economic geography based on investigations of southern Germany. The emergence of hexagonal agglomeration in economic geography models was envisaged by Krugman. In this book, after a brief introduction of central place theory and new economic geography, the missing link between them is discovered by elucidating the mechanism of the evolution of bifurcating hexagonal patterns. Pattern formation by such bifurcation is a well-studied topic in nonlinear mathematics, and group-theoretic bifurcation analysis is a well-developed theoretical tool. A finite hexagonal lattice is used to express uniformly distri...

  19. Comparison of fuel assemblies in lead cooled fast reactors

    Energy Technology Data Exchange (ETDEWEB)

    Perez, A.; Sanchez, H.; Aguilar, L.; Espinosa P, G., E-mail: alejandria.peval@gmail.com [Universidad Autonoma Metropolitana, Unidad Iztapalapa, San Rafael Atlixco No. 186, Col. Vicentina, 09340 Ciudad de Mexico (Mexico)

    2016-09-15

    This paper presents a comparison of the thermal-fluid processes in the core, fuel heat transfer, and thermal power between two fuel assemblies: square and hexagonal, in a lead-cooled fast reactor (Lfr). A multi-physics reduced order model for the analysis of Lfr single channel is developed in this work. The work focused on a coupling between process of neutron kinetic, fuel heat transfer process and thermal-fluid, in a single channel. The thermal power is obtained from neutron point kinetics model, considering a non-uniform power distribution. The analysis of the processes of thermal-fluid considers thermal expansion effects. The transient heat transfer in fuel is carried out in an annular geometry, and one-dimensional in radial direction for each axial node. The results presented in comparing these assemblies consider the temperature field in the fuel, in the thermal fluid and under steady state, and transient conditions. Transients consider flow of coolant and inlet temperature of coolant. The mathematical model of Lfr considers three main modules: the heat transfer in the annular fuel, the power generation with feedback effects on neutronic, and the thermal-fluid in the single channel. The modeling of nuclear reactors in general, the coupling is crucial by the feedback between the neutron processes with fuel heat transfer, and thermo-fluid, where is very common the numerical instabilities, after all it has to refine the model to achieve the design data. In this work is considered as a reference the ELSY reactor for the heat transfer analysis in the fuel and pure lead properties for analyzing the thermal-fluid. The results found shows that the hexagonal array has highest temperature in the fuel, respect to square array. (Author)

  20. Comparison of fuel assemblies in lead cooled fast reactors

    International Nuclear Information System (INIS)

    Perez, A.; Sanchez, H.; Aguilar, L.; Espinosa P, G.

    2016-09-01

    This paper presents a comparison of the thermal-fluid processes in the core, fuel heat transfer, and thermal power between two fuel assemblies: square and hexagonal, in a lead-cooled fast reactor (Lfr). A multi-physics reduced order model for the analysis of Lfr single channel is developed in this work. The work focused on a coupling between process of neutron kinetic, fuel heat transfer process and thermal-fluid, in a single channel. The thermal power is obtained from neutron point kinetics model, considering a non-uniform power distribution. The analysis of the processes of thermal-fluid considers thermal expansion effects. The transient heat transfer in fuel is carried out in an annular geometry, and one-dimensional in radial direction for each axial node. The results presented in comparing these assemblies consider the temperature field in the fuel, in the thermal fluid and under steady state, and transient conditions. Transients consider flow of coolant and inlet temperature of coolant. The mathematical model of Lfr considers three main modules: the heat transfer in the annular fuel, the power generation with feedback effects on neutronic, and the thermal-fluid in the single channel. The modeling of nuclear reactors in general, the coupling is crucial by the feedback between the neutron processes with fuel heat transfer, and thermo-fluid, where is very common the numerical instabilities, after all it has to refine the model to achieve the design data. In this work is considered as a reference the ELSY reactor for the heat transfer analysis in the fuel and pure lead properties for analyzing the thermal-fluid. The results found shows that the hexagonal array has highest temperature in the fuel, respect to square array. (Author)

  1. MOCUM: A two-dimensional method of characteristics code based on constructive solid geometry and unstructured meshing for general geometries

    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.

  2. The Geometry Conference

    CERN Document Server

    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.

  3. The extended family of hexagonal molybdenum oxide

    Energy Technology Data Exchange (ETDEWEB)

    Hartl, Monika [Los Alamos National Laboratory; Daemen, Luke [Los Alamos National Laboratory; Lunk, J H [NON LANL; Hartl, H [NON LANL; Frisk, A T [NON LANL; Shendervich, I [NON LANL; Mauder, D [NON LANL; Feist, M [NON LANL; Eckelt, R [NON LANL

    2009-01-01

    Over the last 40 years, a large number of isostructural compounds in the system MoO{sub 3}-NH{sub 3}-H{sub 2}O have been published. The reported molecular formulae of 'hexagonal molybdenum oxide' (HEMO) varied from MoO{sub 3}, MoO{sub 3} {center_dot} 0.33NH{sub 3}, MoO{sub 3} {center_dot} nH{sub 2}O (0.09 {le} n {le} 0.69) to MoO{sub 3} {center_dot} mNH{sub 3} {center_dot} nH{sub 2}O (0.09 {le} m {le} 0.20; 0.18 {le} n {le} 0.60). Samples, prepared by the acidification route, were investigated using thermal analysis coupled on-line to a mass spectrometer for evolved gas analysis; X-ray powder diffraction; Fourier Transform Infrared, Raman and Magic-Angle-Spinning {sup 1}H-NMR spectroscopy; Incoherent Inelastic Neutron Scattering. The X-ray study of a selected monocrystal confirmed the presence of the well-known framework of edge-sharing MoO{sub 6} octahedra: Space group P6{sub 3}/m, a = 10.527(1), c =3.7245(7) {angstrom}, {gamma} = 120{sup o}. The structure of the synthesized samples can best be described by the structural formula (NH{sub 4})[Mo{sub x}{open_square}{sub 1/2+p/2}(O{sub 3x + 1/2-p/2})(OH){sub p}] {center_dot} yH{sub 2}O (x 5.9-7.1; p {approx} 0.1; y = 1.2-2.6), which is consistent with the existence of one vacancy for 12-15 molybdenum sites. The 'chimie douce' reaction of MoO{sub 3} {center_dot} 0.155NH{sub 3} {center_dot} 0.440H{sub 2}O with a 1:1 mixture of NO/NO{sub 2} at 100 C resulted in the synthesis of MoO{sub 3} {center_dot} 0.539H{sub 2}O. Tailored nano-sized molybdenum powders can be produced using HEMO as precursor.

  4. Algorithms in Algebraic Geometry

    CERN Document Server

    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

  5. Revolutions of Geometry

    CERN Document Server

    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

  6. Fundamental concepts of geometry

    CERN Document Server

    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.

  7. Developments in special geometry

    International Nuclear Information System (INIS)

    Mohaupt, Thomas; Vaughan, Owen

    2012-01-01

    We review the special geometry of N = 2 supersymmetric vector and hypermultiplets with emphasis on recent developments and applications. A new formulation of the local c-map based on the Hesse potential and special real coordinates is presented. Other recent developments include the Euclidean version of special geometry, and generalizations of special geometry to non-supersymmetric theories. As applications we discuss the proof that the local r-map and c-map preserve geodesic completeness, and the construction of four- and five-dimensional static solutions through dimensional reduction over time. The shared features of the real, complex and quaternionic version of special geometry are stressed throughout.

  8. Elastic plastic analysis of fuel element assemblies - hexagonal claddings and fuel rods

    International Nuclear Information System (INIS)

    Mamoun, M.M.; Wu, T.S.; Chopra, P.S.; Rardin, D.C.

    1979-01-01

    Analytical studies have been conducted to investigate the structural, thermal, and mechanical behavior of fuel rods, claddings and fuel element assemblies of several designs for a conceptual Safety Test Facility (STF). One of the design objectives was to seek a geometrical configuration for a clad by maximizing the volume fraction of fuel and minimizing the resultant stresses set-up in the clad. The results of studies conducted on various geometrical configurations showed that the latter design objective can be achieved by selecting a clad of an hexagonal geometry. The analytical studies necessitated developing solutions for determining the stresses, strains, and displacements experienced by fuel rods and an hexagonal cladding subjected to thermal fuel-bowing loads acting on its internal surface, the external pressure of the coolant, and elevated temperatures. This paper presents some of the initially formulated analytical methods and results. It should be emphasized that the geometrical configuration considered in this paper may not necessarily be similar to that of the final design. Several variables have been taken into consideration including cladding thickness, the dimensions of the fuel rod, the temperature of the fuel and cladding, the external pressure of the cooling fluid, and the mechanical strength properties of fuel and cladding. A finite-element computer program, STRAW Code, has also been employed to generate several numerical results which have been compared with those predicted by employing the initially formulated solutions. The theoretically predicted results are in good agreement with those of the STRAW Code. (orig.)

  9. On the extension of the analytic nodal diffusion solver ANDES to sodium fast reactors

    International Nuclear Information System (INIS)

    Ochoa, R.; Herrero, J.J.; Garcia-Herranz, N.

    2011-01-01

    Within the framework of the Collaborative Project for a European Sodium Fast Reactor, the reactor physics group at UPM is working on the extension of its in-house multi-scale advanced deterministic code COBAYA3 to Sodium Fast Reactors (SFR). COBAYA3 is a 3D multigroup neutron kinetics diffusion code that can be used either as a pin-by-pin code or as a stand-alone nodal code by using the analytic nodal diffusion solver ANDES. It is coupled with thermal-hydraulics codes such as COBRA-TF and FLICA, allowing transient analysis of LWR at both fine-mesh and coarse-mesh scales. In order to enable also 3D pin-by-pin and nodal coupled NK-TH simulations of SFR, different developments are in progress. This paper presents the first steps towards the application of COBAYA3 to this type of reactors. ANDES solver, already extended to triangular-Z geometry, has been applied to fast reactor steady-state calculations. The required cross section libraries were generated with ERANOS code for several configurations. Here some of the limitations encountered when attempting to apply the Analytical Coarse Mesh Finite Difference (ACMFD) method - implemented inside ANDES - to fast reactor calculations are discussed and the sensitivity of the method to the energy-group structure is studied. In order to reinforce some of the conclusions obtained two calculations are presented. The first one involves a 3D mini-core model in 33 groups, where the ANDES solver presents several issues. And secondly, a benchmark from the NEA for a small 3D FBR in hexagonal-Z geometry in 4 energy groups is used to verify the good convergence of the code in a few-energy-group structure. (author)

  10. Intrinsic magnetic properties of hexagonal LuFeO3 and the effects of nonstoichiometry

    Directory of Open Access Journals (Sweden)

    Jarrett A. Moyer

    2014-01-01

    Full Text Available We used oxide molecular-beam epitaxy in a composition-spread geometry to deposit hexagonal LuFeO3 (h-LuFeO3 thin films with a monotonic variation in the Lu/Fe cation ratio, creating a mosaic of samples that ranged from iron rich to lutetium rich. We characterized the effects of composition variation with x-ray diffraction, atomic force microscopy, scanning transmission electron microscopy, and superconducting quantum interference device magnetometry. After identifying growth conditions leading to stoichiometric film growth, an additional sample was grown with a rotating sample stage. From this stoichiometric sample, we determined stoichiometric h-LuFeO3 to have a TN = 147 K and Ms = 0.018 μB/Fe.

  11. Theoretical prediction of low-density hexagonal ZnO hollow structures

    Energy Technology Data Exchange (ETDEWEB)

    Tuoc, Vu Ngoc, E-mail: tuoc.vungoc@hust.edu.vn [Institute of Engineering Physics, Hanoi University of Science and Technology, 1 Dai Co Viet Road, Hanoi (Viet Nam); Huan, Tran Doan [Institute of Materials Science, University of Connecticut, Storrs, Connecticut 06269-3136 (United States); Thao, Nguyen Thi [Institute of Engineering Physics, Hanoi University of Science and Technology, 1 Dai Co Viet Road, Hanoi (Viet Nam); Hong Duc University, 307 Le Lai, Thanh Hoa City (Viet Nam); Tuan, Le Manh [Hong Duc University, 307 Le Lai, Thanh Hoa City (Viet Nam)

    2016-10-14

    Along with wurtzite and zinc blende, zinc oxide (ZnO) has been found in a large number of polymorphs with substantially different properties and, hence, applications. Therefore, predicting and synthesizing new classes of ZnO polymorphs are of great significance and have been gaining considerable interest. Herein, we perform a density functional theory based tight-binding study, predicting several new series of ZnO hollow structures using the bottom-up approach. The geometry of the building blocks allows for obtaining a variety of hexagonal, low-density nanoporous, and flexible ZnO hollow structures. Their stability is discussed by means of the free energy computed within the lattice-dynamics approach. Our calculations also indicate that all the reported hollow structures are wide band gap semiconductors in the same fashion with bulk ZnO. The electronic band structures of the ZnO hollow structures are finally examined in detail.

  12. Geometry of multihadron production

    Energy Technology Data Exchange (ETDEWEB)

    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.

  13. Designs and finite geometries

    CERN Document Server

    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.

  14. 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

  15. The Beauty of Geometry

    Science.gov (United States)

    Morris, Barbara H.

    2004-01-01

    This article describes a geometry project that used the beauty of stained-glass-window designs to teach middle school students about geometric figures and concepts. Three honors prealgebra teachers and a middle school mathematics gifted intervention specialist created a geometry project that covered the curriculum and also assessed students'…

  16. Inserting Stress Analysis of Combined Hexagonal Aluminum Honeycombs

    Directory of Open Access Journals (Sweden)

    Xiangcheng Li

    2016-01-01

    Full Text Available Two kinds of hexagonal aluminum honeycombs are tested to study their out-of-plane crushing behavior. In the tests, honeycomb samples, including single hexagonal aluminum honeycomb (SHAH samples and two stack-up combined hexagonal aluminum honeycombs (CHAH samples, are compressed at a fixed quasistatic loading rate. The results show that the inserting process of CHAH can erase the initial peak stress that occurred in SHAH. Meanwhile, energy-absorbing property of combined honeycomb samples is more beneficial than the one of single honeycomb sample with the same thickness if the two types of honeycomb samples are completely crushed. Then, the applicability of the existing theoretical model for single hexagonal honeycomb is discussed, and an area equivalent method is proposed to calculate the crushing stress for nearly regular hexagonal honeycombs. Furthermore, a semiempirical formula is proposed to calculate the inserting plateau stress of two stack-up CHAH, in which structural parameters and mechanics properties of base material are concerned. The results show that the predicted stresses of three kinds of two stack-up combined honeycombs are in good agreement with the experimental data. Based on this study, stress-displacement curve of aluminum honeycombs can be designed in detail, which is very beneficial to optimize the energy-absorbing structures in engineering fields.

  17. Hexagonal OsB2: Sintering, microstructure and mechanical properties

    International Nuclear Information System (INIS)

    Xie, Zhilin; Lugovy, Mykola; Orlovskaya, Nina; Graule, Thomas; Kuebler, Jakob; Mueller, Martin; Gao, Huili; Radovic, Miladin; Cullen, David A.

    2015-01-01

    Highlights: • ReB 2 -type hexagonal OsB 2 powder has been densified by spark plasma sintering. • The sintered OsB 2 contains ∼80 wt.% hexagonal and ∼20 wt.% orthorhombic phases. • The average grain size of the sintered OsB 2 sample was 0.56 ± 0.26 μm. • H = 31 ± 9 GPa and E = 574 ± 112 GPa measured by nanoindentation. - Abstract: The metastable high pressure ReB 2 -type hexagonal OsB 2 bulk ceramics was produced by spark plasma sintering. The phase composition, microstructure, and mechanical behavior of the sintered OsB 2 were studied by X-ray diffraction, optical microscopy, TEM, SEM, EDS, and nanoindentation. The produced ceramics was rather porous and contained a mixture of hexagonal (∼80 wt.%) and orthorhombic (∼20 wt.%) phases as identified by X-ray diffraction and EBSD analysis. Two boron-rich phases, which do not contain Os, were also identified by TEM and SEM/EDS analysis. Nanoindentation measurements yielded a hardness of 31 ± 9 GPa and Young’s modulus of 574 ± 112 GPa, indicating that the material is rather hard and very stiff; however, it is very prone to crack formation and propagation, which is indicative of a very brittle nature of this material. Improvements in the sintering regime are required in order to produce dense, homogeneous and single phase hexagonal OsB 2 bulk ceramics

  18. A Lorentzian quantum geometry

    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.

  19. Methods of information geometry

    CERN Document Server

    Amari, Shun-Ichi

    2000-01-01

    Information geometry provides the mathematical sciences with a new framework of analysis. It has emerged from the investigation of the natural differential geometric structure on manifolds of probability distributions, which consists of a Riemannian metric defined by the Fisher information and a one-parameter family of affine connections called the \\alpha-connections. The duality between the \\alpha-connection and the (-\\alpha)-connection together with the metric play an essential role in this geometry. This kind of duality, having emerged from manifolds of probability distributions, is ubiquitous, appearing in a variety of problems which might have no explicit relation to probability theory. Through the duality, it is possible to analyze various fundamental problems in a unified perspective. The first half of this book is devoted to a comprehensive introduction to the mathematical foundation of information geometry, including preliminaries from differential geometry, the geometry of manifolds or probability d...

  20. A Lorentzian quantum geometry

    International Nuclear Information System (INIS)

    Grotz, Andreas

    2011-01-01

    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.

  1. 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

  2. Steady squares and hexagons on a subcritical ramp

    International Nuclear Information System (INIS)

    Hoyle, R.B.

    1995-01-01

    Steady squares and hexagons on a subcritical ramp are studied, both analytically and numerically, within the framework of the lowest-order amplitude equations. On the subcritical ramp, the external stress or control parameter varies continuously in space from subcritical to supercritical values. At the subcritical end of the ramp, pattern formation is suppressed, and patterns fade away into the conduction solution. It is shown that three-dimensional patterns may change shape on a subcritical ramp. A square pattern becomes a pattern of rolls as it fades, with the roll axes aligned in the direction orthogonal to that in which the control parameter varies. Hexagons in systems with horizontal midplane symmetry become a pattern of rectangles before reaching the conduction solution. There is a suggestion that hexagons in systems which lack this symmetry might fade away through a roll pattern. Numerical simulations are used to illustrate these phenomena

  3. Additive Manufacturing of Dense Hexagonal Boron Nitride Objects

    Energy Technology Data Exchange (ETDEWEB)

    Marquez Rossy, Andres E [ORNL; Armstrong, Beth L [ORNL; Elliott, Amy M [ORNL; Lara-Curzio, Edgar [ORNL

    2017-05-12

    The feasibility of manufacturing hexagonal boron nitride objects via additive manufacturing techniques was investigated. It was demonstrated that it is possible to hot-extrude thermoplastic filaments containing uniformly distributed boron nitride particles with a volume concentration as high as 60% and that these thermoplastic filaments can be used as feedstock for 3D-printing objects using a fused deposition system. Objects 3D-printed by fused deposition were subsequently sintered at high temperature to obtain dense ceramic products. In a parallel study the behavior of hexagonal boron nitride in aqueous solutions was investigated. It was shown that the addition of a cationic dispersant to an azeotrope enabled the formulation of slurries with a volume concentration of boron nitride as high as 33%. Although these slurries exhibited complex rheological behavior, the results from this study are encouraging and provide a pathway for manufacturing hexagonal boron nitride objects via robocasting.

  4. New results for loop integrals. AMBRE, CSectors, hexagon

    International Nuclear Information System (INIS)

    Gluza, Janusz; Kajda, Krzysztof

    2009-03-01

    We report on the three Mathematica packages hexagon, CSectors, AMBRE. They are useful for the evaluation of one- and two-loop Feynman integrals with a dependence on several kinematical scales. These integrals are typically needed for LHC and ILC applications, but also for higher order corrections at meson factories. hexagon is a new package for the tensor reduction of one-loop 5-point and 6-point functions with rank R=3 and R=4, respectively; AMBRE is a tool for derivations of Mellin-Barnes representations; CSectors is an interface for the package sectordecomposition and allows a convenient, direct evaluation of tensor Feynman integrals. (orig.)

  5. Communication: Water on hexagonal boron nitride from diffusion Monte Carlo

    Energy Technology Data Exchange (ETDEWEB)

    Al-Hamdani, Yasmine S.; Ma, Ming; Michaelides, Angelos, E-mail: angelos.michaelides@ucl.ac.uk [Thomas Young Centre and London Centre for Nanotechnology, 17–19 Gordon Street, London WC1H 0AH (United Kingdom); Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ (United Kingdom); Alfè, Dario [Thomas Young Centre and London Centre for Nanotechnology, 17–19 Gordon Street, London WC1H 0AH (United Kingdom); Department of Earth Sciences, University College London, Gower Street, London WC1E 6BT (United Kingdom); Lilienfeld, O. Anatole von [Institute of Physical Chemistry and National Center for Computational Design and Discovery of Novel Materials, Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel (Switzerland); Argonne Leadership Computing Facility, Argonne National Laboratories, 9700 S. Cass Avenue Argonne, Lemont, Illinois 60439 (United States)

    2015-05-14

    Despite a recent flurry of experimental and simulation studies, an accurate estimate of the interaction strength of water molecules with hexagonal boron nitride is lacking. Here, we report quantum Monte Carlo results for the adsorption of a water monomer on a periodic hexagonal boron nitride sheet, which yield a water monomer interaction energy of −84 ± 5 meV. We use the results to evaluate the performance of several widely used density functional theory (DFT) exchange correlation functionals and find that they all deviate substantially. Differences in interaction energies between different adsorption sites are however better reproduced by DFT.

  6. Complex and symplectic geometry

    CERN Document Server

    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.

  7. Non-Euclidean geometry

    CERN Document Server

    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

  8. Lectures on coarse geometry

    CERN Document Server

    Roe, John

    2003-01-01

    Coarse geometry is the study of spaces (particularly metric spaces) from a 'large scale' point of view, so that two spaces that look the same from a great distance are actually equivalent. This point of view is effective because it is often true that the relevant geometric properties of metric spaces are determined by their coarse geometry. Two examples of important uses of coarse geometry are Gromov's beautiful notion of a hyperbolic group and Mostow's proof of his famous rigidity theorem. The first few chapters of the book provide a general perspective on coarse structures. Even when only metric coarse structures are in view, the abstract framework brings the same simplification as does the passage from epsilons and deltas to open sets when speaking of continuity. The middle section reviews notions of negative curvature and rigidity. Modern interest in large scale geometry derives in large part from Mostow's rigidity theorem and from Gromov's subsequent 'large scale' rendition of the crucial properties of n...

  9. Complex algebraic geometry

    CERN Document Server

    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.

  10. Geometry and Combinatorics

    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...

  11. The geometry of geodesics

    CERN Document Server

    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.

  12. Geometry and billiards

    CERN Document Server

    Tabachnikov, Serge

    2005-01-01

    Mathematical billiards describe the motion of a mass point in a domain with elastic reflections off the boundary or, equivalently, the behavior of rays of light in a domain with ideally reflecting boundary. From the point of view of differential geometry, the billiard flow is the geodesic flow on a manifold with boundary. This book is devoted to billiards in their relation with differential geometry, classical mechanics, and geometrical optics. The topics covered include variational principles of billiard motion, symplectic geometry of rays of light and integral geometry, existence and nonexistence of caustics, optical properties of conics and quadrics and completely integrable billiards, periodic billiard trajectories, polygonal billiards, mechanisms of chaos in billiard dynamics, and the lesser-known subject of dual (or outer) billiards. The book is based on an advanced undergraduate topics course (but contains more material than can be realistically taught in one semester). Although the minimum prerequisit...

  13. Introduction to tropical geometry

    CERN Document Server

    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...

  14. Rudiments of algebraic geometry

    CERN Document Server

    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.

  15. 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....

  16. Intermediate algebra & analytic geometry

    CERN Document Server

    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

  17. d-geometries revisited

    CERN Document Server

    Ceresole, Anna; Gnecchi, Alessandra; Marrani, Alessio

    2013-01-01

    We analyze some properties of the four dimensional supergravity theories which originate from five dimensions upon reduction. They generalize to N>2 extended supersymmetries the d-geometries with cubic prepotentials, familiar from N=2 special K\\"ahler geometry. We emphasize the role of a suitable parametrization of the scalar fields and the corresponding triangular symplectic basis. We also consider applications to the first order flow equations for non-BPS extremal black holes.

  18. Fast geometric algorithms

    International Nuclear Information System (INIS)

    Noga, M.T.

    1984-01-01

    This thesis addresses a number of important problems that fall within the framework of the new discipline of Computational Geometry. The list of topics covered includes sorting and selection, convex hull algorithms, the L 1 hull, determination of the minimum encasing rectangle of a set of points, the Euclidean and L 1 diameter of a set of points, the metric traveling salesman problem, and finding the superrange of star-shaped and monotype polygons. The main theme of all the work was to develop a set of very fast state-of-the-art algorithms that supersede any rivals in terms of speed and ease of implementation. In some cases existing algorithms were refined; for others new techniques were developed that add to the present database of fast adaptive geometric algorithms. What emerges is a collection of techniques that is successful at merging modern tools developed in analysis of algorithms with those of classical geometry

  19. Fourier rebinning algorithm for inverse geometry CT.

    Science.gov (United States)

    Mazin, Samuel R; Pele, Norbert J

    2008-11-01

    Inverse geometry computed tomography (IGCT) is a new type of volumetric CT geometry that employs a large array of x-ray sources opposite a smaller detector array. Volumetric coverage and high isotropic resolution produce very large data sets and therefore require a computationally efficient three-dimensional reconstruction algorithm. The purpose of this work was to adapt and evaluate a fast algorithm based on Defrise's Fourier rebinning (FORE), originally developed for positron emission tomography. The results were compared with the average of FDK reconstructions from each source row. The FORE algorithm is an order of magnitude faster than the FDK-type method for the case of 11 source rows. In the center of the field-of-view both algorithms exhibited the same resolution and noise performance. FORE exhibited some resolution loss (and less noise) in the periphery of the field-of-view. FORE appears to be a fast and reasonably accurate reconstruction method for IGCT.

  20. CMS geometry through 2020

    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.

  1. Software Geometry in Simulations

    Science.gov (United States)

    Alion, Tyler; Viren, Brett; Junk, Tom

    2015-04-01

    The Long Baseline Neutrino Experiment (LBNE) involves many detectors. The experiment's near detector (ND) facility, may ultimately involve several detectors. The far detector (FD) will be significantly larger than any other Liquid Argon (LAr) detector yet constructed; many prototype detectors are being constructed and studied to motivate a plethora of proposed FD designs. Whether it be a constructed prototype or a proposed ND/FD design, every design must be simulated and analyzed. This presents a considerable challenge to LBNE software experts; each detector geometry must be described to the simulation software in an efficient way which allows for multiple authors to easily collaborate. Furthermore, different geometry versions must be tracked throughout their use. We present a framework called General Geometry Description (GGD), written and developed by LBNE software collaborators for managing software to generate geometries. Though GGD is flexible enough to be used by any experiment working with detectors, we present it's first use in generating Geometry Description Markup Language (GDML) files to interface with LArSoft, a framework of detector simulations, event reconstruction, and data analyses written for all LAr technology users at Fermilab. Brett is the other of the framework discussed here, the General Geometry Description (GGD).

  2. 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

  3. Hexagon and stripe patterns in dielectric barrier streamer discharge

    International Nuclear Information System (INIS)

    Dong Lifang; He Yafeng; Yin Zengqian; Chai Zhifang

    2004-01-01

    We present a specially designed dielectric barrier discharge (DBD) system for the study of pattern formation. Hexagon and stripe patterns have been observed in a streamer discharge in a DBD for the first time. The phase diagram of pattern types as a function of applied voltage is given

  4. Moving antiplane shear crack in hexagonal piezoelectric crystals

    International Nuclear Information System (INIS)

    Tupholme, G.

    1998-01-01

    Closed form solutions are obtained and discussed for the stress and electric displacement fields around a loaded Griffith-type antiplane shear strip crack moving in hexagonal piezoelectric crystals. Representative numerical results are presented for ZnO and PZT-5H. (author)

  5. Coherent memory functions for finite systems: hexagonal photosynthetic unit

    International Nuclear Information System (INIS)

    Barvik, I.; Herman, P.

    1990-10-01

    Coherent memory functions entering the Generalized Master Equation are presented for an hexagonal model of a photosynthetic unit. Influence of an energy heterogeneity on an exciton transfer is an antenna system as well as to a reaction center is investigated. (author). 9 refs, 3 figs

  6. Scanning tunneling microscopy of hexagonal BN grown on graphite

    International Nuclear Information System (INIS)

    Fukumoto, H.; Hamada, T.; Endo, T.; Osaka, Y.

    1991-01-01

    The microscopic surface topography of thin BN x films grown on graphite by electron cyclotron resonance plasma chemical vapor deposition have been imaged with scanning tunneling microscopy in air. The scanning tunneling microscope has generated images of hexagonal BN with atomic resolution

  7. Epitaxial hexagonal materials on IBAD-textured substrates

    Science.gov (United States)

    Matias, Vladimir; Yung, Christopher

    2017-08-15

    A multilayer structure including a hexagonal epitaxial layer, such as GaN or other group III-nitride (III-N) semiconductors, a oriented textured layer, and a non-single crystal substrate, and methods for making the same. The textured layer has a crystalline alignment preferably formed by the ion-beam assisted deposition (IBAD) texturing process and can be biaxially aligned. The in-plane crystalline texture of the textured layer is sufficiently low to allow growth of high quality hexagonal material, but can still be significantly greater than the required in-plane crystalline texture of the hexagonal material. The IBAD process enables low-cost, large-area, flexible metal foil substrates to be used as potential alternatives to single-crystal sapphire and silicon for manufacture of electronic devices, enabling scaled-up roll-to-roll, sheet-to-sheet, or similar fabrication processes to be used. The user is able to choose a substrate for its mechanical and thermal properties, such as how well its coefficient of thermal expansion matches that of the hexagonal epitaxial layer, while choosing a textured layer that more closely lattice matches that layer.

  8. Lattice-polarity-driven epitaxy of hexagonal semiconductor nanowires

    KAUST Repository

    Wang, Ping

    2015-12-22

    Lattice-polarity-driven epitaxy of hexagonal semiconductor nanowires (NWs) is demonstrated on InN NWs. In-polarity InN NWs form typical hexagonal structure with pyramidal growth front, whereas N-polarity InN NWs slowly turn to the shape of hexagonal pyramid and then convert to an inverted pyramid growth, forming diagonal pyramids with flat surfaces and finally coalescence with each other. This contrary growth behavior driven by lattice-polarity is most likely due to the relatively lower growth rate of the (0001 ̅) plane, which results from the fact that the diffusion barriers of In and N adatoms on the (0001) plane (0.18 and 1.0 eV, respectively) are about two-fold larger in magnitude than those on the (0001 ̅) plane (0.07 and 0.52 eV), as calculated by first-principles density functional theory (DFT). The formation of diagonal pyramids for the N-polarity hexagonal NWs affords a novel way to locate quantum dot in the kink position, suggesting a new recipe for the fabrication of dot-based devices.

  9. Synthesis of hexagonal boron nitride graphene-like few layers

    Science.gov (United States)

    Yuan, S.; Toury, B.; Journet, C.; Brioude, A.

    2014-06-01

    Self-standing highly crystallized hexagonal boron nitride (h-BN) mono-, bi- and few-layers have been obtained for the first time via the Polymer Derived Ceramics (PDCs) route by adding lithium nitride (Li3N) micropowders to liquid-state polyborazylene (PBN). Incorporation of Li3N as a crystallization promoter allows the onset of crystallization of h-BN at a lower temperature (1200 °C) than under classical conditions (1800 °C). The hexagonal structure was confirmed by both electron and X-ray diffraction.Self-standing highly crystallized hexagonal boron nitride (h-BN) mono-, bi- and few-layers have been obtained for the first time via the Polymer Derived Ceramics (PDCs) route by adding lithium nitride (Li3N) micropowders to liquid-state polyborazylene (PBN). Incorporation of Li3N as a crystallization promoter allows the onset of crystallization of h-BN at a lower temperature (1200 °C) than under classical conditions (1800 °C). The hexagonal structure was confirmed by both electron and X-ray diffraction. Electronic supplementary information (ESI) available: See DOI: 10.1039/c4nr01017e

  10. Influence of strontium on the cubic to ordered hexagonal phase

    Indian Academy of Sciences (India)

    ... Refresher Courses · Symposia · Live Streaming. Home; Journals; Bulletin of Materials Science; Volume 23; Issue 6. Influence of strontium on the cubic to ordered hexagonal phase transformation in barium magnesium niobate. M Thirumal A K Ganguli. Phase Transitions Volume 23 Issue 6 December 2000 pp 495-498 ...

  11. New approach for direct chemical synthesis of hexagonal Co nanoparticles

    Energy Technology Data Exchange (ETDEWEB)

    Abel, Frank M., E-mail: fabel@udel.edu [Physics and Astronomy, University of Delaware (United States); Tzitzios, Vasilis [Institute of Nanoscience and Nanotechnology, NCSR, Demokritos (Greece); Hadjipanayis, George C. [Physics and Astronomy, University of Delaware (United States)

    2016-02-15

    In this paper, we explore the possibility of producing hexagonal Cobalt nanoparticles, with high saturation magnetization by direct chemical synthesis. The nanoparticles were synthesized by reduction of anhydrous cobalt (II) chloride by NaBH{sub 4} in tetraglyme at temperatures in the range of 200–270 °C under a nitrogen–hydrogen atmosphere. The reactions were done at high temperatures to allow for the formation of as-made hexagonal cobalt. The size of the particles was controlled by the addition of different surfactants. The best magnetic properties so far were obtained on spherical hexagonal Co nanoparticles with an average size of 45 nm, a saturation magnetization of 143 emu/g and coercivity of 500 Oe. the saturation magnetization and coercivity were further improved by annealing the Co nanoparticles leading to saturation magnetization of 160 emu/g and coercivity of 540 Oe. - Highlights: • We synthesized hexagonal cobalt nanoparticles by a new wet chemical method. • We considered the effects of different surfactants on particles magnetic properties. • The as-made Co nanoparticles had magnetic properties of 143 emu/g and 500 Oe. • After annealing magnetic properties of 160 emu/g and 540 Oe were obtained.

  12. Model for lattice dynamics of hexagonal close packed metals

    Energy Technology Data Exchange (ETDEWEB)

    Singh, R K [Tata Inst. of Fundamental Research, Bombay (India); Kumar, S [Meerut Coll. (India). Dept. of Physics

    1977-11-19

    A lattice dynamical model, which satisfies the requirements of translational invariance as well as the static equilibrium of hexagonal close packed lattice, has been proposed and applied to study the phonon dispersion relations in magnesium. The results revealed by this model have been claimed to be better than earlier ones.

  13. Lattice-polarity-driven epitaxy of hexagonal semiconductor nanowires

    KAUST Repository

    Wang, Ping; Yuan, Ying; Zhao, Chao; Wang, Xinqiang; Zheng, Xiantong; Rong, Xin; Wang, Tao; Sheng, Bowen; Wang, Qingxiao; Zhang, Yongqiang; Bian, Lifeng; Yang, Xue-Lin; Xu, Fu-Jun; Qin, Zhixin; Li, Xin-Zheng; Zhang, Xixiang; Shen, Bo

    2015-01-01

    by first-principles density functional theory (DFT). The formation of diagonal pyramids for the N-polarity hexagonal NWs affords a novel way to locate quantum dot in the kink position, suggesting a new recipe for the fabrication of dot-based devices.

  14. Epitaxial hexagonal materials on IBAD-textured substrates

    Energy Technology Data Exchange (ETDEWEB)

    Matias, Vladimir; Yung, Christopher

    2017-08-15

    A multilayer structure including a hexagonal epitaxial layer, such as GaN or other group III-nitride (III-N) semiconductors, a <111> oriented textured layer, and a non-single crystal substrate, and methods for making the same. The textured layer has a crystalline alignment preferably formed by the ion-beam assisted deposition (IBAD) texturing process and can be biaxially aligned. The in-plane crystalline texture of the textured layer is sufficiently low to allow growth of high quality hexagonal material, but can still be significantly greater than the required in-plane crystalline texture of the hexagonal material. The IBAD process enables low-cost, large-area, flexible metal foil substrates to be used as potential alternatives to single-crystal sapphire and silicon for manufacture of electronic devices, enabling scaled-up roll-to-roll, sheet-to-sheet, or similar fabrication processes to be used. The user is able to choose a substrate for its mechanical and thermal properties, such as how well its coefficient of thermal expansion matches that of the hexagonal epitaxial layer, while choosing a textured layer that more closely lattice matches that layer.

  15. Global aspects of complex geometry

    CERN Document Server

    Catanese, Fabrizio; Huckleberry, Alan T

    2006-01-01

    Present an overview of developments in Complex Geometry. This book covers topics that range from curve and surface theory through special varieties in higher dimensions, moduli theory, Kahler geometry, and group actions to Hodge theory and characteristic p-geometry.

  16. Characterization of the secondary flow in hexagonal ducts

    Science.gov (United States)

    Marin, O.; Vinuesa, R.; Obabko, A. V.; Schlatter, P.

    2016-12-01

    In this work we report the results of DNSs and LESs of the turbulent flow through hexagonal ducts at friction Reynolds numbers based on centerplane wall shear and duct half-height Reτ,c ≃ 180, 360, and 550. The evolution of the Fanning friction factor f with Re is in very good agreement with experimental measurements. A significant disagreement between the DNS and previous RANS simulations was found in the prediction of the in-plane velocity, and is explained through the inability of the RANS model to properly reproduce the secondary flow present in the hexagon. The kinetic energy of the secondary flow integrated over the cross-sectional area yz decreases with Re in the hexagon, whereas it remains constant with Re in square ducts at comparable Reynolds numbers. Close connection between the values of Reynolds stress u w ¯ on the horizontal wall close to the corner and the interaction of bursting events between the horizontal and inclined walls is found. This interaction leads to the formation of the secondary flow, and is less frequent in the hexagon as Re increases due to the 120∘ aperture of its vertex, whereas in the square duct the 90∘ corner leads to the same level of interaction with increasing Re. Analysis of turbulence statistics at the centerplane and the azimuthal variance of the mean flow and the fluctuations shows a close connection between hexagonal ducts and pipe flows, since the hexagon exhibits near-axisymmetric conditions up to a distance of around 0.15DH measured from its center. Spanwise distributions of wall-shear stress show that in square ducts the 90∘ corner sets the location of a high-speed streak at a distance zv+≃50 from it, whereas in hexagons the 120∘ aperture leads to a shorter distance of zv+≃38 . At these locations the root mean square of the wall-shear stresses exhibits an inflection point, which further shows the connections between the near-wall structures and the large-scale motions in the outer flow.

  17. Chemical trends of Schottky barrier behavior on monolayer hexagonal B, Al, and Ga nitrides

    Science.gov (United States)

    Lu, Haichang; Guo, Yuzheng; Robertson, John

    2016-08-01

    The Schottky Barrier Heights (SBH) of metal layers on top of monolayer hexagonal X-nitrides (X = B, Al, Ga, and h-XN) are calculated using supercells and density functional theory so as to understand the chemical trends of contact formation on graphene and the 2D layered semiconductors such as the transition metal dichalcogenides. The Fermi level pinning factor S of SBHs on h-BN is calculated to be nearly 1, indicating no pinning. For h-AlN and h-GaN, the calculated pinning factor is about 0.63, less than for h-BN. We attribute this to the formation of stronger, chemisorptive bonds between the nitrides and the contact metal layer. Generally, the h-BN layer remains in a planar sp2 geometry and has weak physisorptive bonds to the metals, whereas h-AlN and h-GaN buckle out of their planar geometry which enables them to form the chemisorptive bonds to the metals.

  18. Design considerations for quasi-phase-matching in doubly resonant lithium niobate hexagonal microresonators

    CSIR Research Space (South Africa)

    Sono, Tleyane J

    2017-08-01

    Full Text Available Fabrication capabilities of high optical quality hexagonal superstructures by chemical etching of inverted ferroelectric domains in lithium niobate platform suggests a route for efficient implementation of compact hexagonal microcavities...

  19. Energetics of a hexagonal-lamellar-hexagonal-phase transition sequence in dioleoylphosphatidylethanolamine membranes

    International Nuclear Information System (INIS)

    Gawrisch, K.; Parsegian, V.A.; Hajduk, D.A.; Tate, M.W.; Gruner, S.M.; Fuller, N.L.; Rand, R.P.

    1992-01-01

    The phase diagram of DOPE/water dispersions was investigated by NMR and X-ray diffraction in the water concentration range from 2 to 20 water molecules per lipid and in the temperature range from -5 to +50C. At temperature above 22C, the dispersions form an inverse (H II ) phase at all water concentrations. Below 25C, an H II phase occurs at high water concentrations, an L α phase is formed at intermediate water concentrations, and finally the system switches back to an H II phase at low water concentrations. The enthalpy of the L α -H II -phase transition is +0.3 kcal/mol as measured by differential scanning calorimetry. Using 31 P and 2 H NMR and X-ray diffraction. The authors measured the trapped water volumes in H II and L α phases as a function of osmotic pressure. The change of the H II -phase free energy as a function of hydration was calculated by integrating the osmotic pressure vs trapped water volume curve. The phase diagram calculated on the basis of the known enthalpy of transition and the osmotic pressure vs water volume curves is in good agreement with the measured one. The H II -L α -H II double-phase transition at temperatures below 22C can be shown to be a consequence of (1) the greater degree of hydration of the H II phase in excess water and (2) the relative sensitivities with which the lamellar and hexagonal phases dehydrate with increasing osmotic pressure. These results demonstrate the usefulness of osmotic stress measurements to understand lipid-phase diagrams

  20. Sources of hyperbolic geometry

    CERN Document Server

    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...

  1. Generalizing optical geometry

    International Nuclear Information System (INIS)

    Jonsson, Rickard; Westman, Hans

    2006-01-01

    We show that by employing the standard projected curvature as a measure of spatial curvature, we can make a certain generalization of optical geometry (Abramowicz M A and Lasota J-P 1997 Class. Quantum Grav. A 14 23-30). This generalization applies to any spacetime that admits a hypersurface orthogonal shearfree congruence of worldlines. This is a somewhat larger class of spacetimes than the conformally static spacetimes assumed in standard optical geometry. In the generalized optical geometry, which in the generic case is time dependent, photons move with unit speed along spatial geodesics and the sideways force experienced by a particle following a spatially straight line is independent of the velocity. Also gyroscopes moving along spatial geodesics do not precess (relative to the forward direction). Gyroscopes that follow a curved spatial trajectory precess according to a very simple law of three-rotation. We also present an inertial force formalism in coordinate representation for this generalization. Furthermore, we show that by employing a new sense of spatial curvature (Jonsson R 2006 Class. Quantum Grav. 23 1)) closely connected to Fermat's principle, we can make a more extensive generalization of optical geometry that applies to arbitrary spacetimes. In general this optical geometry will be time dependent, but still geodesic photons move with unit speed and follow lines that are spatially straight in the new sense. Also, the sideways experienced (comoving) force on a test particle following a line that is straight in the new sense will be independent of the velocity

  2. Computational synthetic geometry

    CERN Document Server

    Bokowski, Jürgen

    1989-01-01

    Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces. This research monograph considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids. It turns out that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field. Besides such complexity theorems a variety of symbolic algorithms are discussed, and the methods are applied to obtain new mathematical results on convex polytopes, projective configurations and the combinatorics of Grassmann varieties. Finally algebraic varieties characterizing matroids and oriented matroids are introduced providing a new basis for applying computer algebra methods in this field. The necessary background knowledge is reviewed briefly. The text is accessible to stud...

  3. Discrete and computational geometry

    CERN Document Server

    Devadoss, Satyan L

    2011-01-01

    Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also fe...

  4. Geometry and Cloaking Devices

    Science.gov (United States)

    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.

  5. Lectures on discrete geometry

    CERN Document Server

    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...

  6. Complex differential geometry

    CERN Document Server

    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...

  7. Geometry and symmetry

    CERN Document Server

    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

  8. COREMAP: Graphical user interface for displaying reactor core data in an interactive hexagon map

    International Nuclear Information System (INIS)

    Muscat, F.L.; Derstine, K.L.

    1995-01-01

    COREMAP is a Graphical User Interface (GUI) designed to assist users read and check reactor core data from multidimensional neutronic simulation models in color and/or as text in an interactive 2D planar grid of hexagonal subassemblies. COREMAP is a complete GEODST/RUNDESC viewing tool which enables the user to access multi data set files (e.g. planes, moments, energy groups ,... ) and display up to two data sets simultaneously, one as color and the other as text. The user (1) controls color scale characteristics such as type (linear or logarithmic) and range limits, (2) controls the text display based upon conditional statements on data spelling, and value. (3) chooses zoom features such as core map size, number of rings and surrounding subassemblies, and (4) specifies the data selection for supplied popup subwindows which display a selection of data currently off-screen for a selected cell, as a list of data and/or as a graph. COREMAP includes a RUNDESC file editing tool which creates ''proposed'' Run-description files by point and click revisions to subassembly assignments in an existing EBRII Run-description file. COREMAP includes a fully automated printing option which creates high quality PostScript color or greyscale images of the core map independent of the monitor used, e.g. color prints can be generated with a session from a color or monochrome monitor. The automated PostScript output is an alternative to the xgrabsc based printing option. COREMAP includes a plotting option which creates graphs related to a selected cell. The user specifies the X and Y coordinates types (planes, moment, group, flux ,... ) and a parameter, P, when displaying several curves for the specified (X, Y) pair COREMAP supports hexagonal geometry reactor core configurations specified by: the GEODST file and binary Standard Interface Files and the RUNDESC ordering

  9. 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.

  10. Multiplicity in difference geometry

    OpenAIRE

    Tomasic, Ivan

    2011-01-01

    We prove a first principle of preservation of multiplicity in difference geometry, paving the way for the development of a more general intersection theory. In particular, the fibres of a \\sigma-finite morphism between difference curves are all of the same size, when counted with correct multiplicities.

  11. Spacetime and Euclidean geometry

    Science.gov (United States)

    Brill, Dieter; Jacobson, Ted

    2006-04-01

    Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the spacetime Pythagoras theorem.

  12. Physics and geometry

    International Nuclear Information System (INIS)

    Konopleva, N.P.

    2009-01-01

    The basic ideas of description methods of physical fields and elementary particle interactions are discussed. One of such ideas is the conception of space-time geometry. In this connection experimental measurement methods are analyzed. It is shown that measure procedures are the origin of geometrical axioms. The connection between space symmetry properties and the conservation laws is considered

  13. Origami, Geometry and Art

    Science.gov (United States)

    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…

  14. Gravity is Geometry.

    Science.gov (United States)

    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)

  15. Towards a Nano Geometry?

    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...

  16. Diophantine geometry an introduction

    CERN Document Server

    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.

  17. Sliding vane geometry turbines

    Science.gov (United States)

    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.

  18. History of analytic geometry

    CERN Document Server

    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.

  19. Non-euclidean geometry

    CERN Document Server

    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.

  20. Topics in Riemannian geometry

    International Nuclear Information System (INIS)

    Ezin, J.P.

    1988-08-01

    The lectures given at the ''5th Symposium of Mathematics in Abidjan: Differential Geometry and Mechanics'' are presented. They are divided into four chapters: Riemannian metric on a differential manifold, curvature tensor fields on a Riemannian manifold, some classical functionals on Riemannian manifolds and questions. 11 refs

  1. Geometry Euclid and beyond

    CERN Document Server

    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 ...

  2. The Formation and Characterization of GaN Hexagonal Pyramids

    Science.gov (United States)

    Zhang, Shi-Ying; Xiu, Xiang-Qian; Lin, Zeng-Qin; Hua, Xue-Mei; Xie, Zi-Li; Zhang, Rong; Zheng, You-Dou

    2013-05-01

    GaN with hexagonal pyramids is fabricated using the photo-assisted electroless chemical etching method. Defective areas of the GaN substrate are selectively etched in a mixed solution of KOH and K2S2O8 under ultraviolet illumination, producing submicron-sized pyramids. Hexagonal pyramids on the etched GaN with well-defined {101¯1¯} facets and very sharp tips are formed. High-resolution x-ray diffraction shows that etched GaN with pyramids has a higher crystal quality, and micro-Raman spectra reveal a tensile stress relaxation in GaN with pyramids compared with normal GaN. The cathodoluminescence intensity of GaN after etching is significantly increased by three times, which is attributed to the reduction in the internal reflection, high-quality GaN with pyramids and the Bragg effect.

  3. Switching behavior and novel stable states of magnetic hexagonal nanorings

    Energy Technology Data Exchange (ETDEWEB)

    Yasir Rafique, M., E-mail: myasir.rafique@ciitlahore.edu.pk [Department of Physics, COMSATS Institute of Information Technology, Lahore 54000 (Pakistan); Pan, Liqing; Guo, Zhengang [College of Science and Research Institute for New Energy, China Three Gorges University, Yichang 443002 (China)

    2017-06-15

    Micromagnetic simulations for Cobalt hexagonal shape nanorings show onion (O) and vortex state (V) along with new state named “tri-domain state”. The tri-domain state is observed in sufficiently large width of ring. The magnetic reversible mechanism and transition of states are explained with help of vector field display. The transitions from one state to other occur by propagation of domain wall. The vertical parts of hexagonal rings play important role in developing the new “tri-domain” state. The behaviors of switching fields from onion to tri-domain (HO-Tr), tri-domain to vortex state (HTr-V) and vortex to onion state and “states size” are discussed in term of geometrical parameter of ring.

  4. Hexagon OPE resummation and multi-Regge kinematics

    Energy Technology Data Exchange (ETDEWEB)

    Drummond, J.M. [School of Physics & Astronomy, University of Southampton,Highfield, Southampton, SO17 1BJ (United Kingdom); Theory Division, Physics Department, CERN,CH-1211 Geneva 23 (Switzerland); LAPTh, CNRS, Université de Savoie,9 Chemin de Bellevue, F-74941 Annecy-le-Vieux Cedex (France); Papathanasiou, G. [LAPTh, CNRS, Université de Savoie,9 Chemin de Bellevue, F-74941 Annecy-le-Vieux Cedex (France)

    2016-02-29

    We analyse the OPE contribution of gluon bound states in the double scaling limit of the hexagonal Wilson loop in planar N=4 super Yang-Mills theory. We provide a systematic procedure for perturbatively resumming the contributions from single-particle bound states of gluons and expressing the result order by order in terms of two-variable polylogarithms. We also analyse certain contributions from two-particle gluon bound states and find that, after analytic continuation to the 2→4 Mandelstam region and passing to multi-Regge kinematics (MRK), only the single-particle gluon bound states contribute. From this double-scaled version of MRK we are able to reconstruct the full hexagon remainder function in MRK up to five loops by invoking single-valuedness of the results.

  5. Polymer- and salt-induced toroids of hexagonal DNA.

    OpenAIRE

    Ubbink, J; Odijk, T

    1995-01-01

    A model is proposed for polymer- and salt-induced toroidal condensates of DNA, based on a recent theory of the undulation enhancement of the electrostatic interaction in the bulk hexagonal phase of semiflexible polyions. In a continuum approximation, the thermodynamic potential of a monomolecular toroid may be split up in bulk, surface, and curvature contributions. With the help of an approximate analytical minimization procedure, the optimal torus dimensions are calculated as a function of t...

  6. Importance of the hexagonal lipid phase in biological membrane organization

    OpenAIRE

    Jouhet, Juliette

    2013-01-01

    Domains are present in every natural membrane. They are characterized by a distinctive protein and/or lipid composition. Their size is highly variable from the nano- to the micrometer scale. The domains confer specific properties to the membrane leading to original structure and function. The determinants leading to domain organization are therefore important but remain obscure. This review presents how the ability of lipids to organize into hexagonal II or lamellar phases can promote particu...

  7. Electronic structure of nanoparticles of substoichometric hexagonal tungsten oxides

    International Nuclear Information System (INIS)

    Khyzhun, O Y; Solonin, Y M

    2007-01-01

    X-ray photoelectron spectroscopy (XPS), X-ray emission spectroscopy (XES) and X-ray absorption spectroscopy (XAS) methods were used to study the electronic structure of hexagonal h-WO 3 and h-WO 2.8 nanoparticles. For comparison, nanopowder substoichiometric monoclinic tungsten oxides with close content of oxygen atoms, namely m-WO 3 and m-WO 2.77 compounds, were also investigated. For the mentioned oxides, XPS valence-band and corelevel spectra, XES O Kα bands and XAS W L III and O 1s edges were derived. The XPS valence-band spectra and O Kα emission bands in the mentioned hexagonal and monoclinic tungsten oxides were compared on a common energy scale. Both the O Kα bands and XPS valence-band spectra broaden somewhat in the sequences h-WO 3 → h-WO 2.8 and m-WO 3 → m-WO 2.77 , with the half-widths of the spectra being somewhat higher for the hexagonal oxides as compared with those for the monoclinic compounds. The effective positive charge state of tungsten atoms in h-WO 2.8 is very close to that in m-WO 2.77 , but the negative charge states of oxygen atoms are close to each other for all the tungsten oxides under consideration

  8. Hexagonal undersampling for faster MRI near metallic implants.

    Science.gov (United States)

    Sveinsson, Bragi; Worters, Pauline W; Gold, Garry E; Hargreaves, Brian A

    2015-02-01

    Slice encoding for metal artifact correction acquires a three-dimensional image of each excited slice with view-angle tilting to reduce slice and readout direction artifacts respectively, but requires additional imaging time. The purpose of this study was to provide a technique for faster imaging around metallic implants by undersampling k-space. Assuming that areas of slice distortion are localized, hexagonal sampling can reduce imaging time by 50% compared with conventional scans. This work demonstrates this technique by comparisons of fully sampled images with undersampled images, either from simulations from fully acquired data or from data actually undersampled during acquisition, in patients and phantoms. Hexagonal sampling is also shown to be compatible with parallel imaging and partial Fourier acquisitions. Image quality was evaluated using a structural similarity (SSIM) index. Images acquired with hexagonal undersampling had no visible difference in artifact suppression from fully sampled images. The SSIM index indicated high similarity to fully sampled images in all cases. The study demonstrates the ability to reduce scan time by undersampling without compromising image quality. © 2014 Wiley Periodicals, Inc.

  9. Femtosecond laser direct writing of monocrystalline hexagonal silver prisms

    Energy Technology Data Exchange (ETDEWEB)

    Vora, Kevin; Kang, SeungYeon; Moebius, Michael [School of Engineering and Applied Sciences, Harvard University, 9 Oxford Street, Cambridge, Massachusetts 02138 (United States); Mazur, Eric [School of Engineering and Applied Sciences, Harvard University, 9 Oxford Street, Cambridge, Massachusetts 02138 (United States); Department of Physics, Harvard University, 9 Oxford Street, Cambridge, Massachusetts 02138 (United States)

    2014-10-06

    Bottom-up growth methods and top-down patterning techniques are both used to fabricate metal nanostructures, each with a distinct advantage: One creates crystalline structures and the other offers precise positioning. Here, we present a technique that localizes the growth of metal crystals to the focal volume of a laser beam, combining advantages from both approaches. We report the fabrication of silver nanoprisms—hexagonal nanoscale silver crystals—through irradiation with focused femtosecond laser pulses. The growth of these nanoprisms is due to a nonlinear optical interaction between femtosecond laser pulses and a polyvinylpyrrolidone film doped with silver nitrate. The hexagonal nanoprisms have bases hundreds of nanometers in size and the crystal growth occurs over exposure times of less than 1 ms (8 orders of magnitude faster than traditional chemical techniques). Electron backscatter diffraction analysis shows that the hexagonal nanoprisms are monocrystalline. The fabrication method combines advantages from both wet chemistry and femtosecond laser direct-writing to grow silver crystals in targeted locations. The results presented in this letter offer an approach to directly positioning and growing silver crystals on a substrate, which can be used for plasmonic devices.

  10. Femtosecond laser direct writing of monocrystalline hexagonal silver prisms

    International Nuclear Information System (INIS)

    Vora, Kevin; Kang, SeungYeon; Moebius, Michael; Mazur, Eric

    2014-01-01

    Bottom-up growth methods and top-down patterning techniques are both used to fabricate metal nanostructures, each with a distinct advantage: One creates crystalline structures and the other offers precise positioning. Here, we present a technique that localizes the growth of metal crystals to the focal volume of a laser beam, combining advantages from both approaches. We report the fabrication of silver nanoprisms—hexagonal nanoscale silver crystals—through irradiation with focused femtosecond laser pulses. The growth of these nanoprisms is due to a nonlinear optical interaction between femtosecond laser pulses and a polyvinylpyrrolidone film doped with silver nitrate. The hexagonal nanoprisms have bases hundreds of nanometers in size and the crystal growth occurs over exposure times of less than 1 ms (8 orders of magnitude faster than traditional chemical techniques). Electron backscatter diffraction analysis shows that the hexagonal nanoprisms are monocrystalline. The fabrication method combines advantages from both wet chemistry and femtosecond laser direct-writing to grow silver crystals in targeted locations. The results presented in this letter offer an approach to directly positioning and growing silver crystals on a substrate, which can be used for plasmonic devices.

  11. A voxelization approach to navigate through nested geometries

    CERN Document Server

    Harrison, Brent Andrew

    2016-01-01

    High energy physics experiment software typically implements a detailed description of the geometry of the relevant detector. As modern detectors increase in complexity, modelling them becomes more challenging. Typically such models are built as a nested hierarchy of O(10000) volumes reaching a depth of 10 - 20. It is desirable to develop data structures and algorithms which allow fast and efficient navigation though a given detector geometry model. We investigate the feasibility of voxelisation techniques to this end.

  12. Thermal stability of hexagonal OsB2

    Science.gov (United States)

    Xie, Zhilin; Blair, Richard G.; Orlovskaya, Nina; Cullen, David A.; Andrew Payzant, E.

    2014-11-01

    The synthesis of novel hexagonal ReB2-type OsB2 ceramic powder was performed by high energy ball milling of elemental Os and B powders. Two different sources of B powder have been used for this mechanochemical synthesis. One B powder consisted of a mixture of amorphous and crystalline phases and a mixture of 10B and 11B isotopes with a fine particle size, while another B powder was a purely crystalline (rhombohedral) material consisting of enriched 11B isotope with coarse particle size. The same Os powder was used for the synthesis in both cases. It was established that, in the first case, the hexagonal OsB2 phase was the main product of synthesis with a small quantity of Os2B3 phase present after synthesis as an intermediate product. In the second case, where coarse crystalline 11B powder was used as a raw material, only Os2B3 boride was synthesized mechanochemically. The thermal stability of hexagonal OsB2 powder was studied by heating under argon up to 876 °C and cooling in vacuo down to -225 °C. During the heating, the sacrificial reaction 2OsB2+3O2→2Os+2B2O3 took place due to presence of O2/water vapor molecules in the heating chamber, resulting in the oxidation of B atoms and formation of B2O3 and precipitation of Os metal out of the OsB2 lattice. As a result of such phase changes during heating, the lattice parameters of hexagonal OsB2 changed significantly. The shrinkage of the a lattice parameter was recorded in 276-426 °C temperature range upon heating, which was attributed to the removal of B atoms from the OsB2 lattice due to oxidation followed by the precipitation of Os atoms and formation of Os metal. While significant structural changes occurred upon heating due to presence of O2, the hexagonal OsB2 ceramic demonstrated good phase stability upon cooling in vacuo with linear shrinkage of the lattice parameters and no phase changes detected during cooling.

  13. Multivariate calculus and geometry

    CERN Document Server

    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.

  14. Transformational plane geometry

    CERN Document Server

    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...

  15. Multilevel geometry optimization

    Science.gov (United States)

    Rodgers, Jocelyn M.; Fast, Patton L.; Truhlar, Donald G.

    2000-02-01

    Geometry optimization has been carried out for three test molecules using six multilevel electronic structure methods, in particular Gaussian-2, Gaussian-3, multicoefficient G2, multicoefficient G3, and two multicoefficient correlation methods based on correlation-consistent basis sets. In the Gaussian-2 and Gaussian-3 methods, various levels are added and subtracted with unit coefficients, whereas the multicoefficient Gaussian-x methods involve noninteger parameters as coefficients. The multilevel optimizations drop the average error in the geometry (averaged over the 18 cases) by a factor of about two when compared to the single most expensive component of a given multilevel calculation, and in all 18 cases the accuracy of the atomization energy for the three test molecules improves; with an average improvement of 16.7 kcal/mol.

  16. Multilevel geometry optimization

    Energy Technology Data Exchange (ETDEWEB)

    Rodgers, Jocelyn M. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States); Fast, Patton L. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States); Truhlar, Donald G. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States)

    2000-02-15

    Geometry optimization has been carried out for three test molecules using six multilevel electronic structure methods, in particular Gaussian-2, Gaussian-3, multicoefficient G2, multicoefficient G3, and two multicoefficient correlation methods based on correlation-consistent basis sets. In the Gaussian-2 and Gaussian-3 methods, various levels are added and subtracted with unit coefficients, whereas the multicoefficient Gaussian-x methods involve noninteger parameters as coefficients. The multilevel optimizations drop the average error in the geometry (averaged over the 18 cases) by a factor of about two when compared to the single most expensive component of a given multilevel calculation, and in all 18 cases the accuracy of the atomization energy for the three test molecules improves; with an average improvement of 16.7 kcal/mol. (c) 2000 American Institute of Physics.

  17. Geometry and Destiny

    OpenAIRE

    Krauss, Lawrence M.; Turner, Michael S.

    1999-01-01

    The recognition that the cosmological constant may be non-zero forces us to re-evaluate standard notions about the connection between geometry and the fate of our Universe. An open Universe can recollapse, and a closed Universe can expand forever. As a corollary, we point out that there is no set of cosmological observations we can perform that will unambiguously allow us to determine what the ultimate destiny of the Universe will be.

  18. Complex geometries in wood

    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....

  19. Electroweak vacuum geometry

    International Nuclear Information System (INIS)

    Lepora, N.; Kibble, T.

    1999-01-01

    We analyse symmetry breaking in the Weinberg-Salam model paying particular attention to the underlying geometry of the theory. In this context we find two natural metrics upon the vacuum manifold: an isotropic metric associated with the scalar sector, and a squashed metric associated with the gauge sector. Physically, the interplay between these metrics gives rise to many of the non-perturbative features of Weinberg-Salam theory. (author)

  20. W-geometry

    International Nuclear Information System (INIS)

    Hull, C.M.

    1993-01-01

    The geometric structure of theories with gauge fields of spins two and higher should involve a higher spin generalisation of Riemannian geometry. Such geometries are discussed and the case of W ∝ -gravity is analysed in detail. While the gauge group for gravity in d dimensions is the diffeomorphism group of the space-time, the gauge group for a certain W-gravity theory (which is W ∝ -gravity in the case d=2) is the group of symplectic diffeomorphisms of the cotangent bundle of the space-time. Gauge transformations for W-gravity gauge fields are given by requiring the invariance of a generalised line element. Densities exist and can be constructed from the line element (generalising √detg μν ) only if d=1 or d=2, so that only for d=1,2 can actions be constructed. These two cases and the corresponding W-gravity actions are considered in detail. In d=2, the gauge group is effectively only a subgroup of the symplectic diffeomorphisms group. Some of the constraints that arise for d=2 are similar to equations arising in the study of self-dual four-dimensional geometries and can be analysed using twistor methods, allowing contact to be made with other formulations of W-gravity. While the twistor transform for self-dual spaces with one Killing vector reduces to a Legendre transform, that for two Killing vectors gives a generalisation of the Legendre transform. (orig.)

  1. Integral geometry and valuations

    CERN Document Server

    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...

  2. CBM RICH geometry optimization

    Energy Technology Data Exchange (ETDEWEB)

    Mahmoud, Tariq; Hoehne, Claudia [II. Physikalisches Institut, Giessen Univ. (Germany); Collaboration: CBM-Collaboration

    2016-07-01

    The Compressed Baryonic Matter (CBM) experiment at the future FAIR complex will investigate the phase diagram of strongly interacting matter at high baryon density and moderate temperatures in A+A collisions from 2-11 AGeV (SIS100) beam energy. The main electron identification detector in the CBM experiment will be a RICH detector with a CO{sub 2} gaseous-radiator, focusing spherical glass mirrors, and MAPMT photo-detectors being placed on a PMT-plane. The RICH detector is located directly behind the CBM dipole magnet. As the final magnet geometry is now available, some changes in the RICH geometry become necessary. In order to guarantee a magnetic field of 1 mT at maximum in the PMT plane for effective operation of the MAPMTs, two measures have to be taken: The PMT plane is moved outwards of the stray field by tilting the mirrors by 10 degrees and shielding boxes have been designed. In this contribution the results of the geometry optimization procedure are presented.

  3. Fast reactor programme

    International Nuclear Information System (INIS)

    Slagter, W.; Roodbergen, H.A.

    1975-07-01

    A numerical method has been applied to determine three-dimensional temperature distributions in small regions of hexagonal fuel rod assemblies with liquid metal cooling. The temperature calculations, based on the finite element method, centered on heat transport from the fuel rod surface into the adjacent subchannel and on heat transport between adjacent subchannels. The study is restricted to analysis of steady-state heat transfer in fuel rod assemblies of smooth parallel rods for the condition of prescribed heat flux and slug flow. The computed temperature profiles are expressed in terms of Nusselt or Stanton numbers and amplitudes of circumferential cladding temperature variations as a function of axial distances. In simple geometries like the circular duct, the method is applied to calculate the temperature distribution and the axial variation of the Nusselt number for the condition of laminar flow and uniform heat flux. The flow is hydrodynamically developed. Good agreement between numerical and theoretical solutions confirms the validity of the finite element method. The results obtained for fuel rod assemblies are compared with available experimental and theoretical predictions. It is found that the contribution of turbulence to intersubchannel heat transport in sodium equals that due to conduction. The novel feature of the method applied to convective heat transfer problems is the computation of detailed three-dimensional coolant temperature fields in large regions of fuel rod assemblies

  4. Introducing geometry concept based on history of Islamic geometry

    Science.gov (United States)

    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.

  5. Transmission probability method based on triangle meshes for solving unstructured geometry neutron transport problem

    Energy Technology Data Exchange (ETDEWEB)

    Wu Hongchun [Nuclear Engineering Department, Xi' an Jiaotong University, Xi' an 710049, Shaanxi (China)]. E-mail: hongchun@mail.xjtu.edu.cn; Liu Pingping [Nuclear Engineering Department, Xi' an Jiaotong University, Xi' an 710049, Shaanxi (China); Zhou Yongqiang [Nuclear Engineering Department, Xi' an Jiaotong University, Xi' an 710049, Shaanxi (China); Cao Liangzhi [Nuclear Engineering Department, Xi' an Jiaotong University, Xi' an 710049, Shaanxi (China)

    2007-01-15

    In the advanced reactor, the fuel assembly or core with unstructured geometry is frequently used and for calculating its fuel assembly, the transmission probability method (TPM) has been used widely. However, the rectangle or hexagon meshes are mainly used in the TPM codes for the normal core structure. The triangle meshes are most useful for expressing the complicated unstructured geometry. Even though finite element method and Monte Carlo method is very good at solving unstructured geometry problem, they are very time consuming. So we developed the TPM code based on the triangle meshes. The TPM code based on the triangle meshes was applied to the hybrid fuel geometry, and compared with the results of the MCNP code and other codes. The results of comparison were consistent with each other. The TPM with triangle meshes would thus be expected to be able to apply to the two-dimensional arbitrary fuel assembly.

  6. Transmission probability method for solving neutron transport equation in three-dimensional triangular-z geometry

    Energy Technology Data Exchange (ETDEWEB)

    Liu Guoming [Department of Nuclear Engineering, Xi' an Jiaotong University, Xi' an, Shaanxi 710049 (China)], E-mail: gmliusy@gmail.com; Wu Hongchun; Cao Liangzhi [Department of Nuclear Engineering, Xi' an Jiaotong University, Xi' an, Shaanxi 710049 (China)

    2008-09-15

    This paper presents a transmission probability method (TPM) to solve the neutron transport equation in three-dimensional triangular-z geometry. The source within the mesh is assumed to be spatially uniform and isotropic. At the mesh surface, the constant and the simplified P{sub 1} approximation are invoked for the anisotropic angular flux distribution. Based on this model, a code TPMTDT is encoded. It was verified by three 3D Takeda benchmark problems, in which the first two problems are in XYZ geometry and the last one is in hexagonal-z geometry, and an unstructured geometry problem. The results of the present method agree well with those of Monte-Carlo calculation method and Spherical Harmonics (P{sub N}) method.

  7. 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

  8. Fractal Geometry and Stochastics V

    CERN Document Server

    Falconer, Kenneth; Zähle, Martina

    2015-01-01

    This book brings together leading contributions from the fifth conference on Fractal Geometry and Stochastics held in Tabarz, Germany, in March 2014. The book is divided into five sections covering different facets of this fast developing area: geometric measure theory, self-similar fractals and recurrent structures, analysis and algebra on fractals, multifractal theory, and random constructions. There are state-of-the-art surveys as well as papers highlighting more specific recent advances. The authors are world-experts who present their topics comprehensibly and attractively. The book provides an accessible gateway to the subject for newcomers as well as a reference for recent developments for specialists. Authors include: Krzysztof Barański, Julien Barral, Kenneth Falconer, De-Jun Feng, Peter J. Grabner, Rostislav Grigorchuk, Michael Hinz, Stéphane Jaffard, Maarit Järvenpää, Antti Käenmäki, Marc Kesseböhmer, Michel Lapidus, Klaus Mecke, Mark Pollicott,  Michał Rams, Pablo Shmerkin, and András Te...

  9. Two lectures on D-geometry and noncommutative geometry

    International Nuclear Information System (INIS)

    Douglas, M.R.

    1999-01-01

    This is a write-up of lectures given at the 1998 Spring School at the Abdus Salam ICTP. We give a conceptual introduction to D-geometry, the study of geometry as seen by D-branes in string theory, and to noncommutative geometry as it has appeared in D-brane and Matrix theory physics. (author)

  10. Conference on Complex Geometry and Mirror Symmetry

    CERN Document Server

    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

  11. Geometry of Quantum States

    International Nuclear Information System (INIS)

    Hook, D W

    2008-01-01

    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 framework, and

  12. 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

  13. Kinematic geometry of gearing

    CERN Document Server

    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

  14. From geometry to topology

    CERN Document Server

    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.

  15. Torsional heterotic geometries

    International Nuclear Information System (INIS)

    Becker, Katrin; Sethi, Savdeep

    2009-01-01

    We construct new examples of torsional heterotic backgrounds using duality with orientifold flux compactifications. We explain how duality provides a perturbative solution to the type I/heterotic string Bianchi identity. The choice of connection used in the Bianchi identity plays an important role in the construction. We propose the existence of a much larger landscape of compact torsional geometries using string duality. Finally, we present some quantum exact metrics that correspond to NS5-branes placed on an elliptic space. These metrics describe how torus isometries are broken by NS flux.

  16. Geometrie verstehen: statisch - kinematisch

    Science.gov (United States)

    Kroll, Ekkehard

    Dem Allgemeinen steht begrifflich das Besondere gegenüber. In diesem Sinne sind allgemeine Überlegungen zum Verstehen von Mathematik zu ergänzen durch Untersuchungen hinsichtlich des Verstehens der einzelnen mathematischen Disziplinen, insbesondere der Geometrie. Hier haben viele Schülerinnen und Schüler Probleme. Diese rühren hauptsächlich daher, dass eine fertige geometrische Konstruktion in ihrer statischen Präsentation auf Papier nicht mehr die einzelnen Konstruktionsschritte erkennen lässt; zum Nachvollzug müssen sie daher ergänzend in einer Konstruktionsbeschreibung festgehalten werden.

  17. Elementary algebraic geometry

    CERN Document Server

    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

  18. Local analytic geometry

    CERN Document Server

    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

  19. Geometry of conics

    CERN Document Server

    Akopyan, A V

    2007-01-01

    The book is devoted to the properties of conics (plane curves of second degree) that can be formulated and proved using only elementary geometry. Starting with the well-known optical properties of conics, the authors move to less trivial results, both classical and contemporary. In particular, the chapter on projective properties of conics contains a detailed analysis of the polar correspondence, pencils of conics, and the Poncelet theorem. In the chapter on metric properties of conics the authors discuss, in particular, inscribed conics, normals to conics, and the Poncelet theorem for confoca

  20. Geometry and trigonometry

    CERN Document Server

    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

  1. Geometry I essentials

    CERN Document Server

    REA, The Editors of

    2012-01-01

    REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Geometry I includes methods of proof, points, lines, planes, angles, congruent angles and line segments, triangles, parallelism, quadrilaterals, geometric inequalities, and geometric

  2. Delamination of hexagonal boron nitride in a stirred media mill

    International Nuclear Information System (INIS)

    Damm, C.; Körner, J.; Peukert, W.

    2013-01-01

    A scalable process for delamination of hexagonal boron nitride in an aqueous solution of the non-ionic surfactant TWEEN85 using a stirred media mill is presented. The size of the ZrO 2 beads used as grinding media governs the dimensions of the ground boron nitride particles as atomic force microscopic investigations (AFM) reveal: the mean flakes thickness decreases from 3.5 to 1.5 nm and the ratio between mean flake area and mean flake thickness increases from 2,200 to 5,800 nm if the grinding media size is reduced from 0.8 to 0.1 mm. This result shows that a high number of stress events in combination with low stress energy (small grinding media) facilitate delamination of the layered material whereas at high stress energies in combination with a low number of stress events (large grinding media) breakage of the layers dominates over delamination. The results of particle height analyses by AFM show that few-layer structures have been formed by stirred media milling. This result is in agreement with the layer thickness dependence of the delamination energy for hexagonal boron nitride. The concentration of nanoparticles remaining dispersed after centrifugation of the ground suspension increases with grinding time and with decreasing grinding media size. After 5 h of grinding using 0.1 mm ZrO 2 grinding media the yield of nanoparticle formation is about 5 wt%. The nanoparticles exhibit the typical Raman peak for hexagonal boron nitride at 1,366 cm −1 showing that the in-plane order in the milled platelets is remained.

  3. Hexagon functions and the three-loop remainder function

    Energy Technology Data Exchange (ETDEWEB)

    Dixon, Lance J.; Drummond, James M.; von Hippel, Matt; Pennington, Jeffrey

    2013-12-01

    We present the three-loop remainder function, which describes the scattering of six gluons in the maximally-helicity-violating configuration in planar NN = 4 super-Yang-Mills theory, as a function of the three dual conformal cross ratios. The result can be expressed in terms of multiple Goncharov polylogarithms. We also employ a more restricted class of hexagon functions which have the correct branch cuts and certain other restrictions on their symbols. We classify all the hexagon functions through transcendental weight five, using the coproduct for their Hopf algebra iteratively, which amounts to a set of first-order differential equations. The three-loop remainder function is a particular weight-six hexagon function, whose symbol was determined previously. The differential equations can be integrated numerically for generic values of the cross ratios, or analytically in certain kinematic limits, including the near-collinear and multi-Regge limits. These limits allow us to impose constraints from the operator product expansion and multi-Regge factorization directly at the function level, and thereby to fix uniquely a set of Riemann ζ valued constants that could not be fixed at the level of the symbol. The near-collinear limits agree precisely with recent predictions by Basso, Sever and Vieira based on integrability. The multi-Regge limits agree with the factorization formula of Fadin and Lipatov, and determine three constants entering the impact factor at this order. We plot the three-loop remainder function for various slices of the Euclidean region of positive cross ratios, and compare it to the two-loop one. For large ranges of the cross ratios, the ratio of the three-loop to the two-loop remainder function is relatively constant, and close to -7.

  4. Graded geometry and Poisson reduction

    OpenAIRE

    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

  5. A fast nodal neutron diffusion method for cartesian geometry

    International Nuclear Information System (INIS)

    Makai, M.; Maeder, C.

    1983-01-01

    A numerical method based on an analytical solution to the three-dimensional two-group diffusion equation has been derived assuming that the flux is a sum of the functions of one variable. In each mesh the incoming currents are used as boundary conditions. The final equations for the average flux and the outgoing currents are of the response matrix type. The method is presented in a form that can be extended to the general multigroup case. In the SEXI computer program developed on the basis of this method, the response matrix elements are recalculated in each outer iteration to minimize the data transfer between disk storage and central memory. The efficiency of the method is demonstrated for a light water reactor (LWR) benchmark problem. The SEXI program has been incorporated into the LWR simulator SILWER code as a possible option

  6. Intermediate heat exchanger design study of 25 MW straight-tube hexagonal modular type

    International Nuclear Information System (INIS)

    Okamoto, Masaharu; Tanaka, Toshiyuki

    1983-09-01

    The helium-to-helium Intermediate Heat Exchanger(IHX), straight-tube hexagonal modular type was designed at General Atomic Company(GA), which heat duty is 421 MW. For this type IHX, at the selection of basic design, emphasis is placed on cost reduction and size reduction. Then small diameter tube size(11.1 mm), with wall thickness of 1.2 mm is applied to this IHX, necessary for the compact surface geometry. The other side, the helical-tube type IHX was designed at JAERI, which heat duty is 25 MW. This paper discusses the referance design of 25 MW scale IHX, with GA type application. The basic feature of this type IHX is as follows. (1) Thermal stress is reduced, as a result of using small diameter and thin wall thickness tube. (2) The possible improvements can make for higher heat flux, because of short length tube, compare with helical or U-tube type. (3) The simple tube support can use compare with helical or U-tube type. The conclusion reached is that GA type IHX is about one forth compactness and one forth weight compare with helical tube IHX. (author)

  7. Numerical simulation of a 3-D flow within a storage area hexagonal modular pavement systems

    International Nuclear Information System (INIS)

    Rashid, M A; Abustan, I; Hamzah, M O

    2013-01-01

    This numerical study has been performed to predict the flow patterns and characteristics within a storage area Hexagonal Modular Pavement Systems. Throughout the design and planning period for future construction are increasingly integrating computational fluid dynamics (CFD) into the process. A commercially known software, FLOW-3D, is applied to numerically solve the Navier-stokes equations for solution domains which are separated into three regions with overlapping boundaries to efficiently accommodate the grid resolutions, namely the honeycomb shaped modular, gravel and combined honeycomb shaped modular with gravel fill. The filtration of the fluid within the interstices of a permeable pavement is evaluated by integrating the Reynolds Averaged Navier-Stokes equations (RANS) inside the voids rather than making use of the widespread porous media approach. In conclusion, the results from numerical simulation are generally well agreed with the existing data and flow information such as flow patterns at increased flow, discharge rate and pressure is obtained to be used for engineering design purpose. Overall, the potential for FLOW-3D to model various geometries and configurations appears great. It should be noted that CFD should not be considered a complete replacement for physical modelling; however, it can definitely be used as a supplementary tool throughout the pavement design process.

  8. Multidirection Piezoelectricity in Mono- and Multilayered Hexagonal α-In2Se3

    KAUST Repository

    Xue, Fei

    2018-04-25

    Piezoelectric materials have been widely used for sensors, actuators, electronics, and energy conversion. Two-dimensional (2D) ultrathin semiconductors, such as monolayer h-BN and MoS2 with their atom-level geometry, are currently emerging as new and attractive members of the piezoelectric family. However, their piezoelectric polarization is commonly limited to the in-plane direction of odd-number ultrathin layers, largely restricting their application in integrated nanoelectromechanical systems. Recently, theoretical calculations have predicted the existence of out-of-plane and in-plane piezoelectricity in monolayer α-In2Se3. Here, we experimentally report the coexistence of out-of-plane and in-plane piezoelectricity in monolayer to bulk α-In2Se3, attributed to their noncentrosymmetry originating from the hexagonal stacking. Specifically, the corresponding d33 piezoelectric coefficient of α-In2Se3 increases from 0.34 pm/V (monolayer) to 5.6 pm/V (bulk) without any odd-even effect. In addition, we also demonstrate a type of α-In2Se3-based flexible piezoelectric nanogenerator as an energy-harvesting cell and electronic skin. The out-of-plane and in-plane piezoelectricity in α-In2Se3 flakes offers an opportunity to enable both directional and nondirectional piezoelectric devices to be applicable for self-powered systems and adaptive and strain-tunable electronics/optoelectronics.

  9. Haze and cloud structure of Saturn's North Pole and Hexagon Wave from Cassini/ISS imaging

    Science.gov (United States)

    Sanz-Requena, J. F.; Pérez-Hoyos, S.; Sánchez-Lavega, A.; Antuñano, A.; Irwin, Patrick G. J.

    2018-05-01

    In this paper we present a study of the vertical haze and cloud structure in the upper two bars of Saturn's Northern Polar atmosphere using the Imaging Science Subsystem (ISS) instrument onboard the Cassini spacecraft. We focus on the characterization of latitudes from 53° to 90° N. The observations were taken during June 2013 with five different filters (VIO, BL1, MT2, CB2 and MT3) covering spectral range from the 420 nm to 890 nm (in a deep methane absorption band). Absolute reflectivity measurements of seven selected regions at all wavelengths and several illumination and observation geometries are compared with the values produced by a radiative transfer model. The changes in reflectivity at these latitudes are mostly attributed to changes in the tropospheric haze. This includes the haze base height (from 600 ± 200 mbar at the lowest latitudes to 1000 ± 300 mbar in the pole), its particle number density (from 20 ± 2 particles/cm3 to 2 ± 0.5 particles/cm3 at the haze base) and its scale height (from 18 ± 0.1 km to 50 ± 0.1 km). We also report variability in the retrieved particle size distribution and refractive indices. We find that the Hexagonal Wave dichotomizes the studied stratospheric and tropospheric hazes between the outer, equatorward regions and the inner, Polar Regions. This suggests that the wave or the jet isolates the particle distribution at least at tropospheric levels.

  10. Research on the Method of Urban Waterlogging Flood Routing Based on Hexagonal Grid

    Directory of Open Access Journals (Sweden)

    LAI Guangling

    2016-12-01

    Full Text Available An evolution of the urban waterlogging flood routing was studied in this paper based on the method of hexagonal grid modeling. Using the method of discrete grid, established an urban geometry model on account of the regular multi-scale discrete grid. With the fusion of 3D topographic survey data and 2D building vector data, formed a regular network model of surface. This model took multi special block into account, such as urban terrain and buildings. On this basis, a method of reverse flow deduction was proposed, which was an inverse computation from the state of flood to the evolution process. That is, based on the water depth of flood, made use of the connectivity with the outfall to calculate the range of water logging, and then implemented the urban waterlogging flood simulation deduction. The test indicated that, this method can implement the evolution of urban waterlogging scenario deduction effectively. And the correlational research could provide scientific basis for urban disaster prevention and emergency decision-making.

  11. Topological dynamics of vortex-line networks in hexagonal manganites

    Science.gov (United States)

    Xue, Fei; Wang, Nan; Wang, Xueyun; Ji, Yanzhou; Cheong, Sang-Wook; Chen, Long-Qing

    2018-01-01

    The two-dimensional X Y model is the first well-studied system with topological point defects. On the other hand, although topological line defects are common in three-dimensional systems, the evolution mechanism of line defects is not fully understood. The six domains in hexagonal manganites converge to vortex lines in three dimensions. Using phase-field simulations, we predicted that during the domain coarsening process, the vortex-line network undergoes three types of basic topological changes, i.e., vortex-line loop shrinking, coalescence, and splitting. It is shown that the vortex-antivortex annihilation controls the scaling dynamics.

  12. Inter-layer potential for hexagonal boron nitride

    Energy Technology Data Exchange (ETDEWEB)

    Leven, Itai; Hod, Oded, E-mail: odedhod@tau.ac.il [Department of Chemical Physics, School of Chemistry, The Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv 69978 (Israel); Azuri, Ido; Kronik, Leeor [Department of Materials and Interfaces, Weizmann Institute of Science, Rehovoth 76100 (Israel)

    2014-03-14

    A new interlayer force-field for layered hexagonal boron nitride (h-BN) based structures is presented. The force-field contains three terms representing the interlayer attraction due to dispersive interactions, repulsion due to anisotropic overlaps of electron clouds, and monopolar electrostatic interactions. With appropriate parameterization, the potential is able to simultaneously capture well the binding and lateral sliding energies of planar h-BN based dimer systems as well as the interlayer telescoping and rotation of double walled boron-nitride nanotubes of different crystallographic orientations. The new potential thus allows for the accurate and efficient modeling and simulation of large-scale h-BN based layered structures.

  13. The hexagon gauge anomaly in type 1 superstring theory

    International Nuclear Information System (INIS)

    Green, M.B.; Schwarz, J.H.

    1985-01-01

    Hexagon diagrams with external on-mass-shell Yang-Mills gauge particles are investigated in type I superstring theory. Both the annulus and the Moebuis-strip diagrams are shown to give anomalies, implying that spurious longitudinal modes cannot be consistently decoupled. However, the anomalies cancel when the two diagrams are added together if the gauge group is chosen to be SO(32). In carrying out the analysis, two different regulators are considered, but the same conclusions emerge in both cases. We point out where various terms in the low-energy effective action originate in superstring diagrams. (orig.)

  14. Electronic structure of superlattices of graphene and hexagonal boron nitride

    KAUST Repository

    Kaloni, Thaneshwor P.

    2011-11-14

    We study the electronic structure of superlattices consisting of graphene and hexagonal boron nitride slabs, using ab initio density functional theory. We find that the system favors a short C–B bond length at the interface between the two component materials. A sizeable band gap at the Dirac point is opened for superlattices with single graphene layers but not for superlattices with graphene bilayers. The system is promising for applications in electronic devices such as field effect transistors and metal-oxide semiconductors.

  15. Inter-layer potential for hexagonal boron nitride

    Science.gov (United States)

    Leven, Itai; Azuri, Ido; Kronik, Leeor; Hod, Oded

    2014-03-01

    A new interlayer force-field for layered hexagonal boron nitride (h-BN) based structures is presented. The force-field contains three terms representing the interlayer attraction due to dispersive interactions, repulsion due to anisotropic overlaps of electron clouds, and monopolar electrostatic interactions. With appropriate parameterization, the potential is able to simultaneously capture well the binding and lateral sliding energies of planar h-BN based dimer systems as well as the interlayer telescoping and rotation of double walled boron-nitride nanotubes of different crystallographic orientations. The new potential thus allows for the accurate and efficient modeling and simulation of large-scale h-BN based layered structures.

  16. Chromatic Dispersion Compensation Using Photonic Crystal Fibers with Hexagonal Distribution

    Directory of Open Access Journals (Sweden)

    Erick E. Reyes-Vera

    2013-11-01

    Full Text Available In this paper we show various configurations of photonic crystal fiber with hexagonal holes distribution for compensation of chromatic dispersion in optical communications links. The vectorial finite element method with scattering boundary condition was used for the analysis of the fibers. From these results it was estimated variation of the dispersion and the dispersion slope with respect to change in the diameter of the holes in the microstructure. With the above was possible to obtain values of dispersion in the C and L bands of telecommunications close to -850 ps / nm * km, with confinement losses 10-3 dB / km

  17. Hexagon POPE: effective particles and tree level resummation

    Energy Technology Data Exchange (ETDEWEB)

    Córdova, Lucía [Perimeter Institute for Theoretical Physics,Waterloo, Ontario N2L 2Y5 (Canada); Department of Physics and Astronomy & Guelph-Waterloo Physics Institute,University of Waterloo,Waterloo, Ontario N2L 3G1 (Canada)

    2017-01-12

    We present the resummation of the full Pentagon Operator Product Expansion series of the hexagon Wilson loop in planar N=4 SYM at tree level. We do so by considering the one effective particle states formed by a fundamental flux tube excitation and an arbitrary number of the so called small fermions which are then integrated out. We derive the one effective particle measures at finite coupling. By evaluating these measures at tree level and summing over all one effective particle states we reproduce the full 6 point tree level amplitude.

  18. Inter-layer potential for hexagonal boron nitride

    International Nuclear Information System (INIS)

    Leven, Itai; Hod, Oded; Azuri, Ido; Kronik, Leeor

    2014-01-01

    A new interlayer force-field for layered hexagonal boron nitride (h-BN) based structures is presented. The force-field contains three terms representing the interlayer attraction due to dispersive interactions, repulsion due to anisotropic overlaps of electron clouds, and monopolar electrostatic interactions. With appropriate parameterization, the potential is able to simultaneously capture well the binding and lateral sliding energies of planar h-BN based dimer systems as well as the interlayer telescoping and rotation of double walled boron-nitride nanotubes of different crystallographic orientations. The new potential thus allows for the accurate and efficient modeling and simulation of large-scale h-BN based layered structures

  19. Electronic structure of superlattices of graphene and hexagonal boron nitride

    KAUST Repository

    Kaloni, Thaneshwor P.; Cheng, Yingchun; Schwingenschlö gl, Udo

    2011-01-01

    We study the electronic structure of superlattices consisting of graphene and hexagonal boron nitride slabs, using ab initio density functional theory. We find that the system favors a short C–B bond length at the interface between the two component materials. A sizeable band gap at the Dirac point is opened for superlattices with single graphene layers but not for superlattices with graphene bilayers. The system is promising for applications in electronic devices such as field effect transistors and metal-oxide semiconductors.

  20. Hydraulic characteristics of a fast reactor fuel subassembly: An experimental investigation

    International Nuclear Information System (INIS)

    Padmakumar, G.; Velusamy, K.; Prasad, B.V.S.S.; Rajan, K.K.

    2017-01-01

    Highlights: • Fuel subassembly bundle geometry is studied for its hydraulic behaviour. • The results are also compared with data available in literature. • All flow regimes viz. laminar, transition and turbulent is covered for the study. • Pressure drop across different regions of subassembly was also determined. • The effect of external blockage is also studied and reported. - Abstract: Fuel subassemblies of a fast reactor consist of fuel pin bundle with helically wound spacer wires, arranged in a triangular pitch within a hexagonal wrapper. The fuel pins are located within the subassembly. Further the subassembly comprises of a diffuser where the cross section changes from cylindrical to hexagonal, mixing plenum before the exit of pin bundle and a specially designed blockage adapter. Accurate assessment of the pressure drop in the fuel subassembly is essential to ensure adequate core cooling and design of sodium pump. Experimental determination of pressure drop characteristics in the subassembly by simulating the hydraulic condition in the subassemblies of the reactor core is considered essential as a better choice as correlations reported in the literature cannot be directly used for all the complex regions present in the subassembly. This is due to the fact that flows in the interconnecting sections are highly under developed. Further, the flow regime in a fuel subassembly varies from laminar (during shutdown heat removal under natural convection) to completely turbulent under full power condition. To understand the hydraulic characteristics of the 500 MWe Proto type Fast Breeder Reactor (PFBR) fuel subassembly, an experimental facility has been commissioned. Experiments on full scale subassembly with dummy fuel pins have been performed using water as simulant. Experiments have been conducted covering a wide range of Reynolds number encompassing laminar, transition and turbulent regimes. In the rod bundle, no abrupt changes in friction factor were

  1. Band gap effects of hexagonal boron nitride using oxygen plasma

    Energy Technology Data Exchange (ETDEWEB)

    Sevak Singh, Ram; Leong Chow, Wai [School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798 (Singapore); Yingjie Tay, Roland [School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798 (Singapore); Temasek Laboratories-NTU, 50 Nanyang Avenue, Singapore 639798 (Singapore); Hon Tsang, Siu [Temasek Laboratories-NTU, 50 Nanyang Avenue, Singapore 639798 (Singapore); Mallick, Govind [Temasek Laboratories-NTU, 50 Nanyang Avenue, Singapore 639798 (Singapore); Weapons and Materials Research Directorate, U.S. Army Research Laboratory, Aberdeen Proving Ground, Maryland 21005 (United States); Tong Teo, Edwin Hang, E-mail: htteo@ntu.edu.sg [School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798 (Singapore); School of Materials Science and Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798 (Singapore)

    2014-04-21

    Tuning of band gap of hexagonal boron nitride (h-BN) has been a challenging problem due to its inherent chemical stability and inertness. In this work, we report the changes in band gaps in a few layers of chemical vapor deposition processed as-grown h-BN using a simple oxygen plasma treatment. Optical absorption spectra show a trend of band gap narrowing monotonically from 6 eV of pristine h-BN to 4.31 eV when exposed to oxygen plasma for 12 s. The narrowing of band gap causes the reduction in electrical resistance by ∼100 fold. The x-ray photoelectron spectroscopy results of plasma treated hexagonal boron nitride surface show the predominant doping of oxygen for the nitrogen vacancy. Energy sub-band formations inside the band gap of h-BN, due to the incorporation of oxygen dopants, cause a red shift in absorption edge corresponding to the band gap narrowing.

  2. Band gap effects of hexagonal boron nitride using oxygen plasma

    International Nuclear Information System (INIS)

    Sevak Singh, Ram; Leong Chow, Wai; Yingjie Tay, Roland; Hon Tsang, Siu; Mallick, Govind; Tong Teo, Edwin Hang

    2014-01-01

    Tuning of band gap of hexagonal boron nitride (h-BN) has been a challenging problem due to its inherent chemical stability and inertness. In this work, we report the changes in band gaps in a few layers of chemical vapor deposition processed as-grown h-BN using a simple oxygen plasma treatment. Optical absorption spectra show a trend of band gap narrowing monotonically from 6 eV of pristine h-BN to 4.31 eV when exposed to oxygen plasma for 12 s. The narrowing of band gap causes the reduction in electrical resistance by ∼100 fold. The x-ray photoelectron spectroscopy results of plasma treated hexagonal boron nitride surface show the predominant doping of oxygen for the nitrogen vacancy. Energy sub-band formations inside the band gap of h-BN, due to the incorporation of oxygen dopants, cause a red shift in absorption edge corresponding to the band gap narrowing

  3. Tolerance measurements on internal- and external-hexagon implants.

    Science.gov (United States)

    Braian, Michael; De Bruyn, Hugo; Fransson, Håkan; Christersson, Cecilia; Wennerberg, Ann

    2014-01-01

    To measure the horizontal machining tolerances of the interface between internal- and external-hexagon implants and analogs with corresponding components after delivery from the manufacturer. These values may be a valuable tool for evaluating increasing misfit caused by fabrication, processing, and wear. Seven implants and seven analogs with external- and internal-hexagon connections (Biomet 3i) with corresponding prefabricated gold cylinders and gold screws, prefabricated cylindric plastic cylinders, and laboratory screws were studied. One set of components from the external and internal groups was measured manually and digitally. Measurements from the test subjects were compared with identical measurements from the virtual model to obtain threshold values. The virtual model was then used to obtain optimally oriented cuts. The horizontal machining tolerances for castable plastic abutments on external implants were 12 ± 89 μm, and for internal implants they were 86 ± 47 μm. Tolerance measurements on prefabricated gold abutments for external implants were 44 ± 9 μm, and for internal implants they were 58 ± 28 μm. The groups with metallic components showed the smallest tolerance at external group and internal group. The prefabricated plastic cylinder groups ranged from external and internal connection.

  4. Defect sensitive etching of hexagonal boron nitride single crystals

    Science.gov (United States)

    Edgar, J. H.; Liu, S.; Hoffman, T.; Zhang, Yichao; Twigg, M. E.; Bassim, Nabil D.; Liang, Shenglong; Khan, Neelam

    2017-12-01

    Defect sensitive etching (DSE) was developed to estimate the density of non-basal plane dislocations in hexagonal boron nitride (hBN) single crystals. The crystals employed in this study were precipitated by slowly cooling (2-4 °C/h) a nickel-chromium flux saturated with hBN from 1500 °C under 1 bar of flowing nitrogen. On the (0001) planes, hexagonal-shaped etch pits were formed by etching the crystals in a eutectic mixture of NaOH and KOH between 450 °C and 525 °C for 1-2 min. There were three types of pits: pointed bottom, flat bottom, and mixed shape pits. Cross-sectional transmission electron microscopy revealed that the pointed bottom etch pits examined were associated with threading dislocations. All of these dislocations had an a-type burgers vector (i.e., they were edge dislocations, since the line direction is perpendicular to the [ 2 11 ¯ 0 ]-type direction). The pit widths were much wider than the pit depths as measured by atomic force microscopy, indicating the lateral etch rate was much faster than the vertical etch rate. From an Arrhenius plot of the log of the etch rate versus the inverse temperature, the activation energy was approximately 60 kJ/mol. This work demonstrates that DSE is an effective method for locating threading dislocations in hBN and estimating their densities.

  5. FAINT LUMINESCENT RING OVER SATURN’S POLAR HEXAGON

    Energy Technology Data Exchange (ETDEWEB)

    Adriani, Alberto; D’Aversa, Emiliano; Oliva, Fabrizio; Filacchione, Gianrico [Institute of Space Astrophysics and Planetology of INAF, Via Fosso del Cavaliere 100, I-00133 Rome (Italy); Moriconi, Maria Luisa, E-mail: alberto.adriani@iaps.inaf.it [Institute of Atmospheric Sciences and Climate of CNR, Via Fosso del Cavaliere 100, I-00133 Rome (Italy)

    2015-07-20

    Springtime insolation is presently advancing across Saturn's north polar region. Early solar radiation scattered through the gaseous giant's atmosphere gives a unique opportunity to sound the atmospheric structure at its upper troposphere/lower stratosphere at high latitudes. Here, we report the detection of a tenuous bright structure in Saturn's northern polar cap corresponding to the hexagon equatorward boundary, observed by Cassini Visual and Infrared Mapping Spectrometer on 2013 June. The structure is spectrally characterized by an anomalously enhanced intensity in the 3610–3730 nm wavelength range and near 2500 nm, pertaining to relatively low opacity windows between strong methane absorption bands. Our first results suggest that a strong forward scattering by tropospheric clouds, higher in respect to the surrounding cloud deck, can be responsible for the enhanced intensity of the feature. This can be consistent with the atmospheric dynamics associated with the jet stream embedded in the polar hexagon. Further investigations at higher spectral resolution are needed to better assess the vertical distribution and microphysics of the clouds in this interesting region.

  6. Vortex solitons at the interface separating square and hexagonal lattices

    Energy Technology Data Exchange (ETDEWEB)

    Jović Savić, Dragana, E-mail: jovic@ipb.ac.rs; Piper, Aleksandra; Žikić, Radomir; Timotijević, Dejan

    2015-06-19

    Vortex solitons at the interface separating two different photonic lattices – square and hexagonal – are demonstrated numerically. We consider the conditions for the existence of discrete vortex states at such interfaces and develop a concise picture of different scenarios of the vortex solutions behavior. Various vortices with different size and topological charges are considered, as well as various lattice interfaces. A novel type of discrete vortex surface solitons in a form of five-lobe solution is observed. Besides stable three-lobe and six-lobe discrete surface modes propagating for long distances, we observe various oscillatory vortex surface solitons, as well as dynamical instabilities of different kinds of solutions and study their angular momentum. Dynamical instabilities occur for higher values of the propagation constant, or at higher beam powers. - Highlights: • We demonstrate vortex solitons at the square–hexagonal photonic lattice interface. • A novel type of five-lobe surface vortex solitons is observed. • Different phase structures of surface solutions are studied. • Orbital angular momentum transfer of such solutions is investigated.

  7. Saturnian north polar region: a triangle inside the hexagon?

    Science.gov (United States)

    Kochemasov, Gennady G.

    2010-05-01

    The famous and "mysterious" stable hexagon structure around the North Pole of Saturn was earlier interpreted as projections of faces of a structural tetrahedron [1]. This "hidden" simplest Plato's polyhedron is a result of an interference of four fundamental (wave 1) warping waves having in any rotating celestial body four directions: orthogonal and diagonal. Origin of the warping waves in any celestial body is due to their movements in elliptical keplerian orbits with periodically changing accelerations. The structural tetrahedron is an intrinsic geometric feature marking the celestial bodies ubiquitous tectonic dichotomy as in a tetrahedron always there is an opposition of a face (expansion) and a vertex (contraction). In the saturnian case the tetrahedron shows a face at the north and a vertex at the south. Morphologically this is manifested by the hexagon and opposing it in the south a vertex. Blue and pink hues of the northern and southern hemispheres also underline the tectonic dichotomy. These geometric expressions are enforced by a subtle dark equilateral triangle appearing in the image PIA11682 also around the north pole and inside the hexagon (the triangle side is about 15000 km long). One angle of the triangle is clearly visible, another one just shows itself and the third one is barely distinguished. The sides of the triangle are not strait lines but slightly broken amidst lines what makes the triangle appear a bit hexagonal (spherical) and the angle is a bit bigger than 60 degrees of a classical equilateral triangle (~70 degrees). The central part of the triangle is not imaged (a black hole in the PIA11682). This image also confirms that the wide northern polar region is also densely "peppered" with bright cloudy more or less isometric spots on average 400 to 800 km across as in other latitudinal belts of Saturn [2, 3, 4]. Earlier they were observed in IR wavelengths, now they show themselves in visible wavelengths. Their origin and size were

  8. Thermal stability of hexagonal OsB{sub 2}

    Energy Technology Data Exchange (ETDEWEB)

    Xie, Zhilin [Department of Mechanical and Aerospace Engineering, University of Central Florida, Orlando, FL 32816 (United States); Blair, Richard G. [Department of Mechanical and Aerospace Engineering, University of Central Florida, Orlando, FL 32816 (United States); Department of Physics, University of Central Florida, Orlando, FL 32816 (United States); Orlovskaya, Nina, E-mail: Nina.Orlovskaya@ucf.edu [Department of Mechanical and Aerospace Engineering, University of Central Florida, Orlando, FL 32816 (United States); Cullen, David A. [Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831 (United States); Andrew Payzant, E. [Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN 37831 (United States)

    2014-11-15

    The synthesis of novel hexagonal ReB{sub 2}-type OsB{sub 2} ceramic powder was performed by high energy ball milling of elemental Os and B powders. Two different sources of B powder have been used for this mechanochemical synthesis. One B powder consisted of a mixture of amorphous and crystalline phases and a mixture of {sup 10}B and {sup 11}B isotopes with a fine particle size, while another B powder was a purely crystalline (rhombohedral) material consisting of enriched {sup 11}B isotope with coarse particle size. The same Os powder was used for the synthesis in both cases. It was established that, in the first case, the hexagonal OsB{sub 2} phase was the main product of synthesis with a small quantity of Os{sub 2}B{sub 3} phase present after synthesis as an intermediate product. In the second case, where coarse crystalline {sup 11}B powder was used as a raw material, only Os{sub 2}B{sub 3} boride was synthesized mechanochemically. The thermal stability of hexagonal OsB{sub 2} powder was studied by heating under argon up to 876 °C and cooling in vacuo down to −225 °C. During the heating, the sacrificial reaction 2OsB{sub 2}+3O{sub 2}→2Os+2B{sub 2}O{sub 3} took place due to presence of O{sub 2}/water vapor molecules in the heating chamber, resulting in the oxidation of B atoms and formation of B{sub 2}O{sub 3} and precipitation of Os metal out of the OsB{sub 2} lattice. As a result of such phase changes during heating, the lattice parameters of hexagonal OsB{sub 2} changed significantly. The shrinkage of the a lattice parameter was recorded in 276–426 °C temperature range upon heating, which was attributed to the removal of B atoms from the OsB{sub 2} lattice due to oxidation followed by the precipitation of Os atoms and formation of Os metal. While significant structural changes occurred upon heating due to presence of O{sub 2}, the hexagonal OsB{sub 2} ceramic demonstrated good phase stability upon cooling in vacuo with linear shrinkage of the lattice

  9. Thermal stability of hexagonal OsB2

    International Nuclear Information System (INIS)

    Xie, Zhilin; Blair, Richard G.; Orlovskaya, Nina; Cullen, David A.; Andrew Payzant, E.

    2014-01-01

    The synthesis of novel hexagonal ReB 2 -type OsB 2 ceramic powder was performed by high energy ball milling of elemental Os and B powders. Two different sources of B powder have been used for this mechanochemical synthesis. One B powder consisted of a mixture of amorphous and crystalline phases and a mixture of 10 B and 11 B isotopes with a fine particle size, while another B powder was a purely crystalline (rhombohedral) material consisting of enriched 11 B isotope with coarse particle size. The same Os powder was used for the synthesis in both cases. It was established that, in the first case, the hexagonal OsB 2 phase was the main product of synthesis with a small quantity of Os 2 B 3 phase present after synthesis as an intermediate product. In the second case, where coarse crystalline 11 B powder was used as a raw material, only Os 2 B 3 boride was synthesized mechanochemically. The thermal stability of hexagonal OsB 2 powder was studied by heating under argon up to 876 °C and cooling in vacuo down to −225 °C. During the heating, the sacrificial reaction 2OsB 2 +3O 2 →2Os+2B 2 O 3 took place due to presence of O 2 /water vapor molecules in the heating chamber, resulting in the oxidation of B atoms and formation of B 2 O 3 and precipitation of Os metal out of the OsB 2 lattice. As a result of such phase changes during heating, the lattice parameters of hexagonal OsB 2 changed significantly. The shrinkage of the a lattice parameter was recorded in 276–426 °C temperature range upon heating, which was attributed to the removal of B atoms from the OsB 2 lattice due to oxidation followed by the precipitation of Os atoms and formation of Os metal. While significant structural changes occurred upon heating due to presence of O 2 , the hexagonal OsB 2 ceramic demonstrated good phase stability upon cooling in vacuo with linear shrinkage of the lattice parameters and no phase changes detected during cooling. - Graphical abstract: The in situ high temperature XRD

  10. Anisotropic Hexagonal Boron Nitride Nanomaterials - Synthesis and Applications

    Energy Technology Data Exchange (ETDEWEB)

    Han,W.Q.

    2008-08-01

    Boron nitride (BN) is a synthetic binary compound located between III and V group elements in the Periodic Table. However, its properties, in terms of polymorphism and mechanical characteristics, are rather close to those of carbon compared with other III-V compounds, such as gallium nitride. BN crystallizes into a layered or a tetrahedrally linked structure, like those of graphite and diamond, respectively, depending on the conditions of its preparation, especially the pressure applied. Such correspondence between BN and carbon readily can be understood from their isoelectronic structures [1, 2]. On the other hand, in contrast to graphite, layered BN is transparent and is an insulator. This material has attracted great interest because, similar to carbon, it exists in various polymorphic forms exhibiting very different properties; however, these forms do not correspond strictly to those of carbon. Crystallographically, BN is classified into four polymorphic forms: Hexagonal BN (h-BN) (Figure 1(b)); rhombohedral BN (r-BN); cubic BN (c-BN); and wurtzite BN (w-BN). BN does not occur in nature. In 1842, Balmain [3] obtained BN as a reaction product between molten boric oxide and potassium cyanide under atmospheric pressure. Thereafter, many methods for its synthesis were reported. h-BN and r-BN are formed under ambient pressure. c-BN is synthesized from h-BN under high pressure at high temperature while w-BN is prepared from h-BN under high pressure at room temperature [1]. Each BN layer consists of stacks of hexagonal plate-like units of boron and nitrogen atoms linked by SP{sup 2} hybridized orbits and held together mainly by Van der Waals force (Fig 1(b)). The hexagonal polymorph has two-layered repeating units: AA'AA'... that differ from those in graphite: ABAB... (Figure 1(a)). Within the layers of h-BN there is coincidence between the same phases of the hexagons, although the boron atoms and nitrogen atoms are alternatively located along the c

  11. Real algebraic geometry

    CERN Document Server

    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.

  12. Critique of information geometry

    International Nuclear Information System (INIS)

    Skilling, John

    2014-01-01

    As applied to probability, information geometry fails because probability distributions do not form a metric space. Probability theory rests on a compelling foundation of elementary symmetries, which also support information (aka minus entropy, Kullback-Leibler) H(p;q) as the unique measure of divergence from source probability distribution q to destination p. Because the only compatible connective H is from≠to asymmetric, H(p;q)≠H(q;p), there can be no compatible geometrical distance (which would necessarily be from=to symmetric). Hence there is no distance relationship compatible with the structure of probability theory. Metrics g and densities sqrt(det(g)) interpreted as prior probabilities follow from the definition of distance, and must fail likewise. Various metrics and corresponding priors have been proposed, Fisher's being the most popular, but all must behave unacceptably. This is illustrated with simple counter-examples

  13. Geometry from Gauge Theory

    International Nuclear Information System (INIS)

    Correa, Diego H.; Silva, Guillermo A.

    2008-01-01

    We discuss how geometrical and topological aspects of certain (1/2)-BPS type IIB geometries are captured by their dual operators in N = 4 Super Yang-Mills theory. The type IIB solutions are characterized by arbitrary droplet pictures in a plane and we consider, in particular, axially symmetric droplets. The 1-loop anomalous dimension of the dual gauge theory operators probed with single traces is described by some bosonic lattice Hamiltonians. These Hamiltonians are shown to encode the topology of the droplets. In appropriate BMN limits, the Hamiltonians spectrum reproduces the spectrum of near-BPS string excitations propagating along each of the individual edges of the droplet. We also study semiclassical regimes for the Hamiltonians. For droplets having disconnected constituents, the Hamiltonian admits different complimentary semiclassical descriptions, each one replicating the semiclassical description for closed strings extending in each of the constituents

  14. Emergent geometry of membranes

    Energy Technology Data Exchange (ETDEWEB)

    Badyn, Mathias Hudoba de; Karczmarek, Joanna L.; Sabella-Garnier, Philippe; Yeh, Ken Huai-Che [Department of Physics and Astronomy, University of British Columbia,6224 Agricultural Road, Vancouver (Canada)

    2015-11-13

    In work http://dx.doi.org/10.1103/PhysRevD.86.086001, a surface embedded in flat ℝ{sup 3} is associated to any three hermitian matrices. We study this emergent surface when the matrices are large, by constructing coherent states corresponding to points in the emergent geometry. We find the original matrices determine not only shape of the emergent surface, but also a unique Poisson structure. We prove that commutators of matrix operators correspond to Poisson brackets. Through our construction, we can realize arbitrary noncommutative membranes: for example, we examine a round sphere with a non-spherically symmetric Poisson structure. We also give a natural construction for a noncommutative torus embedded in ℝ{sup 3}. Finally, we make remarks about area and find matrix equations for minimal area surfaces.

  15. Super low threshold plasmonic WGM lasing from an individual ZnO hexagonal microrod on an Au substrate for plasmon lasers.

    Science.gov (United States)

    Dong, H M; Yang, Y H; Yang, G W

    2015-03-05

    We demonstrate an individual ZnO hexagonal microrod on the surface of an Au substrate which can become new sources for manufacturing miniature ZnO plasmon lasers by surface plasmon polariton coupling to whispering-gallery modes (WGMs). We also demonstrate that the rough surface of Au substrates can acquire a more satisfied enhancement of ZnO emission if the surface geometry of Au substrates is appropriate. Furthermore, we achieve high Q factor and super low threshold plasmonic WGM lasing from an individual ZnO hexagonal microrod on the surface of the Au substrate, in which Q factor can reach 5790 and threshold is 0.45 KW/cm(2) which is the lowest value reported to date for ZnO nanostructures lasing, at least 10 times smaller than that of ZnO at the nanometer. Electron transfer mechanisms are proposed to understand the physical origin of quenching and enhancement of ZnO emission on the surface of Au substrates. These investigations show that this novel coupling mode holds a great potential of ZnO hexagonal micro- and nanorods for data storage, bio-sensing, optical communications as well as all-optic integrated circuits.

  16. Geometry through history Euclidean, hyperbolic, and projective geometries

    CERN Document Server

    Dillon, Meighan I

    2018-01-01

    Presented as an engaging discourse, this textbook invites readers to delve into the historical origins and uses of geometry. The narrative traces the influence of Euclid’s system of geometry, as developed in his classic text The Elements, through the Arabic period, the modern era in the West, and up to twentieth century mathematics. Axioms and proof methods used by mathematicians from those periods are explored alongside the problems in Euclidean geometry that lead to their work. Students cultivate skills applicable to much of modern mathematics through sections that integrate concepts like projective and hyperbolic geometry with representative proof-based exercises. For its sophisticated account of ancient to modern geometries, this text assumes only a year of college mathematics as it builds towards its conclusion with algebraic curves and quaternions. Euclid’s work has affected geometry for thousands of years, so this text has something to offer to anyone who wants to broaden their appreciation for the...

  17. On organizing principles of discrete differential geometry. Geometry of spheres

    International Nuclear Information System (INIS)

    Bobenko, Alexander I; Suris, Yury B

    2007-01-01

    Discrete differential geometry aims to develop discrete equivalents of the geometric notions and methods of classical differential geometry. This survey contains a discussion of the following two fundamental discretization principles: the transformation group principle (smooth geometric objects and their discretizations are invariant with respect to the same transformation group) and the consistency principle (discretizations of smooth parametrized geometries can be extended to multidimensional consistent nets). The main concrete geometric problem treated here is discretization of curvature-line parametrized surfaces in Lie geometry. Systematic use of the discretization principles leads to a discretization of curvature-line parametrization which unifies circular and conical nets.

  18. Higher geometry an introduction to advanced methods in analytic geometry

    CERN Document Server

    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

  19. A Multi-Dimensional Heat Transfer Model of a Tie-Tube and Hexagonal Fuel Element for Nuclear Thermal Propulsion

    Science.gov (United States)

    Gomez, C. F.; Mireles, O. R.; Stewart, E.

    2016-01-01

    The Space Capable Cryogenic Thermal Engine (SCCTE) effort considers a nuclear thermal rocket design based around a Low-Enriched Uranium (LEU) design fission reactor. The reactor core is comprised of bundled hexagonal fuel elements that directly heat hydrogen for expansion in a thrust chamber and hexagonal tie-tubes that house zirconium hydride moderator mass for the purpose of thermalizing fast neutrons resulting from fission events. Created 3D steady state Hex fuel rod model with 1D flow channels. Hand Calculation were used to set up initial conditions for fluid flow. The Hex Fuel rod uses 1D flow paths to model the channels using empirical correlations for heat transfer in a pipe. Created a 2-D axisymmetric transient to steady state model using the CFD turbulent flow and Heat Transfer module in COMSOL. This model was developed to find and understand the hydrogen flow that might effect the thermal gradients axially and at the end of the tie tube where the flow turns and enters an annulus. The Hex fuel rod and Tie tube models were made based on requirements given to us by CSNR and the SCCTE team. The models helped simplify and understand the physics and assumptions. Using pipe correlations reduced the complexity of the 3-D fuel rod model and is numerically more stable and computationally more time-efficient compared to the CFD approach. The 2-D axisymmetric tie tube model can be used as a reference "Virtual test model" for comparing and improving 3-D Models.

  20. Strong 3D and 1D magnetism in hexagonal Fe-chalcogenides FeS and FeSe vs. weak magnetism in hexagonal FeTe

    Energy Technology Data Exchange (ETDEWEB)

    Parker, David S. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

    2017-06-13

    We present a comparative theoretical study of the hexagonal forms of the Fe-chalcogenides FeS, FeSe and FeTe with their better known tetragonal forms. While the tetragonal forms exhibit only an incipient antiferromagnetism and experimentally show superconductivity when doped, the hexagonal forms of FeS and FeSe display a robust magnetism. We show that this strong magnetism arises from a van Hove singularity associated with the direct Fe-Fe c-axis chains in the generally more three-dimensional NiAs structure. We also find that hexagonal FeTe is much less magnetic than the other two hexagonal materials, so that unconventional magnetically-mediated superconductivity is possible, although a large Tc value is unlikely.

  1. Strong 3D and 1D magnetism in hexagonal Fe-chalcogenides FeS and FeSe vs. weak magnetism in hexagonal FeTe.

    Science.gov (United States)

    Parker, David S

    2017-06-13

    We present a comparative theoretical study of the hexagonal forms of the Fe-chalcogenides FeS, FeSe and FeTe with their better known tetragonal forms. While the tetragonal forms exhibit only an incipient antiferromagnetism and experimentally show superconductivity when doped, the hexagonal forms of FeS and FeSe display a robust magnetism. We show that this strong magnetism arises from a van Hove singularity associated with the direct Fe-Fe c-axis chains in the generally more three-dimensional NiAs structure. We also find that hexagonal FeTe is much less magnetic than the other two hexagonal materials, so that unconventional magnetically-mediated superconductivity is possible, although a large T c value is unlikely.

  2. An introduction to incidence geometry

    CERN Document Server

    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...

  3. Casimir forces and geometry

    International Nuclear Information System (INIS)

    Buescher, R.

    2005-01-01

    Casimir interactions are interactions induced by quantum vacuum fluctuations and thermal fluctuations of the electromagnetic field. Using a path integral quantization for the gauge field, an effective Gaussian action will be derived which is the starting point to compute Casimir forces between macroscopic objects analytically and numerically. No assumptions about the independence of the material and shape dependent contributions to the interaction are made. We study the limit of flat surfaces in further detail and obtain a concise derivation of Lifshitz' theory of molecular forces. For the case of ideally conducting boundaries, the Gaussian action will be calculated explicitly. Both limiting cases are also discussed within the framework of a scalar field quantization approach, which is applicable for translationally invariant geometries. We develop a non-perturbative approach to calculate the Casimir interaction from the Gaussian action for periodically deformed and ideally conducting objects numerically. The obtained results reveal two different scaling regimes for the Casimir force as a function of the distance between the objects, their deformation wavelength and -amplitude. The results confirm that the interaction is non-additive, especially in the presence of strong geometric deformations. Furthermore, the numerical approach is extended to calculate lateral Casimir forces. The results are consistent with the results of the proximity-force approximation for large deformation wavelengths. A qualitatively different behaviour between the normal and lateral force is revealed. We also establish a relation between the boundary induced change of the of the density of states for the scalar Helmholtz equation and the Casimir interaction using the path integral method. For statically deformed boundaries, this relation can be expressed as a novel trace formula, which is formally similar to the so-called Krein-Friedel-Lloyd formula. While the latter formula describes the

  4. Planetary Image Geometry Library

    Science.gov (United States)

    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

  5. Initiation to global Finslerian geometry

    CERN Document Server

    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

  6. High-Entropy Alloys in Hexagonal Close-Packed Structure

    Science.gov (United States)

    Gao, M. C.; Zhang, B.; Guo, S. M.; Qiao, J. W.; Hawk, J. A.

    2016-07-01

    The microstructures and properties of high-entropy alloys (HEAs) based on the face-centered cubic and body-centered cubic structures have been studied extensively in the literature, but reports on HEAs in the hexagonal close-packed (HCP) structure are very limited. Using an efficient strategy in combining phase diagram inspection, CALPHAD modeling, and ab initio molecular dynamics simulations, a variety of new compositions are suggested that may hold great potentials in forming single-phase HCP HEAs that comprise rare earth elements and transition metals, respectively. Experimental verification was carried out on CoFeReRu and CoReRuV using X-ray diffraction, scanning electron microscopy, and energy dispersion spectroscopy.

  7. A Computational Study of the Growth of Hexagonal Ice

    Science.gov (United States)

    Fulford, Maxwell; Salvalaglio, Matteo; Parrinello, Michele; Molteni, Carla

    Hexagonal ice (Ih) has two distinct crystallographic surfaces; a basal and prism surface. At low vapour pressures, Ih forms thin plates and elongated prisms, depending on the temperature. The macroscopic shape depends on the relative rate of growth of the basal and prism surfaces. The aim of our research is to estimate the relative rate of growth of the two surfaces for a range of temperatures and ultimately predict the shape of Ih, using computer simulations. Our simulations show the well-know phenomenon that the surface of ice lowers its interfacial free energy by forming a stable quasi-liquid layer (QLL). The QLL mediates crystal growth and has a thickness which varies with temperature and crystallographic surface. We use a combination of Molecular Dynamics and Metadynamics to study how the interfacial structure at the ice/quasi-liquid and quasi-liquid/vapour interfaces influence the adsorption potential, surface transport properties and growth shape..

  8. Critical heat flux in tubes and tight hexagonal rod lattices

    International Nuclear Information System (INIS)

    Erbacher, F.J.; Cheng Xu; Zeggel, W.

    1994-01-01

    The critical heat flux (CHF) in small-diameter tubes and in tight hexagonal 7-rod and 37-rod bundles was investigated in the KRISTA test facility, using Freon 12 as the working fluid. The measurements in tubes showed that the influence of the tube diameter on CHF cannot be described as suggested by earlier publications with sufficient accuracy. CHF in bundles is lower than in tubes under comparable conditions. The influence of spacers (grid spacers, wire wraps) on CHF was found to be governed by local steam qualities. A comparison of the test results with some CHF prediction methods showed that the look-up table method reproduces the test results in circular tubes most accurately. Combined with CHF look-up tables, subchannel analysis and Ahmad's fluid-to-fluid scaling law, Freon experiments have proven to be a suitable tool for CHF prediction in water-cooled rod bundles. (orig.) [de

  9. Chemical synthesis of hexagonal indium nitride nanocrystallines at low temperature

    Science.gov (United States)

    Wang, Liangbiao; Shen, Qianli; Zhao, Dejian; Lu, Juanjuan; Liu, Weiqiao; Zhang, Junhao; Bao, Keyan; Zhou, Quanfa

    2017-08-01

    In this study, hexagonal indium nitride nanocystallines with high crystallinity have been prepared by the reaction of InCl3·4H2O, sulfur and NaNH2 in an autoclave at 160 °C. The crystal structures and morphologies of the obtained InN sample are characterized by X-ray diffraction and scanning electron microscope. As InCl3·4H2O is substituted by In(NO3)3·4.5H2O, InN nanocrystallines could also be obtained by using the similar method. The photoluminescence spectrum shows that the InN emits a broad peak positioned at 2.3 eV.

  10. Hydroxyapatite: Vibrational spectra and monoclinic to hexagonal phase transition

    Science.gov (United States)

    Slepko, Alexander; Demkov, Alexander A.

    2015-02-01

    Fundamental studies of biomaterials are necessary to deepen our understanding of their degradation and to develop cure for related illnesses. Biomineral hydroxyapatite Ca10(PO4)6(OH)2 is the main mineral constituent of mammal bone, and its synthetic analogues are used in biomedical applications. The mineral can be found in either hexagonal or monoclinic form. The transformation between these two phases is poorly understood, but knowing its mechanism may be critical to reversing processes in bone related to aging. Using density functional theory, we investigate the mechanisms of the phase transformation and estimate the transition temperature to be 680 K in fair agreement with the experimental temperature of 470 K. We also report the heat capacity of hydroxyapatite and a peculiarity in its phonon dispersion that might allow for non-destructive measurements of the crystal composition with applications in preventive medical screening for bone mineral loss.

  11. Fractional Dynamics of Genetic Algorithms Using Hexagonal Space Tessellation

    Directory of Open Access Journals (Sweden)

    J. A. Tenreiro Machado

    2013-01-01

    Full Text Available The paper formulates a genetic algorithm that evolves two types of objects in a plane. The fitness function promotes a relationship between the objects that is optimal when some kind of interface between them occurs. Furthermore, the algorithm adopts an hexagonal tessellation of the two-dimensional space for promoting an efficient method of the neighbour modelling. The genetic algorithm produces special patterns with resemblances to those revealed in percolation phenomena or in the symbiosis found in lichens. Besides the analysis of the spacial layout, a modelling of the time evolution is performed by adopting a distance measure and the modelling in the Fourier domain in the perspective of fractional calculus. The results reveal a consistent, and easy to interpret, set of model parameters for distinct operating conditions.

  12. Magnetic tunnel junctions with monolayer hexagonal boron nitride tunnel barriers

    Energy Technology Data Exchange (ETDEWEB)

    Piquemal-Banci, M.; Galceran, R.; Bouzehouane, K.; Anane, A.; Petroff, F.; Fert, A.; Dlubak, B.; Seneor, P. [Unité Mixte de Physique, CNRS, Thales, Univ. Paris-Sud, Université Paris-Saclay, Palaiseau 91767 (France); Caneva, S.; Martin, M.-B.; Weatherup, R. S.; Kidambi, P. R.; Robertson, J.; Hofmann, S. [Department of Engineering, University of Cambridge, Cambridge CB21PZ (United Kingdom); Xavier, S. [Thales Research and Technology, 1 avenue Augustin Fresnel, Palaiseau 91767 (France)

    2016-03-07

    We report on the integration of atomically thin 2D insulating hexagonal boron nitride (h-BN) tunnel barriers into Co/h-BN/Fe magnetic tunnel junctions (MTJs). The h-BN monolayer is directly grown by chemical vapor deposition on Fe. The Conductive Tip Atomic Force Microscopy (CT-AFM) measurements reveal the homogeneity of the tunnel behavior of our h-BN layers. As expected for tunneling, the resistance depends exponentially on the number of h-BN layers. The h-BN monolayer properties are also characterized through integration into complete MTJ devices. A Tunnel Magnetoresistance of up to 6% is observed for a MTJ based on a single atomically thin h-BN layer.

  13. Effective cleaning of hexagonal boron nitride for graphene devices.

    Science.gov (United States)

    Garcia, Andrei G F; Neumann, Michael; Amet, François; Williams, James R; Watanabe, Kenji; Taniguchi, Takashi; Goldhaber-Gordon, David

    2012-09-12

    Hexagonal boron nitride (h-BN) films have attracted considerable interest as substrates for graphene. ( Dean, C. R. et al. Nat. Nanotechnol. 2010 , 5 , 722 - 6 ; Wang, H. et al. Electron Device Lett. 2011 , 32 , 1209 - 1211 ; Sanchez-Yamagishi, J. et al. Phys. Rev. Lett. 2012 , 108 , 1 - 5 .) We study the presence of organic contaminants introduced by standard lithography and substrate transfer processing on h-BN films exfoliated on silicon oxide substrates. Exposure to photoresist processing adds a large broad luminescence peak to the Raman spectrum of the h-BN flake. This signal persists through typical furnace annealing recipes (Ar/H(2)). A recipe that successfully removes organic contaminants and results in clean h-BN flakes involves treatment in Ar/O(2) at 500 °C.

  14. Superior thermal conductivity in suspended bilayer hexagonal boron nitride

    Science.gov (United States)

    Wang, Chengru; Guo, Jie; Dong, Lan; Aiyiti, Adili; Xu, Xiangfan; Li, Baowen

    2016-01-01

    We reported the basal-plane thermal conductivity in exfoliated bilayer hexagonal boron nitride h-BN that was measured using suspended prepatterned microstructures. The h-BN sample suitable for thermal measurements was fabricated by dry-transfer method, whose sample quality, due to less polymer residues on surfaces, is believed to be superior to that of PMMA-mediated samples. The measured room temperature thermal conductivity is around 484 Wm−1K−1(+141 Wm−1K−1/ −24 Wm−1K−1) which exceeds that in bulk h-BN, providing experimental observation of the thickness-dependent thermal conductivity in suspended few-layer h-BN. PMID:27142571

  15. A modified hexagonal photonic crystal fiber for terahertz applications

    Science.gov (United States)

    Islam, Md. Saiful; Sultana, Jakeya; Faisal, Mohammad; Islam, Mohammad Rakibul; Dinovitser, Alex; Ng, Brian W.-H.; Abbott, Derek

    2018-05-01

    We present a Zeonex based highly birefringent and dispersion flattened porous core photonic crystal fiber (PC-PCF) for polarization preserving applications in the terahertz region. In order to facilitate birefringence, an array of elliptical shaped air holes surrounded by porous cladding is introduced. The porous cladding comprises circular air-holes in a modified hexagonal arrangement. The transmission characteristics of the proposed PCF are investigated using a full-vector finite element method with perfectly matched layer (PML) absorbing boundary conditions. Simulation results show a high birefringence of 0.086 and an ultra-flattened dispersion variation of ± 0.03 ps/THz/cm at optimal design parameters. Besides, a number of other important wave-guiding properties including frequency dependence of the effective material loss (EML), confinement loss, and effective area are also investigated to assess the fiber's effectiveness as a terahertz waveguide.

  16. Importance of the hexagonal lipid phase in biological membrane organisation

    Directory of Open Access Journals (Sweden)

    Juliette eJouhet

    2013-12-01

    Full Text Available Abstract:Domains are present in every natural membrane. They are characterised by a distinctive protein and/or lipid composition. Their size is highly variable from the nano- to the micrometer scale. The domains confer specific properties to the membrane leading to original structure and function. The determinants leading to domain organisation are therefore important but remain obscure. This review presents how the ability of lipids to organize into hexagonal II or lamellar phases can promote particular local structures within membranes. Since biological membranes are composed of a mixture of lipids, each with distinctive biophysical properties, lateral and transversal sorting of lipids can promote creation of domains inside the membrane through local modulation of the lipid phase. Lipid biophysical properties have been characterized for long based on in vitro analyses using non-natural lipid molecules; their re-examinations using natural lipids might open interesting perspectives on membrane architecture occurring in vivo in various cellular and physiological contexts.

  17. Spin-density wave state in simple hexagonal graphite

    Science.gov (United States)

    Mosoyan, K. S.; Rozhkov, A. V.; Sboychakov, A. O.; Rakhmanov, A. L.

    2018-02-01

    Simple hexagonal graphite, also known as AA graphite, is a metastable configuration of graphite. Using tight-binding approximation, it is easy to show that AA graphite is a metal with well-defined Fermi surface. The Fermi surface consists of two sheets, each shaped like a rugby ball. One sheet corresponds to electron states, another corresponds to hole states. The Fermi surface demonstrates good nesting: a suitable translation in the reciprocal space superposes one sheet onto another. In the presence of the electron-electron repulsion, a nested Fermi surface is unstable with respect to spin-density-wave ordering. This instability is studied using the mean-field theory at zero temperature, and the spin-density-wave order parameter is evaluated.

  18. Importance of the hexagonal lipid phase in biological membrane organization.

    Science.gov (United States)

    Jouhet, Juliette

    2013-01-01

    Domains are present in every natural membrane. They are characterized by a distinctive protein and/or lipid composition. Their size is highly variable from the nano- to the micrometer scale. The domains confer specific properties to the membrane leading to original structure and function. The determinants leading to domain organization are therefore important but remain obscure. This review presents how the ability of lipids to organize into hexagonal II or lamellar phases can promote particular local structures within membranes. Since biological membranes are composed of a mixture of lipids, each with distinctive biophysical properties, lateral and transversal sorting of lipids can promote creation of domains inside the membrane through local modulation of the lipid phase. Lipid biophysical properties have been characterized for long based on in vitro analyses using non-natural lipid molecules; their re-examinations using natural lipids might open interesting perspectives on membrane architecture occurring in vivo in various cellular and physiological contexts.

  19. Finite dipolar hexagonal columns on piled layers of triangular lattice

    International Nuclear Information System (INIS)

    Matsushita, Katsuyoshi; Sugano, Ryoko; Kuroda, Akiyoshi; Tomita, Yusuke; Takayama, Hajime

    2007-01-01

    We have investigated, by the Monte Carlo simulation, spin systems which represent moments of arrayed magnetic nanoparticles interacting with each other only by the dipole-dipole interaction. In the present paper we aim the understanding of finite size effects on the magnetic nanoparticles arrayed in hexagonal columns cut out from the close-packing structures or from those with uniaxial compression. In columns with the genuine close-packing structures, we observe a single vortex state which is also observed previously in finite two-dimensional systems. On the other hand in the system with the inter-layer distance set 1/2 times of the close-packing one, we found ground states which depend on the number of layers. The dependence is induced by a finite size effect and is related to a orientation transition in the corresponding bulk system

  20. Modeling photonic crystal waveguides with noncircular geometry using green function method

    International Nuclear Information System (INIS)

    Uvarovaa, I.; Tsyganok, B.; Bashkatov, Y.; Khomenko, V.

    2012-01-01

    Currently in the field of photonics is an acute problem fast and accurate simulation photonic crystal waveguides with complex geometry. This paper describes an improved method of Green's functions for non-circular geometries. Based on comparison of selected efficient numerical method for finding the eigenvalues for the Green's function method for non-circular holes chosen effective method for our purposes. Simulation is realized in Maple environment. The simulation results confirmed experimentally. Key words: photonic crystal, waveguide, modeling, Green function, complex geometry

  1. Ostrich eggs geometry

    Directory of Open Access Journals (Sweden)

    Šárka Nedomová

    2013-01-01

    Full Text Available Precise quantification of the profile of egg can provide a powerful tool for the analysis of egg shape for various biological problems. A new approach to the geometry of a Ostrich’s egg profile is presented here using an analysing the egg’s digital photo by edge detection techniques. The obtained points on the eggshell counter are fitted by the Fourier series. The obtained equations describing an egg profile have been used to calculate radii of curvature. The radii of the curvature at the important point of the egg profile (sharp end, blunt end and maximum thickness are independent on the egg shape index. The exact values of the egg surface and the egg volume have been obtained. These quantities are also independent on the egg shape index. These quantities can be successively estimated on the basis of simplified equations which are expressed in terms of the egg length, L¸ and its width, B. The surface area of the eggshells also exhibits good correlation with the egg long circumference length. Some limitations of the most used procedures have been also shown.

  2. Nonperturbative quantum geometries

    International Nuclear Information System (INIS)

    Jacobson, T.; California Univ., Santa Barbara; Smolin, L.; California Univ., Santa Barbara

    1988-01-01

    Using the self-dual representation of quantum general relativity, based on Ashtekar's new phase space variables, we present an infinite dimensional family of quantum states of the gravitational field which are exactly annihilated by the hamiltonian constraint. These states are constructed from Wilson loops for Ashtekar's connection (which is the spatial part of the left handed spin connection). We propose a new regularization procedure which allows us to evaluate the action of the hamiltonian constraint on these states. Infinite linear combinations of these states which are formally annihilated by the diffeomorphism constraints as well are also described. These are explicit examples of physical states of the gravitational field - and for the compact case are exact zero eigenstates of the hamiltonian of quantum general relativity. Several different approaches to constructing diffeomorphism invariant states in the self dual representation are also described. The physical interpretation of the states described here is discussed. However, as we do not yet know the physical inner product, any interpretation is at this stage speculative. Nevertheless, this work suggests that quantum geometry at Planck scales might be much simpler when explored in terms of the parallel transport of left-handed spinors than when explored in terms of the three metric. (orig.)

  3. Matrix Information Geometry

    CERN Document Server

    Bhatia, Rajendra

    2013-01-01

    This book is an outcome of the Indo-French Workshop on Matrix Information Geometries (MIG): Applications in Sensor and Cognitive Systems Engineering, which was held in Ecole Polytechnique and Thales Research and Technology Center, Palaiseau, France, in February 23-25, 2011. The workshop was generously funded by the Indo-French Centre for the Promotion of Advanced Research (IFCPAR).  During the event, 22 renowned invited french or indian speakers gave lectures on their areas of expertise within the field of matrix analysis or processing. From these talks, a total of 17 original contribution or state-of-the-art chapters have been assembled in this volume. All articles were thoroughly peer-reviewed and improved, according to the suggestions of the international referees. The 17 contributions presented  are organized in three parts: (1) State-of-the-art surveys & original matrix theory work, (2) Advanced matrix theory for radar processing, and (3) Matrix-based signal processing applications.  

  4. Fabrication of nickel hydroxide electrodes with open-ended hexagonal nanotube arrays for high capacitance supercapacitors.

    Science.gov (United States)

    Wu, Mao-Sung; Huang, Kuo-Chih

    2011-11-28

    A nickel hydroxide electrode with open-ended hexagonal nanotube arrays, prepared by hydrolysis of nickel chloride in the presence of hexagonal ZnO nanorods, shows a very high capacitance of 1328 F g(-1) at a discharge current density of 1 A g(-1) due to the significantly improved ion transport.

  5. Micromolding in inverted polymer opals (MIPO): synthesis of hexagonal mesoporous silica opals

    Energy Technology Data Exchange (ETDEWEB)

    Yang Sanming; Coombs, N.; Ozin, G.A. [Toronto Univ., Ont. (Canada). Materials Chemistry Research Group

    2000-12-15

    Regular arrays of hexagonal mesoporous silica spheres are crucial for a number of applications, but until now control of the diameter, dispersity, and packing of the spheres has not proved possible. These authors report a new method-micromolding in inverted polymer opals-that allows the synthesis of such hexagonal mesoporous silica opals for the first time. (orig.)

  6. Photon-counting hexagonal pixel array CdTe detector: Spatial resolution characteristics for image-guided interventional applications.

    Science.gov (United States)

    Vedantham, Srinivasan; Shrestha, Suman; Karellas, Andrew; Shi, Linxi; Gounis, Matthew J; Bellazzini, Ronaldo; Spandre, Gloria; Brez, Alessandro; Minuti, Massimo

    2016-05-01

    High-resolution, photon-counting, energy-resolved detector with fast-framing capability can facilitate simultaneous acquisition of precontrast and postcontrast images for subtraction angiography without pixel registration artifacts and can facilitate high-resolution real-time imaging during image-guided interventions. Hence, this study was conducted to determine the spatial resolution characteristics of a hexagonal pixel array photon-counting cadmium telluride (CdTe) detector. A 650 μm thick CdTe Schottky photon-counting detector capable of concurrently acquiring up to two energy-windowed images was operated in a single energy-window mode to include photons of 10 keV or higher. The detector had hexagonal pixels with apothem of 30 μm resulting in pixel pitch of 60 and 51.96 μm along the two orthogonal directions. The detector was characterized at IEC-RQA5 spectral conditions. Linear response of the detector was determined over the air kerma rate relevant to image-guided interventional procedures ranging from 1.3 nGy/frame to 91.4 μGy/frame. Presampled modulation transfer was determined using a tungsten edge test device. The edge-spread function and the finely sampled line spread function accounted for hexagonal sampling, from which the presampled modulation transfer function (MTF) was determined. Since detectors with hexagonal pixels require resampling to square pixels for distortion-free display, the optimal square pixel size was determined by minimizing the root-mean-squared-error of the aperture functions for the square and hexagonal pixels up to the Nyquist limit. At Nyquist frequencies of 8.33 and 9.62 cycles/mm along the apothem and orthogonal to the apothem directions, the modulation factors were 0.397 and 0.228, respectively. For the corresponding axis, the limiting resolution defined as 10% MTF occurred at 13.3 and 12 cycles/mm, respectively. Evaluation of the aperture functions yielded an optimal square pixel size of 54 μm. After resampling to 54

  7. Photon-counting hexagonal pixel array CdTe detector: Spatial resolution characteristics for image-guided interventional applications

    Energy Technology Data Exchange (ETDEWEB)

    Vedantham, Srinivasan; Shrestha, Suman; Karellas, Andrew, E-mail: andrew.karellas@umassmed.edu; Shi, Linxi; Gounis, Matthew J. [Department of Radiology, University of Massachusetts Medical School, Worcester, Massachusetts 01655 (United States); Bellazzini, Ronaldo; Spandre, Gloria; Brez, Alessandro; Minuti, Massimo [Istituto Nazionale di Fisica Nucleare (INFN), Pisa 56127, Italy and Pixirad Imaging Counters s.r.l., L. Pontecorvo 3, Pisa 56127 (Italy)

    2016-05-15

    Purpose: High-resolution, photon-counting, energy-resolved detector with fast-framing capability can facilitate simultaneous acquisition of precontrast and postcontrast images for subtraction angiography without pixel registration artifacts and can facilitate high-resolution real-time imaging during image-guided interventions. Hence, this study was conducted to determine the spatial resolution characteristics of a hexagonal pixel array photon-counting cadmium telluride (CdTe) detector. Methods: A 650 μm thick CdTe Schottky photon-counting detector capable of concurrently acquiring up to two energy-windowed images was operated in a single energy-window mode to include photons of 10 keV or higher. The detector had hexagonal pixels with apothem of 30 μm resulting in pixel pitch of 60 and 51.96 μm along the two orthogonal directions. The detector was characterized at IEC-RQA5 spectral conditions. Linear response of the detector was determined over the air kerma rate relevant to image-guided interventional procedures ranging from 1.3 nGy/frame to 91.4 μGy/frame. Presampled modulation transfer was determined using a tungsten edge test device. The edge-spread function and the finely sampled line spread function accounted for hexagonal sampling, from which the presampled modulation transfer function (MTF) was determined. Since detectors with hexagonal pixels require resampling to square pixels for distortion-free display, the optimal square pixel size was determined by minimizing the root-mean-squared-error of the aperture functions for the square and hexagonal pixels up to the Nyquist limit. Results: At Nyquist frequencies of 8.33 and 9.62 cycles/mm along the apothem and orthogonal to the apothem directions, the modulation factors were 0.397 and 0.228, respectively. For the corresponding axis, the limiting resolution defined as 10% MTF occurred at 13.3 and 12 cycles/mm, respectively. Evaluation of the aperture functions yielded an optimal square pixel size of 54

  8. SU-E-T-558: Monte Carlo Photon Transport Simulations On GPU with Quadric Geometry

    International Nuclear Information System (INIS)

    Chi, Y; Tian, Z; Jiang, S; Jia, X

    2015-01-01

    Purpose: Monte Carlo simulation on GPU has experienced rapid advancements over the past a few years and tremendous accelerations have been achieved. Yet existing packages were developed only in voxelized geometry. In some applications, e.g. radioactive seed modeling, simulations in more complicated geometry are needed. This abstract reports our initial efforts towards developing a quadric geometry module aiming at expanding the application scope of GPU-based MC simulations. Methods: We defined the simulation geometry consisting of a number of homogeneous bodies, each specified by its material composition and limiting surfaces characterized by quadric functions. A tree data structure was utilized to define geometric relationship between different bodies. We modified our GPU-based photon MC transport package to incorporate this geometry. Specifically, geometry parameters were loaded into GPU’s shared memory for fast access. Geometry functions were rewritten to enable the identification of the body that contains the current particle location via a fast searching algorithm based on the tree data structure. Results: We tested our package in an example problem of HDR-brachytherapy dose calculation for shielded cylinder. The dose under the quadric geometry and that under the voxelized geometry agreed in 94.2% of total voxels within 20% isodose line based on a statistical t-test (95% confidence level), where the reference dose was defined to be the one at 0.5cm away from the cylinder surface. It took 243sec to transport 100million source photons under this quadric geometry on an NVidia Titan GPU card. Compared with simulation time of 99.6sec in the voxelized geometry, including quadric geometry reduced efficiency due to the complicated geometry-related computations. Conclusion: Our GPU-based MC package has been extended to support photon transport simulation in quadric geometry. Satisfactory accuracy was observed with a reduced efficiency. Developments for charged

  9. SU-E-T-558: Monte Carlo Photon Transport Simulations On GPU with Quadric Geometry

    Energy Technology Data Exchange (ETDEWEB)

    Chi, Y; Tian, Z; Jiang, S; Jia, X [The University of Texas Southwestern Medical Ctr, Dallas, TX (United States)

    2015-06-15

    Purpose: Monte Carlo simulation on GPU has experienced rapid advancements over the past a few years and tremendous accelerations have been achieved. Yet existing packages were developed only in voxelized geometry. In some applications, e.g. radioactive seed modeling, simulations in more complicated geometry are needed. This abstract reports our initial efforts towards developing a quadric geometry module aiming at expanding the application scope of GPU-based MC simulations. Methods: We defined the simulation geometry consisting of a number of homogeneous bodies, each specified by its material composition and limiting surfaces characterized by quadric functions. A tree data structure was utilized to define geometric relationship between different bodies. We modified our GPU-based photon MC transport package to incorporate this geometry. Specifically, geometry parameters were loaded into GPU’s shared memory for fast access. Geometry functions were rewritten to enable the identification of the body that contains the current particle location via a fast searching algorithm based on the tree data structure. Results: We tested our package in an example problem of HDR-brachytherapy dose calculation for shielded cylinder. The dose under the quadric geometry and that under the voxelized geometry agreed in 94.2% of total voxels within 20% isodose line based on a statistical t-test (95% confidence level), where the reference dose was defined to be the one at 0.5cm away from the cylinder surface. It took 243sec to transport 100million source photons under this quadric geometry on an NVidia Titan GPU card. Compared with simulation time of 99.6sec in the voxelized geometry, including quadric geometry reduced efficiency due to the complicated geometry-related computations. Conclusion: Our GPU-based MC package has been extended to support photon transport simulation in quadric geometry. Satisfactory accuracy was observed with a reduced efficiency. Developments for charged

  10. Experiments and correlations of pressure loss coefficients for hexagonal arranged rod bundles (P/D > 1.02) with helical wire spacers in laminar and turbulent flows

    International Nuclear Information System (INIS)

    Marten, K.; Yonekawa, S.; Hoffmann, H.

    1987-05-01

    Advanced pressurized water reactors as well as sodium cooled fast reactors, in their breeding and absorber elements, use tightly packed rod bundles with hexagonally arranged rods. Helical wires or helical fins serve as spacers. The pressure loss coefficients of twelve bundles with helical wires were determined systematically in water experiments. High measuring accuracy was achieved by very precise fabrication of the bundles and the shroud as well as by investigations of the proper measuring techniques. The results show a dependency of the loss coefficients on the Reynolds number and on the P/D and H/D ratios of the bundles. These results together with available systematic experimental results of investigations at P/D > 1.1 were used to develop a correlation to determine the pressure loss coefficients of tightly and widely packed hexagonally arranged rod bundles with helical wire spacers. These correlations were used to recalculate and compare results of pressure loss investigations found in the literature; good agreement was demonstrated. Hence, calculation methods exist for a broad range of applications to determine the pressure loss coefficients of hexagonally arranged rod bundles with helical wires for spacers. (orig./HP) [de

  11. GPS: Geometry, Probability, and Statistics

    Science.gov (United States)

    Field, Mike

    2012-01-01

    It might be said that for most occupations there is now less of a need for mathematics than there was say fifty years ago. But, the author argues, geometry, probability, and statistics constitute essential knowledge for everyone. Maybe not the geometry of Euclid, but certainly geometrical ways of thinking that might enable us to describe the world…

  12. Surrogate Modeling for Geometry Optimization

    DEFF Research Database (Denmark)

    Rojas Larrazabal, Marielba de la Caridad; Abraham, Yonas; Holzwarth, Natalie

    2009-01-01

    A new approach for optimizing the nuclear geometry of an atomic system is described. Instead of the original expensive objective function (energy functional), a small number of simpler surrogates is used.......A new approach for optimizing the nuclear geometry of an atomic system is described. Instead of the original expensive objective function (energy functional), a small number of simpler surrogates is used....

  13. Kaehler geometry and SUSY mechanics

    International Nuclear Information System (INIS)

    Bellucci, Stefano; Nersessian, Armen

    2001-01-01

    We present two examples of SUSY mechanics related with Kaehler geometry. The first system is the N = 4 supersymmetric one-dimensional sigma-model proposed in hep-th/0101065. Another system is the N = 2 SUSY mechanics whose phase space is the external algebra of an arbitrary Kaehler manifold. The relation of these models with antisymplectic geometry is discussed

  14. A prediction for bubbling geometries

    OpenAIRE

    Okuda, Takuya

    2007-01-01

    We study the supersymmetric circular Wilson loops in N=4 Yang-Mills theory. Their vacuum expectation values are computed in the parameter region that admits smooth bubbling geometry duals. The results are a prediction for the supergravity action evaluated on the bubbling geometries for Wilson loops.

  15. Molecular motion in restricted geometries

    Indian Academy of Sciences (India)

    Molecular dynamics in restricted geometries is known to exhibit anomalous behaviour. Diffusion, translational or rotational, of molecules is altered significantly on confinement in restricted geometries. Quasielastic neutron scattering (QENS) offers a unique possibility of studying molecular motion in such systems. Both time ...

  16. Behavior of a bundle of fast fuel pins under irradiation

    International Nuclear Information System (INIS)

    Marbach, G.; Millet, P.; Robert, J.; Languille, A.

    1979-01-01

    In the French design of fuel elements for fast reactors, great deformation of pins can bring about interaction with the hexagonal tube through the spacer wires. The change in such bundles is described here when the diameter of the cladding increases and the outcome of this reaction (bending and ovalization of pins) is calculated with a simplified model. It is shown that the results achieved agree well with the experimental observations [fr

  17. Basic algebraic geometry, v.2

    CERN Document Server

    Shafarevich, Igor Rostislavovich

    1994-01-01

    Shafarevich Basic Algebraic Geometry 2 The second edition of Shafarevich's introduction to algebraic geometry is in two volumes. The second volume covers schemes and complex manifolds, generalisations in two different directions of the affine and projective varieties that form the material of the first volume. Two notable additions in this second edition are the section on moduli spaces and representable functors, motivated by a discussion of the Hilbert scheme, and the section on Kähler geometry. The book ends with a historical sketch discussing the origins of algebraic geometry. From the Zentralblatt review of this volume: "... one can only respectfully repeat what has been said about the first part of the book (...): a great textbook, written by one of the leading algebraic geometers and teachers himself, has been reworked and updated. As a result the author's standard textbook on algebraic geometry has become even more important and valuable. Students, teachers, and active researchers using methods of al...

  18. 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

  19. Concept of a subcritical transmutation system with fast neutron spectrum and liquid fuel

    International Nuclear Information System (INIS)

    Tittelbach, S.

    2002-11-01

    The annual amount of nearly 9500 t of spent fuel from worldwide industrial nuclear energy utilization has to be disposed as high level waste. The retention of nuclear waste from the biosphere has to be assured until the radiological risk decreases to tolerable levels. The long-term radiological risk of spent fuel is dominated by actinide elements, i.e. plutonium, americium and curium. It is intended to reduce this amount of high level waste by Partitioning and Transmutation, so that the radiotoxicity of the disposed waste falls short of the reference value of fresh fuel decaying naturally after about thousand years. For this time period the retention of high level waste can be assured by technical means. The scope of this work is the design of a subcritical fast transmutation system with liquid metal cooling and liquid metal fuel. The lead bismuth eutectic has been choosen as the liquid metal coolant and fuel carrier. To dissolve at least 3 at% of transuran elements, a minimum fuel temperature of 600 C is required. The calculations were carried out with a fuel composition, which results from two plutonium recycling steps in a thorium fuel cycle. Two homogeneous and two heterogeneous blankets have been designed and evaluated leading to one preferred heterogeneous blanket design, which has been investigated in more detail. This blanket design merges the positive properties of a solid fuel system (better control of fuel and reactivity because of smaller and closed fuel volumina) and a liquid fuel system (continous charge and discharge or extraction of fission products). The blanket design is based on the core design of fast breeder liquid metal reactors. It consists of hexagonal fuel elements housing up to six annular shaped fuel cylinders. The hexagonal shape of the fuel elements leads to three fuel zones positioned concentrically around the central spallation target. There is a strong heterogeneous distribution of power and heat flux in this blanket design. Besides

  20. The AFEN Method in Cylindrical (r,θ ,z) Geometry for Pebble Bed Reactors -Incorporation of Acceleration and Discontinuity Factor

    International Nuclear Information System (INIS)

    Lee, Jaejun; Cho, Namzin

    2007-01-01

    Most existing methods of nuclear design analysis for pebble bed reactors (PBRs) are based on old finite difference solvers or on statistical methods. These methods require very long computer times. Therefore, there is strong desire of making available high fidelity coarse-mesh nodal computer codes. Recently, we extended the analytic function expansion nodal (AFEN) method developed quite extensively in Cartesian (x,y,z) geometry and in hexagonal-z geometry to the treatment of the full three dimensional cylindrical (r,θ,z) geometry for pebble bed reactors(PBRs). The AFEN methodology in this geometry as in hexagonal geometry is 'robust', due to the unique feature of the AFEN method that it does not use the transverse integration. This paper presents an acceleration scheme based on the coarse-group rebalance (CGR) concept and provides test results verifying the method and its implementation in the TOPS code. Also, we implemented discontinuity factors in the TOPS code and tested on benchmark problems. The TOPS results are in excellent agreement with those of the VENTURE code, using significantly less computer time

  1. Complex analysis and CR geometry

    CERN Document Server

    Zampieri, Giuseppe

    2008-01-01

    Cauchy-Riemann (CR) geometry is the study of manifolds equipped with a system of CR-type equations. Compared to the early days when the purpose of CR geometry was to supply tools for the analysis of the existence and regularity of solutions to the \\bar\\partial-Neumann problem, it has rapidly acquired a life of its own and has became an important topic in differential geometry and the study of non-linear partial differential equations. A full understanding of modern CR geometry requires knowledge of various topics such as real/complex differential and symplectic geometry, foliation theory, the geometric theory of PDE's, and microlocal analysis. Nowadays, the subject of CR geometry is very rich in results, and the amount of material required to reach competence is daunting to graduate students who wish to learn it. However, the present book does not aim at introducing all the topics of current interest in CR geometry. Instead, an attempt is made to be friendly to the novice by moving, in a fairly relaxed way, f...

  2. 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

  3. Survival and failure modes: platform-switching for internal and external hexagon cemented fixed dental prostheses.

    Science.gov (United States)

    Anchieta, Rodolfo B; Machado, Lucas S; Hirata, Ronaldo; Coelho, Paulo G; Bonfante, Estevam A

    2016-10-01

    This study evaluated the probability of survival (reliability) of platform-switched fixed dental prostheses (FDPs) cemented on different implant-abutment connection designs. Eighty-four-three-unit FDPs (molar pontic) were cemented on abutments connected to two implants of external or internal hexagon connection. Four groups (n = 21 each) were established: external hexagon connection and regular platform (ERC); external hexagon connection and switched platform (ESC); internal hexagon and regular platform (IRC); and internal hexagon and switched platform (ISC). Prostheses were subjected to step-stress accelerated life testing in water. Weibull curves and probability of survival for a mission of 100,000 cycles at 400 N (two-sided 90% CI) were calculated. The beta values of 0.22, 0.48, 0.50, and 1.25 for groups ERC, ESC, IRC, and ISC, respectively, indicated a limited role of fatigue in damage accumulation, except for group ISC. Survival decreased for both platform-switched groups (ESC: 74%, and ISC: 59%) compared with the regular matching platform counterparts (ERC: 95%, and IRC: 98%). Characteristic strength was higher only for ERC compared with ESC, but not different between internal connections. Failures chiefly involved the abutment screw. Platform switching decreased the probability of survival of FDPs on both external and internal connections. The absence in loss of characteristic strength observed in internal hexagon connections favor their use compared with platform-switched external hexagon connections. © 2016 Eur J Oral Sci.

  4. Fast reactors

    International Nuclear Information System (INIS)

    Vasile, A.

    2001-01-01

    Fast reactors have capacities to spare uranium natural resources by their breeding property and to propose solutions to the management of radioactive wastes by limiting the inventory of heavy nuclei. This article highlights the role that fast reactors could play for reducing the radiotoxicity of wastes. The conversion of 238 U into 239 Pu by neutron capture is more efficient in fast reactors than in light water reactors. In fast reactors multi-recycling of U + Pu leads to fissioning up to 95% of the initial fuel ( 238 U + 235 U). 2 strategies have been studied to burn actinides: - the multi-recycling of heavy nuclei is made inside the fuel element (homogeneous option); - the unique recycling is made in special irradiation targets placed inside the core or at its surroundings (heterogeneous option). Simulations have shown that, for the same amount of energy produced (400 TWhe), the mass of transuranium elements (Pu + Np + Am + Cm) sent to waste disposal is 60,9 Kg in the homogeneous option and 204.4 Kg in the heterogeneous option. Experimental programs are carried out in Phenix and BOR60 reactors in order to study the feasibility of such strategies. (A.C.)

  5. Fast ejendom

    DEFF Research Database (Denmark)

    Pagh, Peter

    Bogen omfatter en gennemgang af lovgivning, praksis og teori vedrørende køb af fast ejendom og offentligretlig og privatretlig regulering. Bogen belyser bl.a. de privatretlige emner: købers misligholdelsesbeføjelser, servitutter, naboret, hævd og erstatningsansvar for miljøskader samt den...

  6. Head First 2D Geometry

    CERN Document Server

    Fallow), Stray

    2009-01-01

    Having trouble with geometry? Do Pi, The Pythagorean Theorem, and angle calculations just make your head spin? Relax. With Head First 2D Geometry, you'll master everything from triangles, quads and polygons to the time-saving secrets of similar and congruent angles -- and it'll be quick, painless, and fun. Through entertaining stories and practical examples from the world around you, this book takes you beyond boring problems. You'll actually use what you learn to make real-life decisions, like using angles and parallel lines to crack a mysterious CSI case. Put geometry to work for you, and

  7. A first course in geometry

    CERN Document Server

    Walsh, Edward T

    2014-01-01

    This introductory text is designed to help undergraduate students develop a solid foundation in geometry. Early chapters progress slowly, cultivating the necessary understanding and self-confidence for the more rapid development that follows. The extensive treatment can be easily adapted to accommodate shorter courses. Starting with the language of mathematics as expressed in the algebra of logic and sets, the text covers geometric sets of points, separation and angles, triangles, parallel lines, similarity, polygons and area, circles, space geometry, and coordinate geometry. Each chapter incl

  8. Differential geometry curves, surfaces, manifolds

    CERN Document Server

    Kohnel, Wolfgang

    2002-01-01

    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. Special topics that are explored include Frenet frames, ruled surfaces, minimal surfaces and the Gauss-Bonnet theorem. The second part is an introduction to the geometry of general manifolds, with particular emphasis on connections and curvature. The final two chapters are insightful examinations of the special cases of spaces of constant curvature and Einstein manifolds. The text is illustrated with many figures and examples. The prerequisites are undergraduate analysis and linear algebra.

  9. Universal Fast Breeder Reactor Subassembly Counter manual

    International Nuclear Information System (INIS)

    Menlove, H.O.; Eccleston, G.W.; Swansen, J.E.; Goris, P.; Abedin-Zadeh, R.; Ramalho, A.

    1984-08-01

    A neutron coincidence counter has been designed for the measurement of fast breeder reactor fuel assemblies. This assay system can accommodate the full range of geometries and masses found in fast breeder subassemblies under IAEA safeguards. The system's high-performance capability accommodates high plutonium loadings of up to 16 kg. This manual describes the system and its operation and gives performance and calibration parameters for typical applications

  10. Universal Fast Breeder Reactor Subassembly Counter manual

    Energy Technology Data Exchange (ETDEWEB)

    Menlove, H.O.; Eccleston, G.W.; Swansen, J.E.; Goris, P.; Abedin-Zadeh, R.; Ramalho, A.

    1984-08-01

    A neutron coincidence counter has been designed for the measurement of fast breeder reactor fuel assemblies. This assay system can accommodate the full range of geometries and masses found in fast breeder subassemblies under IAEA safeguards. The system's high-performance capability accommodates high plutonium loadings of up to 16 kg. This manual describes the system and its operation and gives performance and calibration parameters for typical applications.

  11. Controllable synthesis of hexagonal ZnO–carbon core–shell microrods and the removal of ZnO to form hexagonal carbon microtubes

    Energy Technology Data Exchange (ETDEWEB)

    Xiao, Yong, E-mail: xy91007@163.com [Department of Applied Chemistry, South China Agricultural University, Guangzhou 510642 (China); He, Wenqi; Gao, Chuang [Department of Chemistry and Institute of Nanochemistry, Jinan University, Guangzhou 510632 (China); Zheng, Mingtao; Lie, Bingfu; Liu, Xiaotang [Department of Applied Chemistry, South China Agricultural University, Guangzhou 510642 (China); Liu, Yingliang, E-mail: tliuyl@163.com [Department of Applied Chemistry, South China Agricultural University, Guangzhou 510642 (China)

    2013-06-15

    A simple and efficient approach was developed to produce regular and uniform shaped hexagonal ZnO–C core–shell micro-rods and carbon micro-tubes. A single-source raw material, zinc acetate dihydrate, has been used for the in situ generation of the hexagonal ZnO–C micro-rods in a sealed autoclave system at 500 °C for 12 h without a catalyst. The resulting products were characterized by X-ray powder diffraction, scanning and transmission electron microscopy, energy-dispersive X-ray analysis and room-temperature photoluminescence spectroscopy (PL). The partial or complete carbon coating on the ZnO surfaces plays an important role in modifying the PL properties. Impacting factors including thermolysis temperature, time and dose of the reactant on the evolution of the hexagonal shape were investigated. A possible formation diagram for the materials has been proposed and discussed based on the features of the reaction system. - Highlights: • Hexagonal ZnO–C core–shell microrods were synthesized by the lower temperature decomposition of zinc acetate. • The novel hexagonal carbon microtubes can gain by simply handling with dilute acid. • The partial or complete carbon coating on the ZnO surfaces plays an important role in modifying the PL properties. • A possible formation diagram for the materials has been proposed.

  12. Fast multilevel radiative transfer

    International Nuclear Information System (INIS)

    Paletou, Frederic; Leger, Ludovick

    2007-01-01

    The vast majority of recent advances in the field of numerical radiative transfer relies on approximate operator methods better known in astrophysics as Accelerated Lambda-Iteration (ALI). A superior class of iterative schemes, in term of rates of convergence, such as Gauss-Seidel and successive overrelaxation methods were therefore quite naturally introduced in the field of radiative transfer by Trujillo Bueno and Fabiani Bendicho [A novel iterative scheme for the very fast and accurate solution of non-LTE radiative transfer problems. Astrophys J 1995;455:646]; it was thoroughly described for the non-LTE two-level atom case. We describe hereafter in details how such methods can be generalized when dealing with non-LTE unpolarised radiation transfer with multilevel atomic models, in monodimensional geometry

  13. Micro vertex detector design for collider geometries

    International Nuclear Information System (INIS)

    Atkinson, M.; Crennell, D.; Fisher, C.M.; Hughes, P.; Kurtz, N.

    1984-05-01

    Previously the analysis of fixed target jet events using a scintillating optical fibre target to provide a projection of the topology on the plane transverse to the event axis has been considered. It was argued that this transverse plane projection is optimal for the detection of charm or beauty particle decay vertices. The idea is generalised to a jet analysis in a collider geometry particularly when associated with a high Psub(perpendicular to) or missing Esub(T) trigger. This report proposes a simple arrangement of fibres to give high precision track elements in the transverse plane projection coupled with a fast read-out capability. The principle physics aim of the design is to provide a tag for selecting top quark jets by detecting a beauty flavoured particle in the jet. (U.K.)

  14. Absorbing CAD system geometries into GEANT

    International Nuclear Information System (INIS)

    Womersley, J.; Dragovitsch, P.; Youssef, S.

    1991-01-01

    The simulation community has for many years discussed the possibility of direct conversion of geometrical detector models from computer- aided design and engineering systems (CAD systems) to the simulation packages (which we shall assume means GEANT). This would allow fast and simultaneous optimization of the physics performance and structural integrity of detector designs. The benefit that this would offer is the avoidance of such problems as the late discovery of the rather thick cryostats in the D-Zero detector. Recent progress in the absorption of CAD geometries into GEANT models is reviewed, including descriptions of the additions to the I-DEAS solid modeller package developed for the EMPACT SSC proposal, the COGENT CAD-to-GEANT interpreter developed by Quantum Research Services, and the OCTAGON package for representing arbitrary shapes in GEANT. Likely future directions of development are described. 2 refs., 7 figs

  15. Verification of a neutronic code for transient analysis in reactors with Hex-z geometry

    Energy Technology Data Exchange (ETDEWEB)

    Gonzalez-Pintor, S.; Verdu, G. [Departamento de Ingenieria Quimica Y Nuclear, Universitat Politecnica de Valencia, Cami de Vera, 14, 46022. Valencia (Spain); Ginestar, D. [Departamento de Matematica Aplicada, Universitat Politecnica de Valencia, Cami de Vera, 14, 46022. Valencia (Spain)

    2012-07-01

    Due to the geometry of the fuel bundles, to simulate reactors such as VVER reactors it is necessary to develop methods that can deal with hexagonal prisms as basic elements of the spatial discretization. The main features of a code based on a high order finite element method for the spatial discretization of the neutron diffusion equation and an implicit difference method for the time discretization of this equation are presented and the performance of the code is tested solving the first exercise of the AER transient benchmark. The obtained results are compared with the reference results of the benchmark and with the results provided by PARCS code. (authors)

  16. Properties of the center of gravity as an algorithm for position measurements: Two-dimensional geometry

    CERN Document Server

    Landi, Gregorio

    2003-01-01

    The center of gravity as an algorithm for position measurements is analyzed for a two-dimensional geometry. Several mathematical consequences of discretization for various types of detector arrays are extracted. Arrays with rectangular, hexagonal, and triangular detectors are analytically studied, and tools are given to simulate their discretization properties. Special signal distributions free of discretized error are isolated. It is proved that some crosstalk spreads are able to eliminate the center of gravity discretization error for any signal distribution. Simulations, adapted to the CMS em-calorimeter and to a triangular detector array, are provided for energy and position reconstruction algorithms with a finite number of detectors.

  17. Glider-based computing in reaction-diffusion hexagonal cellular automata

    International Nuclear Information System (INIS)

    Adamatzky, Andrew; Wuensche, Andrew; De Lacy Costello, Benjamin

    2006-01-01

    A three-state hexagonal cellular automaton, discovered in [Wuensche A. Glider dynamics in 3-value hexagonal cellular automata: the beehive rule. Int J Unconvention Comput, in press], presents a conceptual discrete model of a reaction-diffusion system with inhibitor and activator reagents. The automaton model of reaction-diffusion exhibits mobile localized patterns (gliders) in its space-time dynamics. We show how to implement the basic computational operations with these mobile localizations, and thus demonstrate collision-based logical universality of the hexagonal reaction-diffusion cellular automaton

  18. Preparation of triangular and hexagonal silver nanoplates on the surface of quartz substrate

    International Nuclear Information System (INIS)

    Jia Huiying; Zeng Jianbo; An Jing; Song Wei; Xu Weiqing; Zhao Bing

    2008-01-01

    In this paper, triangular and hexagonal silver nanoplates were prepared on the surface of quartz substrate using photoreduction of silver ions in the presence of silver seeds. The obtained silver nanoplates were characterized by atomic force microscopy and UV-vis spectroscopy. It was found that the silver seeds played an important role in the formation of triangular and hexagonal silver nanoplates. By varying the irradiation time, nanoplates with different sizes and shapes could be obtained. The growth mechanism for triangular and hexagonal nanoplates prepared on quartz substrate was discussed

  19. Thermal transport across graphene and single layer hexagonal boron nitride

    International Nuclear Information System (INIS)

    Zhang, Jingchao; Hong, Yang; Yue, Yanan

    2015-01-01

    As the dimensions of nanocircuits and nanoelectronics shrink, thermal energies are being generated in more confined spaces, making it extremely important and urgent to explore for efficient heat dissipation pathways. In this work, the phonon energy transport across graphene and hexagonal boron-nitride (h-BN) interface is studied using classic molecular dynamics simulations. Effects of temperature, interatomic bond strength, heat flux direction, and functionalization on interfacial thermal transport are investigated. It is found out that by hydrogenating graphene in the hybrid structure, the interfacial thermal resistance (R) between graphene and h-BN can be reduced by 76.3%, indicating an effective approach to manipulate the interfacial thermal transport. Improved in-plane/out-of-plane phonon couplings and broadened phonon channels are observed in the hydrogenated graphene system by analyzing its phonon power spectra. The reported R results monotonically decrease with temperature and interatomic bond strengths. No thermal rectification phenomenon is observed in this interfacial thermal transport. Results reported in this work give the fundamental knowledge on graphene and h-BN thermal transport and provide rational guidelines for next generation thermal interface material designs

  20. Thermal stability of simple tetragonal and hexagonal diamond germanium

    Science.gov (United States)

    Huston, L. Q.; Johnson, B. C.; Haberl, B.; Wong, S.; Williams, J. S.; Bradby, J. E.

    2017-11-01

    Exotic phases of germanium, that form under high pressure but persist under ambient conditions, are of technological interest due to their unique optical and electrical properties. The thermal evolution and stability of two of these exotic Ge phases, the simple tetragonal (st12) and hexagonal diamond (hd) phases, are investigated in detail. These metastable phases, formed by high pressure decompression in either a diamond anvil cell or by nanoindentation, are annealed at temperatures ranging from 280 to 320 °C for st12-Ge and 200 to 550 °C for hd-Ge. In both cases, the exotic phases originated from entirely pure Ge precursor materials. Raman microspectroscopy is used to monitor the phase changes ex situ following annealing. Our results show that hd-Ge synthesized via a pure form of a-Ge first undergoes a subtle change in structure and then an irreversible phase transformation to dc-Ge with an activation energy of (4.3 ± 0.2) eV at higher temperatures. St12-Ge was found to transform to dc-Ge with an activation energy of (1.44 ± 0.08) eV. Taken together with results from previous studies, this study allows for intriguing comparisons with silicon and suggests promising technological applications.

  1. Hexagonal type Ising nanowire with mixed spins: Some dynamic behaviors

    International Nuclear Information System (INIS)

    Kantar, Ersin; Kocakaplan, Yusuf

    2015-01-01

    The dynamic behaviors of a mixed spin (1/2–1) hexagonal Ising nanowire (HIN) with core–shell structure in the presence of a time dependent magnetic field are investigated by using the effective-field theory with correlations based on the Glauber-type stochastic dynamics (DEFT). According to the values of interaction parameters, temperature dependence of the dynamic magnetizations, the hysteresis loop areas and the dynamic correlations are investigated to characterize the nature (first- or second-order) of the dynamic phase transitions (DPTs). Dynamic phase diagrams, including compensation points, are also obtained. Moreover, from the thermal variations of the dynamic total magnetization, the five compensation types can be found under certain conditions, namely the Q-, R-, S-, P-, and N-types. - Highlights: • Dynamic behaviors of mixed spin HIN system are obtained within the EFT. • The system exhibits i, p and nm fundamental phases. • The dynamic phase diagrams are presented in (h, T), (D, T), (Δ S , T) and (r, T) planes. • The dynamic phase diagrams exhibit the dynamic tricritical point (TCP). • Different dynamic compensation types are obtained

  2. Strain, stabilities and electronic properties of hexagonal BN bilayers

    Science.gov (United States)

    Fujimoto, Yoshitaka; Saito, Susumu

    Hexagonal boron nitride (h-BN) atomic layers have been regarded as fascinating materials both scientifically and technologically due to the sizable band gap. This sizable band-gap nature of the h-BN atomic layers would provide not only new physical properties but also novel nano- and/or opto-electronics applications. Here, we study the first-principles density-functional study that clarifies the biaxial strain effects on the energetics and the electronic properties of h-BN bilayers. We show that the band gaps of the h-BN bilayers are tunable by applying strains. Furthermore, we show that the biaxial strains can produce a transition from indirect to direct band gaps of the h-BN bilayer. We also discuss that both AA and AB stacking patterns of h-BN bilayer become feasible structures because h-BN bilayers possess two different directions in the stacking patterns. Supported by MEXT Elements Strategy Initiative to Form Core Research Center through Tokodai Institute for Element Strategy, JSPS KAKENHI Grant Numbers JP26390062 and JP25107005.

  3. Synthesis of hexagonal gold nanoparticles using a microfluidic reaction system

    International Nuclear Information System (INIS)

    Weng, Chen-Hsun; Lee, Gwo-Bin; Huang, Chih-Chia; Yeh, Chen-Sheng; Lei, Huan-Yao

    2008-01-01

    A new microfluidic reaction system capable of mixing, transporting and reacting is developed for the synthesis of gold nanoparticles. It allows for a rapid and a cost-effective approach to accelerate the synthesis of gold nanoparticles. The microfluidic reaction chip is made from micro-electro-mechanical-system technologies which integrate a micro-mixer, micro-pumps, a micro-valve, micro-heaters and a micro temperature sensor on a single chip. Successful synthesis of dispersed gold nanoparticles has been demonstrated within a shorter period of time, as compared to traditional methods. It is experimentally found that precise control of the mixing/heating time for gold salts and reducing agents plays an essential role in the synthesis of gold nanoparticles. The growth process of hexagonal gold nanoparticles by a thermal aqueous approach is also systematically studied by using the same microfluidic reaction system. The development of the microfluidic reaction system could be promising for the synthesis of functional nanoparticles for future biomedical applications

  4. Magnetic structure and resonance properties of hexagonal antidot lattice

    International Nuclear Information System (INIS)

    Marchenko, A.I.; Krivoruchko, V.N.

    2012-01-01

    Static and resonance properties of ferromagnetic films with an antidot lattice (pores in the film) are studied. The description of the system is based on micromagnetic modeling and analytical solution of the Landau-Lifshitz equation. The dependences of ferromagnetic resonance spectra on the in-plane direction of applied magnetic field and on the lattice parameters are investigated. The dependences of a dynamic system response on frequency at fixed magnetic field and on field at fixed frequency, when the field changes cause the static magnetic order to change are explored. It is found that the specific peculiarities of the system dynamics leave unchange for both of these experimental conditions. Namely, for low damping the resonance spectra contain three quasi-homogeneous modes which are due to the resonance of different regions (domains) of the antidot lattice cell. It is shown the angular field dependences of each mode are characterized by a twofold symmetry and the related easy axes are mutually rotated by 60 degrees. As the result, a hexagonal symmetry of the system static and dynamic magnetic characteristics is realized. The existence in the resonance spectrum of several quasi-homogeneous modes related to different regions of the unit cell could be fundamental for working elements of magnonic devices.

  5. Tilted hexagonal post arrays: DNA electrophoresis in anisotropic media.

    Science.gov (United States)

    Chen, Zhen; Dorfman, Kevin D

    2014-02-01

    Using Brownian dynamics simulations, we show that DNA electrophoresis in a hexagonal array of micron-sized posts changes qualitatively when the applied electric field vector is not coincident with the lattice vectors of the array. DNA electrophoresis in such "tilted" post arrays is superior to the standard "un-tilted" approach; while the time required to achieve a resolution of unity in a tilted post array is similar to an un-tilted array at a low-electric field strengths, this time (i) decreases exponentially with electric field strength in a tilted array and (ii) increases exponentially with electric field strength in an un-tilted array. Although the DNA dynamics in a post array are complicated, the electrophoretic mobility results indicate that the "free path," i.e. the average distance of ballistic trajectories of point-sized particles launched from random positions in the unit cell until they intersect the next post, is a useful proxy for the detailed DNA trajectories. The analysis of the free path reveals a fundamental connection between anisotropy of the medium and DNA transport therein that goes beyond simply improving the separation device. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  6. Transport properties of ultrathin black phosphorus on hexagonal boron nitride

    Energy Technology Data Exchange (ETDEWEB)

    Doganov, Rostislav A.; Özyilmaz, Barbaros [Centre for Advanced 2D Materials and Graphene Research Centre, National University of Singapore, 6 Science Drive 2, 117546 Singapore (Singapore); Department of Physics, National University of Singapore, 2 Science Drive 3, 117542 Singapore (Singapore); Graduate School for Integrative Sciences and Engineering (NGS), National University of Singapore, 28 Medical Drive, 117456 Singapore (Singapore); Koenig, Steven P.; Yeo, Yuting [Centre for Advanced 2D Materials and Graphene Research Centre, National University of Singapore, 6 Science Drive 2, 117546 Singapore (Singapore); Department of Physics, National University of Singapore, 2 Science Drive 3, 117542 Singapore (Singapore); Watanabe, Kenji; Taniguchi, Takashi [National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044 (Japan)

    2015-02-23

    Ultrathin black phosphorus, or phosphorene, is a two-dimensional material that allows both high carrier mobility and large on/off ratios. Similar to other atomic crystals, like graphene or layered transition metal dichalcogenides, the transport behavior of few-layer black phosphorus is expected to be affected by the underlying substrate. The properties of black phosphorus have so far been studied on the widely utilized SiO{sub 2} substrate. Here, we characterize few-layer black phosphorus field effect transistors on hexagonal boron nitride—an atomically smooth and charge trap-free substrate. We measure the temperature dependence of the field effect mobility for both holes and electrons and explain the observed behavior in terms of charged impurity limited transport. We find that in-situ vacuum annealing at 400 K removes the p-doping of few-layer black phosphorus on both boron nitride and SiO{sub 2} substrates and reduces the hysteresis at room temperature.

  7. Hyperbolic phonon polaritons in hexagonal boron nitride (Conference Presentation)

    Science.gov (United States)

    Dai, Siyuan; Ma, Qiong; Fei, Zhe; Liu, Mengkun; Goldflam, Michael D.; Andersen, Trond; Garnett, William; Regan, Will; Wagner, Martin; McLeod, Alexander S.; Rodin, Alexandr; Zhu, Shou-En; Watanabe, Kenji; Taniguchi, T.; Dominguez, Gerado; Thiemens, Mark; Castro Neto, Antonio H.; Janssen, Guido C. A. M.; Zettl, Alex; Keilmann, Fritz; Jarillo-Herrero, Pablo; Fogler, Michael M.; Basov, Dmitri N.

    2016-09-01

    Uniaxial materials whose axial and tangential permittivities have opposite signs are referred to as indefinite or hyperbolic media. While hyperbolic responses are normally achieved with metamaterials, hexagonal boron nitride (hBN) naturally possesses this property due to the anisotropic phonons in the mid-infrared. Using scattering-type scanning near-field optical microscopy, we studied polaritonic phenomena in hBN. We performed infrared nano-imaging of highly confined and low-loss hyperbolic phonon polaritons in hBN. The polariton wavelength was shown to be governed by the hBN thickness according to a linear law persisting down to few atomic layers [1]. Additionally, we carried out the modification of hyperbolic response in meta-structures comprised of a mononlayer graphene deposited on hBN [2]. Electrostatic gating of the top graphene layer allows for the modification of wavelength and intensity of hyperbolic phonon polaritons in bulk hBN. The physics of the modification originates from the plasmon-phonon coupling in the hyperbolic medium. Furthermore, we demonstrated the "hyperlens" for subdiffractional focusing and imaging using a slab of hBN [3]. References [1] S. Dai et al., Science, 343, 1125 (2014). [2] S. Dai et al., Nature Nanotechnology, 10, 682 (2015). [3] S. Dai et al., Nature Communications, 6, 6963 (2015).

  8. Nonlinear coupling of flow harmonics: Hexagonal flow and beyond

    Science.gov (United States)

    Giacalone, Giuliano; Yan, Li; Ollitrault, Jean-Yves

    2018-05-01

    Higher Fourier harmonics of anisotropic flow (v4 and beyond) get large contributions induced by elliptic and triangular flow through nonlinear response. We present a general framework of nonlinear hydrodynamic response which encompasses the existing one and allows us to take into account the mutual correlation between the nonlinear couplings affecting Fourier harmonics of any order. Using Large Hadron Collider data on Pb+Pb collisions at s =2.76 TeV, we perform an application of our formalism to hexagonal flow, v6, a coefficient affected by several nonlinear contributions which are of the same order of magnitude. We obtain the first experimental measure of the coefficient χ624, which couples v6 to v2 and v4. This is achieved by putting together the information from several analyses: event-plane correlations, symmetric cumulants, and higher order moments recently analyzed by the ALICE Collaboration. The value of χ624 extracted from data is in fair agreement with hydrodynamic calculations, although with large error bars, which would be dramatically reduced by a dedicated analysis. We argue that within our formalism the nonlinear structure of a given higher order harmonic can be determined more accurately than the harmonic itself, and we emphasize potential applications to future measurements of v7 and v8.

  9. Advances in discrete differential geometry

    CERN Document Server

    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, ...

  10. 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...

  11. An introduction to differential geometry

    CERN Document Server

    Willmore, T J

    2012-01-01

    This text employs vector methods to explore the classical theory of curves and surfaces. Topics include basic theory of tensor algebra, tensor calculus, calculus of differential forms, and elements of Riemannian geometry. 1959 edition.

  12. Symplectic geometry and Fourier analysis

    CERN Document Server

    Wallach, Nolan R

    2018-01-01

    Suitable for graduate students in mathematics, this monograph covers differential and symplectic geometry, homogeneous symplectic manifolds, Fourier analysis, metaplectic representation, quantization, Kirillov theory. Includes Appendix on Quantum Mechanics by Robert Hermann. 1977 edition.

  13. Topology and geometry for physicists

    CERN Document Server

    Nash, Charles

    1983-01-01

    Differential geometry and topology are essential tools for many theoretical physicists, particularly in the study of condensed matter physics, gravity, and particle physics. Written by physicists for physics students, this text introduces geometrical and topological methods in theoretical physics and applied mathematics. It assumes no detailed background in topology or geometry, and it emphasizes physical motivations, enabling students to apply the techniques to their physics formulas and research. ""Thoroughly recommended"" by The Physics Bulletin, this volume's physics applications range fr

  14. Spectral dimension of quantum geometries

    International Nuclear Information System (INIS)

    Calcagni, Gianluca; Oriti, Daniele; Thürigen, Johannes

    2014-01-01

    The spectral dimension is an indicator of geometry and topology of spacetime and a tool to compare the description of quantum geometry in various approaches to quantum gravity. This is possible because it can be defined not only on smooth geometries but also on discrete (e.g., simplicial) ones. In this paper, we consider the spectral dimension of quantum states of spatial geometry defined on combinatorial complexes endowed with additional algebraic data: the kinematical quantum states of loop quantum gravity (LQG). Preliminarily, the effects of topology and discreteness of classical discrete geometries are studied in a systematic manner. We look for states reproducing the spectral dimension of a classical space in the appropriate regime. We also test the hypothesis that in LQG, as in other approaches, there is a scale dependence of the spectral dimension, which runs from the topological dimension at large scales to a smaller one at short distances. While our results do not give any strong support to this hypothesis, we can however pinpoint when the topological dimension is reproduced by LQG quantum states. Overall, by exploring the interplay of combinatorial, topological and geometrical effects, and by considering various kinds of quantum states such as coherent states and their superpositions, we find that the spectral dimension of discrete quantum geometries is more sensitive to the underlying combinatorial structures than to the details of the additional data associated with them. (paper)

  15. Comparative analysis of a fusion reactor blanket in cylindrical and toroidal geometry using Monte Carlo

    International Nuclear Information System (INIS)

    Chapin, D.L.

    1976-03-01

    Differences in neutron fluxes and nuclear reaction rates in a noncircular fusion reactor blanket when analyzed in cylindrical and toroidal geometry are studied using Monte Carlo. The investigation consists of three phases--a one-dimensional calculation using a circular approximation to a hexagonal shaped blanket; a two-dimensional calculation of a hexagonal blanket in an infinite cylinder; and a three-dimensional calculation of the blanket in tori of aspect ratios 3 and 5. The total blanket reaction rate in the two-dimensional model is found to be in good agreement with the circular model. The toroidal calculations reveal large variations in reaction rates at different blanket locations as compared to the hexagonal cylinder model, although the total reaction rate is nearly the same for both models. It is shown that the local perturbations in the toroidal blanket are due mainly to volumetric effects, and can be predicted by modifying the results of the infinite cylinder calculation by simple volume factors dependent on the blanket location and the torus major radius

  16. Quasi free-standing silicene in a superlattice with hexagonal boron nitride

    KAUST Repository

    Kaloni, T. P.; Tahir, M.; Schwingenschlö gl, Udo

    2013-01-01

    We study a superlattice of silicene and hexagonal boron nitride by first principles calculations and demonstrate that the interaction between the layers of the superlattice is very small. As a consequence, quasi free-standing silicene is realized

  17. Vibrational effects on surface energies and band gaps in hexagonal and cubic ice

    International Nuclear Information System (INIS)

    Engel, Edgar A.; Needs, Richard J.; Monserrat, Bartomeu

    2016-01-01

    Surface energies of hexagonal and cubic water ice are calculated using first-principles quantum mechanical methods, including an accurate description of anharmonic nuclear vibrations. We consider two proton-orderings of the hexagonal and cubic ice basal surfaces and three proton-orderings of hexagonal ice prism surfaces, finding that vibrations reduce the surface energies by more than 10%. We compare our vibrational densities of states to recent sum frequency generation absorption measurements and identify surface proton-orderings of experimental ice samples and the origins of characteristic absorption peaks. We also calculate zero point quantum vibrational corrections to the surface electronic band gaps, which range from −1.2 eV for the cubic ice basal surface up to −1.4 eV for the hexagonal ice prism surface. The vibrational corrections to the surface band gaps are up to 12% smaller than for bulk ice.

  18. Large scale graphene/hexagonal boron nitride heterostructure for tunable plasmonics

    KAUST Repository

    Zhang, Kai; Yap, Fungling; Li, Kun; Ng, Changtai; Li, Linjun; Loh, Kianping

    2013-01-01

    Vertical integration of hexagonal boron nitride (h-BN) and graphene for the fabrication of vertical field-effect transistors or tunneling diodes has stimulated intense interest recently due to the enhanced performance offered by combining

  19. A thermo mechanical benchmark calculation of a hexagonal can in the BTI accident with INCA code

    International Nuclear Information System (INIS)

    Zucchini, A.

    1988-01-01

    The thermomechanical behaviour of an hexagonal can in a benchmark problem (simulating the conditions of a BTI accident in a fuel assembly) is examined by means of the INCA code and the results systematically compared with those of ADINA

  20. Pressure-induced structural change from hexagonal to fcc metal lattice in scandium trihydride

    International Nuclear Information System (INIS)

    Ohmura, A.; Machida, A.; Watanuki, T.; Aoki, K.; Nakano, S.; Takemura, K.

    2007-01-01

    We synthesized scandium hydrides by hydrogenation of a scandium foil with hydrogen fluid under high pressure at ambient temperature. Scandium dihydride (ScH 2 ) and trihydride (ScH 3 ) were prepared near 4 and 5 GPa, respectively. The hydrogenation process and pressure-induced structural changes in ScH 3 were investigated by synchrotron radiation X-ray diffraction measurements up to 54.7 GPa. A structural transition from hexagonal to the fcc lattice began at 30 GPa and was completed at 46 GPa via an intermediate state similar to those reported for other hexagonal trihydrides. The intermediate state was not interpreted in terms of a coexisting state for the low-pressure hexagonal and the high-pressure fcc structures. The onset transition pressure of ScH 3 supported the previously proposed relation that the hexagonal-fcc transition pressure is inversely proportional to the ionic radius of the trihydride

  1. Multiple-view, Multiple-selection Visualization of Simulation Geometry in CMS

    International Nuclear Information System (INIS)

    Bauerdick, L A T; Eulisse, G; Jones, C; McCauley, T; Osborne, I; Kovalskyi, D; Mrak Tadel, A; Tadel, M; Yagil, A

    2012-01-01

    Fireworks, the event-display program of CMS, was extended with an advanced geometry visualization package. ROOT's TGeo geometry is used as internal representation, shared among several geometry views. Each view is represented by a GUI list-tree widget, implemented as a flat vector to allow for fast searching, selection, and filtering by material type, node name, and shape type. Display of logical and physical volumes is supported. Color, transparency, and visibility flags can be modified for each node or for a selection of nodes. Further operations, like opening of a new view or changing of the root node, can be performed via a context menu. Node selection and graphical properties determined by the list-tree view can be visualized in any 3D graphics view of Fireworks. As each 3D view can display any number of geometry views, a user is free to combine different geometry-view selections within the same 3D view. Node-selection by proximity to a given point is possible. A visual clipping box can be set for each geometry view to limit geometry drawing into a specified region. Visualization of geometric overlaps, as detected by TGeo, is also supported. The geometry visualization package is used for detailed inspection and display of simulation geometry with or without the event data. It also serves as a tool for geometry debugging and inspection, facilitating development of geometries for CMS detector upgrades and for SLHC.

  2. Adiabatic demagnetization of the antiferromagnetic spin-1/2 Heisenberg hexagonal cluster

    International Nuclear Information System (INIS)

    Deb, Moumita; Ghosh, Asim Kumar

    2016-01-01

    Exact analytic expressions of eigenvalues of the antiferromagnetic spin-1/2 Heisenberg hexagon in the presence of uniform magnetic field have been obtained. Magnetization process, nature of isentrops and properties of magneto caloric effect in terms of adiabatic demagnetization have been investigated. Theoretical results have been used to study the magneto caloric effect of the spin-1/2 Heisenberg hexagonal compound Cu_3WO_6.

  3. Electronic properties of Mn-decorated silicene on hexagonal boron nitride

    KAUST Repository

    Kaloni, Thaneshwor P.; Gangopadhyay, S.; Jones, Burton; Schwingenschlö gl, Udo; Singh, Nirpendra

    2013-01-01

    We study silicene on hexagonal boron nitride, using first-principles calculations. Since hexagonal boron nitride is semiconducting, the interaction with silicene is weaker than for metallic substrates. It therefore is possible to open a 50 meV band gap in the silicene. We further address the effect of Mn decoration by determining the onsite Hubbard interaction parameter, which turns out to differ significantly for decoration at the top and hollow sites. The induced magnetism in the system is analyzed in detail.

  4. Electronic properties of Mn-decorated silicene on hexagonal boron nitride

    KAUST Repository

    Kaloni, Thaneshwor P.

    2013-12-17

    We study silicene on hexagonal boron nitride, using first-principles calculations. Since hexagonal boron nitride is semiconducting, the interaction with silicene is weaker than for metallic substrates. It therefore is possible to open a 50 meV band gap in the silicene. We further address the effect of Mn decoration by determining the onsite Hubbard interaction parameter, which turns out to differ significantly for decoration at the top and hollow sites. The induced magnetism in the system is analyzed in detail.

  5. Growth and Brilliant Photo-Emission of Crystalline Hexagonal Column of Alq3 Microwires

    OpenAIRE

    Seokho Kim; Do Hyoung Kim; Jinho Choi; Hojin Lee; Sun-Young Kim; Jung Woon Park; Dong Hyuk Park

    2018-01-01

    We report the growth and nanoscale luminescence characteristics of 8-hydroxyquinolinato aluminum (Alq3) with a crystalline hexagonal column morphology. Pristine Alq3 nanoparticles (NPs) were prepared using a conventional reprecipitation method. Crystal hexagonal columns of Alq3 were grown by using a surfactant-assisted self-assembly technique as an adjunct to the aforementioned reprecipitation method. The formation and structural properties of the crystalline and non-crystalline Alq3 NPs were...

  6. Dynamic response of single hexagonal LMFBR core subassembly wrappers

    Energy Technology Data Exchange (ETDEWEB)

    Ash, J. E.; Marciniak, T. J.; (Argonne National Lab., IL (United States))

    1977-07-01

    To analyze the dynamic structural response of the LMFBR core subassembly hexagonal wrappers to postulated local energy releases and the sensitivity of the response to variations in both the pressure loading and the material properties of the stainless steel, a finite-element computer code STRAW has been developed. A series of experiments was performed to study the effects of variations in material properties. The amount of coldworking to which the Type 316 stainless steel is subjected has a strong influence upon the ductility and the elastic yield point. The usual fabrication process produced a nominally 20% coldworking with a yield point of about 680 MPa. By designing a special set of dies for the drawing process, a very low ductility hexcan was produced for which the yield point was raised to 820 MPa. Conversely, the yield point was lowered to 170 MPa by a solution annealing process producing a highly ductile test hexcan. A metallurgical study was conducted to find a representative brittle simulant material for the irradiated end-of-life steel properties. An aging treatment for Type 446 stainless steel was developed which reproduced the expected tensile-flow behavior of the in-pile subassembly. Further study is underway to investigate the fracture properties of the simulant material. The pressure pulses were generated by the controlled expansion of high-pressure detonation poducts from low-density explosives detonated inside a vented steel cannister. The orifice configuration of the cannister and the charge mixture ratio were designed to produce two specified pulse shapes. A charge containing 37,7 g PETN mixed with 35 wt % inert, hollow-glass microballoons developed a pressure pulse peak of 9.5 MPa at 1.0 ms. Increasing the PETN to 41 g resulted in a 14.6 MPa peak pressure, and increasing the explosive concentration to 90 wt % in the mixture increased the burning rate and the pulse risetime, so that the peak occurred at 0.6 ms.

  7. Charge carrier transport properties in layer structured hexagonal boron nitride

    Directory of Open Access Journals (Sweden)

    T. C. Doan

    2014-10-01

    Full Text Available Due to its large in-plane thermal conductivity, high temperature and chemical stability, large energy band gap (˜ 6.4 eV, hexagonal boron nitride (hBN has emerged as an important material for applications in deep ultraviolet photonic devices. Among the members of the III-nitride material system, hBN is the least studied and understood. The study of the electrical transport properties of hBN is of utmost importance with a view to realizing practical device applications. Wafer-scale hBN epilayers have been successfully synthesized by metal organic chemical deposition and their electrical transport properties have been probed by variable temperature Hall effect measurements. The results demonstrate that undoped hBN is a semiconductor exhibiting weak p-type at high temperatures (> 700 °K. The measured acceptor energy level is about 0.68 eV above the valence band. In contrast to the electrical transport properties of traditional III-nitride wide bandgap semiconductors, the temperature dependence of the hole mobility in hBN can be described by the form of μ ∝ (T/T0−α with α = 3.02, satisfying the two-dimensional (2D carrier transport limit dominated by the polar optical phonon scattering. This behavior is a direct consequence of the fact that hBN is a layer structured material. The optical phonon energy deduced from the temperature dependence of the hole mobility is ħω = 192 meV (or 1546 cm-1, which is consistent with values previously obtained using other techniques. The present results extend our understanding of the charge carrier transport properties beyond the traditional III-nitride semiconductors.

  8. Passivation of hexagonal SiC surfaces by hydrogen termination

    International Nuclear Information System (INIS)

    Seyller, Thomas

    2004-01-01

    Surface hydrogenation is a well established technique in silicon technology. It is easily accomplished by wet-chemical procedures and results in clean and unreconstructed surfaces, which are extremely low in charged surface states and stable against oxidation in air, thus constituting an ideal surface preparation. As a consequence, methods for hydrogenation have been sought for preparing silicon carbide (SiC) surfaces with similar well defined properties. It was soon recognized, however, that due to different surface chemistry new ground had to be broken in order to find a method leading to the desired monatomic hydrogen saturation. In this paper the results of H passivation of SiC surfaces by high-temperature hydrogen annealing will be discussed, thereby placing emphasis on chemical, structural and electronic properties of the resulting surfaces. In addition to their unique properties, hydrogenated hexagonal SiC {0001} surfaces offer the interesting possibility of gaining insight into the formation of silicon- and carbon-rich reconstructions as well. This is due to the fact that to date hydrogenation is the only method providing oxygen-free surfaces with a C to Si ratio of 1:1. Last but not least, the electronic properties of hydrogen-free SiC {0001} surfaces will be alluded to. SiC {0001} surfaces are the only known semiconductor surfaces that can be prepared in their unreconstructed (1 x 1) state with one dangling bond per unit cell by photon induced hydrogen desorption. These surfaces give indications of a Mott-Hubbard surface band structure

  9. Hexagonal pixel detector with time encoded binary readout

    International Nuclear Information System (INIS)

    Hoedlmoser, H.; Varner, G.; Cooney, M.

    2009-01-01

    The University of Hawaii is developing continuous acquisition pixel (CAP) detectors for vertexing applications in lepton colliding experiments such as SuperBelle or ILC. In parallel to the investigation of different technology options such as MAPS or SOI, both analog and binary readout concepts have been tested. First results with a binary readout scheme in which the hit information is time encoded by means of a signal shifting mechanism have recently been published. This paper explains the hit reconstruction for such a binary detector with an emphasis on fake hit reconstruction probabilities in order to evaluate the rate capability in a high background environment such as the planned SuperB factory at KEK. The results show that the binary concept is at least comparable to any analog readout strategy if not better in terms of occupancy. Furthermore, we present a completely new binary readout strategy in which the pixel cells are arranged in a hexagonal grid allowing the use of three independent output directions to reduce reconstruction ambiguities. The new concept uses the same signal shifting mechanism for time encoding, however, in dedicated transfer lines on the periphery of the detector, which enables higher shifting frequencies. Detailed Monte Carlo simulations of full size pixel matrices including hit and BG generation, signal generation, and data reconstruction show that by means of multiple signal transfer lines on the periphery the pixel can be made smaller (higher resolution), the number of output channels and the data volume per triggered event can be reduced dramatically, fake hit reconstruction is lowered to a minimum and the resulting effective occupancies are less than 10 -4 . A prototype detector has been designed in the AMS 0.35μm Opto process and is currently under fabrication.

  10. Hexagonal boron nitride neutron detectors with high detection efficiencies

    Science.gov (United States)

    Maity, A.; Grenadier, S. J.; Li, J.; Lin, J. Y.; Jiang, H. X.

    2018-01-01

    Neutron detectors fabricated from 10B enriched hexagonal boron nitride (h-10BN or h-BN) epilayers have demonstrated the highest thermal neutron detection efficiency among solid-state neutron detectors to date at about 53%. In this work, photoconductive-like vertical detectors with a detection area of 1 × 1 mm2 were fabricated from 50 μm thick free-standing h-BN epilayers using Ni/Au and Ti/Al bilayers as ohmic contacts. Leakage currents, mobility-lifetime (μτ) products under UV photoexcitation, and neutron detection efficiencies have been measured for a total of 16 different device configurations. The results have unambiguously identified that detectors incorporating the Ni/Au bilayer on both surfaces as ohmic contacts and using the negatively biased top surface for neutron irradiation are the most desired device configurations. It was noted that high growth temperatures of h-10BN epilayers on sapphire substrates tend to yield a higher concentration of oxygen impurities near the bottom surface, leading to a better device performance by the chosen top surface for irradiation than by the bottom. Preferential scattering of oxygen donors tends to reduce the mobility of holes more than that of electrons, making the biasing scheme with the ability of rapidly extracting holes at the irradiated surface while leaving the electrons to travel a large average distance inside the detector at a preferred choice. When measured against a calibrated 6LiF filled micro-structured semiconductor neutron detector, it was shown that the optimized configuration has pushed the detection efficiency of h-BN neutron detectors to 58%. These detailed studies also provided a better understanding of growth-mediated impurities in h-BN epilayers and their effects on the charge collection and neutron detection efficiencies.

  11. In situ hydrothermal crystallization of hexagonal hydroxyapatite tubes from yttrium ion-doped hydroxyapatite by the Kirkendall effect

    International Nuclear Information System (INIS)

    Li, Chengfeng; Ge, Xiaolu; Li, Guochang; Lu, Hao; Ding, Rui

    2014-01-01

    An in situ hydrothermal crystallization method with presence of glutamic acid, urea and yttrium ions was employed to fabricate hexagonal hydroxyapatite (HAp, Ca 5 (PO 4 ) 3 (OH)) tubes with length of 200 nm–1 μm. Firstly, yttrium ion-doped HAp (Y-HAp, Ca 5−x Y x (PO 4 ) 3 (OH)) was synthesized after hydrolysis of urea and HPO 4 2− ions at 100 °C with a dwell time of 24 h. The shift of X-ray diffraction peaks of HAp to high angle was caused the substitution of Ca 2+ ions by small-sized Y 3+ ions. At 160 °C, further hydrolysis reactions of urea and HPO 4 2− ions resulted in the generation of ample OH − and PO 4 3− ions, which provided a high chemical potential for the dissolution of Y-HAp and recrystallization of HAp and YPO 4 . Finally, HAp tubes were formed in situ on Y-HAp according to the Kirkendall effect as a result of the difference of diffusion rate of cations (Ca 2+ ions, outward and slow) and anions (OH − and PO 4 3− ions, inward and fast). The formation process of HAp tube was simulated by the encapsulation of fluorescein molecules in precipitates. Photoluminescence properties were enhanced for HAp tubes with thick and dense walls. This novel tubular material could find wide applications as carriers of drugs, dyes and catalysts. - Highlights: • Hexagonal HAp tubes with adjustable sizes are prepared by a hydrothermal method. • A dissolution-recrystallization process occurs during hydrothermal treatment. • The formation mechanism is explained by the Kirkendall effect. • The crystallization is simulated by the encapsulation and release of fluorescein

  12. Anomalous lattice compressibility of hexagonal Eu{sub 2}O{sub 3}

    Energy Technology Data Exchange (ETDEWEB)

    Irshad, K.A.; Chandra Shekar, N.V., E-mail: chandru@igcar.gov.in

    2017-07-01

    Monoclinic Eu{sub 2}O{sub 3} was investigated in a Mao-Bell type diamond anvil cell using angle dispersive x-ray diffraction up to a pressure of 26 GPa. Pressure induced structural phase transition from monoclinic to hexagonal phase was observed at 4.3 GPa with 2% volume collapse. Birch –Murnaghan equation of state fit to the pressure volume data yielded a bulk modulus of 159(9) GPa and 165(6) GPa for the monoclinic and hexagonal phases respectively. Equation of state fitting to the structural parameters yielded an axial compressibility of β{sub a} > β{sub c} > β{sub b} for the parent monoclinic phase, showing the least compressibility along b axis. Contrary to the available reports, an anomalous lattice compressibility behavior is observed for the high pressure hexagonal phase, characterized by pronounced hardening of a axis above 15 GPa. The observed incompressible nature of the hexagonal a axis in the pressure range 15–25 GPa is found to be compensated by doubling the compressibility along the c axis. - Highlights: • Structural phase transition in Eu{sub 2}O{sub 3} from monoclinic to hexagonal phase. • Anomalous lattice compressibility in the hexagonal phase has reported first time. • Quantitative analysis of lattice compressibility.

  13. Fast tomosynthesis

    International Nuclear Information System (INIS)

    Klotz, E.; Linde, R.; Tiemens, U.; Weiss, H.

    1978-01-01

    A system has been constructed for fast tomosynthesis, whereby X-ray photographs are made of a single layer of an object. Twenty five X-ray tubes illuminate the object simultaneously at different angles. The resulting coded image is decoded by projecting it with a pattern of lenses that have the same form as the pattern of X-ray tubes. The coded image is optically correlated with the pattern of the sources. The scale of this can be adjusted so that the desired layer of the object is portrayed. Experimental results of its use in a hospital are presented. (C.F.)

  14. Variable geometry Darrieus wind machine

    Science.gov (United States)

    Pytlinski, J. T.; Serrano, D.

    1983-08-01

    A variable geometry Darrieus wind machine is proposed. The lower attachment of the blades to the rotor can move freely up and down the axle allowing the blades of change shape during rotation. Experimental data for a 17 m. diameter Darrieus rotor and a theoretical model for multiple streamtube performance prediction were used to develop a computer simulation program for studying parameters that affect the machine's performance. This new variable geometry concept is described and interrelated with multiple streamtube theory through aerodynamic parameters. The computer simulation study shows that governor behavior of a Darrieus turbine can not be attained by a standard turbine operating within normally occurring rotational velocity limits. A second generation variable geometry Darrieus wind turbine which uses a telescopic blade is proposed as a potential improvement on the studied concept.

  15. 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

  16. Flux compactifications and generalized geometries

    Energy Technology Data Exchange (ETDEWEB)

    Grana, Mariana [Service de Physique Theorique, CEA/Saclay, 91191 Gif-sur-Yvette Cedex (France)

    2006-11-07

    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{sup 6} /(Z{sub 3} x Z{sub 3}) torus in IIA. We finish by studying the effective action and flux vacua for generalized geometries in the context of generalized complex geometry.

  17. Euclidean geometry and its subgeometries

    CERN Document Server

    Specht, Edward John; Calkins, Keith G; Rhoads, Donald H

    2015-01-01

    In this monograph, the authors present a modern development of Euclidean geometry from independent axioms, using up-to-date language and providing detailed proofs. The axioms for incidence, betweenness, and plane separation are close to those of Hilbert. This is the only axiomatic treatment of Euclidean geometry that uses axioms not involving metric notions and that explores congruence and isometries by means of reflection mappings. The authors present thirteen axioms in sequence, proving as many theorems as possible at each stage and, in the process, building up subgeometries, most notably the Pasch and neutral geometries. Standard topics such as the congruence theorems for triangles, embedding the real numbers in a line, and coordinatization of the plane are included, as well as theorems of Pythagoras, Desargues, Pappas, Menelaus, and Ceva. The final chapter covers consistency and independence of axioms, as well as independence of definition properties. There are over 300 exercises; solutions to many of the...

  18. Guide to Computational Geometry Processing

    DEFF Research Database (Denmark)

    Bærentzen, Jakob Andreas; Gravesen, Jens; Anton, François

    be processed before it is useful. This Guide to Computational Geometry Processing reviews the algorithms for processing geometric data, with a practical focus on important techniques not covered by traditional courses on computer vision and computer graphics. This is balanced with an introduction...... to the theoretical and mathematical underpinnings of each technique, enabling the reader to not only implement a given method, but also to understand the ideas behind it, its limitations and its advantages. Topics and features: Presents an overview of the underlying mathematical theory, covering vector spaces......, metric space, affine spaces, differential geometry, and finite difference methods for derivatives and differential equations Reviews geometry representations, including polygonal meshes, splines, and subdivision surfaces Examines techniques for computing curvature from polygonal meshes Describes...

  19. Electrodynamics and Spacetime Geometry: Foundations

    Science.gov (United States)

    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.

  20. Dayside merging and cusp geometry

    International Nuclear Information System (INIS)

    Crooker, N.U.

    1979-01-01

    Geometrical considerations are presented to show that dayside magnetic merging when constrained to act only where the fields are antiparallel results in lines of merging that converge at the polar cusps. An important consequence of this geometry is that no accelerated flows are predicted across the dayside magnetopause. Acceleration owing to merging acts in opposition to the magnetosheath flow at the merging point and produces the variably directed, slower-than-magnetosheath flows observed in the entry layer. Another consequence of the merging geometry is that much of the time closed field lines constitute the subsolar region of the magnetopause. The manner in which the polar cap convection patterns predicted by the proposed geometry change as the interplanetary field is rotated through 360 0 provides a unifying description of how the observed single circular vortex and the crescent-shaped double vortex patterns mutually evolve under the influence of a single operating principle

  1. DOGBONE GEOMETRY FOR RECIRCULATING ACCELERATORS

    International Nuclear Information System (INIS)

    BERG, J.S.; JOHNSTONE, C.; SUMMERS, D.

    2001-01-01

    Most scenarios for accelerating muons require recirculating acceleration. A racetrack shape for the accelerator requires particles with lower energy in early passes to traverse almost the same length of arc as particles with the highest energy. This extra arc length may lead to excess decays and excess cost. Changing the geometry to a dogbone shape, where there is a single linac and the beam turns completely around at the end of the linac, returning to the same end of the linac from which it exited, addresses this problem. In this design, the arc lengths can be proportional to the particle's momentum. This paper proposes an approximate cost model for a recirculating accelerator, attempts to make cost-optimized designs for both racetrack and dogbone geometries, and demonstrates that the dogbone geometry does appear to be more cost effective

  2. Concept on coupled spectrum B/T (burning and/or transmutation) reactor for treatment of minor actinides by thermal and fast neutrons

    International Nuclear Information System (INIS)

    Aziz, Ferhat; Kitamoto, Asashi

    1996-01-01

    A conceptual design of B/T (burning and/or transmutation) reactor based on a modified conventional 1150 MWe-PWR system, with core consisted of two concentric regions for thermal and fast neutrons, was proposed herein for B/T treatment of MA (minor actinides). The B/T fuel considered was supposed such that MA discharged from 1 GWe-LWR was blended homogeneously with the composition of LWR fuel. In the outer region 23- Np, 241 Am and 243 Am were loaded and burned by thermal neutron, while in the inner region 244 Cm was loaded and burned mainly by fast neutron. The geometry of B/T fuel and the fuel assembly in the outer region was left in the same condition to those of standard PWR while in the inner region the B/T fuel was arranged in the hexagonal geometry, allowed high fuel to coolant volume ratio (V m /V f ), to keep the harder neutron spectrum. Two cases of the Coupled Spectrum B/T Reactor (CSR) with different (V m 1 f ) ratio in the inner region were studied, and the results for the tight lattice with (V m /V f ) = 0.5 showed that those isotopes approached the equilibrium composition after about 5 recycle period, when the CSR was operated under the reactivity swing of 2.8 % dk/k. The evaluations on the void coefficient of reactivity, the Doppler effect and the reactivity swing showed that the CSR concept has the inherent safety and can burn and/or transmute all kind of MA in a single reactor. This CSR can burn about 808 kg of MA in one recycle period of 3 years, which is equivalent to the discharged fuel from about 12 units of LWR in a year. (author)

  3. Geometric Transformations in Engineering Geometry

    Directory of Open Access Journals (Sweden)

    I. F. Borovikov

    2015-01-01

    Full Text Available Recently, for business purposes, in view of current trends and world experience in training engineers, research and faculty staff there has been a need to transform traditional courses of descriptive geometry into the course of engineering geometry in which the geometrical transformations have to become its main section. On the basis of critical analysis the paper gives suggestions to improve a presentation technique of this section both in the classroom and in academic literature, extend an application scope of geometrical transformations to solve the position and metric tasks and simulation of surfaces, as well as to design complex engineering configurations, which meet a number of pre-specified conditions.The article offers to make a number of considerable amendments to the terms and definitions used in the existing courses of descriptive geometry. It draws some conclusions and makes the appropriate proposals on feasibility of coordination in teaching the movement transformation in the courses of analytical and descriptive geometry. This will provide interdisciplinary team teaching and allow students to be convinced that a combination of analytical and graphic ways to solve geometric tasks is useful and reasonable.The traditional sections of learning courses need to be added with a theory of projective and bi-rational transformations. In terms of application simplicity and convenience it is enough to consider the central transformations when solving the applied tasks. These transformations contain a beam of sub-invariant (low-invariant straight lines on which the invariant curve induces non-involution and involution projectivities. The expediency of nonlinear transformations application is shown in the article by a specific example of geometric modeling of the interfacing surface "spar-blade".Implementation of these suggestions will contribute to a real transformation of a traditional course of descriptive geometry to the engineering geometry

  4. KEMAJUAN BELAJAR SISWA PADA GEOMETRI TRANSFORMASI MENGGUNAKAN AKTIVITAS REFLEKSI GEOMETRI

    Directory of Open Access Journals (Sweden)

    Irkham Ulil Albab

    2014-10-01

    Full Text Available Abstrak: Penelitian ini bertujuan untuk mendeskripsikan kemajuan belajar siswa pada materi geometri transformasi yang didukung dengan serangkaian aktivitas belajar berdasarkan Pendidikan Matematika Realistik Indonesia. Penelitian didesain melalui tiga tahap, yaitu tahapan perancangan desain awal, pengujian desain melalui pembelajaran awal dan pembelajaran eksperimental, dan tahap analisis retrospektif. Dalam penelitian ini, Hypothetical Learning Trajectory, HLT (HLT berperan penting sebagai desain pembelajaran sekaligus instrumen penelitian. HLT diujikan terhadap 26 siswa kelas VII. Data dikumpulkan dengan teknik wawancara, pengamatan, dan catatan lapangan. Hasil penelitian menunjukkan bahwa desain pembelajaran ini mampu menstimulasi siswa untuk memberikan karakteristik refleksi dan transformasi geometri lainnya secara informal, mengklasifikasikannya dalam transformasi isometri pada level kedua, dan menemukan garis bantuan refleksi pada level yang lebih formal. Selain itu, garis bantuan refleksi digunakan oleh siswa untuk menggambar bayangan refleksi dan pola pencerminan serta memahami bentuk rotasi dan translasi sebagai kombinasi refleksi adalah level tertinggi. Keyword: transformasi geometri, kombinasi refleksi, rotasi, translasi, design research, HLT STUDENTS’ LEARNING PROGRESS ON TRANSFORMATION GEOMETRY USING THE GEOMETRY REFLECTION ACTIVITIES Abstract: This study was aimed at describing the students’ learning progress on transformation geometry supported by a set of learning activities based on Indonesian Realistic Mathematics Education. The study was designed into three stages, that is, the preliminary design stage, the design testing through initial instruction and experiment, and the restrospective analysis stage. In this study, Hypothetical Learning Trajectory (HLT played an important role as an instructional design and a research instrument. HLT was tested to 26 seventh grade students. The data were collected through interviews

  5. Graphical debugging of combinational geometry

    International Nuclear Information System (INIS)

    Burns, T.J.; Smith, M.S.

    1992-01-01

    A graphical debugger for combinatorial geometry being developed at Oak Ridge National Laboratory is described. The prototype debugger consists of two parts: a FORTRAN-based ''view'' generator and a Microsoft Windows application for displaying the geometry. Options and features of both modules are discussed. Examples illustrating the various options available are presented. The potential for utilizing the images produced using the debugger as a visualization tool for the output of the radiation transport codes is discussed as is the future direction of the development

  6. Lectures on Algebraic Geometry I

    CERN Document Server

    Harder, Gunter

    2012-01-01

    This book and the following second volume is an introduction into modern algebraic geometry. In the first volume the methods of homological algebra, theory of sheaves, and sheaf cohomology are developed. These methods are indispensable for modern algebraic geometry, but they are also fundamental for other branches of mathematics and of great interest in their own. In the last chapter of volume I these concepts are applied to the theory of compact Riemann surfaces. In this chapter the author makes clear how influential the ideas of Abel, Riemann and Jacobi were and that many of the modern metho

  7. Combinatorial geometry in the plane

    CERN Document Server

    Hadwiger, Hugo; Klee, Victor

    2014-01-01

    Geared toward advanced undergraduates familiar with analysis and college geometry, this concise book discusses theorems on topics restricted to the plane such as convexity, coverings, and graphs. In addition to helping students cultivate rigorous thought, the text encourages the development of mathematical intuition and clarifies the nature of mathematical research.The two-part treatment begins with specific topics including integral distances, covering problems, point set geometry and convexity, simple paradoxes involving point sets, and pure combinatorics, among other subjects. The second pa

  8. Modern differential geometry for physicists

    CERN Document Server

    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

  9. Comparison theorems in Riemannian geometry

    CERN Document Server

    Cheeger, Jeff

    2008-01-01

    The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem-the first such treatment in a book in English. Next comes a detailed presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one on the injectivity radius. Chapters 6-9 deal with many of the most re

  10. Geometry, topology, and string theory

    Energy Technology Data Exchange (ETDEWEB)

    Varadarajan, Uday [Univ. of California, Berkeley, CA (United States)

    2003-01-01

    A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated.

  11. Spatial geometry and special relativity

    DEFF Research Database (Denmark)

    Kneubil, Fabiana Botelho

    2016-01-01

    In this work, it is shown the interplay of relative and absolute entities, which are present in both spatial geometry and special relativity. In order to strengthen the understanding of special relativity, we discuss firstly an instance of geometry and the existence of both frame......-dependent and frame-independent entities. We depart from a subject well known by students, which is the three-dimensional geometric space in order to compare, afterwards, with the treatment of four-dimensional space in the special relativity. The differences and similarities between these two subjects are also...

  12. Stochastic geometry and its applications

    CERN Document Server

    Chiu, Sung Nok; Kendall, Wilfrid S; Mecke, Joseph

    2013-01-01

    An extensive update to a classic text Stochastic geometry and spatial statistics play a fundamental role in many modern branches of physics, materials sciences, engineering, biology and environmental sciences. They offer successful models for the description of random two- and three-dimensional micro and macro structures and statistical methods for their analysis. The previous edition of this book has served as the key reference in its field for over 18 years and is regarded as the best treatment of the subject of stochastic geometry, both as a subject with vital a

  13. Introduction to topology and geometry

    CERN Document Server

    Stahl, Saul

    2014-01-01

    An easily accessible introduction to over three centuries of innovations in geometry Praise for the First Edition ". . . a welcome alternative to compartmentalized treatments bound to the old thinking. This clearly written, well-illustrated book supplies sufficient background to be self-contained." -CHOICE This fully revised new edition offers the most comprehensive coverage of modern geometry currently available at an introductory level. The book strikes a welcome balance between academic rigor and accessibility, providing a complete and cohesive picture of the science with an unparallele

  14. Algebraic geometry and theta functions

    CERN Document Server

    Coble, Arthur B

    1929-01-01

    This book is the result of extending and deepening all questions from algebraic geometry that are connected to the central problem of this book: the determination of the tritangent planes of a space curve of order six and genus four, which the author treated in his Colloquium Lecture in 1928 at Amherst. The first two chapters recall fundamental ideas of algebraic geometry and theta functions in such fashion as will be most helpful in later applications. In order to clearly present the state of the central problem, the author first presents the better-known cases of genus two (Chapter III) and

  15. Geometry, topology, and string theory

    International Nuclear Information System (INIS)

    Varadarajan, Uday

    2003-01-01

    A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated

  16. Characterization of new hexagonal large area Geiger Avalanche Photodiodes

    International Nuclear Information System (INIS)

    Boccone, V.; Aguilar, J.A.; Della Volpe, D.; Christov, A.; Montaruli, T.; Rameez, M.; Basili, A.

    2013-06-01

    Photomultipliers (PMTs) are the standard detector for construction of the current generation of imaging Atmospheric Cherenkov Telescopes (IACTs). Despite impressive improvements in QE and reliability in the last years, these devices suffer from the limitation of being unable to operate in the partially illuminated sky (during full or partial moon periods) as the excess light leads to a significant increase in the rate of ageing of the devices themselves and consequently limit the life of the camera. A viable alternative is the large area Geiger-mode avalanche photodiodes (G-APDs also known as Silicon Photomultipliers or SiPMs) that are commercially available from different producers in various types and dimensions. The sufficiency of the maturity of this technology for application to Cherenkov Astronomy has already been demonstrated by the FACT telescope. One of the camera designs under study for the 4 m Davies Cotton Telescope foresees the utilization of a large area G-APDs coupled to non imaging light concentrators. In collaboration with Hamamatsu and deriving from their current technology, we have designed a new hexagonal shaped large area G-APD HEX S12516 which when coupled to a Winston cone of 24 degrees cutting angle allows for a pixel angular resolution of 0.25 degrees for a f/D 1.4 telescope with a diameter of 4 m. The device, available in 2 different cell size configurations (50 μm and 100 μm), is divided into 4 different channels powered in common cathode mode. A temperature sensor was included for a better temperature evaluation in the characterization phase. The first 3 prototypes were fully characterized and the results are compared to the larger area devices commercially available such as the S10985-050C (2x2 array of 3x3 mm 2 G-APDs). The photo-detection efficiency is measured applying the Poisson statistics method using pulsed LED at 7 different wavelengths from 355 to 670 nm and for different bias over-voltages (V ov ). Optical crosstalk and

  17. Achieving Ohmic Contact for High-quality MoS2 Devices on Hexagonal Boron Nitride

    Science.gov (United States)

    Cui, Xu

    MoS2, among many other transition metal dichalcogenides (TMDCs), holds great promise for future applications in nano-electronics, opto-electronics and mechanical devices due to its ultra-thin nature, flexibility, sizable band-gap, and unique spin-valley coupled physics. However, there are two main challenges that hinder careful study of this material. Firstly, it is hard to achieve Ohmic contacts to mono-layer MoS2, particularly at low temperatures (T) and low carrier densities. Secondly, materials' low quality and impurities introduced during the fabrication significantly limit the electron mobility of mono- and few-layer MoS2 to be substantially below theoretically predicted limits, which has hampered efforts to observe its novel quantum transport behaviours. Traditional low work function metals doesn't necessary provide good electron injection to thin MoS2 due to metal oxidation, Fermi level pinning, etc. To address the first challenge, we tried multiple contact schemes and found that mono-layer hexagonal boron nitride (h-BN) and cobalt (Co) provide robust Ohmic contact. The mono-layer spacer serves two advantageous purposes: it strongly interacts with the transition metal, reducing its work function by over 1 eV; and breaks the metal-TMDCs interaction to eliminate the interfacial states that cause Fermi level pinning. We measure a flat-band Schottky barrier of 16 meV, which makes thin tunnel barriers upon doping the channels, and thus achieve low-T contact resistance of 3 kohm.um at a carrier density of 5.3x10. 12/cm. 2. Similar to graphene, eliminating all potential sources of disorder and scattering is the key to achieving high performance in MoS2 devices. We developed a van der Waals heterostructure device platform where MoS2 layers are fully encapsulated within h-BN and electrically contacted in a multi-terminal geometry using gate-tunable graphene electrodes. The h-BN-encapsulation provides excellent protection from environmental factors, resulting in

  18. Hydrothermal synthesis and magneto-optical properties of Ni-doped ZnO hexagonal columns

    International Nuclear Information System (INIS)

    Xu, Xingyan; Cao, Chuanbao

    2015-01-01

    Single crystal Zn 1−x Ni x O (x=0, 0.02, 0.04, 0.06) hexagonal columns have been synthesized by a simple hydrothermal route. The hexagonal columns of the products are about 3 μm in diameter and about 2 μm in thickness. X-ray diffraction (XRD), Ni K-edge XANES spectra and TEM indicate that the as-prepared samples are single-crystalline wurtzite structure and no metallic Ni or other secondary phases are found in the hexagonal columns. Optical absorption and Raman results further confirm the incorporation of Ni 2+ ions in the ZnO lattice. Magnetic measurements indicate that the Zn 1−x Ni x O hexagonal columns exhibited obvious ferromagnetic characteristic at room temperature. The coercive fields (H c ) were obtained to be 135.3, 327.79 and 127.29 Oe for x=0.02, 0.04 and 0.06, respectively. The ferromagnetism was assumed to originate from the exchange interaction between free carriers (holes or electrons) from the valence band and the localized d spins on the Ni ions. - Highlights: • Single crystal Zn 1−x Ni x O (x=0, 0.02, 0.04, 0.06) hexagonal columns were synthesized by a simple hydrothermal method. • The layer-by-layer growth manner of the Zn 1−x Ni x O hexagonal columns was proposed. • Obvious room-temperature ferromagnetic characteristic of Zn 1−x Ni x O are observed and the coercivity (H c ) are 135.3,327.79 and 127.29 Oe for x=0.02, 0.04 and 0.06, respectively. • The exchange interaction between local-spin polarized electrons and conduction electrons is responsible for the room-temperature ferromagnetism in the Zn 1−x Ni x O hexagonal columns

  19. The Idea of Order at Geometry Class.

    Science.gov (United States)

    Rishel, Thomas

    The idea of order in geometry is explored using the experience of assignments given to undergraduates in a college geometry course "From Space to Geometry." Discussed are the definition of geometry, and earth measurement using architecture, art, and common experience. This discussion concludes with a consideration of the question of whether…

  20. Teaching Spatial Geometry in a Virtual World

    DEFF Research Database (Denmark)

    Förster, Klaus-Tycho

    2017-01-01

    Spatial geometry is one of the fundamental mathematical building blocks of any engineering education. However, it is overshadowed by planar geometry in the curriculum between playful early primary education and later analytical geometry, leaving a multi-year gap where spatial geometry is absent...

  1. Stationary Liquid Fuel Fast Reactor

    International Nuclear Information System (INIS)

    Yang, Won Sik; Grandy, Andrew; Boroski, Andrew; Krajtl, Lubomir; Johnson, Terry

    2015-01-01

    For effective burning of hazardous transuranic (TRU) elements of used nuclear fuel, a transformational advanced reactor concept named SLFFR (Stationary Liquid Fuel Fast Reactor) was proposed based on stationary molten metallic fuel. The fuel enters the reactor vessel in a solid form, and then it is heated to molten temperature in a small melting heater. The fuel is contained within a closed, thick container with penetrating coolant channels, and thus it is not mixed with coolant nor flow through the primary heat transfer circuit. The makeup fuel is semi- continuously added to the system, and thus a very small excess reactivity is required. Gaseous fission products are also removed continuously, and a fraction of the fuel is periodically drawn off from the fuel container to a processing facility where non-gaseous mixed fission products and other impurities are removed and then the cleaned fuel is recycled into the fuel container. A reference core design and a preliminary plant system design of a 1000 MWt TRU- burning SLFFR concept were developed using TRU-Ce-Co fuel, Ta-10W fuel container, and sodium coolant. Conservative design approaches were adopted to stay within the current material performance database. Detailed neutronics and thermal-fluidic analyses were performed to develop a reference core design. Region-dependent 33-group cross sections were generated based on the ENDF/B-VII.0 data using the MC2-3 code. Core and fuel cycle analyses were performed in theta-r-z geometries using the DIF3D and REBUS-3 codes. Reactivity coefficients and kinetics parameters were calculated using the VARI3D perturbation theory code. Thermo-fluidic analyses were performed using the ANSYS FLUENT computational fluid dynamics (CFD) code. Figure 0.1 shows a schematic radial layout of the reference 1000 MWt SLFFR core, and Table 0.1 summarizes the main design parameters of SLFFR-1000 loop plant. The fuel container is a 2.5 cm thick cylinder with an inner radius of 87.5 cm. The fuel

  2. Stationary Liquid Fuel Fast Reactor

    Energy Technology Data Exchange (ETDEWEB)

    Yang, Won Sik [Purdue Univ., West Lafayette, IN (United States); Grandy, Andrew [Argonne National Lab. (ANL), Argonne, IL (United States); Boroski, Andrew [Argonne National Lab. (ANL), Argonne, IL (United States); Krajtl, Lubomir [Argonne National Lab. (ANL), Argonne, IL (United States); Johnson, Terry [Argonne National Lab. (ANL), Argonne, IL (United States)

    2015-09-30

    For effective burning of hazardous transuranic (TRU) elements of used nuclear fuel, a transformational advanced reactor concept named SLFFR (Stationary Liquid Fuel Fast Reactor) was proposed based on stationary molten metallic fuel. The fuel enters the reactor vessel in a solid form, and then it is heated to molten temperature in a small melting heater. The fuel is contained within a closed, thick container with penetrating coolant channels, and thus it is not mixed with coolant nor flow through the primary heat transfer circuit. The makeup fuel is semi- continuously added to the system, and thus a very small excess reactivity is required. Gaseous fission products are also removed continuously, and a fraction of the fuel is periodically drawn off from the fuel container to a processing facility where non-gaseous mixed fission products and other impurities are removed and then the cleaned fuel is recycled into the fuel container. A reference core design and a preliminary plant system design of a 1000 MWt TRU- burning SLFFR concept were developed using TRU-Ce-Co fuel, Ta-10W fuel container, and sodium coolant. Conservative design approaches were adopted to stay within the current material performance database. Detailed neutronics and thermal-fluidic analyses were performed to develop a reference core design. Region-dependent 33-group cross sections were generated based on the ENDF/B-VII.0 data using the MC2-3 code. Core and fuel cycle analyses were performed in theta-r-z geometries using the DIF3D and REBUS-3 codes. Reactivity coefficients and kinetics parameters were calculated using the VARI3D perturbation theory code. Thermo-fluidic analyses were performed using the ANSYS FLUENT computational fluid dynamics (CFD) code. Figure 0.1 shows a schematic radial layout of the reference 1000 MWt SLFFR core, and Table 0.1 summarizes the main design parameters of SLFFR-1000 loop plant. The fuel container is a 2.5 cm thick cylinder with an inner radius of 87.5 cm. The fuel

  3. Analogical Reasoning in Geometry Education

    Science.gov (United States)

    Magdas, Ioana

    2015-01-01

    The analogical reasoning isn't used only in mathematics but also in everyday life. In this article we approach the analogical reasoning in Geometry Education. The novelty of this article is a classification of geometrical analogies by reasoning type and their exemplification. Our classification includes: analogies for understanding and setting a…

  4. Normal forms in Poisson geometry

    NARCIS (Netherlands)

    Marcut, I.T.

    2013-01-01

    The structure of Poisson manifolds is highly nontrivial even locally. The first important result in this direction is Conn's linearization theorem around fixed points. One of the main results of this thesis (Theorem 2) is a normal form theorem in Poisson geometry, which is the Poisson-geometric

  5. Exploring Bundling Theory with Geometry

    Science.gov (United States)

    Eckalbar, John C.

    2006-01-01

    The author shows how instructors might successfully introduce students in principles and intermediate microeconomic theory classes to the topic of bundling (i.e., the selling of two or more goods as a package, rather than separately). It is surprising how much students can learn using only the tools of high school geometry. To be specific, one can…

  6. Stochastic Modelling of River Geometry

    DEFF Research Database (Denmark)

    Sørensen, John Dalsgaard; Schaarup-Jensen, K.

    1996-01-01

    Numerical hydrodynamic river models are used in a large number of applications to estimate critical events for rivers. These estimates are subject to a number of uncertainties. In this paper, the problem to evaluate these estimates using probabilistic methods is considered. Stochastic models for ...... for river geometries are formulated and a coupling between hydraulic computational methods and numerical reliability methods is presented....

  7. Matter in toy dynamical geometries

    NARCIS (Netherlands)

    Konopka, T.J.

    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

  8. Let??s teach geometry

    OpenAIRE

    Ca??adas, Mar??a C.; Molina, Marta; Gallardo, Sandra; Mart??nez-Santaolalla, Manuel J.; Pe??as, Mar??a

    2010-01-01

    In this work we present an activity for High School students in which various mathematical concepts of plane and spatial geometry are involved. The final objective of the proposed tasks is constructing a particular polyhedron, the cube, by using a modality of origami called modular origami.

  9. Granular flows in constrained geometries

    Science.gov (United States)

    Murthy, Tejas; Viswanathan, Koushik

    Confined geometries are widespread in granular processing applications. The deformation and flow fields in such a geometry, with non-trivial boundary conditions, determine the resultant mechanical properties of the material (local porosity, density, residual stresses etc.). We present experimental studies of deformation and plastic flow of a prototypical granular medium in different nontrivial geometries- flat-punch compression, Couette-shear flow and a rigid body sliding past a granular half-space. These geometries represent simplified scaled-down versions of common industrial configurations such as compaction and dredging. The corresponding granular flows show a rich variety of flow features, representing the entire gamut of material types, from elastic solids (beam buckling) to fluids (vortex-formation, boundary layers) and even plastically deforming metals (dead material zone, pile-up). The effect of changing particle-level properties (e.g., shape, size, density) on the observed flows is also explicitly demonstrated. Non-smooth contact dynamics particle simulations are shown to reproduce some of the observed flow features quantitatively. These results showcase some central challenges facing continuum-scale constitutive theories for dynamic granular flows.

  10. General Relativity: Geometry Meets Physics

    Science.gov (United States)

    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…

  11. Learners engaging with transformation geometry

    African Journals Online (AJOL)

    participants engaged in investigative semi-structured interviews with the resear- chers. ... Keywords: analysis; conversions; transformation geometry; transformations; treatments .... semiotic systems of representation is not only to designate mathematical objects or to com- municate but also to ... Research design. We believe ...

  12. Multivariable calculus and differential geometry

    CERN Document Server

    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.

  13. College geometry a unified development

    CERN Document Server

    Kay, David C

    2011-01-01

    ""The book is a comprehensive textbook on basic geometry. … Key features of the book include numerous figures and many problems, more than half of which come with hints or even complete solutions. Frequent historical comments add to making the reading a pleasant one.""-Michael Joswig, Zentralblatt MATH 1273

  14. Geometry.

    Science.gov (United States)

    Mahaffey, Michael L.

    One of a series of experimental units for children at the preschool level, this booklet deals with geometric concepts. A unit on volume and a unit on linear measurement are covered; for each unit a discussion of mathematical objectives, a list of materials needed, and a sequence of learning activities are provided. Directions are specified for the…

  15. Geometri

    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...

  16. Discrete differential geometry. Consistency as integrability

    OpenAIRE

    Bobenko, Alexander I.; Suris, Yuri B.

    2005-01-01

    A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete geometry studies geometric shapes with finite number of elements (such as polyhedra), the discrete differential geometry aims at the development of discrete equivalents of notions and methods of smooth surface theory. Current interest in this field derives not ...

  17. Investigation of velocity distribution in an inner subchannel of wire wrapped fuel pin bundle of sodium-cooled fast reactor

    International Nuclear Information System (INIS)

    Nishimura, Masahiro; Kamide, Hideki; Ohshima, Hiroyuki; Kobayashi, Jun; Sato, Hiroyuki

    2011-01-01

    A sodium cooled fast reactor is designed to attain a high burn-up of core fuel in commercialized fast reactor cycle systems. In high burn-up fuel subassemblies, deformation of fuel pin due to the swelling and thermal bowing may decrease local flow velocity via change of flow area in the subassembly and influence the heat removal capability. Therefore, it is important to obtain the detail of flow velocity distribution in a wire wrapped pin bundle. In this study, water experiments were carried out to investigate the detailed velocity distribution in a subchannel of nominal pin geometry as the first step. These basic data are not only useful for understanding of pin bundle thermal hydraulics but also a code validation. A wire-wrapped 3-pin bundle water model was applied to investigate the detailed velocity distribution in the subchannel which is surrounded by 3 pins with wrapping wire. The test section consists of an irregular hexagonal acrylic duct tube and three pins made of fluorinated resin pins which has nearly the same refractive index with that of water and a high light transmission rate. This enables to visualize the central subchannel through the pins. The velocity distribution in the central subchannel with the wrapping wire was measured by PIV (Particle Image Velocimetry) through a side wall of the duct tube. Typical flow velocity conditions in the pin bundle were 0.36m/s (Re=2,700) and 1.6m/s (Re=13,500). Influence of the wrapping wire on the velocity distributions in vertical and horizontal directions was confirmed. A clockwise swirl flow around the wire was found in subchannel. Significant differences were not recognized between the two cases of Re=2,700 and 13,500 concerning flow patterns. (author)

  18. Code subspaces for LLM geometries

    Science.gov (United States)

    Berenstein, David; Miller, Alexandra

    2018-03-01

    We consider effective field theory around classical background geometries with a gauge theory dual, specifically those in the class of LLM geometries. These are dual to half-BPS states of N= 4 SYM. We find that the language of code subspaces is natural for discussing the set of nearby states, which are built by acting with effective fields on these backgrounds. This work extends our previous work by going beyond the strict infinite N limit. We further discuss how one can extract the topology of the state beyond N→∞ and find that, as before, uncertainty and entanglement entropy calculations provide a useful tool to do so. Finally, we discuss obstructions to writing down a globally defined metric operator. We find that the answer depends on the choice of reference state that one starts with. Therefore, within this setup, there is ambiguity in trying to write an operator that describes the metric globally.

  19. Euclidean distance geometry an introduction

    CERN Document Server

    Liberti, Leo

    2017-01-01

    This textbook, the first of its kind, presents the fundamentals of distance geometry:  theory, useful methodologies for obtaining solutions, and real world applications. Concise proofs are given and step-by-step algorithms for solving fundamental problems efficiently and precisely are presented in Mathematica®, enabling the reader to experiment with concepts and methods as they are introduced. Descriptive graphics, examples, and problems, accompany the real gems of the text, namely the applications in visualization of graphs, localization of sensor networks, protein conformation from distance data, clock synchronization protocols, robotics, and control of unmanned underwater vehicles, to name several.  Aimed at intermediate undergraduates, beginning graduate students, researchers, and practitioners, the reader with a basic knowledge of linear algebra will gain an understanding of the basic theories of distance geometry and why they work in real life.

  20. Fractal geometry and computer graphics

    CERN Document Server

    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...