Geometric numerical integration applied to the elastic pendulum at higher order resonance
Tuwankotta, J.M.; Quispel, G.R.W.
2000-01-01
In this paper we study the performance of a symplectic numerical integrator based on the splitting method This method is applied to a subtle problem ie higher order resonance of the elastic pendulum In order to numerically study the phase space of the elastic pendulum at higher order resonance a
On the numerical evaluation of algebro-geometric solutions to integrable equations
International Nuclear Information System (INIS)
Kalla, C; Klein, C
2012-01-01
Physically meaningful periodic solutions to certain integrable partial differential equations are given in terms of multi-dimensional theta functions associated with real Riemann surfaces. Typical analytical problems in the numerical evaluation of these solutions are studied. In the case of hyperelliptic surfaces efficient algorithms exist even for almost degenerate surfaces. This allows the numerical study of solitonic limits. For general real Riemann surfaces, the choice of a homology basis adapted to the anti-holomorphic involution is important for a convenient formulation of the solutions and smoothness conditions. Since existing algorithms for algebraic curves produce a homology basis not related to automorphisms of the curve, we study symplectic transformations to an adapted basis and give explicit formulae for M-curves. As examples we discuss solutions of the Davey–Stewartson and the multi-component nonlinear Schrödinger equations
Geometric and numerical foundations of movements
Mansard, Nicolas; Lasserre, Jean-Bernard
2017-01-01
This book aims at gathering roboticists, control theorists, neuroscientists, and mathematicians, in order to promote a multidisciplinary research on movement analysis. It follows the workshop “ Geometric and Numerical Foundations of Movements ” held at LAAS-CNRS in Toulouse in November 2015[1]. Its objective is to lay the foundations for a mutual understanding that is essential for synergetic development in motion research. In particular, the book promotes applications to robotics --and control in general-- of new optimization techniques based on recent results from real algebraic geometry.
Geometric integrators for stochastic rigid body dynamics
Tretyakov, Mikhail
2016-01-05
Geometric integrators play an important role in simulating dynamical systems on long time intervals with high accuracy. We will illustrate geometric integration ideas within the stochastic context, mostly on examples of stochastic thermostats for rigid body dynamics. The talk will be mainly based on joint recent work with Rusland Davidchak and Tom Ouldridge.
Geometric transitions and integrable systems
Diaconescu, D.-E.; Dijkgraaf, R.H.; Donagi, R.; Hofman, C.; Pantev, T.
2006-01-01
We consider B-model large N duality for a new class of noncompact Calabi-Yau spaces modeled on the neighborhood of a ruled surface in a Calabi-Yau threefold. The closed string side of the transition is governed at genus zero by an A(1) Hitchin integrable system on a genus g Riemann surface Sigma.
Geometric transitions and integrable systems
International Nuclear Information System (INIS)
Diaconescu, D.-E.; Dijkgraaf, R.; Donagi, R.; Hofman, C.; Pantev, T.
2006-01-01
We consider B-model large N duality for a new class of noncompact Calabi-Yau spaces modeled on the neighborhood of a ruled surface in a Calabi-Yau threefold. The closed string side of the transition is governed at genus zero by an A 1 Hitchin integrable system on a genus g Riemann surface Σ. The open string side is described by a holomorphic Chern-Simons theory which reduces to a generalized matrix model in which the eigenvalues lie on the compact Riemann surface Σ. We show that the large N planar limit of the generalized matrix model is governed by the same A 1 Hitchin system therefore proving genus zero large N duality for this class of transitions
Numerical and experimental investigation of geometric parameters in projection welding
DEFF Research Database (Denmark)
Kristensen, Lars; Zhang, Wenqi; Bay, Niels
2000-01-01
Resistance projection welding is widely used for joining of workpieces with almost any geometric combination. This makes standardization of projection welding impossible. In order to facilitate industrial applications of projection welding, systematic investigations are carried out on the geometric...... parameters by numerical modeling and experimental studies. SORPAS, an FEM program for numerical modeling of resistance welding, is developed as a tool to help in the phase of product design and process optimization in both spot and projection welding. A systematic experimental investigation of projection...... welding a disc to a ring with a triangular ring projection has been carried out to study the influence of the geometric parameters in various metal combinations. In these studies, SORPAS has been used as a supporting tool to understand the relationship of the parameters and the phenomena occurring...
Geometric, control and numeric aspects of nonholonomic systems
Cortés Monforte, Jorge
2002-01-01
Nonholonomic systems are a widespread topic in several scientific and commercial domains, including robotics, locomotion and space exploration. This work sheds new light on this interdisciplinary character through the investigation of a variety of aspects coming from several disciplines. The main aim is to illustrate the idea that a better understanding of the geometric structures of mechanical systems unveils new and unknown aspects to them, and helps both analysis and design to solve standing problems and identify new challenges. In this way, separate areas of research such as Classical Mechanics, Differential Geometry, Numerical Analysis or Control Theory are brought together in this study of nonholonomic systems.
Numerical Contour Integration for Loop Integrals
Kurihara, Y.; Kaneko, T.
2005-01-01
A fully numerical method to calculate loop integrals, a numerical contour-integration method, is proposed. Loop integrals can be interpreted as a contour integral in a complex plane for an integrand with multi-poles in the plane. Stable and efficient numerical integrations an along appropriate contour can be performed for tensor integrals as well as for scalar ones appearing in loop calculations of the standard model. Examples of 3- and 4-point diagrams in 1-loop integrals and 2- and 3-point ...
Numerical nonlinear complex geometrical optics algorithm for the 3D Calderón problem
DEFF Research Database (Denmark)
Delbary, Fabrice; Knudsen, Kim
2014-01-01
computer implementation of the full nonlinear algorithm is given. First a boundary integral equation is solved by a Nystrom method for the traces of the complex geometrical optics solutions, second the scattering transform is computed and inverted using fast Fourier transform, and finally a boundary value...... to the generalized Laplace equation. The 3D problem was solved in theory in late 1980s using complex geometrical optics solutions and a scattering transform. Several approximations to the reconstruction method have been suggested and implemented numerically in the literature, but here, for the first time, a complete...... to the simpler approximations. In addition, convergence of the numerical solution towards the exact solution of the boundary integral equation is proved....
Geometric integrator for simulations in the canonical ensemble
International Nuclear Information System (INIS)
Tapias, Diego; Sanders, David P.; Bravetti, Alessandro
2016-01-01
We introduce a geometric integrator for molecular dynamics simulations of physical systems in the canonical ensemble that preserves the invariant distribution in equations arising from the density dynamics algorithm, with any possible type of thermostat. Our integrator thus constitutes a unified framework that allows the study and comparison of different thermostats and of their influence on the equilibrium and non-equilibrium (thermo-)dynamic properties of a system. To show the validity and the generality of the integrator, we implement it with a second-order, time-reversible method and apply it to the simulation of a Lennard-Jones system with three different thermostats, obtaining good conservation of the geometrical properties and recovering the expected thermodynamic results. Moreover, to show the advantage of our geometric integrator over a non-geometric one, we compare the results with those obtained by using the non-geometric Gear integrator, which is frequently used to perform simulations in the canonical ensemble. The non-geometric integrator induces a drift in the invariant quantity, while our integrator has no such drift, thus ensuring that the system is effectively sampling the correct ensemble.
Numerical integration of variational equations.
Skokos, Ch; Gerlach, E
2010-09-01
We present and compare different numerical schemes for the integration of the variational equations of autonomous Hamiltonian systems whose kinetic energy is quadratic in the generalized momenta and whose potential is a function of the generalized positions. We apply these techniques to Hamiltonian systems of various degrees of freedom and investigate their efficiency in accurately reproducing well-known properties of chaos indicators such as the Lyapunov characteristic exponents and the generalized alignment indices. We find that the best numerical performance is exhibited by the "tangent map method," a scheme based on symplectic integration techniques which proves to be optimal in speed and accuracy. According to this method, a symplectic integrator is used to approximate the solution of the Hamilton equations of motion by the repeated action of a symplectic map S , while the corresponding tangent map TS is used for the integration of the variational equations. A simple and systematic technique to construct TS is also presented.
Cuba: Multidimensional numerical integration library
Hahn, Thomas
2016-08-01
The Cuba library offers four independent routines for multidimensional numerical integration: Vegas, Suave, Divonne, and Cuhre. The four algorithms work by very different methods, and can integrate vector integrands and have very similar Fortran, C/C++, and Mathematica interfaces. Their invocation is very similar, making it easy to cross-check by substituting one method by another. For further safeguarding, the output is supplemented by a chi-square probability which quantifies the reliability of the error estimate.
International Nuclear Information System (INIS)
Wilson, O.J.
1980-05-01
This report describes a numerical technique of determining the geometric efficiency of circular detector and various surface source arrangements. Circular sources are primarily discussed, but most other surface shapes can be accommodated by the technique
A simple numerical model of a geometrically nonlinear Timoshenko beam
Keijdener, C.; Metrikine, A.
2015-01-01
In the original problem for which this model was developed, onedimensional flexible objects interact through a non-linear contact model. Due to the non-linear nature of the contact model, a numerical time-domain approach was adopted. One of the goals was to see if the coupling between axial and
Davidchack, R. L.; Ouldridge, T. E.; Tretyakov, M. V.
2017-12-01
We introduce new Langevin-type equations describing the rotational and translational motion of rigid bodies interacting through conservative and non-conservative forces and hydrodynamic coupling. In the absence of non-conservative forces, the Langevin-type equations sample from the canonical ensemble. The rotational degrees of freedom are described using quaternions, the lengths of which are exactly preserved by the stochastic dynamics. For the proposed Langevin-type equations, we construct a weak 2nd order geometric integrator that preserves the main geometric features of the continuous dynamics. The integrator uses Verlet-type splitting for the deterministic part of Langevin equations appropriately combined with an exactly integrated Ornstein-Uhlenbeck process. Numerical experiments are presented to illustrate both the new Langevin model and the numerical method for it, as well as to demonstrate how inertia and the coupling of rotational and translational motion can introduce qualitatively distinct behaviours.
Purely geometric path integral for spin-foams
International Nuclear Information System (INIS)
Shirazi, Atousa Chaharsough; Engle, Jonathan
2014-01-01
Spin-foams are a proposal for defining the dynamics of loop quantum gravity via path integral. In order for a path integral to be at least formally equivalent to the corresponding canonical quantization, at each point in the space of histories it is important that the integrand have not only the correct phase—a topic of recent focus in spin-foams—but also the correct modulus, usually referred to as the measure factor. The correct measure factor descends from the Liouville measure on the reduced phase space, and its calculation is a task of canonical analysis. The covariant formulation of gravity from which spin-foams are derived is the Plebanski–Holst formulation, in which the basic variables are a Lorentz connection and a Lorentz-algebra valued 2-form, called the Plebanski 2-form. However, in the final spin-foam sum, one usually sums over only spins and intertwiners, which label eigenstates of the Plebanski 2-form alone. The spin-foam sum is therefore a discretized version of a Plebanski–Holst path integral in which only the Plebanski 2-form appears, and in which the connection degrees of freedom have been integrated out. We call this a purely geometric Plebanski–Holst path integral. In prior work in which one of the authors was involved, the measure factor for the Plebanski–Holst path integral with both connection and 2-form variables was calculated. Before one discretizes this measure and incorporates it into a spin-foam sum, however, one must integrate out the connection in order to obtain the purely geometric version of the path integral. To calculate this purely geometric path integral is the principal task of the present paper, and it is done in two independent ways. Background independence of the resulting path integral is discussed in the final section, and gauge-fixing is discussed in appendix B. (paper)
Numerical Quadrature of Periodic Singular Integral Equations
DEFF Research Database (Denmark)
Krenk, Steen
1978-01-01
This paper presents quadrature formulae for the numerical integration of a singular integral equation with Hilbert kernel. The formulae are based on trigonometric interpolation. By integration a quadrature formula for an integral with a logarithmic singularity is obtained. Finally it is demonstra......This paper presents quadrature formulae for the numerical integration of a singular integral equation with Hilbert kernel. The formulae are based on trigonometric interpolation. By integration a quadrature formula for an integral with a logarithmic singularity is obtained. Finally...... it is demonstrated how a singular integral equation with infinite support can be solved by use of the preceding formulae....
Geometric Realizations of Bi-Hamiltonian Completely Integrable Systems
Directory of Open Access Journals (Sweden)
Gloria Marí Beffa
2008-03-01
Full Text Available In this paper we present an overview of the connection between completely integrable systems and the background geometry of the flow. This relation is better seen when using a group-based concept of moving frame introduced by Fels and Olver in [Acta Appl. Math. 51 (1998, 161-213; 55 (1999, 127-208]. The paper discusses the close connection between different types of geometries and the type of equations they realize. In particular, we describe the direct relation between symmetric spaces and equations of KdV-type, and the possible geometric origins of this connection.
An integrated introduction to computer graphics and geometric modeling
Goldman, Ronald
2009-01-01
… this book may be the first book on geometric modelling that also covers computer graphics. In addition, it may be the first book on computer graphics that integrates a thorough introduction to 'freedom' curves and surfaces and to the mathematical foundations for computer graphics. … the book is well suited for an undergraduate course. … The entire book is very well presented and obviously written by a distinguished and creative researcher and educator. It certainly is a textbook I would recommend. …-Computer-Aided Design, 42, 2010… Many books concentrate on computer programming and soon beco
International Nuclear Information System (INIS)
Chen, Wei-Hsin; Wang, Chien-Chang; Hung, Chen-I
2014-01-01
Graphical abstract: - Highlights: • An integrated thermoelectric generation-cooling system is analyzed numerically. • The system performance is improved through the geometric design. • The effects of contact resistance and heat convection on performance are considered. • With varied TEG length, the system performance depends on boundary conditions. • The study provides a useful insight into the design of integrated TEG–TEC systems. - Abstract: Geometric design of an integrated thermoelectric generation-cooling system is performed numerically using a finite element method. In the system, a thermoelectric cooler (TEC) is powered directly by a thermoelectric generator (TEG). Two different boundary conditions in association with the effects of contact resistance and heat convection on system performance are taken into account. The results suggest that the characteristics of system performance under varying TEG length are significantly different from those under altering TEC length. When the TEG length is changed, the entire behavior of system performance depends highly on the boundary conditions. On the other hand, the maximum distributions of cooling power and coefficient of performance (COP) are exhibited when the TEC length is altered, whether the hot surface of TEG is given by a fixed temperature or heat transfer rate. The system performance will be reduced once the contact resistance and heat convection are considered. When the lengths of TEG and TEC vary, the maximum reduction percentages of system performance are 12.45% and 18.67%, respectively. The numerical predictions have provided a useful insight into the design of integrated TEG–TEC systems
Combinatorial and geometric aspects of Feynman graphs and Feynman integrals
International Nuclear Information System (INIS)
Bergbauer, Christoph
2009-01-01
The integrals associated to Feynman graphs must have been a source of frustration for particle physicists ever since. Indeed there is a delicate difference between being able to draw a Feynman graph and being able to compute the associated Feynman integral. Although perturbation theory has brought enormous breakthroughs, many physicists turned to more abstract developments in quantum field theory, looked for other ways to produce perturbational results, or left the field entirely. Nonetheless there is a significant number of physicists, computational and theoretical, who pursue the quest for concepts and algorithms to compute and understand those integrals to higher and higher orders. Their motivation is to help test the validity of the underlying physical theory. For a mathematician, Feynman graphs and their integrals provide a rich subject in their own right, independent of their computability. It was only recently though that the work of Bloch, Esnault and Kreimer has brought a growing interest of mathematicians from various disciplines to the subject. In fact it opened up a completely new direction of research: a motivic interpretation of Feynman graphs that unites their combinatorial, geometric and arithmetic aspects. This idea had been in the air for a while, based on computational results of Broadhurst and Kreimer, and on a theorem of Belkale and Brosnan related to a conjecture of Kontsevich about the generality of the underlying motives. A prerequisite for the motivic approach is a profound understanding of renormalization that was established less recently in a modern language by Connes and Kreimer. This dissertation studies the renormalization of Feynman graphs in position space using an adapted resolution of singularities, and makes two other contributions of mostly combinatorial nature to the subject. I hope this may serve as a reference for somebody who feels comfortable with the traditional position space literature and looks for a transition to the
Numerical time integration for air pollution models
J.G. Verwer (Jan); W. Hundsdorfer (Willem); J.G. Blom (Joke)
1998-01-01
textabstractDue to the large number of chemical species and the three space dimensions, off-the-shelf stiff ODE integrators are not feasible for the numerical time integration of stiff systems of advection-diffusion-reaction equations [ fracpar{c{t + nabla cdot left( vu{u c right) = nabla cdot left(
A numerical method for resonance integral calculations
International Nuclear Information System (INIS)
Tanbay, Tayfun; Ozgener, Bilge
2013-01-01
A numerical method has been proposed for resonance integral calculations and a cubic fit based on least squares approximation to compute the optimum Bell factor is given. The numerical method is based on the discretization of the neutron slowing down equation. The scattering integral is approximated by taking into account the location of the upper limit in energy domain. The accuracy of the method has been tested by performing computations of resonance integrals for uranium dioxide isolated rods and comparing the results with empirical values. (orig.)
Fibonacci numerical integration on a sphere
International Nuclear Information System (INIS)
Hannay, J H; Nye, J F
2004-01-01
For elementary numerical integration on a sphere, there is a distinct advantage in using an oblique array of integration sampling points based on a chosen pair of successive Fibonacci numbers. The pattern has a familiar appearance of intersecting spirals, avoiding the local anisotropy of a conventional latitude-longitude array. Besides the oblique Fibonacci array, the prescription we give is also based on a non-uniform scaling used for one-dimensional numerical integration, and indeed achieves the same order of accuracy as for one dimension: error ∼N -6 for N points. This benefit of Fibonacci is not shared by domains of integration with boundaries (e.g., a square, for which it was originally proposed); with non-uniform scaling the error goes as N -3 , with or without Fibonacci. For experimental measurements over a sphere our prescription is realized by a non-uniform Fibonacci array of weighted sampling points
The dynamical systems approach to numerical integration
Wisdom, Jack
2018-03-01
The dynamical systems approach to numerical integration is reviewed and extended. The new method is compared to some alternative methods based on the Lie series approach. The test problem is the motion of the outer planets. The algorithms developed using the dynamical systems approach perform well.
Automatic numerical integration methods for Feynman integrals through 3-loop
International Nuclear Information System (INIS)
De Doncker, E; Olagbemi, O; Yuasa, F; Ishikawa, T; Kato, K
2015-01-01
We give numerical integration results for Feynman loop diagrams through 3-loop such as those covered by Laporta [1]. The methods are based on automatic adaptive integration, using iterated integration and extrapolation with programs from the QUADPACK package, or multivariate techniques from the ParInt package. The Dqags algorithm from QuadPack accommodates boundary singularities of fairly general types. PARINT is a package for multivariate integration layered over MPI (Message Passing Interface), which runs on clusters and incorporates advanced parallel/distributed techniques such as load balancing among processes that may be distributed over a network of nodes. Results are included for 3-loop self-energy diagrams without IR (infra-red) or UV (ultra-violet) singularities. A procedure based on iterated integration and extrapolation yields a novel method of numerical regularization for integrals with UV terms, and is applied to a set of 2-loop self-energy diagrams with UV singularities. (paper)
Kou, Jisheng
2015-07-16
In this paper, we consider an interface model for multicomponent two-phase fluids with geometric mean influence parameters, which is popularly used to model and predict surface tension in practical applications. For this model, there are two major challenges in theoretical analysis and numerical simulation: the first one is that the influence parameter matrix is not positive definite; the second one is the complicated structure of the energy function, which requires us to find out a physically consistent treatment. To overcome these two challenging problems, we reduce the formulation of the energy function by employing a linear transformation and a weighted molar density, and furthermore, we propose a local minimum grand potential energy condition to establish the relation between the weighted molar density and mixture compositions. From this, we prove the existence of the solution under proper conditions and prove the maximum principle of the weighted molar density. For numerical simulation, we propose a modified Newton\\'s method for solving this nonlinear model and analyze its properties; we also analyze a finite element method with a physical-based adaptive mesh-refinement technique. Numerical examples are tested to verify the theoretical results and the efficiency of the proposed methods.
International Nuclear Information System (INIS)
Bona, Carles; Lehner, Luis; Palenzuela-Luque, Carlos
2005-01-01
We study the implications of adopting hyperbolic-driver coordinate conditions motivated by geometrical considerations. In particular, conditions that minimize the rate of change of the metric variables. We analyze the properties of the resulting system of equations and their effect when implementing excision techniques. We find that commonly used coordinate conditions lead to a characteristic structure at the excision surface where some modes are not of outflow type with respect to any excision boundary chosen inside the horizon. Thus, boundary conditions are required for these modes. Unfortunately, the specification of these conditions is a delicate issue as the outflow modes involve both gauge and main variables. As an alternative to these driver equations, we examine conditions derived from extremizing a scalar constructed from Killing's equation and present specific numerical examples
An integrated numerical protection system (SPIN)
International Nuclear Information System (INIS)
Savornin, J.L.; Bouchet, J.M.; Furet, J.L.; Jover, P.; Sala, A.
1978-01-01
Developments in technology have now made it possible to perform more sophisticated protection functions which follow more closely the physical phenomena to be monitored. For this reason the Commissariat a l'energie atomique, Merlin-Gerin, Cerci and Framatome have embarked on the joint development of an Integrated Numerical Protection System (SPIN) which will fulfil this objective and will improve the safety and availability of power stations. The system described involves the use of programmed numerical techniques and a structure based on multiprocessors. The architecture has a redundancy of four. Throughout the development of the project the validity of the studies was confirmed by experiments. A first numerical model of a protection function was tested in the laboratory and is now in operation in a power station. A set of models was then introduced for checking the main components of the equipment finally chosen prior to building and testing a prototype. (author)
Directory of Open Access Journals (Sweden)
Ye-Wei Zhang
2017-01-01
Full Text Available This paper presents a novel design by integrating geometrical and material nonlinear energy sink (NES with a piezoelectric-based vibration energy harvester under shock excitation, which can realize vibration control and energy harvesting. The nonlinear spring and hysteresis behavior of the NES could reflect geometrical and material nonlinearity, respectively. Two configurations of the piezoelectric device, including the piezoelectric element embedded between the NES mass and the single-degree-of-freedom system or ground, are utilised to examine the energy dissipated by damper and hysteresis behavior of NES and the energy harvested by the piezoelectric element. Similar numerical research methods of Runge-Kutta algorithm are used to investigate the two configurations. The energy transaction measure (ETM is adopted to examine the instantaneous energy transaction between the primary and the NES-piezoelectricity system. And it demonstrates that the dissipated and harvested energy transaction is transferred from the primary system to the NES-piezoelectricity system and the instantaneous transaction of mechanical energy occupies a major part of the energy of transaction. Both figurations could realize vibration control efficiently.
Geometrical-integrability constraints and equations of motion in four plus extended super spaces
International Nuclear Information System (INIS)
Chau, L.L.
1987-01-01
It is pointed out that many equations of motion in physics, including gravitational and Yang-Mills equations, have a common origin: i.e. they are the results of certain geometrical integrability conditions. These integrability conditions lead to linear systems and conservation laws that are important in integrating these equations of motion
Su, Lijuan; Wang, Fei; He, Peng; Dambon, Olaf; Klocke, Fritz; Yi, Allen Y.
2014-02-01
In precision glass molding, refractive index change and geometric deviation (or curve change as often referred to in industry) occurred during molding process can result in substantial amount of aberrations. Previously, refractive index change and geometric deviation were investigated in separate studies by the authors. However, optical performance of a molded glass lens depends on both refractive index and geometry. In order to mold lenses with optimal performance, both refractive index change and geometric deviation have to be taken into consideration simultaneously and compensated. This paper presented an integrated compensation procedure for modifying molds to compensate both refractive index change and geometric deviation. Group refractive index change predicted by the finite element method simulation was used to provide a modified geometry design for a desired lens. Geometric deviations of molded glass lenses with the modified design were analyzed with a previously developed numerical simulation approach, which is used to modify the mold shape. This procedure was validated by molding a generic aspherical glass lens. Both geometry and optical measurement results confirmed that the molded lens performed as specified by the original design. It also demonstrated that finite element method assisted compensation procedure can be used to predict the final optical performance of compression molded glass components. This research provided an opportunity for optics manufacturers to achieve better performance lens while maintaining lower cost and a shorter cycle time.
Parker, Jeffrey B.
2018-05-01
Zonal flows have been observed to appear spontaneously from turbulence in a number of physical settings. A complete theory for their behavior is still lacking. Recently, a number of studies have investigated the dynamics of zonal flows using quasilinear (QL) theories and the statistical framework of a second-order cumulant expansion (CE2). A geometrical-optics (GO) reduction of CE2, derived under an assumption of separation of scales between the fluctuations and the zonal flow, is studied here numerically. The reduced model, CE2-GO, has a similar phase-space mathematical structure to the traditional wave-kinetic equation, but that wave-kinetic equation has been shown to fail to preserve enstrophy conservation and to exhibit an ultraviolet catastrophe. CE2-GO, in contrast, preserves nonlinear conservation of both energy and enstrophy. We show here how to retain these conservation properties in a pseudospectral simulation of CE2-GO. We then present nonlinear simulations of CE2-GO and compare with direct simulations of quasilinear (QL) dynamics. We find that CE2-GO retains some similarities to QL. The partitioning of energy that resides in the zonal flow is in good quantitative agreement between CE2-GO and QL. On the other hand, the length scale of the zonal flow does not follow the same qualitative trend in the two models. Overall, these simulations indicate that CE2-GO provides a simpler and more tractable statistical paradigm than CE2, but CE2-GO is missing important physics.
Applying recursive numerical integration techniques for solving high dimensional integrals
Energy Technology Data Exchange (ETDEWEB)
Ammon, Andreas [IVU Traffic Technologies AG, Berlin (Germany); Genz, Alan [Washington State Univ., Pullman, WA (United States). Dept. of Mathematics; Hartung, Tobias [King' s College, London (United Kingdom). Dept. of Mathematics; Jansen, Karl; Volmer, Julia [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Leoevey, Hernan [Humboldt Univ. Berlin (Germany). Inst. fuer Mathematik
2016-11-15
The error scaling for Markov-Chain Monte Carlo techniques (MCMC) with N samples behaves like 1/√(N). This scaling makes it often very time intensive to reduce the error of computed observables, in particular for applications in lattice QCD. It is therefore highly desirable to have alternative methods at hand which show an improved error scaling. One candidate for such an alternative integration technique is the method of recursive numerical integration (RNI). The basic idea of this method is to use an efficient low-dimensional quadrature rule (usually of Gaussian type) and apply it iteratively to integrate over high-dimensional observables and Boltzmann weights. We present the application of such an algorithm to the topological rotor and the anharmonic oscillator and compare the error scaling to MCMC results. In particular, we demonstrate that the RNI technique shows an error scaling in the number of integration points m that is at least exponential.
Applying recursive numerical integration techniques for solving high dimensional integrals
International Nuclear Information System (INIS)
Ammon, Andreas; Genz, Alan; Hartung, Tobias; Jansen, Karl; Volmer, Julia; Leoevey, Hernan
2016-11-01
The error scaling for Markov-Chain Monte Carlo techniques (MCMC) with N samples behaves like 1/√(N). This scaling makes it often very time intensive to reduce the error of computed observables, in particular for applications in lattice QCD. It is therefore highly desirable to have alternative methods at hand which show an improved error scaling. One candidate for such an alternative integration technique is the method of recursive numerical integration (RNI). The basic idea of this method is to use an efficient low-dimensional quadrature rule (usually of Gaussian type) and apply it iteratively to integrate over high-dimensional observables and Boltzmann weights. We present the application of such an algorithm to the topological rotor and the anharmonic oscillator and compare the error scaling to MCMC results. In particular, we demonstrate that the RNI technique shows an error scaling in the number of integration points m that is at least exponential.
Numerical Integration with GeoGebra in High School
Herceg, Dorde; Herceg, Dragoslav
2010-01-01
The concept of definite integral is almost always introduced as the Riemann integral, which is defined in terms of the Riemann sum, and its geometric interpretation. This definition is hard to understand for high school students. With the aid of mathematical software for visualisation and computation of approximate integrals, the notion of…
Spatiotemporal feature integration shapes approximate numerical processing.
Fornaciai, Michele; Park, Joonkoo
2017-11-01
Numerosity perception involves a complex cascade of processing stages comprising an early sensory representation stage followed by a later stage providing a conceptual representation of numerical magnitude. While much recent work has focused on understanding how nonnumerical spatial features (e.g., density, area) influence numerosity perception in this processing cascade, little is known about how the spatiotemporal properties of the stimuli affect numerosity processing. Whether numerosity information is integrated over space and time in the processing cascade is an important question as it can provide insights into how the system dedicated for numerosity interacts with other perceptual systems. To address these issues, in four independent experiments, we asked participants to judge the numerosities of various different kinds of dynamically presented dot arrays, such as dots randomly changing in their locations, moving in smooth trajectories, or flickering on and off. The results revealed a systematic overestimation of dynamically presented dot arrays, which implicates the existence of spatiotemporal integration mechanisms, both at the early sensory representation stage and the later conceptual representation stage. The results also revealed the influence of motion and color processing areas on numerosity processing. The findings thus provide empirical evidence that numerosity perception arises from a complex interaction between multiple perceptual mechanisms in the visual stream, and that it is shaped by the integration of spatiotemporal properties of visual stimuli.
The Neumann Type Systems and Algebro-Geometric Solutions of a System of Coupled Integrable Equations
International Nuclear Information System (INIS)
Chen Jinbing; Qiao Zhijun
2011-01-01
A system of (1+1)-dimensional coupled integrable equations is decomposed into a pair of new Neumann type systems that separate the spatial and temporal variables for this system over a symplectic submanifold. Then, the Neumann type flows associated with the coupled integrable equations are integrated on the complex tour of a Riemann surface. Finally, the algebro-geometric solutions expressed by Riemann theta functions of the system of coupled integrable equations are obtained by means of the Jacobi inversion.
Wang, Zheng; Xu, Xiaochuan; Fan, Donglei; Wang, Yaguo; Subbaraman, Harish; Chen, Ray T
2016-05-05
Subwavelength grating (SWG) waveguide is an intriguing alternative to conventional optical waveguides due to the extra degree of freedom it offers in tuning a few important waveguide properties, such as dispersion and refractive index. Devices based on SWG waveguides have demonstrated impressive performances compared to conventional waveguides. However, the high loss of SWG waveguide bends jeopardizes their applications in integrated photonic circuits. In this work, we propose a geometrical tuning art, which realizes a pre-distorted refractive index profile in SWG waveguide bends. The pre-distorted refractive index profile can effectively reduce the mode mismatch and radiation loss simultaneously, thus significantly reduce the bend loss. This geometry tuning art has been numerically optimized and experimentally demonstrated in present study. Through such tuning, the average insertion loss of a 5 μm SWG waveguide bend is reduced drastically from 5.43 dB to 1.10 dB per 90° bend for quasi-TE polarization. In the future, the proposed scheme will be utilized to enhance performance of a wide range of SWG waveguide based photonics devices.
Numerical Differentiation and Integration through Aitken-Neville Schemes
Directory of Open Access Journals (Sweden)
Ramesh Kumar Muthumalai
2013-09-01
Full Text Available Some new formulas are given to approximate higher order derivatives and integrals through Aitken-Neville iterative schemes for arbitrary spaced grids. An algorithm is given in MATLAB for numerical differentiation. Also, numerical examples are provided to study error analysis of new formulas for numerical differentiation and integration.
Directory of Open Access Journals (Sweden)
Guliar O.
2015-12-01
Full Text Available On the basis of virtual work variations a new finite element with a variable crosssectional area along a generation, which due to numerical integration takes into account the variability of mechanical and geometrical parameters in cross-section was developed. In the process of test problem solving the correctness of the results, which allows to get this version of FE, was confirmed.
Towards AN Integration of GIS and Bim Data: what are the Geometric and Topological Issues?
Arroyo Ohori, K.; Biljecki, F.; Diakité, A.; Krijnen, T.; Ledoux, H.; Stoter, J.
2017-10-01
Geographic information and building information modelling both model buildings and infrastructure, but the way in which they are modelled is usually complimentary and BIM-GIS integration is widely considered as a way forward for both domains. For one, more detailed BIM data can feed more general GIS data and GIS data can provide the context that is necessary to BIM data. While previous studies have focused on the theoretical aspects of such an integration at a schema level, in this paper we focus on explaining the geometric and topological issues we have found while trying to develop software to realise such an integration in practice and at a data level. In our preliminary results, which are presented here, we have found that many issues for such an integration remain: handling the geometric and topological problems in BIM models, dealing with bad georeferencing and figuring out the best way to convert data between IFC and CityGML are all open issues.
A Generalized Technique in Numerical Integration
Safouhi, Hassan
2018-02-01
Integration by parts is one of the most popular techniques in the analysis of integrals and is one of the simplest methods to generate asymptotic expansions of integral representations. The product of the technique is usually a divergent series formed from evaluating boundary terms; however, sometimes the remaining integral is also evaluated. Due to the successive differentiation and anti-differentiation required to form the series or the remaining integral, the technique is difficult to apply to problems more complicated than the simplest. In this contribution, we explore a generalized and formalized integration by parts to create equivalent representations to some challenging integrals. As a demonstrative archetype, we examine Bessel integrals, Fresnel integrals and Airy functions.
IsoGeometric Analysis : a New Paradigm in the Numerical Approximation of PDEs : a CIME school
Sangalli, Giancarlo
2016-01-01
Providing an introduction to isogeometric methods with a focus on their mathematical foundations, this book is composed of four chapters, each devoted to a topic of special interests for isogeometric methods and their theoretical understanding. It contains a tutorial on splines and generalizations that are used in CAD parametrizations, and gives an overview of geometric modeling techniques that can be used within the isogeometric approach, with a focus on non-tensor product splines. Finally, it presents the mathematical properties of isogeometric spaces and spline spaces for vector field approximations, and treats in detail an application of fundamental importance: the isogeometric simulation of a viscous incompressible flow.
Geometric and approximation properties of some singular integrals in the unit disk
Directory of Open Access Journals (Sweden)
Gal Sorin G
2006-01-01
Full Text Available The purpose of this paper is to prove several results in approximation by complex Picard, Poisson-Cauchy, and Gauss-Weierstrass singular integrals with Jackson-type rate, having the quality of preservation of some properties in geometric function theory, like the preservation of coefficients' bounds, positive real part, bounded turn, starlikeness, and convexity. Also, some sufficient conditions for starlikeness and univalence of analytic functions are preserved.
Directory of Open Access Journals (Sweden)
HE Handong
2017-08-01
Full Text Available Using GIS, data models of geology via geometric descriptions and expressions are being developed. However, the role played by these data models in terms of the description and expression of geological structure phenomenon is limited. To improve the semantic information in geological GIS data models, this study adopts an object-oriented method that describes and expresses the geometric and semantic features of the geological structure phenomenon using geological objects and designs a data model of regional geological structures by integrating geometry and semantics. Moreover, the study designs a semantic "vocabulary-explanation-graph" method for describing the geological phenomenon of structures. Based on the semantic features of regional geological structures and a linear classification method, it divides the regional geological structure phenomenon into 3 divisions, 10 groups, 33 classes and defines the element set and element class. Moreover, it builds the basic geometric network for geological elements based on the geometric and semantic relations among geological objects. Using the ArcGIS Diagrammer Geodatabase, it considers the regional geological structure of the Ning-Zhen Mountains to verify the data model, and the results indicate a high practicability.
DEFF Research Database (Denmark)
Gorji, Mofid; Mirgolbabaei, Hessam; Barari, Amin
2010-01-01
In this paper a two-dimensional numerical simulation of a steady incompressible and turbulent model has been carried out to study the effects of vortex generators in a compact heat exchanger in a curvilinear coordinate system. The mesh which is applied in this study is boundary fitted and has been...
Integrating spatial and numerical structure in mathematical patterning
Ni’mah, K.; Purwanto; Irawan, E. B.; Hidayanto, E.
2018-03-01
This paper reports a study monitoring the integrating spatial and numerical structure in mathematical patterning skills of 30 students grade 7th of junior high school. The purpose of this research is to clarify the processes by which learners construct new knowledge in mathematical patterning. Findings indicate that: (1) students are unable to organize the structure of spatial and numerical, (2) students were only able to organize the spatial structure, but the numerical structure is still incorrect, (3) students were only able to organize numerical structure, but its spatial structure is still incorrect, (4) students were able to organize both of the spatial and numerical structure.
International Nuclear Information System (INIS)
Dolly, S; Chen, H; Mutic, S; Anastasio, M; Li, H
2016-01-01
Purpose: A persistent challenge for the quality assessment of radiation therapy treatments (e.g. contouring accuracy) is the absence of the known, ground truth for patient data. Moreover, assessment results are often patient-dependent. Computer simulation studies utilizing numerical phantoms can be performed for quality assessment with a known ground truth. However, previously reported numerical phantoms do not include the statistical properties of inter-patient variations, as their models are based on only one patient. In addition, these models do not incorporate tumor data. In this study, a methodology was developed for generating numerical phantoms which encapsulate the statistical variations of patients within radiation therapy, including tumors. Methods: Based on previous work in contouring assessment, geometric attribute distribution (GAD) models were employed to model both the deterministic and stochastic properties of individual organs via principle component analysis. Using pre-existing radiation therapy contour data, the GAD models are trained to model the shape and centroid distributions of each organ. Then, organs with different shapes and positions can be generated by assigning statistically sound weights to the GAD model parameters. Organ contour data from 20 retrospective prostate patient cases were manually extracted and utilized to train the GAD models. As a demonstration, computer-simulated CT images of generated numerical phantoms were calculated and assessed subjectively and objectively for realism. Results: A cohort of numerical phantoms of the male human pelvis was generated. CT images were deemed realistic both subjectively and objectively in terms of image noise power spectrum. Conclusion: A methodology has been developed to generate realistic numerical anthropomorphic phantoms using pre-existing radiation therapy data. The GAD models guarantee that generated organs span the statistical distribution of observed radiation therapy patients
Parallel Algorithm for Adaptive Numerical Integration
International Nuclear Information System (INIS)
Sujatmiko, M.; Basarudin, T.
1997-01-01
This paper presents an automation algorithm for integration using adaptive trapezoidal method. The interval is adaptively divided where the width of sub interval are different and fit to the behavior of its function. For a function f, an integration on interval [a,b] can be obtained, with maximum tolerance ε, using estimation (f, a, b, ε). The estimated solution is valid if the error is still in a reasonable range, fulfil certain criteria. If the error is big, however, the problem is solved by dividing it into to similar and independent sub problem on to separate [a, (a+b)/2] and [(a+b)/2, b] interval, i. e. ( f, a, (a+b)/2, ε/2) and (f, (a+b)/2, b, ε/2) estimations. The problems are solved in two different kinds of processor, root processor and worker processor. Root processor function ti divide a main problem into sub problems and distribute them to worker processor. The division mechanism may go further until all of the sub problem are resolved. The solution of each sub problem is then submitted to the root processor such that the solution for the main problem can be obtained. The algorithm is implemented on C-programming-base distributed computer networking system under parallel virtual machine platform
Case studies in the numerical solution of oscillatory integrals
International Nuclear Information System (INIS)
Adam, G.
1992-06-01
A numerical solution of a number of 53,249 test integrals belonging to nine parametric classes was attempted by two computer codes: EAQWOM (Adam and Nobile, IMA Journ. Numer. Anal. (1991) 11, 271-296) and DO1ANF (Mark 13, 1988) from the NAG library software. For the considered test integrals, EAQWOM was found to be superior to DO1ANF as it concerns robustness, reliability, and friendly user information in case of failure. (author). 9 refs, 3 tabs
Numerical integrators for Stiff and Stiff oscillatory First Order initial ...
African Journals Online (AJOL)
Numerical integrators for Stiff and Stiff oscillatory First Order initial value problems. ... Journal of the Nigerian Association of Mathematical Physics ... In this paper, efforts are geared towards the numerical solution of the first order initial value problem (I.V.P) of the form Y\\' = F(X,Y), X∈[ a, b] , Y(a) = Y0, where Y\\' is the total ...
Directory of Open Access Journals (Sweden)
Chuan Wang
2013-01-01
Full Text Available In order to improve the efficiency of stainless steel stamping multistage pump, quadratic regression orthogonal test, hydraulic design, and computational fluid dynamics (CFD are used to analyze the effect of pump geometric parameters. Sixteen impellers are designed based on the quadratic regression orthogonal test, which have three factors including impeller outlet slope, impeller blade outlet stagger angle, and impeller blade outlet width. Through quadratic regression equation, the function relationship between efficiency values and three factors is established. The optimal combination of geometric parameters is found through the analysis of the regression equation. To further study the influence of blade thickness on the performance of multistage pump, numerical simulations of multistage pump with different blade thicknesses are carried out. The influence law of blade thickness on pump performance is built from the external characteristics and internal flow field. In conclusion, with the increase of blade thickness, the best efficiency point of the pump shifts to the small flow rate direction, and the vortex regions inside the pump at rated flow gradually increase, which is the main reason that pump efficiency decreases along with the increase of the blade thickness at rated flow.
Image Retrieval based on Integration between Color and Geometric Moment Features
International Nuclear Information System (INIS)
Saad, M.H.; Saleh, H.I.; Konbor, H.; Ashour, M.
2012-01-01
Content based image retrieval is the retrieval of images based on visual features such as colour, texture and shape. .the Current approaches to CBIR differ in terms of which image features are extracted; recent work deals with combination of distances or scores from different and usually independent representations in an attempt to induce high level semantics from the low level descriptors of the images. content-based image retrieval has many application areas such as, education, commerce, military, searching, commerce, and biomedicine and Web image classification. This paper proposes a new image retrieval system, which uses color and geometric moment feature to form the feature vectors. Bhattacharyya distance and histogram intersection are used to perform feature matching. This framework integrates the color histogram which represents the global feature and geometric moment as local descriptor to enhance the retrieval results. The proposed technique is proper for precisely retrieving images even in deformation cases such as geometric deformations and noise. It is tested on a standard the results shows that a combination of our approach as a local image descriptor with other global descriptors outperforms other approaches.
Translation and integration of numerical atomic orbitals in linear molecules
International Nuclear Information System (INIS)
Heinäsmäki, Sami
2014-01-01
We present algorithms for translation and integration of atomic orbitals for LCAO calculations in linear molecules. The method applies to arbitrary radial functions given on a numerical mesh. The algorithms are based on pseudospectral differentiation matrices in two dimensions and the corresponding two-dimensional Gaussian quadratures. As a result, multicenter overlap and Coulomb integrals can be evaluated effectively
Translation and integration of numerical atomic orbitals in linear molecules
Energy Technology Data Exchange (ETDEWEB)
Heinäsmäki, Sami, E-mail: sami.heinasmaki@gmail.com [Department of Physics, University of Oulu, FIN-90014, Oulu (Finland)
2014-02-14
We present algorithms for translation and integration of atomic orbitals for LCAO calculations in linear molecules. The method applies to arbitrary radial functions given on a numerical mesh. The algorithms are based on pseudospectral differentiation matrices in two dimensions and the corresponding two-dimensional Gaussian quadratures. As a result, multicenter overlap and Coulomb integrals can be evaluated effectively.
Translation and integration of numerical atomic orbitals in linear molecules.
Heinäsmäki, Sami
2014-02-14
We present algorithms for translation and integration of atomic orbitals for LCAO calculations in linear molecules. The method applies to arbitrary radial functions given on a numerical mesh. The algorithms are based on pseudospectral differentiation matrices in two dimensions and the corresponding two-dimensional Gaussian quadratures. As a result, multicenter overlap and Coulomb integrals can be evaluated effectively.
Translation and integration of numerical atomic orbitals in linear molecules
Heinäsmäki, Sami
2014-02-01
We present algorithms for translation and integration of atomic orbitals for LCAO calculations in linear molecules. The method applies to arbitrary radial functions given on a numerical mesh. The algorithms are based on pseudospectral differentiation matrices in two dimensions and the corresponding two-dimensional Gaussian quadratures. As a result, multicenter overlap and Coulomb integrals can be evaluated effectively.
Canonical algorithms for numerical integration of charged particle motion equations
Efimov, I. N.; Morozov, E. A.; Morozova, A. R.
2017-02-01
A technique for numerically integrating the equation of charged particle motion in a magnetic field is considered. It is based on the canonical transformations of the phase space in Hamiltonian mechanics. The canonical transformations make the integration process stable against counting error accumulation. The integration algorithms contain a minimum possible amount of arithmetics and can be used to design accelerators and devices of electron and ion optics.
Numerical Integration of the Transport Equation For Infinite Homogeneous Media
Energy Technology Data Exchange (ETDEWEB)
Haakansson, Rune
1962-01-15
The transport equation for neutrons in infinite homogeneous media is solved by direct numerical integration. Accounts are taken to the anisotropy and the inelastic scattering. The integration has been performed by means of the trapezoidal rule and the length of the energy intervals are constant in lethargy scale. The machine used is a Ferranti Mercury computer. Results are given for water, heavy water, aluminium water mixture and iron-aluminium-water mixture.
International Nuclear Information System (INIS)
Witkowski, W.R.; Eldred, M.S.; Harding, D.C.
1994-01-01
The use of state-of-the-art numerical analysis tools to determine the optimal design of a radioactive material (RAM) transportation container is investigated. The design of a RAM package's components involves a complex coupling of structural, thermal, and radioactive shielding analyses. The final design must adhere to very strict design constraints. The current technique used by cask designers is uncoupled and involves designing each component separately with respect to its driving constraint. With the use of numerical optimization schemes, the complex couplings can be considered directly, and the performance of the integrated package can be maximized with respect to the analysis conditions. This can lead to more efficient package designs. Thermal and structural accident conditions are analyzed in the shape optimization of a simplified cask design. In this paper, details of the integration of numerical analysis tools, development of a process model, nonsmoothness difficulties with the optimization of the cask, and preliminary results are discussed
Monograph - The Numerical Integration of Ordinary Differential Equations.
Hull, T. E.
The materials presented in this monograph are intended to be included in a course on ordinary differential equations at the upper division level in a college mathematics program. These materials provide an introduction to the numerical integration of ordinary differential equations, and they can be used to supplement a regular text on this…
Preserving Simplecticity in the Numerical Integration of Linear Beam Optics
Energy Technology Data Exchange (ETDEWEB)
Allen, Christopher K. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
2017-07-01
Presented are mathematical tools and methods for the development of numerical integration techniques that preserve the symplectic condition inherent to mechanics. The intended audience is for beam physicists with backgrounds in numerical modeling and simulation with particular attention to beam optics applications. The paper focuses on Lie methods that are inherently symplectic regardless of the integration accuracy order. Section 2 provides the mathematically tools used in the sequel and necessary for the reader to extend the covered techniques. Section 3 places those tools in the context of charged-particle beam optics; in particular linear beam optics is presented in terms of a Lie algebraic matrix representation. Section 4 presents numerical stepping techniques with particular emphasis on a third-order leapfrog method. Section 5 discusses the modeling of field imperfections with particular attention to the fringe fields of quadrupole focusing magnets. The direct computation of a third order transfer matrix for a fringe field is shown.
Notes on the integration of numerical relativity waveforms
Energy Technology Data Exchange (ETDEWEB)
Reisswig, Christian [Theoretical Astrophysics Including Relativity, California Institute of Technology, Pasadena, CA 91125 (United States); Pollney, Denis, E-mail: reisswig@tapir.caltech.edu [Departament de Fisica, Universitat de les Illes Balears, Palma de Mallorca E-07122 (Spain)
2011-10-01
The primary goal of numerical relativity is to provide estimates of the wave strain, h, from strong gravitational wave sources, to be used in detector templates. The simulations, however, typically measure waves in terms of the Weyl curvature component, {psi}{sub 4}. Assuming Bondi gauge, transforming to the strain h reduces to integration of {psi}{sub 4} twice in time. Integrations performed in either the time or frequency domain, however, lead to secular nonlinear drifts in the resulting strain h. These nonlinear drifts are not explained by the two unknown integration constants which can at most result in linear drifts. We identify a number of fundamental difficulties which can arise from integrating finite length, discretely sampled and noisy data streams. These issues are an artifact of post-processing data. They are independent of the characteristics of the original simulation, such as gauge or numerical method used. We suggest, however, a simple procedure for integrating numerical waveforms in the frequency domain, which is effective at strongly reducing spurious secular nonlinear drifts in the resulting strain.
Numerical integration of discontinuous functions: moment fitting and smart octree
Hubrich, Simeon; Di Stolfo, Paolo; Kudela, László; Kollmannsberger, Stefan; Rank, Ernst; Schröder, Andreas; Düster, Alexander
2017-11-01
A fast and simple grid generation can be achieved by non-standard discretization methods where the mesh does not conform to the boundary or the internal interfaces of the problem. However, this simplification leads to discontinuous integrands for intersected elements and, therefore, standard quadrature rules do not perform well anymore. Consequently, special methods are required for the numerical integration. To this end, we present two approaches to obtain quadrature rules for arbitrary domains. The first approach is based on an extension of the moment fitting method combined with an optimization strategy for the position and weights of the quadrature points. In the second approach, we apply the smart octree, which generates curved sub-cells for the integration mesh. To demonstrate the performance of the proposed methods, we consider several numerical examples, showing that the methods lead to efficient quadrature rules, resulting in less integration points and in high accuracy.
Symbolic-Numeric Integration of the Dynamical Cosserat Equations
Lyakhov, Dmitry A.
2017-08-29
We devise a symbolic-numeric approach to the integration of the dynamical part of the Cosserat equations, a system of nonlinear partial differential equations describing the mechanical behavior of slender structures, like fibers and rods. This is based on our previous results on the construction of a closed form general solution to the kinematic part of the Cosserat system. Our approach combines methods of numerical exponential integration and symbolic integration of the intermediate system of nonlinear ordinary differential equations describing the dynamics of one of the arbitrary vector-functions in the general solution of the kinematic part in terms of the module of the twist vector-function. We present an experimental comparison with the well-established generalized \\\\alpha -method illustrating the computational efficiency of our approach for problems in structural mechanics.
Numerical solution of nonlinear Hammerstein fuzzy functional integral equations
Enkov, Svetoslav; Georgieva, Atanaska; Nikolla, Renato
2016-12-01
In this work we investigate nonlinear Hammerstein fuzzy functional integral equation. Our aim is to provide an efficient iterative method of successive approximations by optimal quadrature formula for classes of fuzzy number-valued functions of Lipschitz type to approximate the solution. We prove the convergence of the method by Banach's fixed point theorem and investigate the numerical stability of the presented method with respect to the choice of the first iteration. Finally, illustrative numerical experiment demonstrate the accuracy and the convergence of the proposed method.
Numerical Integration with Graphical Processing Unit for QKD Simulation
2014-03-27
33 NUMERICAL INTEGRATION WITH GRAPHICAL PROCESSING UNIT FOR QKD SIMULATION Virginia R. Garrett, B.S.E.E. Captain, USAF Approved: //signed// Douglas ...17] B. Nelson, R. Kirby , and R. Haimes, “Gpu-based volume visualization from high- order finite element fields,” IEEE Transactions on Visualization and...Intel i7-3610QM CPU. 15. SUBJECT TERMS Software Engineering, GPU Programming, Numerical Methods, Quantum Key Distribution U U U UU 74 Dr. Douglas Hodson, AFIT/ENG (937) 785-3636 x4719
Numerical treatments for solving nonlinear mixed integral equation
Directory of Open Access Journals (Sweden)
M.A. Abdou
2016-12-01
Full Text Available We consider a mixed type of nonlinear integral equation (MNLIE of the second kind in the space C[0,T]×L2(Ω,T<1. The Volterra integral terms (VITs are considered in time with continuous kernels, while the Fredholm integral term (FIT is considered in position with singular general kernel. Using the quadratic method and separation of variables method, we obtain a nonlinear system of Fredholm integral equations (NLSFIEs with singular kernel. A Toeplitz matrix method, in each case, is then used to obtain a nonlinear algebraic system. Numerical results are calculated when the kernels take a logarithmic form or Carleman function. Moreover, the error estimates, in each case, are then computed.
Kaden, R.; Kolbe, T. H.
2012-07-01
Virtual 3D city models are integrated complex compositions of spatial data of different themes, origin, quality, scale, and dimensions. Within this paper, we address the problem of spatial compatibility of geodata aiming to provide support for ad-hoc integration of virtual 3D city models including geodata of different sources and themes like buildings, terrain, and city furniture. In contrast to related work which is dealing with the integration of redundant geodata structured according to different data models and ontologies, we focus on the integration of complex 3D models of the same representation (here: CityGML) but regarding to the geometric-topological consistent matching of non-homologous objects, e.g. a building is connected to a road, and their geometric homogenisation. Therefore, we present an approach including a data model for a Geodata Join and the general concept of an integration procedure using the join information. The Geodata Join aims to bridge the lack of information between fragmented geodata by describing the relationship between adjacent objects from different datasets. The join information includes the geometrical representation of those parts of an object, which have a specific/known topological or geometrical relationship to another object. This part is referred to as a Connector and is either described by points, lines, or surfaces of the existing object geometry or by additional join geometry. In addition, the join information includes the specification of the connected object in the other dataset and the description of the topological and geometrical relationship between both objects, which is used to aid the matching process. Furthermore, the Geodata Join contains object-related information like accuracy values and restrictions of movement and deformation which are used to optimize the integration process. Based on these parameters, a functional model including a matching algorithm, transformation methods, and conditioned adjustment
Gómez-Robles, Aida; Martinón-Torres, María; Bermúdez de Castro, José María; Prado-Simón, Leyre; Arsuaga, Juan Luis
2011-12-01
This paper continues the series of articles initiated in 2006 that analyse hominin dental crown morphology by means of geometric morphometric techniques. The detailed study of both upper premolar occlusal morphologies in a comprehensive sample of hominin fossils, including those coming from the Gran Dolina-TD6 and Sima de los Huesos sites from Atapuerca, Spain, complement previous works on lower first and second premolars and upper first molars. A morphological gradient consisting of the change from asymmetric to symmetric upper premolars and a marked reduction of the lingual cusp in recent Homo species has been observed in both premolars. Although percentages of correct classification based on upper premolar morphologies are not very high, significant morphological differences between Neanderthals (and European middle Pleistocene fossils) and modern humans have been identified, especially in upper second premolars. The study of morphological integration between premolar morphologies reveals significant correlations that are weaker between upper premolars than between lower ones and significant correlations between antagonists. These results have important implications for understanding the genetic and functional factors underlying dental phenotypic variation and covariation. Copyright Â© 2011 Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
S. Merkt
2012-01-01
Full Text Available
ENGLISH ABSTRACT: Selective laser melting (SLM is becoming an economically viable choice for manufacturing complex serial parts. This paper focuses on a geometric complexity analysis as part of the integrative technology evaluation model (ITEM presented here. In contrast to conventional evaluation methodologies, the ITEM considers interactions between product and process innovations generated by SLM. The evaluation of manufacturing processes that compete with SLM is the main goal of ITEM. The paper includes a complexity analysis of a test part from Festo AG. The paper closes with a discussion of how the expanded design freedom of SLM can be used to improve company operations, and how the complexity analysis presented here can be seen as a starting point for feature-based complexity analysis..
AFRIKAANSE OPSOMMING: Selektiewe lasersmelting word geleidelik ’n gangbare ekonomiese keuse vir die vervaar-diging van opeenvolgende komplekse onderdele. Die navorsing is toegespits op die ontleding van meetkundige kompleksiteit as ’n gedeelte van ’n integrerende tegnologiese evalueringsmodel. Gemeet teen konvensionele evalueringsmodelle behandel die genoemde metode interaksies tussen produkte- en prosesinnovasies wat gegenereer word. Die navorsing behandel ’n kompleksiteitsontleding van ’n toetsonderdeel van die firma FESTO AG. Die resultaat toon hoe kompleksiteits-analise gebruik kan word as die vertrekpunt vir eienskapsgebaseerde analise.
Numerical integration of massive two-loop Mellin-Barnes integrals in Minkowskian regions
International Nuclear Information System (INIS)
Dubovyk, Ievgen
2016-07-01
Mellin-Barnes (MB) techniques applied to integrals emerging in particle physics perturbative calculations are summarized. New versions of AMBRE packages which construct planar and nonplanar MB representations are shortly discussed. The numerical package MBnumerics.m is presented for the first time which is able to calculate with a high precision multidimensional MB integrals in Minkowskian regions. Examples are given for massive vertex integrals which include threshold effects and several scale parameters.
Singularity Preserving Numerical Methods for Boundary Integral Equations
Kaneko, Hideaki (Principal Investigator)
1996-01-01
In the past twelve months (May 8, 1995 - May 8, 1996), under the cooperative agreement with Division of Multidisciplinary Optimization at NASA Langley, we have accomplished the following five projects: a note on the finite element method with singular basis functions; numerical quadrature for weakly singular integrals; superconvergence of degenerate kernel method; superconvergence of the iterated collocation method for Hammersteion equations; and singularity preserving Galerkin method for Hammerstein equations with logarithmic kernel. This final report consists of five papers describing these projects. Each project is preceeded by a brief abstract.
Numerical counting ratemeter with variable time constant and integrated circuits
International Nuclear Information System (INIS)
Kaiser, J.; Fuan, J.
1967-01-01
We present here the prototype of a numerical counting ratemeter which is a special version of variable time-constant frequency meter (1). The originality of this work lies in the fact that the change in the time constant is carried out automatically. Since the criterion for this change is the accuracy in the annunciated result, the integration time is varied as a function of the frequency. For the prototype described in this report, the time constant varies from 1 sec to 1 millisec. for frequencies in the range 10 Hz to 10 MHz. This prototype is built entirely of MECL-type integrated circuits from Motorola and is thus contained in two relatively small boxes. (authors) [fr
Numerical integration and optimization of motions for multibody dynamic systems
Aguilar Mayans, Joan
This thesis considers the optimization and simulation of motions involving rigid body systems. It does so in three distinct parts, with the following topics: optimization and analysis of human high-diving motions, efficient numerical integration of rigid body dynamics with contacts, and motion optimization of a two-link robot arm using Finite-Time Lyapunov Analysis. The first part introduces the concept of eigenpostures, which we use to simulate and analyze human high-diving motions. Eigenpostures are used in two different ways: first, to reduce the complexity of the optimal control problem that we solve to obtain such motions, and second, to generate an eigenposture space to which we map existing real world motions to better analyze them. The benefits of using eigenpostures are showcased through different examples. The second part reviews an extensive list of integration algorithms used for the integration of rigid body dynamics. We analyze the accuracy and stability of the different integrators in the three-dimensional space and the rotation space SO(3). Integrators with an accuracy higher than first order perform more efficiently than integrators with first order accuracy, even in the presence of contacts. The third part uses Finite-time Lyapunov Analysis to optimize motions for a two-link robot arm. Finite-Time Lyapunov Analysis diagnoses the presence of time-scale separation in the dynamics of the optimized motion and provides the information and methodology for obtaining an accurate approximation to the optimal solution, avoiding the complications that timescale separation causes for alternative solution methods.
Functional morphology and integration of corvid skulls – a 3D geometric morphometric approach
Directory of Open Access Journals (Sweden)
Gunz Philipp
2009-01-01
Full Text Available Abstract Background Sympatric corvid species have evolved differences in nesting, habitat choice, diet and foraging. Differences in the frequency with which corvid species use their repertoire of feeding techniques is expected to covary with bill-shape and with the frontal binocular field. Species that frequently probe are expected to have a relatively longer bill and more sidewise oriented orbits in contrast to species that frequently peck. We tested this prediction by analyzing computed tomography scans of skulls of six corvid species by means of three-dimensional geometric morphometrics. We (1 explored patterns of major variation using principal component analysis, (2 compared within and between species relationships of size and shape and (3 quantitatively compared patterns of morphological integration between bill and cranium by means of partial least squares (singular warp analysis. Results Major shape variation occurs at the bill, in the orientation of orbits, in the position of the foramen magnum and in the angle between bill and cranium. The first principal component correlated positively with centroid-size, but within-species allometric relationships differed markedly. Major covariation between the bill and cranium lies in the difference in orbit orientation relative to bill-length and in the angle between bill and cranium. Conclusion Corvid species show pronounced differences in skull shape, which covary with foraging mode. Increasing bill-length, bill-curvature and sidewise orientation of the eyes is associated with an increase in the observed frequency in probing (vice versa in pecking. Hence, the frequency of probing, bill-length, bill-curvature and sidewise orientation of the eyes is progressively increased from jackdaw, to Eurasian jay, to black-billed magpie, to hooded crow, to rook and to common raven (when feeding on carcasses is considered as probing. Our results on the morphological integration suggest that most of the
Integrated numerical modeling of a laser gun injector
International Nuclear Information System (INIS)
Liu, H.; Benson, S.; Bisognano, J.; Liger, P.; Neil, G.; Neuffer, D.; Sinclair, C.; Yunn, B.
1993-01-01
CEBAF is planning to incorporate a laser gun injector into the linac front end as a high-charge cw source for a high-power free electron laser and nuclear physics. This injector consists of a DC laser gun, a buncher, a cryounit and a chicane. The performance of the injector is predicted based on integrated numerical modeling using POISSON, SUPERFISH and PARMELA. The point-by-point method incorporated into PARMELA by McDonald is chosen for space charge treatment. The concept of open-quotes conditioning for final bunchingclose quotes is employed to vary several crucial parameters of the system for achieving highest peak current while maintaining low emittance and low energy spread. Extensive parameter variation studies show that the design will perform better than the specifications for FEL operations aimed at industrial applications and fundamental scientific research. The calculation also shows that the injector will perform as an extremely bright cw electron source
Comparison of four stable numerical methods for Abel's integral equation
Murio, Diego A.; Mejia, Carlos E.
1991-01-01
The 3-D image reconstruction from cone-beam projections in computerized tomography leads naturally, in the case of radial symmetry, to the study of Abel-type integral equations. If the experimental information is obtained from measured data, on a discrete set of points, special methods are needed in order to restore continuity with respect to the data. A new combined Regularized-Adjoint-Conjugate Gradient algorithm, together with two different implementations of the Mollification Method (one based on a data filtering technique and the other on the mollification of the kernal function) and a regularization by truncation method (initially proposed for 2-D ray sample schemes and more recently extended to 3-D cone-beam image reconstruction) are extensively tested and compared for accuracy and numerical stability as functions of the level of noise in the data.
Integrated numerical modeling of a laser gun injector
International Nuclear Information System (INIS)
Liu, H.; Benson, S.; Bisognano, J.; Liger, P.; Neil, G.; Neuffer, D.; Sinclair, C.; Yunn, B.
1993-06-01
CEBAF is planning to incorporate a laser gun injector into the linac front end as a high-charge cw source for a high-power free electron laser and nuclear physics. This injector consists of a DC laser gun, a buncher, a cryounit and a chicane. The performance of the injector is predicted based on integrated numerical modeling using POISSON, SUPERFISH and PARMELA. The point-by-point method incorporated into PARMELA by McDonald is chosen for space charge treatment. The concept of ''conditioning for final bunching'' is employed to vary several crucial parameters of the system for achieving highest peak current while maintaining low emittance and low energy spread. Extensive parameter variation studies show that the design will perform beyond the specifications for FEL operations aimed at industrial applications and fundamental scientific research. The calculation also shows that the injector will perform as an extremely bright cw electron source
International Nuclear Information System (INIS)
Jowzani-Moghaddam, A.
1981-01-01
An integral transport method of calculating the geometrical shadowing factor in multiregion annular cells for infinite closely packed lattices in cylindrical geometry is developed. This analytical method has been programmed in the TPGS code. This method is based upon a consideration of the properties of the integral transport method for a nonuniform body, which together with Bonalumi's approximations allows the determination of the approximate multiregion collision probability matrix for infinite closely packed lattices with sufficient accuracy. The multiregion geometrical shadowing factors have been calculated for variations in fuel pin annular segment rings in a geometry of annular cells. These shadowing factors can then be used in the calculation of neutron transport from one annulus to another in an infinite lattice. The result of this new geometrical shadowing and collision probability matrix are compared with the Dancoff-Ginsburg correction and the probability matrix using constant shadowing on Yankee fuel elements in an infinite lattice. In these cases the Dancoff-Ginsburg correction factor and collision probability matrix using constant shadowing are in difference by at most 6.2% and 6%, respectively
Advances in Integrated Vehicle Thermal Management and Numerical Simulation
Directory of Open Access Journals (Sweden)
Yan Wang
2017-10-01
Full Text Available With the increasing demands for vehicle dynamic performance, economy, safety and comfort, and with ever stricter laws concerning energy conservation and emissions, vehicle power systems are becoming much more complex. To pursue high efficiency and light weight in automobile design, the power system and its vehicle integrated thermal management (VITM system have attracted widespread attention as the major components of modern vehicle technology. Regarding the internal combustion engine vehicle (ICEV, its integrated thermal management (ITM mainly contains internal combustion engine (ICE cooling, turbo-charged cooling, exhaust gas recirculation (EGR cooling, lubrication cooling and air conditioning (AC or heat pump (HP. As for electric vehicles (EVs, the ITM mainly includes battery cooling/preheating, electric machines (EM cooling and AC or HP. With the rational effective and comprehensive control over the mentioned dynamic devices and thermal components, the modern VITM can realize collaborative optimization of multiple thermodynamic processes from the aspect of system integration. Furthermore, the computer-aided calculation and numerical simulation have been the significant design methods, especially for complex VITM. The 1D programming can correlate multi-thermal components and the 3D simulating can develop structuralized and modularized design. Additionally, co-simulations can virtualize simulation of various thermo-hydraulic behaviors under the vehicle transient operational conditions. This article reviews relevant researching work and current advances in the ever broadening field of modern vehicle thermal management (VTM. Based on the systematic summaries of the design methods and applications of ITM, future tasks and proposals are presented. This article aims to promote innovation of ITM, strengthen the precise control and the performance predictable ability, furthermore, to enhance the level of research and development (R&D.
Calculus Technique of Integration by Parts, Correlated with a Geometric Picture
Fromhold, Albert T., Jr.
2005-01-01
The method of integration by parts is one of the most useful in integral calculus. Among the most important applications is the integration of differentials involving products, differentials in involving logarithms, and differentials involving inverse circular functions.
How to integrate divergent integrals: a pure numerical approach to complex loop calculations
International Nuclear Information System (INIS)
Caravaglios, F.
2000-01-01
Loop calculations involve the evaluation of divergent integrals. Usually [G. 't Hooft, M. Veltman, Nucl. Phys. B 44 (1972) 189] one computes them in a number of dimensions different than four where the integral is convergent and then one performs the analytical continuation and considers the Laurent expansion in powers of ε=n-4. In this paper we discuss a method to extract directly all coefficients of this expansion by means of concrete and well defined integrals in a five-dimensional space. We by-pass the formal and symbolic procedure of analytic continuation; instead we can numerically compute the integrals to extract directly both the coefficient of the pole 1/ε and the finite part
Directory of Open Access Journals (Sweden)
Masuda Kazuhiko
2016-01-01
Full Text Available Backscattering properties of ice crystal models (Voronoi aggregates (VA, hexagonal columns (COL, and six-branched bullet rosettes (BR6 are calculated by using geometrical-opticsintegral-equation (GOIE method. Characteristics of depolarization ratio (δ and lidar ratio (L of the crystal models are examined. δ (L values are 0.2~0.3 (4~50, 0.3~0.4 (10~25, and 0.5~0.6 (50~100 for COL, BR6, and VA, respectively, at wavelength λ=0.532 μm. It is found that small deformation of COL model could produce significant changes in δ and L.
Lenarda, P; Paggi, M
A comprehensive computational framework based on the finite element method for the simulation of coupled hygro-thermo-mechanical problems in photovoltaic laminates is herein proposed. While the thermo-mechanical problem takes place in the three-dimensional space of the laminate, moisture diffusion occurs in a two-dimensional domain represented by the polymeric layers and by the vertical channel cracks in the solar cells. Therefore, a geometrical multi-scale solution strategy is pursued by solving the partial differential equations governing heat transfer and thermo-elasticity in the three-dimensional space, and the partial differential equation for moisture diffusion in the two dimensional domains. By exploiting a staggered scheme, the thermo-mechanical problem is solved first via a fully implicit solution scheme in space and time, with a specific treatment of the polymeric layers as zero-thickness interfaces whose constitutive response is governed by a novel thermo-visco-elastic cohesive zone model based on fractional calculus. Temperature and relative displacements along the domains where moisture diffusion takes place are then projected to the finite element model of diffusion, coupled with the thermo-mechanical problem by the temperature and crack opening dependent diffusion coefficient. The application of the proposed method to photovoltaic modules pinpoints two important physical aspects: (i) moisture diffusion in humidity freeze tests with a temperature dependent diffusivity is a much slower process than in the case of a constant diffusion coefficient; (ii) channel cracks through Silicon solar cells significantly enhance moisture diffusion and electric degradation, as confirmed by experimental tests.
DEFF Research Database (Denmark)
Madsen, Søren Bøgelund; Ibsen, Claus Hessler; Gervang, Bo
2015-01-01
The focus of this paper is the validation and comparison of simplified numerical models of the mechanical rolling process used in tube to tubesheet joints. The investigated models is an axisymmetric model and planar models with plane strain and stress. There are different pros and cons...... strain and stress assumptions. Therefore, it is desirable to investigate how close these simplified models can predict the geometry changes after expansion measured in the experiment. The conclusion of the paper is that a planer model with plane strain is the best model at predicting the actual...
Integrating Numerical Computation into the Modeling Instruction Curriculum
Caballero, Marcos D.; Burk, John B.; Aiken, John M.; Thoms, Brian D.; Douglas, Scott S.; Scanlon, Erin M.; Schatz, Michael F.
2014-01-01
Numerical computation (the use of a computer to solve, simulate, or visualize a physical problem) has fundamentally changed the way scientific research is done. Systems that are too difficult to solve in closed form are probed using computation. Experiments that are impossible to perform in the laboratory are studied numerically. Consequently, in…
Conservation properties of numerical integrators for highly oscillatory Hamiltonian systems
Cohen, David
2017-01-01
Modulated Fourier expansion is used to show long-time near-conservation of the total and oscillatory energies of numerical methods for Hamiltonian systems with highly oscillatory solutions. The numerical methods considered are an extension of the trigonometric methods. A brief discussion of conservation properties in the continuous problem and in the multi-frequency case is also given
Numerical evaluation of integrals containing a spherical Bessel function by product integration
International Nuclear Information System (INIS)
Lehman, D.R.; Parke, W.C.; Maximon, L.C.
1981-01-01
A method is developed for numerical evaluation of integrals with k-integration range from 0 to infinity that contain a spherical Bessel function j/sub l/(kr) explicitly. The required quadrature weights are easily calculated and the rate of convergence is rapid: only a relatively small number of quadrature points is needed: for an accurate evaluation even when r is large. The quadrature rule is obtained by the method of product integration. With the abscissas chosen to be those of Clenshaw--Curtis and the Chebyshev polynomials as the interpolating polynomials, quadrature weights are obtained that depend on the spherical Bessel function. An inhomogenous recurrence relation is derived from which the weights can be calculated without accumulation of roundoff error. The procedure is summarized as an easily implementable algorithm. Questions of convergence are discussed and the rate of convergence demonstrated for several test integrals. Alternative procedures are given for generating the integration weights and an error analysis of the method is presented
Numerical modeling in photonic crystals integrated technology: the COPERNICUS Project
DEFF Research Database (Denmark)
Malaguti, Stefania; Armaroli, Andrea; Bellanca, Gaetano
2011-01-01
Photonic crystals will play a fundamental role in the future of optical communications. The relevance of the numerical modeling for the success of this technology is assessed by using some examples concerning the experience of the COPERNICUS Project.......Photonic crystals will play a fundamental role in the future of optical communications. The relevance of the numerical modeling for the success of this technology is assessed by using some examples concerning the experience of the COPERNICUS Project....
2016-01-01
The folded paper-size illusion is as easy to demonstrate as it is powerful in generating insights into perceptual processing: First take two A4 sheets of paper, one original sized, another halved by folding, then compare them in terms of area size by centering the halved sheet on the center of the original one! We perceive the larger sheet as far less than double (i.e., 100%) the size of the small one, typically only being about two thirds larger—this illusion is preserved by rotating the inner sheet and even by aligning it to one or two sides, but is dissolved by aligning both sheets to three sides, here documented by 88 participants’ data. A potential explanation might be the general incapability of accurately comparing more than one geometrical dimension at once—in everyday life, we solve this perceptual-cognitive bottleneck by reducing the complexity of such a task via aligning parts with same lengths. PMID:27698977
An efficient numerical integral in three-dimensional electromagnetic field computations
Whetten, Frank L.; Liu, Kefeng; Balanis, Constantine A.
1990-01-01
An improved algorithm for efficiently computing a sinusoid and an exponential integral commonly encountered in method-of-moments solutions is presented. The new algorithm has been tested for accuracy and computer execution time against both numerical integration and other existing numerical algorithms, and has outperformed them. Typical execution time comparisons on several computers are given.
Fauzi, Ahmad
2017-11-01
Numerical computation has many pedagogical advantages: it develops analytical skills and problem-solving skills, helps to learn through visualization, and enhances physics education. Unfortunately, numerical computation is not taught to undergraduate education physics students in Indonesia. Incorporate numerical computation into the undergraduate education physics curriculum presents many challenges. The main challenges are the dense curriculum that makes difficult to put new numerical computation course and most students have no programming experience. In this research, we used case study to review how to integrate numerical computation into undergraduate education physics curriculum. The participants of this research were 54 students of the fourth semester of physics education department. As a result, we concluded that numerical computation could be integrated into undergraduate education physics curriculum using spreadsheet excel combined with another course. The results of this research become complements of the study on how to integrate numerical computation in learning physics using spreadsheet excel.
Directory of Open Access Journals (Sweden)
Qifeng Wang
2018-01-01
Full Text Available With respect to the multiattribute decision-making (MADM problem in which the attributes have interdependent or interactive phenomena under the interval-valued intuitionistic fuzzy environment, we propose a group decision-making approach based on the interval-valued intuitionistic fuzzy Einstein geometric Choquet integral operator (IVIFEGC. Firstly, the Einstein operational laws and some basic principle on interval-valued intuitionistic fuzzy sets are introduced. Then, the IVIFEGC is developed and some desirable properties of the operator are studied. Further, an approach to multiattribute group decision-making with interval-valued intuitionistic fuzzy information is developed, where the attributes have interdependent phenomena. Finally, an illustrative example is used to illustrate the developed approach.
Integrated 6-DOF Orbit-Attitude Dynamical Modeling and Control Using Geometric Mechanics
Directory of Open Access Journals (Sweden)
Ling Jiang
2017-01-01
Full Text Available The integrated 6-DOF orbit-attitude dynamical modeling and control have shown great importance in various missions, for example, formation flying and proximity operations. The integrated approach yields better performances than the separate one in terms of accuracy, efficiency, and agility. One challenge in the integrated approach is to find a unified representation for the 6-DOF motion with configuration space SE(3. Recently, exponential coordinates of SE(3 have been used in dynamics and control of the 6-DOF motion, however, only on the kinematical level. In this paper, we will improve the current method by adopting exponential coordinates on the dynamical level, by giving the relation between the second-order derivative of exponential coordinates and spacecraft’s accelerations. In this way, the 6-DOF motion in terms of exponential coordinates can be written as a second-order system with a quite compact form, to which a broader range of control theories, such as higher-order sliding modes, can be applied. For a demonstration purpose, a simple asymptotic tracking control law with almost global convergence is designed. Finally, the integrated modeling and control are applied to the body-fixed hovering over an asteroid and verified by a simulation, in which absolute motions of the spacecraft and asteroid are simulated separately.
Sotiropoulos, F.; Kang, S.; Chamorro, L. P.; Hill, C.
2011-12-01
The field of MHK energy is still in its infancy lagging approximately a decade or more behind the technology and development progress made in wind energy engineering. Marine environments are characterized by complex topography and three-dimensional (3D) turbulent flows, which can greatly affect the performance and structural integrity of MHK devices and impact the Levelized Cost of Energy (LCoE). Since the deployment of multi-turbine arrays is envisioned for field applications, turbine-to-turbine interactions and turbine-bathymetry interactions need to be understood and properly modeled so that MHK arrays can be optimized on a site specific basis. Furthermore, turbulence induced by MHK turbines alters and interacts with the nearby ecosystem and could potentially impact aquatic habitats. Increased turbulence in the wake of MHK devices can also change the shear stress imposed on the bed ultimately affecting the sediment transport and suspension processes in the wake of these structures. Such effects, however, remain today largely unexplored. In this work a science-based approach integrating state-of-the-art experimentation with high-resolution computational fluid dynamics is proposed as a powerful strategy for optimizing the performance of MHK devices and assessing environmental impacts. A novel numerical framework is developed for carrying out Large-Eddy Simulation (LES) in arbitrarily complex domains with embedded MHK devices. The model is able to resolve the geometrical complexity of real-life MHK devices using the Curvilinear Immersed Boundary (CURVIB) method along with a wall model for handling the flow near solid surfaces. Calculations are carried out for an axial flow hydrokinetic turbine mounted on the bed of rectangular open channel on a grid with nearly 200 million grid nodes. The approach flow corresponds to fully developed turbulent open channel flow and is obtained from a separate LES calculation. The specific case corresponds to that studied
Directory of Open Access Journals (Sweden)
Anatolij K. Prykarpatski
2017-12-01
Full Text Available The classical Lagrange-d’Alembert principle had a decisive influence on formation of modern analytical mechanics which culminated in modern Hamilton and Poisson mechanics. Being mainly interested in the geometric interpretation of this principle, we devoted our review to its deep relationships to modern Lie-algebraic aspects of the integrability theory of nonlinear heavenly type dynamical systems and its so called Lax-Sato counterpart. We have also analyzed old and recent investigations of the classical M. A. Buhl problem of describing compatible linear vector field equations, its general M.G. Pfeiffer and modern Lax-Sato type special solutions. Especially we analyzed the related Lie-algebraic structures and integrability properties of a very interesting class of nonlinear dynamical systems called the dispersionless heavenly type equations, which were initiated by Plebański and later analyzed in a series of articles. As effective tools the AKS-algebraic and related R -structure schemes are used to study the orbits of the corresponding co-adjoint actions, which are intimately related to the classical Lie-Poisson structures on them. It is demonstrated that their compatibility condition coincides with the corresponding heavenly type equations under consideration. It is also shown that all these equations originate in this way and can be represented as a Lax-Sato compatibility condition for specially constructed loop vector fields on the torus. Typical examples of such heavenly type equations, demonstrating in detail their integrability via the scheme devised herein, are presented.
Directory of Open Access Journals (Sweden)
Jin-Xiu Hu
2014-01-01
Full Text Available A new approach is presented for the numerical evaluation of arbitrary singular domain integrals. In this method, singular domain integrals are transformed into a boundary integral and a radial integral which contains singularities by using the radial integration method. The analytical elimination of singularities condensed in the radial integral formulas can be accomplished by expressing the nonsingular part of the integration kernels as a series of cubic B-spline basis functions of the distance r and using the intrinsic features of the radial integral. In the proposed method, singularities involved in the domain integrals are explicitly transformed to the boundary integrals, so no singularities exist at internal points. A few numerical examples are provided to verify the correctness and robustness of the presented method.
Energy Technology Data Exchange (ETDEWEB)
Maljovec, Dan [Univ. of Utah, Salt Lake City, UT (United States); Wang, Bei [Univ. of Utah, Salt Lake City, UT (United States); Pascucci, Valerio [Univ. of Utah, Salt Lake City, UT (United States); Bremer, Peer-Timo [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Mandelli, Diego [Idaho National Lab. (INL), Idaho Falls, ID (United States); Pernice, Michael [Idaho National Lab. (INL), Idaho Falls, ID (United States); Nourgaliev, Robert [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2013-10-01
and 2) topology-based methodologies to interactively visualize multidimensional data and extract risk-informed insights. Regarding item 1) we employ learning algorithms that aim to infer/predict simulation outcome and decide the coordinate in the input space of the next sample that maximize the amount of information that can be gained from it. Such methodologies can be used to both explore and exploit the input space. The later one is especially used for safety analysis scopes to focus samples along the limit surface, i.e. the boundaries in the input space between system failure and system success. Regarding item 2) we present a software tool that is designed to analyze multi-dimensional data. We model a large-scale nuclear simulation dataset as a high-dimensional scalar function defined over a discrete sample of the domain. First, we provide structural analysis of such a function at multiple scales and provide insight into the relationship between the input parameters and the output. Second, we enable exploratory analysis for users, where we help the users to differentiate features from noise through multi-scale analysis on an interactive platform, based on domain knowledge and data characterization. Our analysis is performed by exploiting the topological and geometric properties of the domain, building statistical models based on its topological segmentations and providing interactive visual interfaces to facilitate such explorations.
Numerical Integration of Stiff System of Ordinary Differential ...
African Journals Online (AJOL)
The goal of this work is to develop, analyse and implement a K-step Implicit Rational Runge-Kutta schemes for Integration of Stiff system of Ordinary differential Equations. Its development adopted Taylor and Binomial series expansion Techniques to generate its parameters. The analysis of its basic properties adopted ...
Numerical calculation of path integrals : The small-polaron model
Raedt, Hans De; Lagendijk, Ad
1983-01-01
The thermodynamic properties of the small-polaron model are studied by means of a discrete version of the Feynman path-integral representation of the partition function. This lattice model describes a fermion interacting with a boson field. The bosons are treated analytically, the fermion
Integrated numerical methods for hypersonic aircraft cooling systems analysis
Petley, Dennis H.; Jones, Stuart C.; Dziedzic, William M.
1992-01-01
Numerical methods have been developed for the analysis of hypersonic aircraft cooling systems. A general purpose finite difference thermal analysis code is used to determine areas which must be cooled. Complex cooling networks of series and parallel flow can be analyzed using a finite difference computer program. Both internal fluid flow and heat transfer are analyzed, because increased heat flow causes a decrease in the flow of the coolant. The steady state solution is a successive point iterative method. The transient analysis uses implicit forward-backward differencing. Several examples of the use of the program in studies of hypersonic aircraft and rockets are provided.
Exploiting natural scale separation with efficient asynchronous numerical time integration
Rubel, Michael; Leonard, Anthony
2002-11-01
The systems of ordinary differential equations that arise in problems of computational fluid mechanics often exhibit time-scale separation in addition to being stiff: each solution variable acts at a small range of time scales relative to the problem as a whole. When only a small fraction of the solution variables act at the fastest scales, conventional timestepping algorithms waste a great deal of effort over-resolving the slow variables. In this talk, I will discuss numerical strategies to take advantage of time-scale separation for more efficient computing. In particular, results from the dead-reckoning algorithm will be presented.
Rotenberg, David; Chiew, Mark; Ranieri, Shawn; Tam, Fred; Chopra, Rajiv; Graham, Simon J
2013-03-01
Head motion artifacts are a major problem in functional MRI that limit its use in neuroscience research and clinical settings. Real-time scan-plane correction by optical tracking has been shown to correct slice misalignment and nonlinear spin-history artifacts; however, residual artifacts due to dynamic magnetic field nonuniformity may remain in the data. A recently developed correction technique, Phase Labeling for Additional Coordinate Encoding, can correct for absolute geometric distortion using only the complex image data from two echo planar images with slightly shifted k-space trajectories. An approach is presented that integrates Phase Labeling for Additional Coordinate Encoding into a real-time scan-plane update system by optical tracking, applied to a tissue-equivalent phantom undergoing complex motion and an functional MRI finger tapping experiment with overt head motion to induce dynamic field nonuniformity. Experiments suggest that such integrated volume-by-volume corrections are very effective at artifact suppression, with potential to expand functional MRI applications. Copyright © 2012 Wiley Periodicals, Inc.
Energy Technology Data Exchange (ETDEWEB)
Yasuda, A.; Miyakoshi, H.; Hayashi, K.; Nishimura, M.; Kamide, H.; Hishida, K. [Japan Nuclear Cycle Development Inst., Oarai, Ibaraki (Japan). Oarai Engineering Center
1999-04-01
Investigations on the inter-wrapper flow (IWF) in a liquid metal cooled fast breeder reactor core have been carried out. The IWF is a natural circulation flow between wrapper tubes in the core barrel where cold fluid is coming from a direct heat exchanger (DHX) in the upper plenum. It was shown by the sodium experiment using 7-subassembly core model that the IWF can cool the subassemblies. To clarify thermal-hydraulic characteristics of the IWF in the core, the water experiment was performed using the flow visualization technique. The test rig for IWF (TRIF) has the core simulating the fuel subassemblies and radial reflectors. The subassemblies are constructed featuring transparent heater to enable both Joule heating and flow visualization. The transparent heater was made of glass with thin conductor film coating of tin oxide, and the glass heater was embedded on the wall of modeled wrapper tube made of acrylic plexiglass. In the present experiment, influences of peripheral geometric parameters such as flow holes of core formers on the thermal-hydraulic field were investigated with the button type spacer pads of the wrapper tube. Through the water tests, flow patterns of the IWF were revealed and velocity fields were quantitatively measured with a particle image velocimetry (PIV). Also, no substantial influence of peripheral geometry was found on the temperature field of the IWF, as far as the button type spacer pad was applied. Numerical simulation was applied to the experimental analysis of IWF by using multidimensional code with porous body model. The numerical results reproduced the flow patterns within TRIF and agreed well to experimental temperature distributions, showing capability of predicting IWF with porous body model. (author)
Weres, Jerzy; Kujawa, Sebastian; Olek, Wiesław; Czajkowski, Łukasz
2016-04-01
Knowledge of physical properties of biomaterials is important in understanding and designing agri-food and wood processing industries. In the study presented in this paper computational methods were developed and combined with experiments to enhance identification of agri-food and forest product properties, and to predict heat and water transport in such products. They were based on the finite element model of heat and water transport and supplemented with experimental data. Algorithms were proposed for image processing, geometry meshing, and inverse/direct finite element modelling. The resulting software system was composed of integrated subsystems for 3D geometry data acquisition and mesh generation, for 3D geometry modelling and visualization, and for inverse/direct problem computations for the heat and water transport processes. Auxiliary packages were developed to assess performance, accuracy and unification of data access. The software was validated by identifying selected properties and using the estimated values to predict the examined processes, and then comparing predictions to experimental data. The geometry, thermal conductivity, specific heat, coefficient of water diffusion, equilibrium water content and convective heat and water transfer coefficients in the boundary layer were analysed. The estimated values, used as an input for simulation of the examined processes, enabled reduction in the uncertainty associated with predictions.
International Nuclear Information System (INIS)
Liu, Fang; Lin, Lin; Vigil-Fowler, Derek; Lischner, Johannes; Kemper, Alexander F.; Sharifzadeh, Sahar; Jornada, Felipe H. da; Deslippe, Jack; Yang, Chao
2015-01-01
We present a numerical integration scheme for evaluating the convolution of a Green's function with a screened Coulomb potential on the real axis in the GW approximation of the self energy. Our scheme takes the zero broadening limit in Green's function first, replaces the numerator of the integrand with a piecewise polynomial approximation, and performs principal value integration on subintervals analytically. We give the error bound of our numerical integration scheme and show by numerical examples that it is more reliable and accurate than the standard quadrature rules such as the composite trapezoidal rule. We also discuss the benefit of using different self energy expressions to perform the numerical convolution at different frequencies
Advanced Numerical Integration Techniques for HighFidelity SDE Spacecraft Simulation
National Aeronautics and Space Administration — Classic numerical integration techniques, such as the ones at the heart of several NASA GSFC analysis tools, are known to work well for deterministic differential...
Numerical Evaluation of Stress Intensity Factors (Ki) J-Integral Approach
National Research Council Canada - National Science Library
Riveros, Guillermo A
2006-01-01
The purpose of this Coastal and Hydraulics Engineering Technical Note (CHETN) is to describe the numerical evaluation of the stress intensity factors using the J-integral approach (Rice 1968a, 1968b...
Numerical Solution of The Linear Fredholm Integral Equations of the Second Kind
Directory of Open Access Journals (Sweden)
N. Parandin
2010-03-01
Full Text Available The theory of integral equation is one of the major topics of applied mathematics. The main purpose of this paper is to introduce a numerical method based on the interpolation for approximating the solution of the second kind linear Fredholm integral equation. In this case, the divided differences method is applied. At last, two numerical examples are presented to show the accuracy of the proposed method
Numerical Integration of the Vlasov Equation of Two Colliding Beams
Zorzano-Mier, M P
2000-01-01
In a circular collider the motion of particles of one beam is strongly perturbed at the interaction points by the electro-magnetic field associated with the counter-rotating beam. For any two arbitrary initial particle distributions the time evolution of the two beams can be known by solving the coupled system of two Vlasov equations. This collective description is mandatory when the two beams have similar strengths, as in the case of LEP or LHC. The coherent modes excited by this beam-beam interaction can be a strong limitation for the operation of LHC. In this work, the coupled Vlasov equations of two colliding flat beams are solved numerically using a finite difference scheme. The results suggest that, for the collision of beams with equal tunes, the tune shift between the $\\sigma$- and $\\pi$- coherent dipole mode depends on the unperturbed tune $q$ because of the deformation that the so-called dynamic beta effect induces on the beam distribution. Only when the unperturbed tune $q\\rightarrow 0.25$ this tun...
Numerical method for solving integral equations of neutron transport. II
International Nuclear Information System (INIS)
Loyalka, S.K.; Tsai, R.W.
1975-01-01
In a recent paper it was pointed out that the weakly singular integral equations of neutron transport can be quite conveniently solved by a method based on subtraction of singularity. This previous paper was devoted entirely to the consideration of simple one-dimensional isotropic-scattering and one-group problems. The present paper constitutes interesting extensions of the previous work in that in addition to a typical two-group anisotropic-scattering albedo problem in the slab geometry, the method is also applied to an isotropic-scattering problem in the x-y geometry. These results are compared with discrete S/sub N/ (ANISN or TWOTRAN-II) results, and for the problems considered here, the proposed method is found to be quite effective. Thus, the method appears to hold considerable potential for future applications. (auth)
Optimal stability polynomials for numerical integration of initial value problems
Ketcheson, David I.
2013-01-08
We consider the problem of finding optimally stable polynomial approximations to the exponential for application to one-step integration of initial value ordinary and partial differential equations. The objective is to find the largest stable step size and corresponding method for a given problem when the spectrum of the initial value problem is known. The problem is expressed in terms of a general least deviation feasibility problem. Its solution is obtained by a new fast, accurate, and robust algorithm based on convex optimization techniques. Global convergence of the algorithm is proven in the case that the order of approximation is one and in the case that the spectrum encloses a starlike region. Examples demonstrate the effectiveness of the proposed algorithm even when these conditions are not satisfied.
Griffin, S; Marcus, A; Schulz, T; Walker, S
1999-06-01
The integrated exposure uptake biokinetic (IEUBK) model, recommended for use by the U.S. Environmental Protection Agency at residential Superfund sites to predict potential risks to children from lead exposure and to establish lead remediation levels, requires an interindividual geometric standard deviation (GSDi) as an essential input parameter. The GSDi quantifies the variability of blood lead concentrations for children exposed to similar environmental concentrations of lead. Estimates of potential risks are directly related to the GSDi, and therefore the GSDi directly impacts the scope of remediation at Superfund sites. Site-specific GSDi can be calculated for sites where blood lead and environmental lead have been measured. This paper uses data from blood and environmental lead studies conducted at the Bingham Creek and Sandy, Utah, Superfund sites to calculate GSDi using regression modeling, box modeling, and structural equation modeling. GSDis were calculated using various methods for treating values below the analytical method detection and quantitation limits. Treatment of nonquantifiable blood lead concentrations affected the GSDi more than the statistical method used to calculate the GSDi. For any given treatment, the different statistical methods produced similar GSDis. Because of the uncertainties associated with data in the blood lead studies, we recommend that a range of GSDis be used when analyzing site-specific risks associated with exposure to environmental lead instead of a single estimate. Because the different statistical methods produce similar GSDis, we recommend a simple procedure to calculate site-specific GSDi from a scientifically sound blood and environmental lead study.
Han, Lei; Zhang, Yong-Jun; Song, Jiangning; Liu, Ming S.; Zhang, Ziding
2012-01-01
Enzymes play a fundamental role in almost all biological processes and identification of catalytic residues is a crucial step for deciphering the biological functions and understanding the underlying catalytic mechanisms. In this work, we developed a novel structural feature called MEDscore to identify catalytic residues, which integrated the microenvironment (ME) and geometrical properties of amino acid residues. Firstly, we converted a residue's ME into a series of spatially neighboring residue pairs, whose likelihood of being located in a catalytic ME was deduced from a benchmark enzyme dataset. We then calculated an ME-based score, termed as MEscore, by summing up the likelihood of all residue pairs. Secondly, we defined a parameter called Dscore to measure the relative distance of a residue to the center of the protein, provided that catalytic residues are typically located in the center of the protein structure. Finally, we defined the MEDscore feature based on an effective nonlinear integration of MEscore and Dscore. When evaluated on a well-prepared benchmark dataset using five-fold cross-validation tests, MEDscore achieved a robust performance in identifying catalytic residues with an AUC1.0 of 0.889. At a ≤10% false positive rate control, MEDscore correctly identified approximately 70% of the catalytic residues. Remarkably, MEDscore achieved a competitive performance compared with the residue conservation score (e.g. CONscore), the most informative singular feature predominantly employed to identify catalytic residues. To the best of our knowledge, MEDscore is the first singular structural feature exhibiting such an advantage. More importantly, we found that MEDscore is complementary with CONscore and a significantly improved performance can be achieved by combining CONscore with MEDscore in a linear manner. As an implementation of this work, MEDscore has been made freely accessible at http://protein.cau.edu.cn/mepi/. PMID:22829945
DEFF Research Database (Denmark)
Cook, Gerald; Lin, Ching-Fang
1980-01-01
The local linearization algorithm is presented as a possible numerical integration scheme to be used in real-time simulation. A second-order nonlinear example problem is solved using different methods. The local linearization approach is shown to require less computing time and give significant...... improvement in accuracy over the classical second-order integration methods....
Geometric identities in stereological particle analysis
DEFF Research Database (Denmark)
Kötzer, S.; Jensen, Eva Bjørn Vedel; Baddeley, A.
We review recent findings about geometric identities in integral geometry and geometric tomography, and their statistical application to stereological particle analysis. Open questions are discussed.......We review recent findings about geometric identities in integral geometry and geometric tomography, and their statistical application to stereological particle analysis. Open questions are discussed....
International Nuclear Information System (INIS)
Chernyshenko, Dmitri; Fangohr, Hans
2015-01-01
In the finite difference method which is commonly used in computational micromagnetics, the demagnetizing field is usually computed as a convolution of the magnetization vector field with the demagnetizing tensor that describes the magnetostatic field of a cuboidal cell with constant magnetization. An analytical expression for the demagnetizing tensor is available, however at distances far from the cuboidal cell, the numerical evaluation of the analytical expression can be very inaccurate. Due to this large-distance inaccuracy numerical packages such as OOMMF compute the demagnetizing tensor using the explicit formula at distances close to the originating cell, but at distances far from the originating cell a formula based on an asymptotic expansion has to be used. In this work, we describe a method to calculate the demagnetizing field by numerical evaluation of the multidimensional integral in the demagnetizing tensor terms using a sparse grid integration scheme. This method improves the accuracy of computation at intermediate distances from the origin. We compute and report the accuracy of (i) the numerical evaluation of the exact tensor expression which is best for short distances, (ii) the asymptotic expansion best suited for large distances, and (iii) the new method based on numerical integration, which is superior to methods (i) and (ii) for intermediate distances. For all three methods, we show the measurements of accuracy and execution time as a function of distance, for calculations using single precision (4-byte) and double precision (8-byte) floating point arithmetic. We make recommendations for the choice of scheme order and integrating coefficients for the numerical integration method (iii). - Highlights: • We study the accuracy of demagnetization in finite difference micromagnetics. • We introduce a new sparse integration method to compute the tensor more accurately. • Newell, sparse integration and asymptotic method are compared for all ranges
Analysis of thermal-plastic response of shells of revolution by numerical integration
International Nuclear Information System (INIS)
Leonard, J.W.
1975-01-01
An economic technique for the numerical analysis of the elasto-plastic behaviour of shells of revolution would be of considerable value in the nuclear reactor industry. A numerical method based on the numerical integration of the governing shell equations has been shown, for elastic cases, to be more efficient than the finite element method when applied to shells of revolution. In the numerical integration method, the governing differential equations of motion are converted into a set of initial-value problems. Each initial-value problem is integrated numerically between meridional boundary points and recombined so as to satisfy boundary conditions. For large-deflection elasto-plastic behaviour, the equations are nonlinear and, hence, are recombined in an iterative manner using the Newton-Raphson procedure. Suppression techniques are incorporated in order to eliminate extraneous solutions within the numerical integration procedure. The Reissner-Meissner shell theory for shells of revolution is adopted to account for large deflection and higher-order rotation effects. The computer modelling of the equations is quite general in that specific shell segment geometries, e.g. cylindrical, spherical, toroidal, conical segments, and any combinations thereof can be handled easily. (Auth.)
A comparison of the efficiency of numerical methods for integrating chemical kinetic rate equations
Radhakrishnan, K.
1984-01-01
The efficiency of several algorithms used for numerical integration of stiff ordinary differential equations was compared. The methods examined included two general purpose codes EPISODE and LSODE and three codes (CHEMEQ, CREK1D and GCKP84) developed specifically to integrate chemical kinetic rate equations. The codes were applied to two test problems drawn from combustion kinetics. The comparisons show that LSODE is the fastest code available for the integration of combustion kinetic rate equations. It is shown that an iterative solution of the algebraic energy conservation equation to compute the temperature can be more efficient then evaluating the temperature by integrating its time-derivative.
Wang, Yi
2016-07-21
Velocity of fluid flow in underground porous media is 6~12 orders of magnitudes lower than that in pipelines. If numerical errors are not carefully controlled in this kind of simulations, high distortion of the final results may occur [1-4]. To fit the high accuracy demands of fluid flow simulations in porous media, traditional finite difference methods and numerical integration methods are discussed and corresponding high-accurate methods are developed. When applied to the direct calculation of full-tensor permeability for underground flow, the high-accurate finite difference method is confirmed to have numerical error as low as 10-5% while the high-accurate numerical integration method has numerical error around 0%. Thus, the approach combining the high-accurate finite difference and numerical integration methods is a reliable way to efficiently determine the characteristics of general full-tensor permeability such as maximum and minimum permeability components, principal direction and anisotropic ratio. Copyright © Global-Science Press 2016.
Wang, Jinting; Lu, Liqiao; Zhu, Fei
2018-01-01
Finite element (FE) is a powerful tool and has been applied by investigators to real-time hybrid simulations (RTHSs). This study focuses on the computational efficiency, including the computational time and accuracy, of numerical integrations in solving FE numerical substructure in RTHSs. First, sparse matrix storage schemes are adopted to decrease the computational time of FE numerical substructure. In this way, the task execution time (TET) decreases such that the scale of the numerical substructure model increases. Subsequently, several commonly used explicit numerical integration algorithms, including the central difference method (CDM), the Newmark explicit method, the Chang method and the Gui-λ method, are comprehensively compared to evaluate their computational time in solving FE numerical substructure. CDM is better than the other explicit integration algorithms when the damping matrix is diagonal, while the Gui-λ (λ = 4) method is advantageous when the damping matrix is non-diagonal. Finally, the effect of time delay on the computational accuracy of RTHSs is investigated by simulating structure-foundation systems. Simulation results show that the influences of time delay on the displacement response become obvious with the mass ratio increasing, and delay compensation methods may reduce the relative error of the displacement peak value to less than 5% even under the large time-step and large time delay.
Analysis of thermal-plastic response of shells of revolution by numerical integration
International Nuclear Information System (INIS)
Leonard, J.W.
1975-01-01
A numerical method based instead on the numerical integration of the governing shell equations has been shown, for elastic cases, to be more efficient than the finite element method when applied to shells of revolution. In the numerical integration method, the governing differential equations of motions are converted into a set of initial-value problems. Each initial-value problem is integrated numerically between meridional boundary points and recombined so as to satisfy boundary conditions. For large-deflection elasto-plastic behavior, the equations are nonlinear and, hence, are recombined in an iterative manner using the Newton-Raphson procedure. Suppression techniques are incorporated in order to eliminate extraneous solutions within the numerical integration procedure. The Reissner-Meissner shell theory for shells of revolution is adopted to account for large deflection and higher-order rotation effects. The computer modelling of the equations is quite general in that specific shell segment geometries, e.g. cylindrical, spherical, toroidal, conical segments, and any combinations thereof can be handled easily. The elasto-plastic constitutive relations adopted are in accordance with currently recommended constitutive equations for inelastic design analysis of FFTF Components. The Von Mises yield criteria and associated flow rule is used and the kinematic hardening law is followed. Examples are considered in which stainless steels common to LMFBR application are used
Geometric optical transfer function and tis computation method
International Nuclear Information System (INIS)
Wang Qi
1992-01-01
Geometric Optical Transfer Function formula is derived after expound some content to be easily ignored, and the computation method is given with Bessel function of order zero and numerical integration and Spline interpolation. The method is of advantage to ensure accuracy and to save calculation
International Nuclear Information System (INIS)
Woods, K; DiCostanzo, D; Gupta, N
2016-01-01
Purpose: To test the efficacy of a retrospective metal artifact reduction (MAR) reconstruction algorithm for a commercial computed tomography (CT) scanner for radiation therapy purposes. Methods: High Z geometric integrity and artifact reduction analysis was performed with three phantoms using General Electric’s (GE) Discovery CT. The three phantoms included: a Computerized Imaging Reference Systems (CIRS) electron density phantom (Model 062) with a 6.5 mm diameter titanium rod insert, a custom spine phantom using Synthes Spine hardware submerged in water, and a dental phantom with various high Z fillings submerged in water. Each phantom was reconstructed using MAR and compared against the original scan. Furthermore, each scenario was tested using standard and extended Hounsfield Unit (HU) ranges. High Z geometric integrity was performed using the CIRS phantom, while the artifact reduction was performed using all three phantoms. Results: Geometric integrity of the 6.5 mm diameter rod was slightly overestimated for non-MAR scans for both standard and extended HU. With MAR reconstruction, the rod was underestimated for both standard and extended HU. For artifact reduction, the mean and standard deviation was compared in a volume of interest (VOI) in the surrounding material (water and water equivalent material, ∼0HU). Overall, the mean value of the VOI was closer to 0 HU for the MAR reconstruction compared to the non-MAR scan for most phantoms. Additionally, the standard deviations for all phantoms were greatly reduced using MAR reconstruction. Conclusion: GE’s MAR reconstruction algorithm improves image quality with the presence of high Z material with minimal degradation of its geometric integrity. High Z delineation can be carried out with proper contouring techniques. The effects of beam hardening artifacts are greatly reduced with MAR reconstruction. Tissue corrections due to these artifacts can be eliminated for simple high Z geometries and greatly
Directory of Open Access Journals (Sweden)
Yan Nan
2017-01-01
Full Text Available In order to calculate the dynamometer card of oil well using acceleration sensor, the algorithm which combined by Kalman filter and discrete numerical integration is proposed. It can be applied to calculate the displacement and precipitation displacement period of oil well dynamometer card. The Kalman filter not only filters out the noise of the acceleration signal, but also maintains the original shape feature. The accurate precipitation of the displacement period ensures the correctness of displacement. The discrete numerical integration algorithm can make the relative error of displacement measurement less than 1%, which meets the requirement for dynamometer card accuracy. It is suitable for different types of oil wells.
pySecDec: A toolbox for the numerical evaluation of multi-scale integrals
Borowka, S.; Heinrich, G.; Jahn, S.; Jones, S. P.; Kerner, M.; Schlenk, J.; Zirke, T.
2018-01-01
We present pySECDEC, a new version of the program SECDEC, which performs the factorization of dimensionally regulated poles in parametric integrals, and the subsequent numerical evaluation of the finite coefficients. The algebraic part of the program is now written in the form of python modules, which allow a very flexible usage. The optimization of the C++ code, generated using FORM, is improved, leading to a faster numerical convergence. The new version also creates a library of the integrand functions, such that it can be linked to user-specific codes for the evaluation of matrix elements in a way similar to analytic integral libraries.
Numerical solution of nonlinear Urisohn-Volterra fuzzy functional integral equations
Georgieva, Atanaska; Naydenova, Iva
2017-12-01
In the present paper, we propose an efficient iterative numerical method of successive approximations to approximate solution of nonlinear Urisohn-Volterra fuzzy functional integral equations by fuzzy trapezoidal quadrature formula for classes of fuzzy-number-valued functions of Lipschitz type. We prove the convergence of the method and investigate the numerical stability of the present method with respect to the choice of the first iteration. The convergence of the method is tested through a numerical experiment, that confirms the obtained theoretical results.
Bray, Hubert L; Mazzeo, Rafe; Sesum, Natasa
2015-01-01
This volume includes expanded versions of the lectures delivered in the Graduate Minicourse portion of the 2013 Park City Mathematics Institute session on Geometric Analysis. The papers give excellent high-level introductions, suitable for graduate students wishing to enter the field and experienced researchers alike, to a range of the most important areas of geometric analysis. These include: the general issue of geometric evolution, with more detailed lectures on Ricci flow and Kähler-Ricci flow, new progress on the analytic aspects of the Willmore equation as well as an introduction to the recent proof of the Willmore conjecture and new directions in min-max theory for geometric variational problems, the current state of the art regarding minimal surfaces in R^3, the role of critical metrics in Riemannian geometry, and the modern perspective on the study of eigenfunctions and eigenvalues for Laplace-Beltrami operators.
Mao, Weihua; Speiser, Michael; Medin, Paul; Papiez, Lech; Solberg, Timothy; Xing, Lei
2011-05-01
Several linacs with integrated kilovoltage (kV) imaging have been developed for delivery of image guided radiation therapy (IGRT). High geometric accuracy and coincidence of kV imaging systems and megavoltage (MV) beam delivery are essential for successful image guidance. A geometric QA tool has been adapted for routine QA for evaluating and characterizing the geometric accuracy of kV and MV cone-beam imaging systems. The purpose of this work is to demonstrate the application of methodology to routine QA across three IGRT-dedicated linac platforms. It has been applied to a Varian Trilogy (Varian Medical Systems, Palo Alto, CA), an Elekta SynergyS (Elekta, Stockholm, Sweden), and a Brainlab Vero (Brainlab AG, Feldkirchen, Germany). Both the Trilogy and SynergyS linacs are equipped with a retractable kV x-ray tube and a flat panel detector. The Vero utilizes a rotating, rigid ring structure integrating a MV x-ray head mounted on orthogonal gimbals, an electronic portal imaging device (EPID), two kV x-ray tubes, and two fixed flat panel detectors. This dual kV imaging system provides orthogonal radiographs, CBCT images, and real-time fluoroscopic monitoring. Two QA phantoms were built to suit different field sizes. Projection images of a QA phantom were acquired using MV and kV imaging systems at a series of gantry angles. Software developed for this study was used to analyze the projection images and calculate nine geometric parameters for each projection. The Trilogy was characterized five times over one year, while the SynergyS was characterized four times and the Vero once. Over 6500 individual projections were acquired and analyzed. Quantitative geometric parameters of both MV and kV imaging systems, as well as the isocenter consistency of the imaging systems, were successfully evaluated. A geometric tool has been successfully implemented for calibration and QA of integrated kV and MV across a variety of radiotherapy platforms. X-ray source angle deviations up to
Numerical treatment of Faddeev integral equations for non-separable potentials
International Nuclear Information System (INIS)
Eyre, D.
1986-10-01
A finite element method is used to solve the three-body problem for bound states. Two-dimensional integral equations are approximated in a trial space of piecewise quadratic polynomials. Approximate solutions are obtained for a model problem of three spinless bosons interacting via the sum of S-wave Yukawa potentials. Numerical estimates for rates of convergence of the method are obtained
Numerical solutions of integral and integro-differential equations using Legendre polynomials
Khater, A.; Shamardan, A.; Callebaut, D.; Sakran, M.
2007-11-01
In this paper, a finite Legendre expansion is developed to solve singularly perturbed integral equations, first order integro-differential equations of Volterra type arising in fluid dynamics and Volterra delay integro-differential equations. The error analysis is derived. Numerical results and comparisons with other methods in literature are considered.
Stable unitary integrators for the numerical implementation of continuous unitary transformations
Savitz, Samuel; Refael, Gil
2017-09-01
The technique of continuous unitary transformations has recently been used to provide physical insight into a diverse array of quantum mechanical systems. However, the question of how to best numerically implement the flow equations has received little attention. The most immediately apparent approach, using standard Runge-Kutta numerical integration algorithms, suffers from both severe inefficiency due to stiffness and the loss of unitarity. After reviewing the formalism of continuous unitary transformations and Wegner's original choice for the infinitesimal generator of the flow, we present a number of approaches to resolving these issues including a choice of generator which induces what we call the "uniform tangent decay flow" and three numerical integrators specifically designed to perform continuous unitary transformations efficiently while preserving the unitarity of flow. We conclude by applying one of the flow algorithms to a simple calculation that visually demonstrates the many-body localization transition.
Dose calculation using a numerical method based on Haar wavelets integration
Energy Technology Data Exchange (ETDEWEB)
Belkadhi, K., E-mail: khaled.belkadhi@ult-tunisie.com [Unité de Recherche de Physique Nucléaire et des Hautes Énergies, Faculté des Sciences de Tunis, Université Tunis El-Manar (Tunisia); Manai, K. [Unité de Recherche de Physique Nucléaire et des Hautes Énergies, Faculté des Sciences de Tunis, Université Tunis El-Manar (Tunisia); College of Science and Arts, University of Bisha, Bisha (Saudi Arabia)
2016-03-11
This paper deals with the calculation of the absorbed dose in an irradiation cell of gamma rays. Direct measurement and simulation have shown that they are expensive and time consuming. An alternative to these two operations is numerical methods, a quick and efficient way can furnish an estimation of the absorbed dose by giving an approximation of the photon flux at a specific point of space. To validate the numerical integration method based on the Haar wavelet for absorbed dose estimation, a study with many configurations was performed. The obtained results with the Haar wavelet method showed a very good agreement with the simulation highlighting good efficacy and acceptable accuracy. - Highlights: • A numerical integration method using Haar wavelets is detailed. • Absorbed dose is estimated with Haar wavelets method. • Calculated absorbed dose using Haar wavelets and Monte Carlo simulation using Geant4 are compared.
A variable step method for the numerical integration of the one-dimensional Schroedinger equation
International Nuclear Information System (INIS)
Raptis, A.D.; Cash, J.R.
1985-01-01
Most numerical methods which have been proposed for the approximate integration of the one-dimensional Schroedinger equation use a fixed step length of integration. Such an approach can of course result in gross inefficiency since the small step length which must normally be used in the initial part of the range of integration to obtain the desired accuracy must then be used throughout the integration. In this paper we consider the method of embedding, which is widely used with explicit Runge-Kutta methods for the solution of first order initial value problems, for use with the special formulae used to integrate the Schroedinger equation. By adopting this technique we have available at each step an estimate of the local truncation error and this estimate can be used to automatically control the step length of integration. Also considered is the problem of estimating the global truncation error at the end of the range of integration. The power of the approaches considered is illustrated by means of some numerical examples. (orig.)
An integral equation-based numerical solver for Taylor states in toroidal geometries
O'Neil, Michael; Cerfon, Antoine J.
2018-04-01
We present an algorithm for the numerical calculation of Taylor states in toroidal and toroidal-shell geometries using an analytical framework developed for the solution to the time-harmonic Maxwell equations. Taylor states are a special case of what are known as Beltrami fields, or linear force-free fields. The scheme of this work relies on the generalized Debye source representation of Maxwell fields and an integral representation of Beltrami fields which immediately yields a well-conditioned second-kind integral equation. This integral equation has a unique solution whenever the Beltrami parameter λ is not a member of a discrete, countable set of resonances which physically correspond to spontaneous symmetry breaking. Several numerical examples relevant to magnetohydrodynamic equilibria calculations are provided. Lastly, our approach easily generalizes to arbitrary geometries, both bounded and unbounded, and of varying genus.
Directory of Open Access Journals (Sweden)
Suresh Thenozhi
2012-01-01
Full Text Available An important objective of health monitoring systems for tall buildings is to diagnose the state of the building and to evaluate its possible damage. In this paper, we use our prototype to evaluate our data-mining approach for the fault monitoring. The offset cancellation and high-pass filtering techniques are combined effectively to solve common problems in numerical integration of acceleration signals in real-time applications. The integration accuracy is improved compared with other numerical integrators. Then we introduce a novel method for support vector machine (SVM classification, called convex-concave hull. We use the Jarvis march method to decide the concave (nonconvex hull for the inseparable points. Finally the vertices of the convex-concave hull are applied for SVM training.
Muniz Oliva, Waldyr
2002-01-01
Geometric Mechanics here means mechanics on a pseudo-riemannian manifold and the main goal is the study of some mechanical models and concepts, with emphasis on the intrinsic and geometric aspects arising in classical problems. The first seven chapters are written in the spirit of Newtonian Mechanics while the last two ones as well as two of the four appendices describe the foundations and some aspects of Special and General Relativity. All the material has a coordinate free presentation but, for the sake of motivation, many examples and exercises are included in order to exhibit the desirable flavor of physical applications.
Bogner, Christian; Schweitzer, Armin; Weinzierl, Stefan
2017-09-01
We study the analytic continuation of Feynman integrals from the kite family, expressed in terms of elliptic generalisations of (multiple) polylogarithms. Expressed in this way, the Feynman integrals are functions of two periods of an elliptic curve. We show that all what is required is just the analytic continuation of these two periods. We present an explicit formula for the two periods for all values of t ∈ R. Furthermore, the nome q of the elliptic curve satisfies over the complete range in t the inequality | q | ≤ 1, where | q | = 1 is attained only at the singular points t ∈ {m2 , 9m2 , ∞ }. This ensures the convergence of the q-series expansion of the ELi-functions and provides a fast and efficient evaluation of these Feynman integrals.
Examination of Numerical Integration Accuracy and Modeling for GRACE-FO and GRACE-II
McCullough, C.; Bettadpur, S.
2012-12-01
As technological advances throughout the field of satellite geodesy improve the accuracy of satellite measurements, numerical methods and algorithms must be able to keep pace. Currently, the Gravity Recovery and Climate Experiment's (GRACE) dual one-way microwave ranging system can determine changes in inter-satellite range to a precision of a few microns; however, with the advent of laser measurement systems nanometer precision ranging is a realistic possibility. With this increase in measurement accuracy, a reevaluation of the accuracy inherent in the linear multi-step numerical integration methods is necessary. Two areas where this can be a primary concern are the ability of the numerical integration methods to accurately predict the satellite's state in the presence of numerous small accelerations due to operation of the spacecraft attitude control thrusters, and due to small, point-mass anomalies on the surface of the Earth. This study attempts to quantify and minimize these numerical errors in an effort to improve the accuracy of modeling and propagation of these perturbations; helping to provide further insight into the behavior and evolution of the Earth's gravity field from the more capable gravity missions in the future.
Rosenbaum, J. S.
1976-01-01
If a system of ordinary differential equations represents a property conserving system that can be expressed linearly (e.g., conservation of mass), it is then desirable that the numerical integration method used conserve the same quantity. It is shown that both linear multistep methods and Runge-Kutta methods are 'conservative' and that Newton-type methods used to solve the implicit equations preserve the inherent conservation of the numerical method. It is further shown that a method used by several authors is not conservative.
Projector methods applied to numerical integration of the SN transport equation
International Nuclear Information System (INIS)
Hristea, V.; Covaci, St.
2003-01-01
We are developing two methods of integration for the S N transport equation in x - y geometry, methods based on projector technique. By cellularization of the phase space and by choosing a finite basis of orthogonal functions, which characterize the angular flux, the non-selfadjoint transport equation is reduced to a cellular automaton. This automaton is completely described by the transition Matrix T. Within this paper two distinct methods of projection are described. One of them uses the transversal integration technique. As an alternative to this we applied the method of the projectors for the integral S N transport equation. We show that the constant spatial approximation of the integral S N transport equation does not lead to negative fluxes. One of the problems with the projector method, namely the appearance of numerical instability for small intervals is solved by the Pade representation of the elements for Matrix T. Numerical tests here presented compare the numerical performances of the algorithms obtained by the two projection methods. The Pade representation was also taken into account for these two algorithm types. (authors)
Numerical Study of Two-Dimensional Volterra Integral Equations by RDTM and Comparison with DTM
Directory of Open Access Journals (Sweden)
Reza Abazari
2013-01-01
Full Text Available The two-dimensional Volterra integral equations are solved using more recent semianalytic method, the reduced differential transform method (the so-called RDTM, and compared with the differential transform method (DTM. The concepts of DTM and RDTM are briefly explained, and their application to the two-dimensional Volterra integral equations is studied. The results obtained by DTM and RDTM together are compared with exact solution. As an important result, it is depicted that the RDTM results are more accurate in comparison with those obtained by DTM applied to the same Volterra integral equations. The numerical results reveal that the RDTM is very effective, convenient, and quite accurate compared to the other kind of nonlinear integral equations. It is predicted that the RDTM can be found widely applicable in engineering sciences.
Voytishek, Anton V.; Shipilov, Nikolay M.
2017-11-01
In this paper, the systematization of numerical (implemented on a computer) randomized functional algorithms for approximation of a solution of Fredholm integral equation of the second kind is carried out. Wherein, three types of such algorithms are distinguished: the projection, the mesh and the projection-mesh methods. The possibilities for usage of these algorithms for solution of practically important problems is investigated in detail. The disadvantages of the mesh algorithms, related to the necessity of calculation values of the kernels of integral equations in fixed points, are identified. On practice, these kernels have integrated singularities, and calculation of their values is impossible. Thus, for applied problems, related to solving Fredholm integral equation of the second kind, it is expedient to use not mesh, but the projection and the projection-mesh randomized algorithms.
A numerical integration approach suitable for simulating PWR dynamics using a microcomputer system
International Nuclear Information System (INIS)
Zhiwei, L.; Kerlin, T.W.
1983-01-01
It is attractive to use microcomputer systems to simulate nuclear power plant dynamics for the purpose of teaching and/or control system design. An analysis and a comparison of feasibility of existing numerical integration methods have been made. The criteria for choosing the integration step using various numerical integration methods including the matrix exponential method are derived. In order to speed up the simulation, an approach is presented using the Newton recursion calculus which can avoid convergence limitations in choosing the integration step size. The accuracy consideration will dominate the integration step limited. The advantages of this method have been demonstrated through a case study using CBM model 8032 microcomputer to simulate a reduced order linear PWR model under various perturbations. It has been proven theoretically and practically that the Runge-Kutta method and Adams-Moulton method are not feasible. The matrix exponential method is good at accuracy and fairly good at speed. The Newton recursion method can save 3/4 to 4/5 time compared to the matrix exponential method with reasonable accuracy. Vertical Barhis method can be expanded to deal with nonlinear nuclear power plant models and higher order models as well
Chebyshev Wavelet Method for Numerical Solution of Fredholm Integral Equations of the First Kind
Directory of Open Access Journals (Sweden)
Hojatollah Adibi
2010-01-01
Full Text Available A computational method for solving Fredholm integral equations of the first kind is presented. The method utilizes Chebyshev wavelets constructed on the unit interval as basis in Galerkin method and reduces solving the integral equation to solving a system of algebraic equations. The properties of Chebyshev wavelets are used to make the wavelet coefficient matrices sparse which eventually leads to the sparsity of the coefficients matrix of obtained system. Finally, numerical examples are presented to show the validity and efficiency of the technique.
Directory of Open Access Journals (Sweden)
Mohamed Ali
2017-10-01
Full Text Available This work, Bernoulli wavelet method is formed to solve nonlinear fuzzy Volterra-Fredholm integral equations. Bernoulli wavelets have been Created by dilation and translation of Bernoulli polynomials. First we introduce properties of Bernoulli wavelets and Bernoulli polynomials, and then we used it to transform the integral equations to the system of algebraic equations. We compared the result of the proposed method with the exact solution to show the convergence and advantages of the new method. The results got by present wavelet method are compared with that of by collocation method based on radial basis functions method. Finally, the numerical examples explain the accuracy of this method.
Directory of Open Access Journals (Sweden)
Hussein Rappel
2014-01-01
integration technique (EFIT as well as its validation with analytical results. Lamb wave method is a long range inspection technique which is considered to have unique future in the field of structural health monitoring. One of the main problems facing the lamb wave method is how to choose the most appropriate frequency to generate the waves for adequate transmission capable of properly propagating in the material, interfering with defects/damages, and being received in good conditions. Modern simulation tools based on numerical methods such as finite integration technique (FIT, finite element method (FEM, and boundary element method (BEM may be used for modeling. In this paper, two sets of simulation are performed. In the first set, group velocities of lamb wave in a steel plate are obtained numerically. Results are then compared with analytical results to validate the simulation. In the second set, EFIT is employed to study fundamental symmetric mode interaction with a surface braking defect.
Numerical simulation and experimental research of the integrated high-power LED radiator
Xiang, J. H.; Zhang, C. L.; Gan, Z. J.; Zhou, C.; Chen, C. G.; Chen, S.
2017-01-01
The thermal management has become an urgent problem to be solved with the increasing power and the improving integration of the LED (light emitting diode) chip. In order to eliminate the contact resistance of the radiator, this paper presented an integrated high-power LED radiator based on phase-change heat transfer, which realized the seamless connection between the vapor chamber and the cooling fins. The radiator was optimized by combining the numerical simulation and the experimental research. The effects of the chamber diameter and the parameters of fin on the heat dissipation performance were analyzed. The numerical simulation results were compared with the measured values by experiment. The results showed that the fin thickness, the fin number, the fin height and the chamber diameter were the factors which affected the performance of radiator from primary to secondary.
Fourth-Order Method for Numerical Integration of Age- and Size-Structured Population Models
Energy Technology Data Exchange (ETDEWEB)
Iannelli, M; Kostova, T; Milner, F A
2008-01-08
In many applications of age- and size-structured population models, there is an interest in obtaining good approximations of total population numbers rather than of their densities. Therefore, it is reasonable in such cases to solve numerically not the PDE model equations themselves, but rather their integral equivalents. For this purpose quadrature formulae are used in place of the integrals. Because quadratures can be designed with any order of accuracy, one can obtain numerical approximations of the solutions with very fast convergence. In this article, we present a general framework and a specific example of a fourth-order method based on composite Newton-Cotes quadratures for a size-structured population model.
International Nuclear Information System (INIS)
Adler, A.; Fuchs, B.; Thielheim, K.O.
1977-01-01
The longitudinal development of electromagnetic cascades in air, copper, iron, and lead is studied on the basis of results derived recently by numerical integration of the cascade equations applying rather accurate expressions for the cross-sections involved with the interactions of high energy electrons, positrons, and photons in electromagnetic cascades. Special attention is given to scaling properties of transition curves. It is demonstrated that a good scaling may be achieved by means of the depth of maximum cascade development. (author)
Loureiro, F. S.; Mansur, Webe Joao
2009-09-01
This paper is concerned with the formulation and numerical implementation of a new class of time integration schemes applied to linear heat conduction problems. The temperature field at any time level is calculated in terms of the numerical Green’s function matrix of the model problem by considering an analytical time integral equation. After spatial discretization by the finite element method, the Green’s function matrix which transfers solution from t to t + Δ t is explicitly computed in nodal coordinates using efficient implicit and explicit Runge-Kutta methods. It is shown that the stability and the accuracy of the proposed method are highly improved when a sub-step procedure is used to calculate recursively the Green’s function matrix at the end of the first time step. As a result, with a suitable choice of the number of sub-steps, large time steps can be used without degenerating the numerical solution. Finally, the effectiveness of the present methodology is demonstrated by analyzing two numerical examples.
Discounting model selection with area-based measures: A case for numerical integration.
Gilroy, Shawn P; Hantula, Donald A
2018-03-01
A novel method for analyzing delay discounting data is proposed. This newer metric, a model-based Area Under Curve (AUC) combining approximate Bayesian model selection and numerical integration, was compared to the point-based AUC methods developed by Myerson, Green, and Warusawitharana (2001) and extended by Borges, Kuang, Milhorn, and Yi (2016). Using data from computer simulation and a published study, comparisons of these methods indicated that a model-based form of AUC offered a more consistent and statistically robust measurement of area than provided by using point-based methods alone. Beyond providing a form of AUC directly from a discounting model, numerical integration methods permitted a general calculation in cases when the Effective Delay 50 (ED50) measure could not be calculated. This allowed discounting model selection to proceed in conditions where data are traditionally more challenging to model and measure, a situation where point-based AUC methods are often enlisted. Results from simulation and existing data indicated that numerical integration methods extended both the area-based interpretation of delay discounting as well as the discounting model selection approach. Limitations of point-based AUC as a first-line analysis of discounting and additional extensions of discounting model selection were also discussed. © 2018 Society for the Experimental Analysis of Behavior.
Mario, Hirz; Gfrerrer, Anton; Lang, Johann
2013-01-01
The automotive industry faces constant pressure to reduce development costs and time while still increasing vehicle quality. To meet this challenge, engineers and researchers in both science and industry are developing effective strategies and flexible tools by enhancing and further integrating powerful, computer-aided design technology. This book provides a valuable overview of the development tools and methods of today and tomorrow. It is targeted not only towards professional project and design engineers, but also to students and to anyone who is interested in state-of-the-art computer-aided development. The book begins with an overview of automotive development processes and the principles of virtual product development. Focusing on computer-aided design, a comprehensive outline of the fundamentals of geometry representation provides a deeper insight into the mathematical techniques used to describe and model geometrical elements. The book then explores the link between the demands of integrated design pr...
Ellmer, Matthias; Mayer-Gürr, Torsten
2016-04-01
Future gravity missions like GRACE-FO and beyond will deliver low-low satellite-to-satellite (ll-sst) ranging measurements of much increased precision. This necessitates a re-evaluation of the processes used in gravity field determination with an eye to numerical stability. When computing gravity fields from ll-sst data, precise positions of both satellites are needed in the setup of the observation equations. These positions thus have an immediate effect on the sought-after gravity field parameters. We use reduced-dynamic orbits which are computed through integration of all accelerations experienced by the satellite, as determined through a priori models and observed through the accelerometer. Our simulations showed that computing the orbit of the satellite through complete integration of all acting forces leads to numeric instabilities magnitudes larger than the expected ranging accuracy. We introduce a numerically stable approach employing a best-fit keplerian reference orbit based on Encke's method. Our investigations revealed that using canonical formulations for the evaluation of the reference keplerian orbit and accelerations lead to insufficient precision, necessitating an alternative formulation like the equinoctial elements.
International Nuclear Information System (INIS)
Kiefer, B; Bartel, T; Menzel, A
2012-01-01
Several constitutive models for magnetic shape memory alloys (MSMAs) have been proposed in the literature. The implementation of numerical integration schemes, which allow the prediction of constitutive response for general loading cases and ultimately the incorporation of MSMA response into numerical solution algorithms for fully coupled magneto-mechanical boundary value problems, however, has received only very limited attention. In this work, we establish two algorithmic implementations of the internal variable model for MSMAs proposed in (Kiefer and Lagoudas 2005 Phil. Mag. Spec. Issue: Recent Adv. Theor. Mech. 85 4289–329, Kiefer and Lagoudas 2009 J. Intell. Mater. Syst. 20 143–70), where we restrict our attention to pure martensitic variant reorientation to limit complexity. The first updating scheme is based on the numerical integration of the reorientation strain evolution equation and represents a classical predictor–corrector-type general return mapping algorithm. In the second approach, the inequality-constrained optimization problem associated with internal variable evolution is converted into an unconstrained problem via Fischer–Burmeister complementarity functions and then iteratively solved in standard Newton–Raphson format. Simulations are verified by comparison to closed-form solutions for experimentally relevant loading cases. (paper)
Baczewski, Andrew D.; Bond, Stephen D.
2013-07-01
Generalized Langevin dynamics (GLD) arise in the modeling of a number of systems, ranging from structured fluids that exhibit a viscoelastic mechanical response, to biological systems, and other media that exhibit anomalous diffusive phenomena. Molecular dynamics (MD) simulations that include GLD in conjunction with external and/or pairwise forces require the development of numerical integrators that are efficient, stable, and have known convergence properties. In this article, we derive a family of extended variable integrators for the Generalized Langevin equation with a positive Prony series memory kernel. Using stability and error analysis, we identify a superlative choice of parameters and implement the corresponding numerical algorithm in the LAMMPS MD software package. Salient features of the algorithm include exact conservation of the first and second moments of the equilibrium velocity distribution in some important cases, stable behavior in the limit of conventional Langevin dynamics, and the use of a convolution-free formalism that obviates the need for explicit storage of the time history of particle velocities. Capability is demonstrated with respect to accuracy in numerous canonical examples, stability in certain limits, and an exemplary application in which the effect of a harmonic confining potential is mapped onto a memory kernel.
The numerical analysis of functional integral and integro-differential equations of Volterra type
Brunner, Hermann
The qualitative and quantitative analysis of numerical methods for delay differential equations is now quite well understood, as reflected in the recent monograph by Bellen and Zennaro (2003). This is in remarkable contrast to the situation in the numerical analysis of functional equations, in which delays occur in connection with memory terms described by Volterra integral operators. The complexity of the convergence and asymptotic stability analyses has its roots in new `dimensions' not present in DDEs: the problems have distributed delays; kernels in the Volterra operators may be weakly singular; a second discretization step (approximation of the memory term by feasible quadrature processes) will in general be necessary before solution approximations can be computed.The purpose of this review is to introduce the reader to functional integral and integro-differential equations of Volterra type and their discretization, focusing on collocation techniques; to describe the `state of the art' in the numerical analysis of such problems; and to show that - especially for many `classical' equations whose analysis dates back more than 100 years - we still have a long way to go before we reach a level of insight into their discretized versions to compare with that achieved for DDEs.
Numerical integration and FEM-implementation of a viscoplastic Chaboche-model with static recovery
Kullig, E.; Wippler, S.
2006-11-01
This paper is concerned with the implementation of a viscoplastic material model of the Chaboche type in the framework of the finite element method (FEM). The equations of the used constitutive law, that incorporates isotropic hardening, back stress evolution with static recovery terms and drag stress evolution, are introduced. A representation of their numerical integration using the implicit backward Euler method under the assumption of small deformations and an isothermal formulation follows. The use of the backward Euler method leads to a nonlinear algebraic system of three equations, which is solved by a combination of the Pegasus method and a fixed-point iteration. After considering the accuracy of the presented integration algorithm in form of iso-error maps, the derivation of the consistent viscoplastic tangent operator is shown. The integration scheme and the calculation of the consistent viscoplastic tangent operator are implemented in the commercial finite element code ABAQUS, using the possibility of the user-defined material subroutine (UMAT). Finally a numerical example in form of a notched bar under tension is presented.
Numerical Modeling of an Integrated Vehicle Fluids System Loop for Pressurizing a Cryogenic Tank
LeClair, A. C.; Hedayat, A.; Majumdar, A. K.
2017-01-01
This paper presents a numerical model of the pressurization loop of the Integrated Vehicle Fluids (IVF) system using the Generalized Fluid System Simulation Program (GFSSP). The IVF propulsion system, being developed by United Launch Alliance to reduce system weight and enhance reliability, uses boiloff propellants to drive thrusters for the reaction control system as well as to run internal combustion engines to develop power and drive compressors to pressurize propellant tanks. NASA Marshall Space Flight Center (MSFC) conducted tests to verify the functioning of the IVF system using a flight-like tank. GFSSP, a finite volume based flow network analysis software developed at MSFC, has been used to support the test program. This paper presents the simulation of three different test series, comparison of numerical prediction and test data and a novel method of presenting data in a dimensionless form. The paper also presents a methodology of implementing a compressor map in a system level code.
International Nuclear Information System (INIS)
Furukawa, Masaru; Ohkawa, Yushiro; Matsuyama, Akinobu
2016-01-01
A high-accuracy numerical integration algorithm for a charged particle motion is developed. The algorithm is based on the Hamiltonian mechanics and the operator decomposition. The algorithm is made to be time-reversal symmetric, and its order of accuracy can be increased to any order by using a recurrence formula. One of the advantages is that it is an explicit method. An effective way to decompose the time evolution operator is examined; the Poisson tensor is decomposed and non-canonical variables are adopted. The algorithm is extended to a time dependent fields' case by introducing the extended phase space. Numerical tests showing the performance of the algorithm are presented. One is the pure cyclotron motion for a long time period, and the other is a charged particle motion in a rapidly oscillating field. (author)
Numerical evaluation of Feynman loop integrals by reduction to tree graphs
Energy Technology Data Exchange (ETDEWEB)
Kleinschmidt, T.
2007-12-15
We present a method for the numerical evaluation of loop integrals, based on the Feynman Tree Theorem. This states that loop graphs can be expressed as a sum of tree graphs with additional external on-shell particles. The original loop integral is replaced by a phase space integration over the additional particles. In cross section calculations and for event generation, this phase space can be sampled simultaneously with the phase space of the original external particles. Since very sophisticated matrix element generators for tree graph amplitudes exist and phase space integrations are generically well understood, this method is suited for a future implementation in a fully automated Monte Carlo event generator. A scheme for renormalization and regularization is presented. We show the construction of subtraction graphs which cancel ultraviolet divergences and present a method to cancel internal on-shell singularities. Real emission graphs can be naturally included in the phase space integral of the additional on-shell particles to cancel infrared divergences. As a proof of concept, we apply this method to NLO Bhabha scattering in QED. Cross sections are calculated and are in agreement with results from conventional methods. We also construct a Monte Carlo event generator and present results. (orig.)
Numerical Integration Techniques for Curved-Element Discretizations of Molecule–Solvent Interfaces
Bardhan, Jaydeep P.; Altman, Michael D.; Willis, David J.; Lippow, Shaun M.; Tidor, Bruce; White, Jacob K.
2012-01-01
Surface formulations of biophysical modeling problems offer attractive theoretical and computational properties. Numerical simulations based on these formulations usually begin with discretization of the surface under consideration; often, the surface is curved, possessing complicated structure and possibly singularities. Numerical simulations commonly are based on approximate, rather than exact, discretizations of these surfaces. To assess the strength of the dependence of simulation accuracy on the fidelity of surface representation, we have developed methods to model several important surface formulations using exact surface discretizations. Following and refining Zauhar’s work (J. Comp.-Aid. Mol. Des. 9:149-159, 1995), we define two classes of curved elements that can exactly discretize the van der Waals, solvent-accessible, and solvent-excluded (molecular) surfaces. We then present numerical integration techniques that can accurately evaluate nonsingular and singular integrals over these curved surfaces. After validating the exactness of the surface discretizations and demonstrating the correctness of the presented integration methods, we present a set of calculations that compare the accuracy of approximate, planar-triangle-based discretizations and exact, curved-element-based simulations of surface-generalized-Born (sGB), surface-continuum van der Waals (scvdW), and boundary-element method (BEM) electrostatics problems. Results demonstrate that continuum electrostatic calculations with BEM using curved elements, piecewise-constant basis functions, and centroid collocation are nearly ten times more accurate than planartriangle BEM for basis sets of comparable size. The sGB and scvdW calculations give exceptional accuracy even for the coarsest obtainable discretized surfaces. The extra accuracy is attributed to the exact representation of the solute–solvent interface; in contrast, commonly used planar-triangle discretizations can only offer improved
Time transformations and Cowell's method. [for numerical integration of satellite motion equations
Velez, C. E.; Hilinski, S.
1978-01-01
The precise numerical integration of Cowell's equations of satellite motion is frequently performed with an independent variable s defined by an equation of the form dt = cr to the n-th power ds, where t represents time, r the radial distance from the center of attraction, c is a constant, and n is a parameter. This has been primarily motivated by the 'uniformizing' effects of such a transformation resulting in desirable 'analytic' stepsize control for elliptical orbits. This report discusses the 'proper' choice of the parameter n defining the independent variable s for various types of orbits and perturbation models, and develops a criterion for its selection.
Numerical analysis of diffuse ceiling ventilation and its integration with a radiant ceiling system
DEFF Research Database (Denmark)
Zhang, Chen; Heiselberg, Per Kvols; Chen, Qingyan
2017-01-01
A novel system combining diffuse ceiling ventilation and radiant ceiling was proposed recently, with the aim of providing energy efficient and comfort environment to office buildings. Designing of such a system is challenging because of complex interactions between the two subsystems and a large...... number of design parameters encountered in practice. This study aimed to develop a numerical model that can reliably predict the airflow and thermal performance of the integrated system during the design stage. The model was validated by experiments under different operating conditions. The validated...
DEFF Research Database (Denmark)
Andersen, Jørgen Ellegaard; Borot, Gaëtan; Orantin, Nicolas
We propose a general theory whose main component are functorial assignments ∑→Ω∑ ∈ E (∑), for a large class of functors E from a certain category of bordered surfaces (∑'s) to a suitable a target category of topological vector spaces. The construction is done by summing appropriate compositions...... of the initial data over all homotopy classes of successive excisions of embedded pair of pants. We provide sufficient conditions to guarantee these infinite sums converge and as a result, we can generate mapping class group invariant vectors Ω∑ which we call amplitudes. The initial data encode the amplitude...... for pair of pants and tori with one boundary, as well as the "recursion kernels" used for glueing. We give this construction the name of "geometric recursion", abbreviated GR. As an illustration, we show how to apply our formalism to various spaces of continuous functions over Teichmueller spaces, as well...
Majumdar, Alok K.; LeClair, Andre C.; Hedayat, Ali
2016-01-01
This paper presents a numerical model of pressurization of a cryogenic propellant tank for the Integrated Vehicle Fluid (IVF) system using the Generalized Fluid System Simulation Program (GFSSP). The IVF propulsion system, being developed by United Launch Alliance, uses boiloff propellants to drive thrusters for the reaction control system as well as to run internal combustion engines to develop power and drive compressors to pressurize propellant tanks. NASA Marshall Space Flight Center (MSFC) has been running tests to verify the functioning of the IVF system using a flight tank. GFSSP, a finite volume based flow network analysis software developed at MSFC, has been used to develop an integrated model of the tank and the pressurization system. This paper presents an iterative algorithm for converging the interface boundary conditions between different component models of a large system model. The model results have been compared with test data.
Geometric Computing for Freeform Architecture
Wallner, J.
2011-06-03
Geometric computing has recently found a new field of applications, namely the various geometric problems which lie at the heart of rationalization and construction-aware design processes of freeform architecture. We report on our work in this area, dealing with meshes with planar faces and meshes which allow multilayer constructions (which is related to discrete surfaces and their curvatures), triangles meshes with circle-packing properties (which is related to conformal uniformization), and with the paneling problem. We emphasize the combination of numerical optimization and geometric knowledge.
Smith, Amanda L.; Benazzi, Stefano; Ledogar, Justin A.; Tamvada, Kelli; Smith, Leslie C. Pryor; Weber, Gerhard W.; Spencer, Mark A.; Dechow, Paul C.; Grosse, Ian R.; Ross, Callum F.; Richmond, Brian G.; Wright, Barth W.; Wang, Qian; Byron, Craig; Slice, Dennis E.; Strait, David S.
2014-01-01
In a broad range of evolutionary studies, an understanding of intraspecific variation is needed in order to contextualize and interpret the meaning of variation between species. However, mechanical analyses of primate crania using experimental or modeling methods typically encounter logistical constraints that force them to rely on data gathered from only one or a few individuals. This results in a lack of knowledge concerning the mechanical significance of intraspecific shape variation that limits our ability to infer the significance of interspecific differences. This study uses geometric morphometric methods (GM) and finite element analysis (FEA) to examine the biomechanical implications of shape variation in chimpanzee crania, thereby providing a comparative context in which to interpret shape-related mechanical variation between hominin species. Six finite element models (FEMs) of chimpanzee crania were constructed from CT scans following shape-space Principal Component Analysis (PCA) of a matrix of 709 Procrustes coordinates (digitized onto 21 specimens) to identify the individuals at the extremes of the first three principal components. The FEMs were assigned the material properties of bone and were loaded and constrained to simulate maximal bites on the P3 and M2. Resulting strains indicate that intraspecific cranial variation in morphology is associated with quantitatively high levels of variation in strain magnitudes, but qualitatively little variation in the distribution of strain concentrations. Thus, interspecific comparisons should include considerations of the spatial patterning of strains rather than focus only their magnitude. PMID:25529239
Directory of Open Access Journals (Sweden)
Nikesh S. Dattani
2012-03-01
Full Text Available One of the most successful methods for calculating reduced density operator dynamics in open quantum systems, that can give numerically exact results, uses Feynman integrals. However, when simulating the dynamics for a given amount of time, the number of time steps that can realistically be used with this method is always limited, therefore one often obtains an approximation of the reduced density operator at a sparse grid of points in time. Instead of relying only on ad hoc interpolation methods (such as splines to estimate the system density operator in between these points, I propose a method that uses physical information to assist with this interpolation. This method is tested on a physically significant system, on which its use allows important qualitative features of the density operator dynamics to be captured with as little as two time steps in the Feynman integral. This method allows for an enormous reduction in the amount of memory and CPU time required for approximating density operator dynamics within a desired accuracy. Since this method does not change the way the Feynman integral itself is calculated, the value of the density operator approximation at the points in time used to discretize the Feynamn integral will be the same whether or not this method is used, but its approximation in between these points in time is considerably improved by this method. A list of ways in which this proposed method can be further improved is presented in the last section of the article.
A stable numerical inversion of Abel's integral equation using almost Bernstein operational matrix
International Nuclear Information System (INIS)
Singh, Om P.; Singh, Vineet K.; Pandey, Rajesh K.
2010-01-01
Many problems in physics like reconstruction of the radially distributed emissivity from the line-of-sight projected intensity, the 3-D image reconstruction from cone-beam projections in computerized tomography, etc. lead naturally, in the case of radial symmetry, to the study of Abel's type integral equation. The aim of this communication is to modify the stable algorithm proposed in [Singh VK, Pandey RK, Singh OP. New stable numerical solution of singular integral equations of Abel type by using normalized Bernstein polynomials. Applied Mathematical Sciences 2009;3(5):241-255] which is based on normalized Bernstein polynomial approximation of the projected intensity profile. So, first we construct an orthonormal family {b i5 } i=0 5 of polynomials of degree 5 from the 5th degree Bernstein polynomials B i5 and use them as a basis to approximate the projected intensity profile. Then, a 6x6 matrix P, named as almost Bernstein operational matrix of integration is constructed and used to reduce the integral equation to a system of algebraic equation which can be solved easily. The method is quite accurate and stable even though the approximations are performed by polynomials of degree 5, as illustrated by applying the method to intensity data with and without random noise to invert and compare it with those obtained by the other methods or with the known analytical inverse. Thus it is good method for applying to experimental intensities distorted by noise.
Szerszeń, Krzysztof; Zieniuk, Eugeniusz
2016-06-01
The paper presents a strategy for numerical solving of parametric integral equation system (PIES) for 2D potential problems without explicit calculation of singular integrals. The values of these integrals will be expressed indirectly in terms of easy to compute non-singular integrals. The effectiveness of the proposed strategy is investigated with the example of potential problem modeled by the Laplace equation. The strategy simplifies the structure of the program with good the accuracy of the obtained solutions.
Numerical Modelling of Mechanical Integrity of the Copper-Cast Iron Canister. A Literature Review
International Nuclear Information System (INIS)
Lanru Jing
2004-04-01
This review article presents a summary of the research works on the numerical modelling of the mechanical integrity of the composite copper-cast iron canisters for the final disposal of Swedish nuclear wastes, conducted by SKB and SKI since 1992. The objective of the review is to evaluate the outstanding issues existing today about the basic design concepts and premises, fundamental issues on processes, properties and parameters considered for the functions and requirements of canisters under the conditions of a deep geological repository. The focus is placed on the adequacy of numerical modelling approaches adopted in regards to the overall mechanical integrity of the canisters, especially the initial state of canisters regarding defects and the consequences of their evolution under external and internal loading mechanisms adopted in the design premises. The emphasis is the stress-strain behaviour and failure/strength, with creep and plasticity involved. Corrosion, although one of the major concerns in the field of canister safety, was not included
Werneburg, Ingmar; Wilson, Laura A B; Parr, William C H; Joyce, Walter G
2015-03-01
The unique ability of modern turtles to retract their head and neck into the shell through a side-necked (pleurodiran) or hidden-necked (cryptodiran) motion is thought to have evolved independently in crown turtles. The anatomical changes that led to the vertebral shapes of modern turtles, however, are still poorly understood. Here we present comprehensive geometric morphometric analyses that trace turtle vertebral evolution and reconstruct disparity across phylogeny. Disparity of vertebral shape was high at the dawn of turtle evolution and decreased after the modern groups evolved, reflecting a stabilization of morphotypes that correspond to the two retraction modes. Stem turtles, which had a very simple mode of retraction, the lateral head tuck, show increasing flexibility of the neck through evolution towards a pleurodiran-like morphotype. The latter was the precondition for evolving pleurodiran and cryptodiran vertebrae. There is no correlation between the construction of formed articulations in the cervical centra and neck mobility. An increasing mobility between vertebrae, associated with changes in vertebral shape, resulted in a more advanced ability to retract the neck. In this regard, we hypothesize that the lateral tucking retraction of stem turtles was not only the precondition for pleurodiran but also of cryptodiran retraction. For the former, a kink in the middle third of the neck needed to be acquired, whereas for the latter modification was necessary between the eighth cervical vertebra and first thoracic vertebra. Our paper highlights the utility of 3D shape data, analyzed in a phylogenetic framework, to examine the magnitude and mode of evolutionary modifications to vertebral morphology. By reconstructing and visualizing ancestral anatomical shapes, we provide insight into the anatomical features underlying neck retraction mode, which is a salient component of extant turtle classification. © The Author(s) 2014. Published by Oxford University Press
Kelly, N. M.; Marchi, S.; Mojzsis, S. J.; Flowers, R. M.; Metcalf, J. R.; Bottke, W. F., Jr.
2017-12-01
Impacts have a significant physical and chemical influence on the surface conditions of a planet. The cratering record is used to understand a wide array of impact processes, such as the evolution of the impact flux through time. However, the relationship between impactor size and a resulting impact crater remains controversial (e.g., Bottke et al., 2016). Likewise, small variations in the impact velocity are known to significantly affect the thermal-mechanical disturbances in the aftermath of a collision. Development of more robust numerical models for impact cratering has implications for how we evaluate the disruptive capabilities of impact events, including the extent and duration of thermal anomalies, the volume of ejected material, and the resulting landscape of impacted environments. To address uncertainties in crater scaling relationships, we present an approach and methodology that integrates numerical modeling of the thermal evolution of terrestrial impact craters with low-temperature, (U-Th)/He thermochronometry. The approach uses time-temperature (t-T) paths of crust within an impact crater, generated from numerical simulations of an impact. These t-T paths are then used in forward models to predict the resetting behavior of (U-Th)/He ages in the mineral chronometers apatite and zircon. Differences between the predicted and measured (U-Th)/He ages from a modeled terrestrial impact crater can then be used to evaluate parameters in the original numerical simulations, and refine the crater scaling relationships. We expect our methodology to additionally inform our interpretation of impact products, such as lunar impact breccias and meteorites, providing robust constraints on their thermal histories. In addition, the method is ideal for sample return mission planning - robust "prediction" of ages we expect from a given impact environment enhances our ability to target sampling sites on the Moon, Mars or other solar system bodies where impacts have strongly
International Nuclear Information System (INIS)
Takeda, H.; Isha, H.
1981-01-01
The paper is concerned with the displacement-assumed-finite elements by applying the reduced numerical integration technique in structural problems. The first part is a general consideration on the technique. Its purpose is to examine a variational interpretation of the finite element displacement formulation with the reduced integration technique in structural problems. The formulation is critically studied from a standpoint of the natural stiffness approach. It is shown that these types of elements are equivalent to a certain type of displacement and stress assumed mixed elements. The rank deficiency of the stiffness matrix of these elements is interpreted as a problem in the transformation from the natural system to a Cartesian system. It will be shown that a variational basis of the equivalent mixed formulation is closely related to the Hellinger-Reissner's functional. It is presented that for simple elements, e.g. bilinear quadrilateral plane stress and plate bending there are corresponding mixed elements from the functional. For relatively complex types of these elements, it is shown that they are equivalent to localized mixed elements from the Hellinger-Reissner's functional. In the second part, typical finite elements with the reduced integration technique are studied to demonstrate this equivalence. A bilinear displacement and rotation assumed shear beam element, a bilinear displacement assumed quadrilateral plane stress element and a bilinear deflection and rotation assumed quadrilateral plate bending element are examined to present equivalent mixed elements. Not only the theoretical consideration is presented but numerical studies are shown to demonstrate the effectiveness of these elements in practical analysis. (orig.)
Sendur, Kürşat
2009-04-27
To address the large number of parameters involved in nano-optical problems, a more efficient computational method is necessary. An integral equation based numerical solution is developed when the particles are illuminated with collimated and focused incident beams. The solution procedure uses the method of weighted residuals, in which the integral equation is reduced to a matrix equation and then solved for the unknown electric field distribution. In the solution procedure, the effects of the surrounding medium and boundaries are taken into account using a Green's function formulation. Therefore, there is no additional error due to artificial boundary conditions unlike differential equation based techniques, such as finite difference time domain and finite element method. In this formulation, only the scattering nano-particle is discretized. Such an approach results in a lesser number of unknowns in the resulting matrix equation. The results are compared to the analytical Mie series solution for spherical particles, as well as to the finite element method for rectangular metallic particles. The Richards-Wolf vector field equations are combined with the integral equation based formulation to model the interaction of nanoparticles with linearly and radially polarized incident focused beams.
International Nuclear Information System (INIS)
Bechlars, J.
1978-12-01
1) Integrable (L 1 ) singularities, occuring on the boundary or along the diagonal direction, and jumps along the diagonal direction do not disturb the compactness of otherwise continuous integral operator kernels. So the theory of compact operators can be applied for solving the integral equation. 2) Provided the regular parts of the kernel are sufficiently differentiable, the continuous differentiability (Cn) of the right hand side is transposed to the solution, if the kernel has no singularities or no singularities on the boundary and no jump. In the case of singularities in connection with a jump examples show, that this result is not valid in general. Therefore a second definition of smoothness has been introduced (Csup((n,α)) : continuous differentiability in the interior and 'limitation of derivatives') which can be applied in such cases and on the other side shows satisfactory error behaviour during interpolation and includes singularities from logarithms and negative powers. Provided diagonal singularities or singularities on the boundary can be asigned to Csup((n+1,α-1)) (0 2 also Csup((2,α)) (0 -2 ). This is confirmed by numerical examples. (orig./HSI) [de
Corrochano, Eduardo Bayro
2010-01-01
This book presents contributions from a global selection of experts in the field. This useful text offers new insights and solutions for the development of theorems, algorithms and advanced methods for real-time applications across a range of disciplines. Written in an accessible style, the discussion of all applications is enhanced by the inclusion of numerous examples, figures and experimental analysis. Features: provides a thorough discussion of several tasks for image processing, pattern recognition, computer vision, robotics and computer graphics using the geometric algebra framework; int
Geometric interpretation of the geometric discord
International Nuclear Information System (INIS)
Yao, Yao; Li, Hong-Wei; Yin, Zhen-Qiang; Han, Zheng-Fu
2012-01-01
We investigate the level surfaces of geometric measure of quantum discord, and provide a pictorial interpretation of geometric discord for Bell-diagonal states. We have observed its nonanalytic behavior under decoherence employing this approach and interestingly found if we expect geometric discord to remain constant under phase-flip channel for a finite period, the initial state must be separable. Besides, this geometric understanding can be applied to verify the hierarchical relationships between geometric discord and the original one. The present work makes us conjecture that the incompatibility of these two definitions may originate from the discrepancy of the geometric structures of them. -- Highlights: ► We investigate geometry structure of geometric measure of quantum discord. ► If geometric discord is assumed to remain constant, the initial state must be separable. ► Geometry interpretation can be applied to verify hierarchical relationships between geometric discord and the original one.
On-the-fly Numerical Surface Integration for Finite-Difference Poisson-Boltzmann Methods.
Cai, Qin; Ye, Xiang; Wang, Jun; Luo, Ray
2011-11-01
Most implicit solvation models require the definition of a molecular surface as the interface that separates the solute in atomic detail from the solvent approximated as a continuous medium. Commonly used surface definitions include the solvent accessible surface (SAS), the solvent excluded surface (SES), and the van der Waals surface. In this study, we present an efficient numerical algorithm to compute the SES and SAS areas to facilitate the applications of finite-difference Poisson-Boltzmann methods in biomolecular simulations. Different from previous numerical approaches, our algorithm is physics-inspired and intimately coupled to the finite-difference Poisson-Boltzmann methods to fully take advantage of its existing data structures. Our analysis shows that the algorithm can achieve very good agreement with the analytical method in the calculation of the SES and SAS areas. Specifically, in our comprehensive test of 1,555 molecules, the average unsigned relative error is 0.27% in the SES area calculations and 1.05% in the SAS area calculations at the grid spacing of 1/2Å. In addition, a systematic correction analysis can be used to improve the accuracy for the coarse-grid SES area calculations, with the average unsigned relative error in the SES areas reduced to 0.13%. These validation studies indicate that the proposed algorithm can be applied to biomolecules over a broad range of sizes and structures. Finally, the numerical algorithm can also be adapted to evaluate the surface integral of either a vector field or a scalar field defined on the molecular surface for additional solvation energetics and force calculations.
McBeck, Jessica A.; Cooke, Michele L.; Herbert, Justin W.; Maillot, Bertrand; Souloumiac, Pauline
2017-09-01
We employ work optimization to predict the geometry of frontal thrusts at two stages of an evolving physical accretion experiment. Faults that produce the largest gains in efficiency, or change in external work per new fault area, ΔWext/ΔA, are considered most likely to develop. The predicted thrust geometry matches within 1 mm of the observed position and within a few degrees of the observed fault dip, for both the first forethrust and backthrust when the observed forethrust is active. The positions of the second backthrust and forethrust that produce >90% of the maximum ΔWext/ΔA also overlap the observed thrusts. The work optimal fault dips are within a few degrees of the fault dips that maximize the average Coulomb stress. Slip gradients along the detachment produce local elevated shear stresses and high strain energy density regions that promote thrust initiation near the detachment. The mechanical efficiency (Wext) of the system decreases at each of the two simulated stages of faulting and resembles the evolution of experimental force. The higher ΔWext/ΔA due to the development of the first pair relative to the second pair indicates that the development of new thrusts may lead to diminishing efficiency gains as the wedge evolves. The numerical estimates of work consumed by fault propagation overlap the range calculated from experimental force data and crustal faults. The integration of numerical and physical experiments provides a powerful approach that demonstrates the utility of work optimization to predict the development of faults.
Numerical path integral solution to strong Coulomb correlation in one dimensional Hooke's atom
Ruokosenmäki, Ilkka; Gholizade, Hossein; Kylänpää, Ilkka; Rantala, Tapio T.
2017-01-01
We present a new approach based on real time domain Feynman path integrals (RTPI) for electronic structure calculations and quantum dynamics, which includes correlations between particles exactly but within the numerical accuracy. We demonstrate that incoherent propagation by keeping the wave function real is a novel method for finding and simulation of the ground state, similar to Diffusion Monte Carlo (DMC) method, but introducing new useful tools lacking in DMC. We use 1D Hooke's atom, a two-electron system with very strong correlation, as our test case, which we solve with incoherent RTPI (iRTPI) and compare against DMC. This system provides an excellent test case due to exact solutions for some confinements and because in 1D the Coulomb singularity is stronger than in two or three dimensional space. The use of Monte Carlo grid is shown to be efficient for which we determine useful numerical parameters. Furthermore, we discuss another novel approach achieved by combining the strengths of iRTPI and DMC. We also show usefulness of the perturbation theory for analytical approximates in case of strong confinements.
Numerical analysis of effects of measurement errors on ultrasonic-measurement-integrated simulation.
Funamoto, Kenichi; Hayase, Toshiyuki; Saijo, Yoshifumi; Yambe, Tomoyuki
2011-03-01
Ultrasonic-measurement-integrated (UMI) simulation, in which feedback signals are applied to the governing equations based on errors between ultrasonic measurement and numerical simulation, has been investigated for reproduction of the blood flow field. However, ultrasonic measurement data inherently include some errors. In this study, the effects of four major measurement errors, namely, errors due to gaussian noise, aliasing, wall filter, and lack of data, on UMI simulation were examined by a numerical experiment dealing with the blood flow field in the descending aorta with an aneurysm, the same as in our previous study. While solving the governing equations in UMI simulation, gaussian noise did not prevent the UMI simulation from effectively reproducing the blood flow field. In contrast, aliasing caused significant errors in UMI simulation. Effects of wall filter and lack of data appeared in diastole and in the whole period, respectively. By detecting significantly large feedback signals as a sign of aliasing and by not adding feedback signals where measured Doppler velocities were aliasing or zero, the computational accuracy substantially improved, alleviating the effects of measurement errors. Through these considerations, UMI simulation can provide accurate and detailed information on hemodynamics with suppression of four major measurement errors.
Ramo, Nicole L.; Puttlitz, Christian M.
2018-01-01
Compelling evidence that many biological soft tissues display both strain- and time-dependent behavior has led to the development of fully non-linear viscoelastic modeling techniques to represent the tissue’s mechanical response under dynamic conditions. Since the current stress state of a viscoelastic material is dependent on all previous loading events, numerical analyses are complicated by the requirement of computing and storing the stress at each step throughout the load history. This requirement quickly becomes computationally expensive, and in some cases intractable, for finite element models. Therefore, we have developed a strain-dependent numerical integration approach for capturing non-linear viscoelasticity that enables calculation of the current stress from a strain-dependent history state variable stored from the preceding time step only, which improves both fitting efficiency and computational tractability. This methodology was validated based on its ability to recover non-linear viscoelastic coefficients from simulated stress-relaxation (six strain levels) and dynamic cyclic (three frequencies) experimental stress-strain data. The model successfully fit each data set with average errors in recovered coefficients of 0.3% for stress-relaxation fits and 0.1% for cyclic. The results support the use of the presented methodology to develop linear or non-linear viscoelastic models from stress-relaxation or cyclic experimental data of biological soft tissues. PMID:29293558
Physics-compatible numerical methods
Barry, Koren; Abgrall, Remi; Pavel, Bochev; Jason, Frank; Blair, Perrot
2014-01-01
International audience; Physics-compatible numerical methods are methods that aim to preserve key mathematical and physical properties of continuum physics models in their finite-dimensional algebraic representations. They include methods which preserve properties such as energy, monotonicity, maximum principles, symmetries, and involutions of the continuum models. Examples are mimetic methods for spatial discretizations, variational and geometric integrators, conservative finite-volume and f...
An integrated numerical and physical modeling system for an enhanced in situ bioremediation process
International Nuclear Information System (INIS)
Huang, Y.F.; Huang, G.H.; Wang, G.Q.; Lin, Q.G.; Chakma, A.
2006-01-01
Groundwater contamination due to releases of petroleum products is a major environmental concern in many urban districts and industrial zones. Over the past years, a few studies were undertaken to address in situ bioremediation processes coupled with contaminant transport in two- or three-dimensional domains. However, they were concentrated on natural attenuation processes for petroleum contaminants or enhanced in situ bioremediation processes in laboratory columns. In this study, an integrated numerical and physical modeling system is developed for simulating an enhanced in situ biodegradation (EISB) process coupled with three-dimensional multiphase multicomponent flow and transport simulation in a multi-dimensional pilot-scale physical model. The designed pilot-scale physical model is effective in tackling natural attenuation and EISB processes for site remediation. The simulation results demonstrate that the developed system is effective in modeling the EISB process, and can thus be used for investigating the effects of various uncertainties. - An integrated modeling system was developed to enhance in situ bioremediation processes
An accurate real-time model of maglev planar motor based on compound Simpson numerical integration
Kou, Baoquan; Xing, Feng; Zhang, Lu; Zhou, Yiheng; Liu, Jiaqi
2017-05-01
To realize the high-speed and precise control of the maglev planar motor, a more accurate real-time electromagnetic model, which considers the influence of the coil corners, is proposed in this paper. Three coordinate systems for the stator, mover and corner coil are established. The coil is divided into two segments, the straight coil segment and the corner coil segment, in order to obtain a complete electromagnetic model. When only take the first harmonic of the flux density distribution of a Halbach magnet array into account, the integration method can be carried out towards the two segments according to Lorenz force law. The force and torque analysis formula of the straight coil segment can be derived directly from Newton-Leibniz formula, however, this is not applicable to the corner coil segment. Therefore, Compound Simpson numerical integration method is proposed in this paper to solve the corner segment. With the validation of simulation and experiment, the proposed model has high accuracy and can realize practical application easily.
An accurate real-time model of maglev planar motor based on compound Simpson numerical integration
Directory of Open Access Journals (Sweden)
Baoquan Kou
2017-05-01
Full Text Available To realize the high-speed and precise control of the maglev planar motor, a more accurate real-time electromagnetic model, which considers the influence of the coil corners, is proposed in this paper. Three coordinate systems for the stator, mover and corner coil are established. The coil is divided into two segments, the straight coil segment and the corner coil segment, in order to obtain a complete electromagnetic model. When only take the first harmonic of the flux density distribution of a Halbach magnet array into account, the integration method can be carried out towards the two segments according to Lorenz force law. The force and torque analysis formula of the straight coil segment can be derived directly from Newton-Leibniz formula, however, this is not applicable to the corner coil segment. Therefore, Compound Simpson numerical integration method is proposed in this paper to solve the corner segment. With the validation of simulation and experiment, the proposed model has high accuracy and can realize practical application easily.
Numerical integration methods and layout improvements in the context of dynamic RNA visualization.
Shabash, Boris; Wiese, Kay C
2017-05-30
RNA visualization software tools have traditionally presented a static visualization of RNA molecules with limited ability for users to interact with the resulting image once it is complete. Only a few tools allowed for dynamic structures. One such tool is jViz.RNA. Currently, jViz.RNA employs a unique method for the creation of the RNA molecule layout by mapping the RNA nucleotides into vertexes in a graph, which we call the detailed graph, and then utilizes a Newtonian mechanics inspired system of forces to calculate a layout for the RNA molecule. The work presented here focuses on improvements to jViz.RNA that allow the drawing of RNA secondary structures according to common drawing conventions, as well as dramatic run-time performance improvements. This is done first by presenting an alternative method for mapping the RNA molecule into a graph, which we call the compressed graph, and then employing advanced numerical integration methods for the compressed graph representation. Comparing the compressed graph and detailed graph implementations, we find that the compressed graph produces results more consistent with RNA drawing conventions. However, we also find that employing the compressed graph method requires a more sophisticated initial layout to produce visualizations that would require minimal user interference. Comparing the two numerical integration methods demonstrates the higher stability of the Backward Euler method, and its resulting ability to handle much larger time steps, a high priority feature for any software which entails user interaction. The work in this manuscript presents the preferred use of compressed graphs to detailed ones, as well as the advantages of employing the Backward Euler method over the Forward Euler method. These improvements produce more stable as well as visually aesthetic representations of the RNA secondary structures. The results presented demonstrate that both the compressed graph representation, as well as the Backward
Penenko, Vladimir; Tsvetova, Elena; Penenko, Alexey
2015-04-01
The proposed method is considered on an example of hydrothermodynamics and atmospheric chemistry models [1,2]. In the development of the existing methods for constructing numerical schemes possessing the properties of total approximation for operators of multiscale process models, we have developed a new variational technique, which uses the concept of adjoint integrating factors. The technique is as follows. First, a basic functional of the variational principle (the integral identity that unites the model equations, initial and boundary conditions) is transformed using Lagrange's identity and the second Green's formula. As a result, the action of the operators of main problem in the space of state functions is transferred to the adjoint operators defined in the space of sufficiently smooth adjoint functions. By the choice of adjoint functions the order of the derivatives becomes lower by one than those in the original equations. We obtain a set of new balance relationships that take into account the sources and boundary conditions. Next, we introduce the decomposition of the model domain into a set of finite volumes. For multi-dimensional non-stationary problems, this technique is applied in the framework of the variational principle and schemes of decomposition and splitting on the set of physical processes for each coordinate directions successively at each time step. For each direction within the finite volume, the analytical solutions of one-dimensional homogeneous adjoint equations are constructed. In this case, the solutions of adjoint equations serve as integrating factors. The results are the hybrid discrete-analytical schemes. They have the properties of stability, approximation and unconditional monotony for convection-diffusion operators. These schemes are discrete in time and analytic in the spatial variables. They are exact in case of piecewise-constant coefficients within the finite volume and along the coordinate lines of the grid area in each
Geometrical optical transfer function: is it worth calculating?
Díaz, José A; Mahajan, Virendra N
2017-10-01
In this paper, we explore the merit of calculating the geometrical optical transfer function (GOTF) in optical design by comparing the time to calculate it with the time to calculate the diffraction optical transfer function (DOTF). We determine the DOTF by numerical integration of the pupil function autocorrelation (that reduces to an integration of a complex exponential of the aberration difference function), 2D digital autocorrelation of the pupil function, and the Fourier transform (FT) of the point-spread function (PSF); and we determine the GOTF by the FT of the geometrical PSF (that reduces to an integration over the pupil plane of a complex exponential that is a scalar product of the spatial frequency and transverse ray aberration vectors) and the FT of the spot diagram. Our starting point for calculating the DOTF is the wave aberrations of the system in its pupil plane, and the transverse ray aberrations in the image plane for the GOTF. Numerical results for primary aberrations and some typical imaging systems show that the direct numerical integrations are slow, but the GOTF calculation by a FT of the spot diagram is two or even three times slower than the DOTF calculation by an FT of the PSF, depending on the aberration. We conclude that the calculation of GOTF is, at best, an approximation of the DOTF and only for large aberrations; GOTF does not offer any advantage in the optical design process, and hence negates its utility.
Numerical path integration technique for the calculation of transport properties of proteins.
Kang, Eun-Hee; Mansfield, Marc L; Douglas, Jack F
2004-03-01
We present a new technique for the computation of both the translational diffusivity and the intrinsic viscosity of macromolecules, and apply it here to proteins. Traditional techniques employ finite element representations of the surface of the macromolecule, taking the surface to be a union of spheres or of polygons, and have computation times that are O(m(3)) where m is the number of finite elements. The new technique, a numerical path integration method, has computation times that are only O(m). We have applied the technique to approximately 1000 different protein structures. The computed translational diffusivities and intrinsic viscosities are, to lowest order, proportional respectively to N(-1/3)(R) and N(0)(R), where N(R) is the number of amino acid residues in the protein. Our calculations also show some correlation with the shape of the molecule, as represented by the ratio m(2)/m(3), where m(2) and m(3) are, respectively, the middle and the smallest of the three principal moments of inertia. Comparisons with a number of experimental results are also performed, with results generally consistent to within experimental error.
An Integrated Numerical Hydrodynamic Shallow Flow-Solute Transport Model for Urban Area
Alias, N. A.; Mohd Sidek, L.
2016-03-01
The rapidly changing on land profiles in the some urban areas in Malaysia led to the increasing of flood risk. Extensive developments on densely populated area and urbanization worsen the flood scenario. An early warning system is really important and the popular method is by numerically simulating the river and flood flows. There are lots of two-dimensional (2D) flood model predicting the flood level but in some circumstances, still it is difficult to resolve the river reach in a 2D manner. A systematic early warning system requires a precisely prediction of flow depth. Hence a reliable one-dimensional (1D) model that provides accurate description of the flow is essential. Research also aims to resolve some of raised issues such as the fate of pollutant in river reach by developing the integrated hydrodynamic shallow flow-solute transport model. Presented in this paper are results on flow prediction for Sungai Penchala and the convection-diffusion of solute transports simulated by the developed model.
Boundary integral equation methods and numerical solutions thin plates on an elastic foundation
Constanda, Christian; Hamill, William
2016-01-01
This book presents and explains a general, efficient, and elegant method for solving the Dirichlet, Neumann, and Robin boundary value problems for the extensional deformation of a thin plate on an elastic foundation. The solutions of these problems are obtained both analytically—by means of direct and indirect boundary integral equation methods (BIEMs)—and numerically, through the application of a boundary element technique. The text discusses the methodology for constructing a BIEM, deriving all the attending mathematical properties with full rigor. The model investigated in the book can serve as a template for the study of any linear elliptic two-dimensional problem with constant coefficients. The representation of the solution in terms of single-layer and double-layer potentials is pivotal in the development of a BIEM, which, in turn, forms the basis for the second part of the book, where approximate solutions are computed with a high degree of accuracy. The book is intended for graduate students and r...
Catching homologies by geometric entropy
Felice, Domenico; Franzosi, Roberto; Mancini, Stefano; Pettini, Marco
2018-02-01
A geometric entropy is defined in terms of the Riemannian volume of the parameter space of a statistical manifold associated with a given network. As such it can be a good candidate for measuring networks complexity. Here we investigate its ability to single out topological features of networks proceeding in a bottom-up manner: first we consider small size networks by analytical methods and then large size networks by numerical techniques. Two different classes of networks, the random graphs and the scale-free networks, are investigated computing their Betti numbers and then showing the capability of geometric entropy of detecting homologies.
A numerical study of the integral equations for the laser fields in free-electron lasers
International Nuclear Information System (INIS)
Yoo, J. G.; Park, S. H.; Jeong, Y. U.; Lee, B. C.; Rhee, Y. J.; Cho, S. O.
2004-01-01
The dynamics of the radiation fields in free-electron lasers is investigated on the basis of the integro-differential equations in the one-dimensional formulation. For simple cases we solved the integro-differential equations analytically and numerically to test our numerical procedures developed on the basis of the Filon method. The numerical results showed good agreement with the analytical solutions. To confirm the legitimacy of the numerical package, we carried out numerical studies on the inhomogeneous broadening effects, where no analytic solutions are available, due to the energy spread and the emittance of the electron beam.
Banyukevich, A.; Ziolkovski, K.
1975-01-01
A number of hybrid methods for solving Cauchy problems are described on the basis of an evaluation of advantages of single and multiple-point numerical integration methods. The selection criterion is the principle of minimizing computer time. The methods discussed include the Nordsieck method, the Bulirsch-Stoer extrapolation method, and the method of recursive Taylor-Steffensen power series.
El-Tom, M E A
1974-01-01
A procedure, using spine functions of degree m, deficiency k-1, for obtaining approximate solutions to nonlinear Volterra integral equations of the second kind is presented. The paper is an investigation of the numerical stability of the procedure for various values of m and k. (5 refs).
Bonotto, C.
1995-01-01
Attempted to verify knowledge regarding decimal and rational numbers in children ages 10-14. Discusses how pupils can receive and assimilate extensions of the number system from natural numbers to decimals and fractions and later can integrate this extension into a single and coherent numerical structure. (Author/MKR)
International Nuclear Information System (INIS)
Vlasov, M.N.; Korsun, A.S.; Maslov, Yu.A.; Merinov, I.G.; Kharitonov, V.S.
2013-01-01
Systematic numerical calculations have been performed for studying the longitudinal flow past an array of rods with a corridor or chess-board packing in a broad range of flow Reynolds numbers. Structures with the porosity varied in a broad range have been studied and the main parameters of the proposed integral model of turbulence are determined [ru
National Research Council Canada - National Science Library
Mitchell, Jason
2002-01-01
A method is presented for the generation of exact numerical coefficients found in two families of implicit Chebyshev methods for the numerical integration of first- and second-order ordinary differential equations...
Structure-preserving geometric algorithms for plasma physics and beam physics
Qin, Hong
2017-10-01
Standard algorithms in the plasma physics and beam physics do not possess the long-term accuracy and fidelity required in the study of multi-scale dynamics, because they do not preserve the geometric structures of the physical systems, such as the local energy-momentum conservation, symplectic structure and gauge symmetry. As a result, numerical errors accumulate coherently with time and long-term simulation results are not reliable. To overcome this difficulty, since 2008 structure-preserving geometric algorithms have been developed. This new generation of algorithms utilizes advanced techniques, such as interpolating differential forms, canonical and non-canonical symplectic integrators, and finite element exterior calculus to guarantee gauge symmetry and charge conservation, and the conservation of energy-momentum and symplectic structure. It is our vision that future numerical capabilities in plasma physics and beam physics will be based on the structure-preserving geometric algorithms.
Evans, Tanya M; Kochalka, John; Ngoon, Tricia J; Wu, Sarah S; Qin, Shaozheng; Battista, Christian; Menon, Vinod
2015-08-19
Early numerical proficiency lays the foundation for acquiring quantitative skills essential in today's technological society. Identification of cognitive and brain markers associated with long-term growth of children's basic numerical computation abilities is therefore of utmost importance. Previous attempts to relate brain structure and function to numerical competency have focused on behavioral measures from a single time point. Thus, little is known about the brain predictors of individual differences in growth trajectories of numerical abilities. Using a longitudinal design, with multimodal imaging and machine-learning algorithms, we investigated whether brain structure and intrinsic connectivity in early childhood are predictive of 6 year outcomes in numerical abilities spanning childhood and adolescence. Gray matter volume at age 8 in distributed brain regions, including the ventrotemporal occipital cortex (VTOC), the posterior parietal cortex, and the prefrontal cortex, predicted longitudinal gains in numerical, but not reading, abilities. Remarkably, intrinsic connectivity analysis revealed that the strength of functional coupling among these regions also predicted gains in numerical abilities, providing novel evidence for a network of brain regions that works in concert to promote numerical skill acquisition. VTOC connectivity with posterior parietal, anterior temporal, and dorsolateral prefrontal cortices emerged as the most extensive network predicting individual gains in numerical abilities. Crucially, behavioral measures of mathematics, IQ, working memory, and reading did not predict children's gains in numerical abilities. Our study identifies, for the first time, functional circuits in the human brain that scaffold the development of numerical skills, and highlights potential biomarkers for identifying children at risk for learning difficulties. Children show substantial individual differences in math abilities and ease of math learning. Early
On Geometric Infinite Divisibility
Sandhya, E.; Pillai, R. N.
2014-01-01
The notion of geometric version of an infinitely divisible law is introduced. Concepts parallel to attraction and partial attraction are developed and studied in the setup of geometric summing of random variables.
Federal Laboratory Consortium — Purpose: The mission of the Geometric Design Laboratory (GDL) is to support the Office of Safety Research and Development in research related to the geometric design...
Martínez-Guerra, Rafael; Gómez-Cortés, Gian Carlo
2015-01-01
This book provides a general overview of several concepts of synchronization and brings together related approaches to secure communication in chaotic systems. This is achieved using a combination of analytic, algebraic, geometrical and asymptotical methods to tackle the dynamical feedback stabilization problem. In particular, differential-geometric and algebraic differential concepts reveal important structural properties of chaotic systems and serve as guide for the construction of design procedures for a wide variety of chaotic systems. The basic differential algebraic and geometric concepts are presented in the first few chapters in a novel way as design tools, together with selected experimental studies demonstrating their importance. The subsequent chapters treat recent applications. Written for graduate students in applied physical sciences, systems engineers, and applied mathematicians interested in synchronization of chaotic systems and in secure communications, this self-contained text requires only...
Directory of Open Access Journals (Sweden)
Mehriban Imanova Natiq
2012-03-01
Full Text Available Normal 0 false false false EN-US X-NONE X-NONE As is known, many problems of natural science are reduced mainly to the solution of nonlinear Volterra integral equations. The method of quadratures that was first applied by Volterra to solving variable boundary integral equations is popular among numerical methods for the solution of such equations. At present, there are different modifications of the method of quadratures that have bounded accuracies. Here we suggest a second derivative multistep method for constructing more exact methods.
DEFF Research Database (Denmark)
Elarga, Hagar; Fantucci, Stefano; Serra, Valentina
2017-01-01
The study investigates the thermal performances of Phase Change Materials (PCM) integrated in a roof space to be used as a residential attic in Torino, Italy. Three different solutions were applied to a roof continuously monitored under summer climatic conditions. The roof was divided into three...... portions, one, the bare roof, representing the reference case without PCMs, the other two integrating two PCM's typologies with different melting/solidification temperatures range. A numerical model was furthermore developed implementing the equivalent capacitance numerical method to describe the substance...... phase transition and the measured data set were used for its validation. The study demonstrates that PCM-enhanced components are a promising solution toward a higher thermal performance efficiency in roof attic spaces during the summer season. Experimental results showed a reduction of the ongoing heat...
International Nuclear Information System (INIS)
Cash, J.R.; Raptis, A.D.; Simos, T.E.
1990-01-01
An efficient algorithm is described for the accurate numerical integration of the one-dimensional Schroedinger equation. This algorithm uses a high-order, variable step Runge-Kutta like method in the region where the potential term dominates, and an exponential or Bessel fitted method in the asymptotic region. This approach can be used to compute scattering phase shifts in an efficient and reliable manner. A Fortran program which implements this algorithm is provided and some test results are given. (orig.)
Integration of numerical modeling and observations for the Gulf of Naples monitoring network
Iermano, I.; Uttieri, M.; Zambianchi, E.; Buonocore, B.; Cianelli, D.; Falco, P.; Zambardino, G.
2012-04-01
Lethal effects of mineral oils on fragile marine and coastal ecosystems are now well known. Risks and damages caused by a maritime accident can be reduced with the help of better forecasts and efficient monitoring systems. The MED project TOSCA (Tracking Oil Spills and Coastal Awareness Network), which gathers 13 partners from 4 Mediterranean countries, has been designed to help create a better response system to maritime accidents. Through the construction of an observational network, based on state of the art technology (HF radars and drifters), TOSCA provides real-time observations and forecasts of the Mediterranean coastal marine environmental conditions. The system is installed and assessed in five test sites on the coastal areas of oil spill outlets (Eastern Mediterranean) and on high traffic areas (Western Mediterranean). The Gulf of Naples, a small semi-closed basin opening to the Tyrrhenian Sea is one of the five test-sites. It is of particular interest from both the environmental point of view, due to peculiar ecosystem properties in the area, and because it sustains important touristic and commercial activities. Currently the Gulf of Naples monitoring network is represented by five automatic weather stations distributed along the coasts of the Gulf, one weather radar, two tide gauges, one waverider buoy, and moored physical, chemical and bio-optical instrumentation. In addition, a CODAR-SeaSonde HF coastal radar system composed of three antennas is located in Portici, Massa Lubrense and Castellammare. The system provides hourly data of surface currents over the entire Gulf with a 1km spatial resolution. A numerical modeling implementation based on Regional Ocean Modeling System (ROMS) is actually integrated in the Gulf of Naples monitoring network. ROMS is a 3-D, free-surface, hydrostatic, primitive equation, finite difference ocean model. In our configuration, the model has high horizontal resolution (250m), and 30 sigma levels in the vertical. Thanks
Block-pulse functions approach to numerical solution of Abel’s integral equation
Directory of Open Access Journals (Sweden)
Monireh Nosrati Sahlan
2015-12-01
Full Text Available This study aims to present a computational method for solving Abel’s integral equation of the second kind. The introduced method is based on the use of Block-pulse functions (BPFs via collocation method. Abel’s integral equations as singular Volterra integral equations are hard and heavy in computation, but because of the properties of BPFs, as is reported in examples, this method is more efficient and more accurate than some other methods for solving this class of integral equations. On the other hand, the benefit of this method is low cost of computing operations. The applied method transforms the singular integral equation into triangular linear algebraic system that can be solved easily. An error analysis is worked out and applications are demonstrated through illustrative examples.
Fundamental aspects of the integration of seismic monitoring with numerical modelling.
CSIR Research Space (South Africa)
Mendecki, AJ
2001-06-01
Full Text Available Numerical modelling of rock-mass response to underground excavations is of vital importance for the decision-making process in designing and running a mine. Likewise, seismic monitoring with state-of-the-art local seismic systems is indispensable...
A Numerical Methods Course Based on B-Learning: Integrated Learning Design and Follow Up
Cepeda, Francisco Javier Delgado
2013-01-01
Information and communication technologies advance continuously, providing a real support for learning processes. Learning technologies address areas which previously have corresponded to face-to-face learning, while mobile resources are having a growing impact on education. Numerical Methods is a discipline and profession based on technology. In…
Two-step rational cononical function in the numerical integration of ...
African Journals Online (AJOL)
By collocation, an explicit nonlinerar two-step scheme is obtained. Numerical examples are provided to demonstrate the performance of the scheme. The results obtained were found to be quite comparable with those by existing schemes. Key Words: Collocation two-step scheme. [Global Jnl Mathematical Sci Vol.2(1) 2003: ...
Montagna, Chiara; Perugini, Diego; De Campos, Christina; Longo, Antonella; Dingwell, Donald Bruce; Papale, Paolo
2015-04-01
Arrival of magma from depth into shallow reservoirs and associated mixing processes have been documented as possible triggers of explosive eruptions. Quantifying the timing from beginning of mixing to eruption is of fundamental importance in volcanology in order to put constraints about the possible onset of a new eruption. Here we integrate numerical simulations and high-temperature experiment performed with natural melts with the aim to attempt identifying the mixing-to-eruption timescales. We performed two-dimensional numerical simulations of the arrival of gas-rich magmas into shallow reservoirs. We solve the fluid dynamics for the two interacting magmas evaluating the space-time evolution of the physical properties of the mixture. Convection and mingling develop quickly into the chamber and feeding conduit/dyke. Over time scales of hours, the magmas in the reservoir appear to have mingled throughout, and convective patterns become harder to identify. High-temperature magma mixing experiments have been performed using a centrifuge and using basaltic and phonolitic melts from Campi Flegrei (Italy) as initial end-members. Concentration Variance Decay (CVD), an inevitable consequence of magma mixing, is exponential with time. The rate of CVD is a powerful new geochronometer for the time from mixing to eruption/quenching. The mingling-to-eruption time of three explosive volcanic eruptions from Campi Flegrei (Italy) yield durations on the order of tens of minutes. These results are in perfect agreement with the numerical simulations that suggest a maximum mixing time of a few hours to obtain a hybrid mixture. We show that integration of numerical simulation and high-temperature experiments can provide unprecedented results about mixing processes in volcanic systems. The combined application of numerical simulations and CVD geochronometer to the eruptive products of active volcanoes could be decisive for the preparation of hazard mitigation during volcanic unrest.
CSIR Research Space (South Africa)
Long, CS
2009-01-01
Full Text Available The effects of selected planar finite element formulations, and their associated integration schemes, on the stiffness of a checkerboard material layout are investigated. Standard 4-node bilinear elements, 8- and 9-node quadratic elements, as well...
Numerical calculation of a class of highly oscillatory integrals with the Mathieu function
International Nuclear Information System (INIS)
Long Yongxing
1992-01-01
The author describes a method for computing highly oscillatory integrals with the Mathieu function. The practice proves that not only the results are highly satisfactory, but also the method is time-saving
DEFF Research Database (Denmark)
Saraswathi, Ananthavel; Sanjeevikumar, Padmanaban; Shanmugham, Sutha
2016-01-01
on generation, transmission and distribution etc. This paper exploited the integration of static synchronous compensator (STATCOM) and superconducting magnetic energy storage (SMES) which is then connected to existing power transmission line for enhancing the available power transfer capacity (ATC). STATCOMis...
Altürk, Ahmet
2016-01-01
Mean value theorems for both derivatives and integrals are very useful tools in mathematics. They can be used to obtain very important inequalities and to prove basic theorems of mathematical analysis. In this article, a semi-analytical method that is based on weighted mean-value theorem for obtaining solutions for a wide class of Fredholm integral equations of the second kind is introduced. Illustrative examples are provided to show the significant advantage of the proposed method over some existing techniques.
ICM: an Integrated Compartment Method for numerically solving partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Yeh, G.T.
1981-05-01
An integrated compartment method (ICM) is proposed to construct a set of algebraic equations from a system of partial differential equations. The ICM combines the utility of integral formulation of finite element approach, the simplicity of interpolation of finite difference approximation, and the flexibility of compartment analyses. The integral formulation eases the treatment of boundary conditions, in particular, the Neumann-type boundary conditions. The simplicity of interpolation provides great economy in computation. The flexibility of discretization with irregular compartments of various shapes and sizes offers advantages in resolving complex boundaries enclosing compound regions of interest. The basic procedures of ICM are first to discretize the region of interest into compartments, then to apply three integral theorems of vectors to transform the volume integral to the surface integral, and finally to use interpolation to relate the interfacial values in terms of compartment values to close the system. The Navier-Stokes equations are used as an example of how to derive the corresponding ICM alogrithm for a given set of partial differential equations. Because of the structure of the algorithm, the basic computer program remains the same for cases in one-, two-, or three-dimensional problems.
International Nuclear Information System (INIS)
Tong, S.S.; Powell, D.; Goel, S.
1992-02-01
A new software system called Engineous combines artificial intelligence and numerical methods for the design and optimization of complex aerospace systems. Engineous combines the advanced computational techniques of genetic algorithms, expert systems, and object-oriented programming with the conventional methods of numerical optimization and simulated annealing to create a design optimization environment that can be applied to computational models in various disciplines. Engineous has produced designs with higher predicted performance gains that current manual design processes - on average a 10-to-1 reduction of turnaround time - and has yielded new insights into product design. It has been applied to the aerodynamic preliminary design of an aircraft engine turbine, concurrent aerodynamic and mechanical preliminary design of an aircraft engine turbine blade and disk, a space superconductor generator, a satellite power converter, and a nuclear-powered satellite reactor and shield. 23 refs
Numerical Integration of the Master Equation in Some Models of Stochastic Epidemiology
Jenkinson, Garrett; Goutsias, John
2012-01-01
The processes by which disease spreads in a population of individuals are inherently stochastic. The master equation has proven to be a useful tool for modeling such processes. Unfortunately, solving the master equation analytically is possible only in limited cases (e.g., when the model is linear), and thus numerical procedures or approximation methods must be employed. Available approximation methods, such as the system size expansion method of van Kampen, may fail to provide reliable solutions, whereas current numerical approaches can induce appreciable computational cost. In this paper, we propose a new numerical technique for solving the master equation. Our method is based on a more informative stochastic process than the population process commonly used in the literature. By exploiting the structure of the master equation governing this process, we develop a novel technique for calculating the exact solution of the master equation – up to a desired precision – in certain models of stochastic epidemiology. We demonstrate the potential of our method by solving the master equation associated with the stochastic SIR epidemic model. MATLAB software that implements the methods discussed in this paper is freely available as Supporting Information S1. PMID:22615755
Energy conservation and high-frequency damping in numerical time-integration
DEFF Research Database (Denmark)
Krenk, Steen
2007-01-01
Momentum and energy conserving time integration procedures are receiving increased interest due to the central role of conservation properties in relation to the problems under investigation. However, most problems in structural dynamics are based on models that are first discretized in space, en...... to introduce so-called alpha-damping, and an improved form leading only to high-frequency damping can be obtained by suitable averaging of the equilibrium equation at consecutive time steps. Conservative time integration algorithms are obtained by use of an integral of the equation of motion......, or by introducing additional variables to represent damping. In the present paper it is demonstrated, how damping equivalent to the alpha-damping of the Newmark algorithm can be introduced directly via displacement and velocity dependent terms. It is furthermore shown, how this damping can be improved...
International Nuclear Information System (INIS)
Aviles, B.N.; Sutton, T.M.; Kelly, D.J. III.
1991-09-01
A generalized Runge-Kutta method has been employed in the numerical integration of the stiff space-time diffusion equations. The method is fourth-order accurate, using an embedded third-order solution to arrive at an estimate of the truncation error for automatic timestep control. The efficiency of the Runge-Kutta method is enhanced by a block-factorization technique that exploits the sparse structure of the matrix system resulting from the space and energy discretized form of the time-dependent neutron diffusion equations. Preliminary numerical evaluation using a one-dimensional finite difference code shows the sparse matrix implementation of the generalized Runge-Kutta method to be highly accurate and efficient when compared to an optimized iterative theta method. 12 refs., 5 figs., 4 tabs
An integrated numerical model for the prediction of Gaussian and billet shapes
DEFF Research Database (Denmark)
Hattel, Jesper; Pryds, Nini; Pedersen, Trine Bjerre
2004-01-01
Separate models for the atomisation and the deposition stages were recently integrated by the authors to form a unified model describing the entire spray-forming process. In the present paper, the focus is on describing the shape of the deposited material during the spray-forming process, obtaine...
Optimization of Nordsieck's Method for the Numerical Integration of Ordinary Differential Equations
Gmelig, R.H.J.; Traas, C.R.
1984-01-01
Stability and accuracy of Nordsieck's integration method can be improved by choosing the zero-positions of the extraneous roots of the characteristic equation in a suitable way. Optimum zero-positions have been found by minimizing the lower bound of the interval of absolute stability and the
Numerical Time Integration Methods for a Point Absorber Wave Energy Converter
DEFF Research Database (Denmark)
Zurkinden, Andrew Stephen; Kramer, Morten
2012-01-01
function of the radiation force and the unknown body velocity due to an external force. The convolution integral can be seen as a memory effect where the system response in the past affects the response in the future. Two different time-domain models will be presented. The first one is based...
Energy Technology Data Exchange (ETDEWEB)
Hurd, J.W.
1987-08-15
The first-order transformation matrix is derived for a simple Wien filter. The Wien filter is approximated by square-edged, homogeneous, transverse E and B fields. The results are compared to results of numerical integration through a Wien filter with and without fringe fields. The derived transformation matrix is presently used in the first-order optics code TRACE to tune the 750 keV polarized proton injection transport at LAMPF. The Wien filter is used to precess the spin of the polarized proton beam.
Hurd, James W.
1987-08-01
The first-order transformation matrix is derived for a simple Wien filter. The Wien filter is approximated by square-edged homogeneous, transverse E and B fields. The results are compared to results of numerical integration through a Wien filter with and without fringe fields. The derived transformation matrix is presently used in the first-order optics code TRACE to tune the 750 keV polarized proton injection transport at LAMPF. The Wien filter is used to precess the spin of the polarized proton beam.
Rößler, Thomas; Stein, Olaf; Heng, Yi; Baumeister, Paul; Hoffmann, Lars
2018-02-01
The accuracy of trajectory calculations performed by Lagrangian particle dispersion models (LPDMs) depends on various factors. The optimization of numerical integration schemes used to solve the trajectory equation helps to maximize the computational efficiency of large-scale LPDM simulations. We analyzed global truncation errors of six explicit integration schemes of the Runge-Kutta family, which we implemented in the Massive-Parallel Trajectory Calculations (MPTRAC) advection module. The simulations were driven by wind fields from operational analysis and forecasts of the European Centre for Medium-Range Weather Forecasts (ECMWF) at T1279L137 spatial resolution and 3 h temporal sampling. We defined separate test cases for 15 distinct regions of the atmosphere, covering the polar regions, the midlatitudes, and the tropics in the free troposphere, in the upper troposphere and lower stratosphere (UT/LS) region, and in the middle stratosphere. In total, more than 5000 different transport simulations were performed, covering the months of January, April, July, and October for the years 2014 and 2015. We quantified the accuracy of the trajectories by calculating transport deviations with respect to reference simulations using a fourth-order Runge-Kutta integration scheme with a sufficiently fine time step. Transport deviations were assessed with respect to error limits based on turbulent diffusion. Independent of the numerical scheme, the global truncation errors vary significantly between the different regions. Horizontal transport deviations in the stratosphere are typically an order of magnitude smaller compared with the free troposphere. We found that the truncation errors of the six numerical schemes fall into three distinct groups, which mostly depend on the numerical order of the scheme. Schemes of the same order differ little in accuracy, but some methods need less computational time, which gives them an advantage in efficiency. The selection of the integration
Directory of Open Access Journals (Sweden)
T. Rößler
2018-02-01
Full Text Available The accuracy of trajectory calculations performed by Lagrangian particle dispersion models (LPDMs depends on various factors. The optimization of numerical integration schemes used to solve the trajectory equation helps to maximize the computational efficiency of large-scale LPDM simulations. We analyzed global truncation errors of six explicit integration schemes of the Runge–Kutta family, which we implemented in the Massive-Parallel Trajectory Calculations (MPTRAC advection module. The simulations were driven by wind fields from operational analysis and forecasts of the European Centre for Medium-Range Weather Forecasts (ECMWF at T1279L137 spatial resolution and 3 h temporal sampling. We defined separate test cases for 15 distinct regions of the atmosphere, covering the polar regions, the midlatitudes, and the tropics in the free troposphere, in the upper troposphere and lower stratosphere (UT/LS region, and in the middle stratosphere. In total, more than 5000 different transport simulations were performed, covering the months of January, April, July, and October for the years 2014 and 2015. We quantified the accuracy of the trajectories by calculating transport deviations with respect to reference simulations using a fourth-order Runge–Kutta integration scheme with a sufficiently fine time step. Transport deviations were assessed with respect to error limits based on turbulent diffusion. Independent of the numerical scheme, the global truncation errors vary significantly between the different regions. Horizontal transport deviations in the stratosphere are typically an order of magnitude smaller compared with the free troposphere. We found that the truncation errors of the six numerical schemes fall into three distinct groups, which mostly depend on the numerical order of the scheme. Schemes of the same order differ little in accuracy, but some methods need less computational time, which gives them an advantage in efficiency. The
Energy Technology Data Exchange (ETDEWEB)
Bammann, Douglas J.; Johnson, G. C. (University of California, Berkeley, CA); Marin, Esteban B.; Regueiro, Richard A. (University of Colorado, Boulder, CO)
2006-01-01
In this report we present the formulation of the physically-based Evolving Microstructural Model of Inelasticity (EMMI) . The specific version of the model treated here describes the plasticity and isotropic damage of metals as being currently applied to model the ductile failure process in structural components of the W80 program . The formulation of the EMMI constitutive equations is framed in the context of the large deformation kinematics of solids and the thermodynamics of internal state variables . This formulation is focused first on developing the plasticity equations in both the relaxed (unloaded) and current configurations. The equations in the current configuration, expressed in non-dimensional form, are used to devise the identification procedure for the plasticity parameters. The model is then extended to include a porosity-based isotropic damage state variable to describe the progressive deterioration of the strength and mechanical properties of metals induced by deformation . The numerical treatment of these coupled plasticity-damage constitutive equations is explained in detail. A number of examples are solved to validate the numerical implementation of the model.
Hu, Shaoxing; Xu, Shike; Wang, Duhu; Zhang, Aiwu
2015-11-11
Aiming at addressing the problem of high computational cost of the traditional Kalman filter in SINS/GPS, a practical optimization algorithm with offline-derivation and parallel processing methods based on the numerical characteristics of the system is presented in this paper. The algorithm exploits the sparseness and/or symmetry of matrices to simplify the computational procedure. Thus plenty of invalid operations can be avoided by offline derivation using a block matrix technique. For enhanced efficiency, a new parallel computational mechanism is established by subdividing and restructuring calculation processes after analyzing the extracted "useful" data. As a result, the algorithm saves about 90% of the CPU processing time and 66% of the memory usage needed in a classical Kalman filter. Meanwhile, the method as a numerical approach needs no precise-loss transformation/approximation of system modules and the accuracy suffers little in comparison with the filter before computational optimization. Furthermore, since no complicated matrix theories are needed, the algorithm can be easily transplanted into other modified filters as a secondary optimization method to achieve further efficiency.
Gocad2OGS: Workflow to Integrate Geo-structural Information into Numerical Simulation Models
Fischer, Thomas; Walther, Marc; Naumov, Dmitri; Sattler, Sabine; Kolditz, Olaf
2015-04-01
The investigation of fluid circulation in the Thuringian syncline is one of the INFLUINS project's targets. A 3D geo-structural model including 12 stratigraphic layers and 54 fault zones is created by geologists in the first step using the Gocad software. Within the INFLUINS project a ground-water flow simulation is used to check existing hypotheses and to gain new ideas of the underground fluid flow behaviour. We used the scientific, platform independent, open source software OpenGeoSys that implements the finite element method to solve the governing equations describing fluid flow in porous media. The geo-structural Gocad model is not suitable for the FEM numerical analysis. Therefore it is converted into an unstructured grid satisfying all mesh quality criteria required for the ground-water flow simulation. The resulting grid is stored in an open data format given by the Visualization Toolkit (vtk). In this work we present a workflow to convert geological structural models, created using the Gocad software, into a simulation model that is easy to use from numerical simulation software. We tested our workflow with the 3D geo-structural model of the Thuringian syncline and were able to setup and to evaluate a hydrogeological simulation model successfully.
International Nuclear Information System (INIS)
Glouannec, Patrick; Michel, Benoit; Delamarre, Guillaume; Grohens, Yves
2014-01-01
This paper presents an experimental and numerical design study of an insulation wall for refrigerated vans. The thermophysical properties of the insulating multilayer panel, the external environment impact (solar irradiation, temperature, etc.) and durability are taken into account. Different tools are used to characterize the thermal performances of the insulation walls and the thermal properties of the insulation materials are measured. In addition, an experiment at the wall scale is carried out and a 2D FEM model of heat and mass transfer within the wall is formulated. Three configurations are studied with this design approach. Multilayer insulation walls containing reflective multi-foil insulation, aerogel and phase change materials (PCM) are tested. Promising results are obtained with these materials, especially the reduction of peak heat transfer and energy consumption during the daytime period. Furthermore, the major influence of solar irradiation is highlighted as it can increase the peak heat transfer crossing the insulation wall by up to 43%. Nevertheless, we showed that the use of reflective multi-foil insulation and aerogel layers allowed decreasing this impact by 27%. - Highlights: • A design study of an insulation wall for a refrigerated van is carried out. • Experimental and numerical studies of multilayer insulation walls are performed. • The major influence of solar irradiation is highlighted. • New insulation materials (reflective multi-foil, aerogel and PCM) are tested
Siegler, Robert S.; Braithwaite, David W.
2016-01-01
In this review, we attempt to integrate two crucial aspects of numerical development: learning the magnitudes of individual numbers and learning arithmetic. Numerical magnitude development involves gaining increasingly precise knowledge of increasing ranges and types of numbers: from non-symbolic to small symbolic numbers, from smaller to larger…
Energy conservation and high-frequency damping in numerical time integration
DEFF Research Database (Denmark)
Krenk, Steen
2008-01-01
this often leads to a fairly large number of high-frequency modes, that are not represented well – and occasionally directly erroneously – by the model. It is desirable to cure this problem by devising algorithms that include the possibility of introducing algorithmic energy dissipation of the high-frequency...... to introduce so-called α-damping, and an improved form leading only to high-frequency damping can be obtained by suitable averaging of the equilibrium equation at onsecutive time steps. Conservative time integration algorithms are obtained by use of an integral of the equation of motion and the acceleration...... of variables related to the displacement and velocity vectors by a suitable first order filter with scalar coefficients. By this device an algorithmic damping can be obtained that is of third order in the low-frequency regime. It is an important feature of both algorithms that they can be arranged to require...
On the Numerical Solution of the Integral Equation Formulation for Transient Structural Synthesis
2014-09-01
Keenan L. Coleman Lieutenant, United States Navy B.S., University of Arizona, 2007 Submitted in partial fulfillment of the requirements for...history of integral equations dates back to the early nineteenth century when the profound mathematical insights of Newton and Leibniz were being...Neta for their guidance and patience during this process. Finally, I would like to thank Dr. Richard Feynman, whose marriage of genius and common
Geometric Dimensioning Sentence Structure.
McCuistion, Patrick J.
1991-01-01
Explanations of geometric dimensioning symbols are provided to assist in the comprehension of the implied basic sentence structure of modern geometric dimensioning and tolerance. The proper identification and interpretation of the substantive language within several exemplary engineering drawings, otherwise called feature control frames, is…
Park, Sang-Uk; Kim, Jun-Mo; Kihm, Jung-Hwi
2014-05-01
A series of numerical simulations was performed using a multiphase thermo-hydro-chemical numerical model to predict integratedly and evaluate quantitatively thermo-hydro-chemical phenomena due to heat generation associated with geologic disposal of high-level radioactive waste. The average mineralogical composition of the fifteen unweathered igneous rock bodies, which were classified as granite, in Republic of Korea was adopted as an initial (primary) mineralogical composition of the host rock of the repository of high-level radioactive waste in the numerical simulations. The numerical simulation results show that temperature rises and thus convective groundwater flow occurs near the repository due to heat generation associated with geologic disposal of high-level radioactive waste. Under these circumstances, a series of water-rock interactions take place. As a result, among the primary minerals, quartz, plagioclase (albite), biotite (annite), and muscovite are dissolved. However, orthoclase is initially precipitated and is then dissolved, whereas microcline is initially dissolved and is then precipitated. On the other hand, the secondary minerals such as kaolinite, Na-smectite, chlorite, and hematite are precipitated and are then partly dissolved. In addition, such dissolution and precipitation of the primary and secondary minerals change groundwater chemistry (quality) and induce reactive chemical transport. As a result, in groundwater, Na+, Fe2+, and HCO3- concentrations initially decrease, whereas K+, AlO2-, and aqueous SiO2 concentrations initially increase. On the other hand, H+ concentration initially increases and thus pH initially decreases due to dissociation of groundwater in order to provide OH-, which is essential in precipitation of Na-smectite and chlorite. Thus, the above-mentioned numerical simulation results suggest that thermo-hydro-chemical numerical simulation can provide a better understanding of heat transport, groundwater flow, and reactive
Emerging opportunities in enterprise integration with open architecture computer numerical controls
Hudson, Christopher A.
1997-01-01
The shift to open-architecture machine tool computer numerical controls is providing new opportunities for metal working oriented manufacturers to streamline the entire 'art to part' process. Production cycle times, accuracy, consistency, predictability and process reliability are just some of the factors that can be improved, leading to better manufactured product at lower costs. Open architecture controllers are allowing manufacturers to apply general purpose software and hardware tools increase where previous approaches relied on proprietary and unique hardware and software. This includes DNC, SCADA, CAD, and CAM, where the increasing use of general purpose components is leading to lower cost system that are also more reliable and robust than the past proprietary approaches. In addition, a number of new opportunities exist, which in the past were likely impractical due to cost or performance constraints.
Chan, William M.
1992-01-01
This project forms part of the long term computational effort to simulate the time dependent flow over the integrated Space Shuttle vehicle (orbiter, solid rocket boosters (SRB's), external tank (ET), and attach hardware) during its ascent mode for various nominal and abort flight conditions. Due to the limitations of experimental data such as wind tunnel wall effects and the difficulty of safely obtaining valid flight data, numerical simulations are undertaken to supplement the existing data base. This data can then be used to predict the aerodynamic behavior over a wide range of flight conditions. Existing computational results show relatively good overall comparison with experiments but further refinement is required to reduce numerical errors and to obtain finer agreements over a larger parameter space. One of the important goals of this project is to obtain better comparisons between numerical simulations and experiments. In the simulations performed so far, the geometry has been simplified in various ways to reduce the complexity so that useful results can be obtained in a reasonable time frame due to limitations in computer resources. In this project, the finer details of the major components of the Space Shuttle are modeled better by including more complexity in the geometry definition. Smaller components not included in early Space Shuttle simulations will now be modeled and gridded.
Directory of Open Access Journals (Sweden)
Naumenko Mikhail
2018-01-01
Full Text Available Modern parallel computing algorithm has been applied to the solution of the few-body problem. The approach is based on Feynman’s continual integrals method implemented in C++ programming language using NVIDIA CUDA technology. A wide range of 3-body and 4-body bound systems has been considered including nuclei described as consisting of protons and neutrons (e.g., 3,4He and nuclei described as consisting of clusters and nucleons (e.g., 6He. The correctness of the results was checked by the comparison with the exactly solvable 4-body oscillatory system and experimental data.
Naumenko, Mikhail; Samarin, Viacheslav
2018-02-01
Modern parallel computing algorithm has been applied to the solution of the few-body problem. The approach is based on Feynman's continual integrals method implemented in C++ programming language using NVIDIA CUDA technology. A wide range of 3-body and 4-body bound systems has been considered including nuclei described as consisting of protons and neutrons (e.g., 3,4He) and nuclei described as consisting of clusters and nucleons (e.g., 6He). The correctness of the results was checked by the comparison with the exactly solvable 4-body oscillatory system and experimental data.
Numerical Simulation of Fluidized Bed Gasifier for Integrated Gasification Combined Cycle
Directory of Open Access Journals (Sweden)
CHEN Ju-hui
2017-06-01
Full Text Available The overall thermal efficiency of the integrated gasification combined cycle ( IGCC has not been sufficiently improved. In order to achieve higher power generation efficiency，the advanced technology of IGCC has been developed which is on the basis of the concept of exergy recovery. IGCC systems and devices from the overall structure of opinion，this technology will generate electricity for the integration of advanced technology together，the current utilization of power generation technology and by endothermic reaction of steam in the gasifier，a gas turbine exhaust heat recovery or the solid oxide fuel cell. It is estimated that such the use of exergy recycling has the advantage of being easy to use，separating，collecting fixed CO2，making it very attractive，and can increase the overall efficiency by 10% or more. The characteristics of fluidized bed gasifier，one of the core equipment of the IGCC system，and its effect on the whole system were studied.
Directory of Open Access Journals (Sweden)
Sheam-Chyun Lin
2014-02-01
Full Text Available Since the inlet and outlet of hidden ceiling fan are almost located at the same Plane; thus, an improper housing may cause inhale-return phenomenon which significantly affects its power consumption and performance. In this study, a comprehensive investigation by numerical and experimental techniques was used to predict and identify the flow pattern, airflow rate, efficiency, and noise for ceiling fans with different design parameters. The results showed that the unique inhale-return phenomenon happens for an inappropriate housing. Several key parameters, such as fan guard, housing ring, inlet-to-outlet area ratio, and blockage height, are evaluated for finding out the criterion to avoid the inhale-return flow. Consequently the study finds that fan guard changes the airflow to a wider distribution with a lower velocity. A minimum blockage distance and a maximum height of ring-plate are set at 80 mm and 30 mm, respectively. Also, it is suggested that the inlet area must be bigger than the outlet area. Moreover, all the parameters show the same trend under various rotational speeds. In conclusion, this systematic investigation not only provides the fan engineer's design ability to avoid the inhale-return phenomenon, but also the predicting capability on its aerodynamic and acoustic performances.
Energy Technology Data Exchange (ETDEWEB)
Patrignani, L.; Losurdo, M.; Bruno, C. [Sapienza Univ. de Roma, Rome (Italy)
2010-09-15
Exhaust emissions from furnace burners can be reduced by premixing reactants with combustion products. This paper discussed the use of a trapped vortex combustor (TVC) as a very promising technology for gas turbines. The TVC can reduce emissions and ensure that the temperature is uniform in the exhaust products, which is a key aspect for certain types of heat treatments, such as in steel rolling mills. The TVC for gas turbines is configured to mix air, fuel and hot products at turbulent scales fine enough to render the combustion mode flameless, or close to flameless. The vortex ensures a high recirculation factor between hot combustion products and reactants, and ultimately flame stability. In this study, the TVC configuration for an existing gas turbine was numerically investigated by means of RANS and LES. According to preliminary results of the fast-flameless combustion (FFC) strategy, the proposed TVC is a suitable candidate to reduce nitrogen oxide (NOx) emissions while keeping the pressure drop below 1 per cent. Both RANS and LES show that too much fuel burns along the main duct. Better fuel splitting or a different position for the injectors may enhance combustion inside the recirculation zone. Behaviour of the main vortices showed that a more accurate design of the internal shape of the combustor is needed to prevent excessive velocity fluctuation or vortex instabilities and therefore emissions. 13 refs., 9 figs.
Doubenskaia, M.; Smurov, I.; Nagulin, K. Yu.
2016-04-01
Complimentary optical diagnostic tools are applied to provide comprehensive analysis of thermal phenomena in millisecond Nd:YAG laser irradiation of steel substrates. The following optical devices are employed: (a) infrared camera FLIR Phoenix RDASTM equipped by InSb sensor with 3 to 5 µm band pass arranged on 320 × 256 pixels array, (b) ultra-rapid camera Phantom V7.1 with SR-CMOS monochrome sensor in the visible spectral range, up to 105 frames per second for 64 × 88 pixels array, (c) original multi-wavelength pyrometer in the near-infrared range (1.370-1.531 µm). The following laser radiation parameters are applied: variation of energy per pulse in the range 15-30 J at a constant pulse duration of 10 ms with and without application of protective gas (Ar). The evolution of true temperature is restored based on the method of multi-colour pyrometry; by this way, melting/solidification dynamics is analysed. Emissivity variation with temperature is studied, and hysteresis type functional dependence is found. Variation of intensity of surface evaporation visualised by the camera Phantom V7.1 is registered and linked with the surface temperature evolution, different surface roughness and influence of protective gas atmosphere. Determination of the vapour plume temperature based on relatively intensities of spectral lines is done. The numerical simulation is carried out applying the thermal model with phase transitions taken into account.
Yaros, Steven F.; Carlson, John R.; Chandrasekaran, Balasubramanyan
1986-01-01
An effort has been undertaken at the NASA Langley Research Center to assess the capabilities of available computational methods for use in propulsion integration design studies of transonic transport aircraft, particularly of pylon/nacelle combinations which exhibit essentially no interference drag. The three computer codes selected represent state-of-the-art computational methods for analyzing complex configurations at subsonic and transonic flight conditions. These are: EULER, a finite volume solution of the Euler equation; VSAERO, a panel solution of the Laplace equation; and PPW, a finite difference solution of the small disturbance transonic equations. In general, all three codes have certain capabilities that allow them to be of some value in predicting the flows about transport configurations, but all have limitations. Until more accurate methods are available, careful application and interpretation of the results of these codes are needed.
Yaros, S. F.; Carlson, J. R.; Chandrasekaran, B.
1986-01-01
An effort has been undertaken at the NASA Langley Research Center to assess the capabilities of available computational methods for use in propulsion integration design studies of transonic transport aircraft, particularly of pylon/nacelle combinations which exhibit essentially no interference drag. The three computer codes selected represent state-of-the-art computational methods for analyzing complex configurations at subsonic and transonic flight conditions. These are: EULER, a finitie volume solution of the Euler equation; VSAERO, a panel solution of the Laplace equation; and PPW, a finite difference solution of the small disturbance transonic equations. In general, all three codes have certain capabilities that allow them to be of some value in predicting the flows about transport configurations, but all have limitations. Until more accurate methods are available, careful application and interpretation of the results of these codes are needed.
International Nuclear Information System (INIS)
Kalogiratou, Z.; Monovasilis, Th.; Psihoyios, G.; Simos, T.E.
2014-01-01
In this work we review single step methods of the Runge–Kutta type with special properties. Among them are methods specially tuned to integrate problems that exhibit a pronounced oscillatory character and such problems arise often in celestial mechanics and quantum mechanics. Symplectic methods, exponentially and trigonometrically fitted methods, minimum phase-lag and phase-fitted methods are presented. These are Runge–Kutta, Runge–Kutta–Nyström and Partitioned Runge–Kutta methods. The theory of constructing such methods is given as well as several specific methods. In order to present the performance of the methods we have tested 58 methods from all categories. We consider the two dimensional harmonic oscillator, the two body problem, the pendulum problem and the orbital problem studied by Stiefel and Bettis. Also we have tested the methods on the computation of the eigenvalues of the one dimensional time independent Schrödinger equation with the harmonic oscillator, the doubly anharmonic oscillator and the exponential potentials
Energy Technology Data Exchange (ETDEWEB)
Chen, Xiangyi; Suh, Kune Y. [KAERI, Daejeon (Korea, Republic of)
2016-05-15
In this work, this benchmark problem is conducted to assess the precision of the upgraded in-house code MINA. Comparison of the results from different best estimate codes employed by various grid spacer pressure drop correlations is carried out to suggest the best one. By modifying In's method, it presents good agreement with the experiment data which is shown in Figure 7. The reason for the failure of the prediction in previous work is caused by the utilization of Rehme's method which is categorized into four groups according to different fitting strategy. Through comparison of drag coefficients calculated by four groups of Rheme's method, equivalent drag coefficient calculated by In's method and experiment data shown in Figure 8, we can conclude that Rehme's method considerably underestimate the drag coefficients in grid spacers used in HELIOS and In's method give a reasonable prediction. Starting from the core inlet, the accumulated pressure losses are presented in figure 9 along the accumulated length of the forced convection flow path; the good agreement of the prediction from MINA with the experiment result shows MINA has very good capability in integrated momentum analysis makes it robust in the future design scoping method development of LFR.
Geometric and engineering drawing
Morling, K
2010-01-01
The new edition of this successful text describes all the geometric instructions and engineering drawing information that are likely to be needed by anyone preparing or interpreting drawings or designs with plenty of exercises to practice these principles.
Geometric ghosts and unitarity
International Nuclear Information System (INIS)
Ne'eman, Y.
1980-09-01
A review is given of the geometrical identification of the renormalization ghosts and the resulting derivation of Unitarity equations (BRST) for various gauges: Yang-Mills, Kalb-Ramond, and Soft-Group-Manifold
Differential geometric structures
Poor, Walter A
2007-01-01
This introductory text defines geometric structure by specifying parallel transport in an appropriate fiber bundle and focusing on simplest cases of linear parallel transport in a vector bundle. 1981 edition.
Energy Technology Data Exchange (ETDEWEB)
Yuan, Rong [Univ. of California, Berkeley, CA (United States)
2007-01-01
Linear elastic fracture mechanics is widely used in industry because it established simple and explicit relationships between the permissible loading conditions and the critical crack size that is allowed in a structure. Stress intensity factors are the above-mentioned functional expressions that relate load with crack size through geometric functions or weight functions. Compliance functions are to determine the crack/flaw size in a structure when optical inspection is inconvenient. As a result, geometric functions, weight functions and compliance functions have been intensively studied to determine the stress intensity factor expressions for different geometries. However, the relations between these functions have received less attention. This work is therefore to investigate the intrinsic relationships between these functions. Theoretical derivation was carried out and the results were verified on single-edge cracked plate under tension and bending. It is found out that the geometric function is essentially the non-dimensional weight function at the loading point. The compliance function is composed of two parts: a varying part due to crack extension and a constant part from the intact structure if no crack exists. The derivative of the compliance function at any location is the product of the geometric function and the weight function at the evaluation point. Inversely, the compliance function can be acquired by the integration of the product of the geometric function and the weight function with respect to the crack size. The integral constant is just the unchanging compliance from the intact structure. Consequently, a special application of the relations is to obtain the compliance functions along a crack once the geometric function and weight functions are known. Any of the three special functions can be derived once the other two functions are known. These relations may greatly simplify the numerical process in obtaining either geometric functions, weight
Energy Technology Data Exchange (ETDEWEB)
Hurd, J.V.
1986-01-01
One of the elements of the 750-keV polarized H/sup -/ injection transport at LAMPF is a Wien (E x B) filter. The Wien filter is used to process the spin of the polarized H/sup -/ ions to the appropriate orientation needed by the experiments. The proton-spin orientation is changed several times during a production cycle. At each new setting of the Wien filter, the beam is focused differently and the beam transport must be returned for an optimum match into the linac. The transport is tuned interactively using the first-order optics code TRACE. The first-order transformation matrix for a simple Wien filter is developed for use in TRACE and the transformation is compared to results of numerical integration to determine the validity of the first-order approximation.
Directory of Open Access Journals (Sweden)
Timchenko V.
2015-01-01
Full Text Available Numerical and experimental investigations of the flow and heat transfer in open-ended channel formed by the double skin façade have been undertaken in order to improve understanding of the phenomena and to apply it to passive cooling of building integrated photovoltaic systems. Both uniform heating and non-uniform heating configurations in which heat sources alternated with unheated zones on both skins were studied. Different periodic and asymmetric heating modes have been considered for the same aspect ratio 1/15 of wall distance to wall height and for periodicity 1/15 and 4/15 of heated/unheated zones and heat input, 220 W/m2. In computational study three dimensional transient LES simulation was carried out. It is shown that in comparison to uniformly heating configuration, non-uniformly heating configuration enhances both convective heat transfer and chimney effect.
Pueyo, Emilio L.; Sánchez, Elisa; Oliva-Urcia, Belén; José Ramón, Ma
2014-05-01
Classic 2D approaches have helped the understanding of the geometry and kinematics of fold-and-thrust belts belts (FAT belts) but are insufficient to unravel many natural cases. This is because deformation is 3D from the geometric point of view and, thus, cylindrical features may be considered as a simplification. On the other hand, deformation kinematics is usually complex, diachronic and poliphasic in real cases. Therefore, FAT belts have to be always considered in 4D. In this sense, the Southern Pyrenees is a perfect location to study the evolution of FAT belts because of the exceptional outcropping conditions of growth strata, the proven diachronic kinematics and the non-coaxial interference of deformation events. Within the vast catalogue of complex structures that includes superposed folding, conical and plunging folds, oblique thrust ramps, etc here, we have selected the westernmost termination of the South Pyrenean sole thrust to illustrate how the integration of geometric and kinematic analysis can help unraveling complex structures in FAT belts. The San Marzal pericline (4 km2 surface extension) is the lateral termination of the Sto. Domingo deca-kilometric fold. San Marzal looks like a large 70° plunging cylindrical structure. However the large magnitude (≡ 60-70°) of vertical axis rotations accommodated between its flanks cannot be explained without a conical geometry. In this work we will show how the structural analysis performed on this structure has disentangled its complex geometry. This analyses comprises several hundreds of bedding data, joints and veins and more than 150 standard paleomagnetic and AMS sites. Besides, we will show how the kinematic information derived from magnetostratigraphic sections (more than 8 km of sampled profiles) has helped to constraint the folding and rotation ages and velocities. Finally, all these complex geometric and kinematic features have inspired us to build an analogue model where we can explore the 3D
Geometrical method of decoupling
Directory of Open Access Journals (Sweden)
C. Baumgarten
2012-12-01
Full Text Available The computation of tunes and matched beam distributions are essential steps in the analysis of circular accelerators. If certain symmetries—like midplane symmetry—are present, then it is possible to treat the betatron motion in the horizontal, the vertical plane, and (under certain circumstances the longitudinal motion separately using the well-known Courant-Snyder theory, or to apply transformations that have been described previously as, for instance, the method of Teng and Edwards. In a preceding paper, it has been shown that this method requires a modification for the treatment of isochronous cyclotrons with non-negligible space charge forces. Unfortunately, the modification was numerically not as stable as desired and it was still unclear, if the extension would work for all conceivable cases. Hence, a systematic derivation of a more general treatment seemed advisable. In a second paper, the author suggested the use of real Dirac matrices as basic tools for coupled linear optics and gave a straightforward recipe to decouple positive definite Hamiltonians with imaginary eigenvalues. In this article this method is generalized and simplified in order to formulate a straightforward method to decouple Hamiltonian matrices with eigenvalues on the real and the imaginary axis. The decoupling of symplectic matrices which are exponentials of such Hamiltonian matrices can be deduced from this in a few steps. It is shown that this algebraic decoupling is closely related to a geometric “decoupling” by the orthogonalization of the vectors E[over →], B[over →], and P[over →], which were introduced with the so-called “electromechanical equivalence.” A mathematical analysis of the problem can be traced down to the task of finding a structure-preserving block diagonalization of symplectic or Hamiltonian matrices. Structure preservation means in this context that the (sequence of transformations must be symplectic and hence canonical. When
Directory of Open Access Journals (Sweden)
Poruba Z.
2009-06-01
Full Text Available For the numerical solution of elasto-plastic problems with use of Newton-Raphson method in global equilibrium equation it is necessary to determine the tangent modulus in each integration point. To reach the parabolic convergence of Newton-Raphson method it is convenient to use so called algorithmic tangent modulus which is consistent with used integration scheme. For more simple models for example Chaboche combined hardening model it is possible to determine it in analytical way. In case of more robust macroscopic models it is in many cases necessary to use the approximation approach. This possibility is presented in this contribution for radial return method on Chaboche model. An example solved in software Ansys corresponds to line contact problem with assumption of Coulomb's friction. The study shows at the end that the number of iteration of N-R method is higher in case of continuum tangent modulus and many times higher with use of modified N-R method, initial stiffness method.
Rao, G Shanker
2006-01-01
About the Book: This book provides an introduction to Numerical Analysis for the students of Mathematics and Engineering. The book is designed in accordance with the common core syllabus of Numerical Analysis of Universities of Andhra Pradesh and also the syllabus prescribed in most of the Indian Universities. Salient features: Approximate and Numerical Solutions of Algebraic and Transcendental Equation Interpolation of Functions Numerical Differentiation and Integration and Numerical Solution of Ordinary Differential Equations The last three chapters deal with Curve Fitting, Eigen Values and Eigen Vectors of a Matrix and Regression Analysis. Each chapter is supplemented with a number of worked-out examples as well as number of problems to be solved by the students. This would help in the better understanding of the subject. Contents: Errors Solution of Algebraic and Transcendental Equations Finite Differences Interpolation with Equal Intervals Interpolation with Unequal Int...
Geometrical optical illusionists.
Wade, Nicholas J
2014-01-01
Geometrical optical illusions were given this title by Oppel in 1855. Variants on such small distortions of visual space were illustrated thereafter, many of which bear the names of those who first described them. Some original forms of the geometrical optical illusions are shown together with 'perceptual portraits' of those who described them. These include: Roget, Chevreul, Fick, Zöllner, Poggendorff, Hering, Kundt, Delboeuf Mach, Helmholtz, Hermann, von Bezold, Müller-Lyer, Lipps, Thiéry, Wundt, Münsterberg, Ebbinghaus, Titchener, Ponzo, Luckiesh, Sander, Ehrenstein, Gregory, Heard, White, Shepard, and. Lingelbach. The illusions are grouped under the headings of orientation, size, the combination of size and orientation, and contrast. Early theories of illusions, before geometrical optical illusions were so named, are mentioned briefly.
PREFACE: Geometrically frustrated magnetism Geometrically frustrated magnetism
Gardner, Jason S.
2011-04-01
Frustrated magnetism is an exciting and diverse field in condensed matter physics that has grown tremendously over the past 20 years. This special issue aims to capture some of that excitement in the field of geometrically frustrated magnets and is inspired by the 2010 Highly Frustrated Magnetism (HFM 2010) meeting in Baltimore, MD, USA. Geometric frustration is a broad phenomenon that results from an intrinsic incompatibility between some fundamental interactions and the underlying lattice geometry based on triangles and tetrahedra. Most studies have centred around the kagomé and pyrochlore based magnets but recent work has looked at other structures including the delafossite, langasites, hyper-kagomé, garnets and Laves phase materials to name a few. Personally, I hope this issue serves as a great reference to scientist both new and old to this field, and that we all continue to have fun in this very frustrated playground. Finally, I want to thank the HFM 2010 organizers and all the sponsors whose contributions were an essential part of the success of the meeting in Baltimore. Geometrically frustrated magnetism contents Spangolite: an s = 1/2 maple leaf lattice antiferromagnet? T Fennell, J O Piatek, R A Stephenson, G J Nilsen and H M Rønnow Two-dimensional magnetism and spin-size effect in the S = 1 triangular antiferromagnet NiGa2S4 Yusuke Nambu and Satoru Nakatsuji Short range ordering in the modified honeycomb lattice compound SrHo2O4 S Ghosh, H D Zhou, L Balicas, S Hill, J S Gardner, Y Qi and C R Wiebe Heavy fermion compounds on the geometrically frustrated Shastry-Sutherland lattice M S Kim and M C Aronson A neutron polarization analysis study of moment correlations in (Dy0.4Y0.6)T2 (T = Mn, Al) J R Stewart, J M Hillier, P Manuel and R Cywinski Elemental analysis and magnetism of hydronium jarosites—model kagome antiferromagnets and topological spin glasses A S Wills and W G Bisson The Herbertsmithite Hamiltonian: μSR measurements on single crystals
Geometric Series via Probability
Tesman, Barry
2012-01-01
Infinite series is a challenging topic in the undergraduate mathematics curriculum for many students. In fact, there is a vast literature in mathematics education research on convergence issues. One of the most important types of infinite series is the geometric series. Their beauty lies in the fact that they can be evaluated explicitly and that…
A Geometric Dissection Problem
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 7; Issue 7. A Geometric Dissection Problem. M N Deshpande. Think It Over Volume 7 Issue 7 July 2002 pp 91-91. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/007/07/0091-0091. Author Affiliations.
Geometric statistical inference
International Nuclear Information System (INIS)
Periwal, Vipul
1999-01-01
A reparametrization-covariant formulation of the inverse problem of probability is explicitly solved for finite sample sizes. The inferred distribution is explicitly continuous for finite sample size. A geometric solution of the statistical inference problem in higher dimensions is outlined
Oskouie, M. Faraji; Ansari, R.; Rouhi, H.
2018-04-01
Eringen's nonlocal elasticity theory is extensively employed for the analysis of nanostructures because it is able to capture nanoscale effects. Previous studies have revealed that using the differential form of the strain-driven version of this theory leads to paradoxical results in some cases, such as bending analysis of cantilevers, and recourse must be made to the integral version. In this article, a novel numerical approach is developed for the bending analysis of Euler-Bernoulli nanobeams in the context of strain- and stress-driven integral nonlocal models. This numerical approach is proposed for the direct solution to bypass the difficulties related to converting the integral governing equation into a differential equation. First, the governing equation is derived based on both strain-driven and stress-driven nonlocal models by means of the minimum total potential energy. Also, in each case, the governing equation is obtained in both strong and weak forms. To solve numerically the derived equations, matrix differential and integral operators are constructed based upon the finite difference technique and trapezoidal integration rule. It is shown that the proposed numerical approach can be efficiently applied to the strain-driven nonlocal model with the aim of resolving the mentioned paradoxes. Also, it is able to solve the problem based on the strain-driven model without inconsistencies of the application of this model that are reported in the literature.
International Nuclear Information System (INIS)
Kim, K. S.; Ju, H. G.; Jeon, T. H. and others
2005-03-01
A comprehensive high fidelity reactor core modeling capability has been developed for detailed analysis of current and advanced reactor designs as part of a US-ROK collaborative I-NERI project. High fidelity was accomplished by integrating highly refined solution modules for the coupled neutronic, thermal-hydraulic, and thermo-mechanical phenomena. Each solution module employs methods and models that are formulated faithfully to the first-principles governing the physics, real geometry, and constituents. Specifically, the critical analysis elements that are incorporated in the coupled code capability are whole-core neutron transport solution, ultra-fine-mesh computational fluid dynamics/heat transfer solution, and finite-element-based thermo-mechanics solution, all obtained with explicit (fuel pin cell level) heterogeneous representations of the components of the core. The vast computational problem resulting from such highly refined modeling is solved on massively parallel computers, and serves as the 'numerical nuclear reactor'. Relaxation of modeling parameters were also pursued to make problems run on clusters of workstations and PCs for smaller scale applications as well
Directory of Open Access Journals (Sweden)
L. Malgaca
2009-01-01
Full Text Available Piezoelectric smart structures can be modeled using commercial finite element packages. Integration of control actions into the finite element model solutions (ICFES can be done in ANSYS by using parametric design language. Simulation results can be obtained easily in smart structures by this method. In this work, cantilever smart structures consisting of aluminum beams and lead-zirconate-titanate (PZT patches are considered. Two cases are studied numerically and experimentally in parallel. In the first case, a smart structure with a single PZT patch is used for the free vibration control under an initial tip displacement. In the second case, a smart structure with two PZT patches is used for the forced vibration control under harmonic excitation, where one of the PZT patches is used as vibration generating shaker while the other is used as vibration controlling actuator. For the two cases, modal analyses are done using chirp signals; Control OFF and Control ON responses in the time domain are obtained for various controller gains. A non-contact laser displacement sensor and strain gauges are utilized for the feedback signals. It is observed that all the simulation results agree with the experimental results.
Energy Technology Data Exchange (ETDEWEB)
Azadeh, A.; Amalnick, M.S.; Ghaderi, S.F.; Asadzadeh, S.M. [Department of Industrial Engineering, Faculty of Engineering, Center of Excellence for Intelligent Experimental Mechanics, Research Institute of Energy Management and Planning, P.O. Box 14178-43111, University of Tehran (Iran); Department of Engineering Optimization Research, Faculty of Engineering, Center of Excellence for Intelligent Experimental Mechanics, Research Institute of Energy Management and Planning, P.O. Box 14178-43111, University of Tehran (Iran)
2007-07-15
This paper introduces an integrated approach based on data envelopment analysis (DEA), principal component analysis (PCA) and numerical taxonomy (NT) for total energy efficiency assessment and optimization in energy intensive manufacturing sectors. Total energy efficiency assessment and optimization of the proposed approach considers structural indicators in addition conventional consumption and manufacturing sector output indicators. The validity of the DEA model is verified and validated by PCA and NT through Spearman correlation experiment. Moreover, the proposed approach uses the measure-specific super-efficiency DEA model for sensitivity analysis to determine the critical energy carriers. Four energy intensive manufacturing sectors are discussed in this paper: iron and steel, pulp and paper, petroleum refining and cement manufacturing sectors. To show superiority and applicability, the proposed approach has been applied to refinery sub-sectors of some OECD (Organization for Economic Cooperation and Development) countries. This study has several unique features which are: (1) a total approach which considers structural indicators in addition to conventional energy efficiency indicators; (2) a verification and validation mechanism for DEA by PCA and NT and (3) utilization of DEA for total energy efficiency assessment and consumption optimization of energy intensive manufacturing sectors. (author)
Energy Technology Data Exchange (ETDEWEB)
Kim, K. S.; Ju, H. G.; Jeon, T. H. and others
2005-03-15
A comprehensive high fidelity reactor core modeling capability has been developed for detailed analysis of current and advanced reactor designs as part of a US-ROK collaborative I-NERI project. High fidelity was accomplished by integrating highly refined solution modules for the coupled neutronic, thermal-hydraulic, and thermo-mechanical phenomena. Each solution module employs methods and models that are formulated faithfully to the first-principles governing the physics, real geometry, and constituents. Specifically, the critical analysis elements that are incorporated in the coupled code capability are whole-core neutron transport solution, ultra-fine-mesh computational fluid dynamics/heat transfer solution, and finite-element-based thermo-mechanics solution, all obtained with explicit (fuel pin cell level) heterogeneous representations of the components of the core. The vast computational problem resulting from such highly refined modeling is solved on massively parallel computers, and serves as the 'numerical nuclear reactor'. Relaxation of modeling parameters were also pursued to make problems run on clusters of workstations and PCs for smaller scale applications as well.
International Nuclear Information System (INIS)
Azadeh, A.; Amalnick, M.S.; Ghaderi, S.F.; Asadzadeh, S.M.
2007-01-01
This paper introduces an integrated approach based on data envelopment analysis (DEA), principal component analysis (PCA) and numerical taxonomy (NT) for total energy efficiency assessment and optimization in energy intensive manufacturing sectors. Total energy efficiency assessment and optimization of the proposed approach considers structural indicators in addition conventional consumption and manufacturing sector output indicators. The validity of the DEA model is verified and validated by PCA and NT through Spearman correlation experiment. Moreover, the proposed approach uses the measure-specific super-efficiency DEA model for sensitivity analysis to determine the critical energy carriers. Four energy intensive manufacturing sectors are discussed in this paper: iron and steel, pulp and paper, petroleum refining and cement manufacturing sectors. To show superiority and applicability, the proposed approach has been applied to refinery sub-sectors of some OECD (Organization for Economic Cooperation and Development) countries. This study has several unique features which are: (1) a total approach which considers structural indicators in addition to conventional energy efficiency indicators; (2) a verification and validation mechanism for DEA by PCA and NT and (3) utilization of DEA for total energy efficiency assessment and consumption optimization of energy intensive manufacturing sectors
International Nuclear Information System (INIS)
Ohwada, Hiroshi; Ishihara, Yasutoshi
2010-01-01
To improve the efficacy of hyperthermia treatment, a novel method of noninvasive measurement of body temperature change is proposed. The proposed technology, thermometry, is based on changes in the electromagnetic field distribution inside the heating applicator with temperature changes and the temperature dependence of the dielectric constant. In addition, an image of the temperature change distribution inside a body is reconstructed by applying a computed tomography (CT) algorithm. The proposed thermometry method can serve as a possible noninvasive method to monitor the temperature change distribution inside the body without the use of enormous thermometers such as in the case of magnetic resonance imaging (MRI). Furthermore, this temperature monitoring method can be easily combined with a heating applicator based on a cavity resonator, and the novel integrated treatment system can possibly be used to treat cancer effectively while noninvasively monitoring the heating effect. In this paper, the phase change distributions of the electromagnetic field with temperature changes are simulated by numerical analysis using the finite difference time domain (FDTD) method. Moreover, to estimate the phase change distributions inside a target body, the phase change distributions with temperature changes are reconstructed by a filtered back-projection. In addition, the reconstruction accuracy of the converted temperature change distribution from the phase change is evaluated. (author)
Morphing of geometric composites via residual swelling.
Pezzulla, Matteo; Shillig, Steven A; Nardinocchi, Paola; Holmes, Douglas P
2015-08-07
Understanding and controlling the shape of thin, soft objects has been the focus of significant research efforts among physicists, biologists, and engineers in the last decade. These studies aim to utilize advanced materials in novel, adaptive ways such as fabricating smart actuators or mimicking living tissues. Here, we present the controlled growth-like morphing of 2D sheets into 3D shapes by preparing geometric composite structures that deform by residual swelling. The morphing of these geometric composites is dictated by both swelling and geometry, with diffusion controlling the swelling-induced actuation, and geometric confinement dictating the structure's deformed shape. Building on a simple mechanical analog, we present an analytical model that quantitatively describes how the Gaussian and mean curvatures of a thin disk are affected by the interplay among geometry, mechanics, and swelling. This model is in excellent agreement with our experiments and numerics. We show that the dynamics of residual swelling is dictated by a competition between two characteristic diffusive length scales governed by geometry. Our results provide the first 2D analog of Timoshenko's classical formula for the thermal bending of bimetallic beams - our generalization explains how the Gaussian curvature of a 2D geometric composite is affected by geometry and elasticity. The understanding conferred by these results suggests that the controlled shaping of geometric composites may provide a simple complement to traditional manufacturing techniques.
Geometric allocation approaches in Markov chain Monte Carlo
International Nuclear Information System (INIS)
Todo, S; Suwa, H
2013-01-01
The Markov chain Monte Carlo method is a versatile tool in statistical physics to evaluate multi-dimensional integrals numerically. For the method to work effectively, we must consider the following key issues: the choice of ensemble, the selection of candidate states, the optimization of transition kernel, algorithm for choosing a configuration according to the transition probabilities. We show that the unconventional approaches based on the geometric allocation of probabilities or weights can improve the dynamics and scaling of the Monte Carlo simulation in several aspects. Particularly, the approach using the irreversible kernel can reduce or sometimes completely eliminate the rejection of trial move in the Markov chain. We also discuss how the space-time interchange technique together with Walker's method of aliases can reduce the computational time especially for the case where the number of candidates is large, such as models with long-range interactions
Geometric Sensitivity of a Pinhole Collimator.
Jacobowitz, Howard; Metzler, Scott D
2010-02-19
Geometric sensitivity for single photon emission computerized tomography (SPECT) is given by a double integral over the detection plane. It would be useful to be able to explicitly evaluate this quantity. This paper shows that the inner integral can be evaluated in the situation where there is no gamma ray penetration of the material surrounding the pinhole aperature. This is done by converting the integral to an integral in the complex plane and using Cauchy's theorem to replace it by one which can be evaluated in terms of elliptic functions.
Dynamics in geometrical confinement
Kremer, Friedrich
2014-01-01
This book describes the dynamics of low molecular weight and polymeric molecules when they are constrained under conditions of geometrical confinement. It covers geometrical confinement in different dimensionalities: (i) in nanometer thin layers or self supporting films (1-dimensional confinement) (ii) in pores or tubes with nanometric diameters (2-dimensional confinement) (iii) as micelles embedded in matrices (3-dimensional) or as nanodroplets.The dynamics under such conditions have been a much discussed and central topic in the focus of intense worldwide research activities within the last two decades. The present book discusses how the resulting molecular mobility is influenced by the subtle counterbalance between surface effects (typically slowing down molecular dynamics through attractive guest/host interactions) and confinement effects (typically increasing the mobility). It also explains how these influences can be modified and tuned, e.g. through appropriate surface coatings, film thicknesses or pore...
Bestvina, Mladen; Vogtmann, Karen
2014-01-01
Geometric group theory refers to the study of discrete groups using tools from topology, geometry, dynamics and analysis. The field is evolving very rapidly and the present volume provides an introduction to and overview of various topics which have played critical roles in this evolution. The book contains lecture notes from courses given at the Park City Math Institute on Geometric Group Theory. The institute consists of a set of intensive short courses offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The courses begin at an introductory level suitable for graduate students and lead up to currently active topics of research. The articles in this volume include introductions to CAT(0) cube complexes and groups, to modern small cancellation theory, to isometry groups of general CAT(0) spaces, and a discussion of nilpotent genus in the context of mapping class groups and CAT(0) gro...
Frè, Pietro Giuseppe
2013-01-01
‘Gravity, a Geometrical Course’ presents general relativity (GR) in a systematic and exhaustive way, covering three aspects that are homogenized into a single texture: i) the mathematical, geometrical foundations, exposed in a self consistent contemporary formalism, ii) the main physical, astrophysical and cosmological applications, updated to the issues of contemporary research and observations, with glimpses on supergravity and superstring theory, iii) the historical development of scientific ideas underlying both the birth of general relativity and its subsequent evolution. The book is divided in two volumes. Volume One is dedicated to the development of the theory and basic physical applications. It guides the reader from the foundation of special relativity to Einstein field equations, illustrating some basic applications in astrophysics. A detailed account of the historical and conceptual development of the theory is combined with the presentation of its mathematical foundations. Differe...
International Nuclear Information System (INIS)
Kostroun, V.O.
1980-01-01
Theoretical expressions for the angular and spectral distributions of synchrotron radiation involve modified Bessel functions of fractional order and the integral ∫sup(infinitely)sub(x)Ksub(ν)(eta)d eta. A simple series expression for these quantities which can be evaluated numerically with hand-held programmable calculators is presented. (orig.)
Corver, M.P.; Doust, H.; van Wees, J.D.A.M.; Cloetingh, S.A.P.L.
2011-01-01
We present the results of an integrated analogue and numerical modeling study with a focus on structural, stratigraphic and thermal differences between symmetric and asymmetric grabens. These models enable fault interpretation and subsidence analyses in studies of active rifting and graben
Waerden, B
1996-01-01
From the reviews: "... Federer's timely and beautiful book indeed fills the need for a comprehensive treatise on geometric measure theory, and his detailed exposition leads from the foundations of the theory to the most recent discoveries. ... The author writes with a distinctive style which is both natural and powerfully economical in treating a complicated subject. This book is a major treatise in mathematics and is essential in the working library of the modern analyst." Bulletin of the London Mathematical Society.
Geometric theory of information
2014-01-01
This book brings together geometric tools and their applications for Information analysis. It collects current and many uses of in the interdisciplinary fields of Information Geometry Manifolds in Advanced Signal, Image & Video Processing, Complex Data Modeling and Analysis, Information Ranking and Retrieval, Coding, Cognitive Systems, Optimal Control, Statistics on Manifolds, Machine Learning, Speech/sound recognition, and natural language treatment which are also substantially relevant for the industry.
Geometrically Consistent Mesh Modification
Bonito, A.
2010-01-01
A new paradigm of adaptivity is to execute refinement, coarsening, and smoothing of meshes on manifolds with incomplete information about their geometry and yet preserve position and curvature accuracy. We refer to this collectively as geometrically consistent (GC) mesh modification. We discuss the concept of discrete GC, show the failure of naive approaches, and propose and analyze a simple algorithm that is GC and accuracy preserving. © 2010 Society for Industrial and Applied Mathematics.
Studies in geometric quantization
International Nuclear Information System (INIS)
Tuynman, G.M.
1988-01-01
This thesis contains five chapters, of which the first, entitled 'What is prequantization, and what is geometric quantization?', is meant as an introduction to geometric quantization for the non-specialist. The second chapter, entitled 'Central extensions and physics' deals with the notion of central extensions of manifolds and elaborates and proves the statements made in the first chapter. Central extensions of manifolds occur in physics as the freedom of a phase factor in the quantum mechanical state vector, as the phase factor in the prequantization process of classical mechanics and it appears in mathematics when studying central extension of Lie groups. In this chapter the connection between these central extensions is investigated and a remarkable similarity between classical and quantum mechanics is shown. In chapter three a classical model is given for the hydrogen atom including spin-orbit and spin-spin interaction. The method of geometric quantization is applied to this model and the results are discussed. In the final chapters (4 and 5) an explicit method to calculate the operators corresponding to classical observables is given when the phase space is a Kaehler manifold. The obtained formula are then used to quantise symplectic manifolds which are irreducible hermitian symmetric spaces and the results are compared with other quantization procedures applied to these manifolds (in particular to Berezin's quantization). 91 refs.; 3 tabs
Perspective: Geometrically frustrated assemblies
Grason, Gregory M.
2016-09-01
This perspective will overview an emerging paradigm for self-organized soft materials, geometrically frustrated assemblies, where interactions between self-assembling elements (e.g., particles, macromolecules, proteins) favor local packing motifs that are incompatible with uniform global order in the assembly. This classification applies to a broad range of material assemblies including self-twisting protein filament bundles, amyloid fibers, chiral smectics and membranes, particle-coated droplets, curved protein shells, and phase-separated lipid vesicles. In assemblies, geometric frustration leads to a host of anomalous structural and thermodynamic properties, including heterogeneous and internally stressed equilibrium structures, self-limiting assembly, and topological defects in the equilibrium assembly structures. The purpose of this perspective is to (1) highlight the unifying principles and consequences of geometric frustration in soft matter assemblies; (2) classify the known distinct modes of frustration and review corresponding experimental examples; and (3) describe outstanding questions not yet addressed about the unique properties and behaviors of this broad class of systems.
Geometric Methods in Physics XXXV
Odzijewicz, Anatol; Previato, Emma
2018-01-01
This book features a selection of articles based on the XXXV Białowieża Workshop on Geometric Methods in Physics, 2016. The series of Białowieża workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. The works in this book, based on presentations given at the workshop, are previously unpublished, at the cutting edge of current research, typically grounded in geometry and analysis, and with applications to classical and quantum physics. In 2016 the special session "Integrability and Geometry" in particular attracted pioneers and leading specialists in the field. Traditionally, the Białowieża Workshop is followed by a School on Geometry and Physics, for advanced graduate students and early-career researchers, and the book also includes extended abstracts of the lecture series.
Directory of Open Access Journals (Sweden)
Suguru Arimoto
2011-01-01
Full Text Available A computable model of grasping and manipulation of a 3D rigid object with arbitrary smooth surfaces by multiple robot fingers with smooth fingertip surfaces is derived under rolling contact constraints between surfaces. Geometrical conditions of pure rolling contacts are described through the moving-frame coordinates at each rolling contact point under the postulates: (1 two surfaces share a common single contact point without any mutual penetration and a common tangent plane at the contact point and (2 each path length of running of the contact point on the robot fingertip surface and the object surface is equal. It is shown that a set of Euler-Lagrange equations of motion of the fingers-object system can be derived by introducing Lagrange multipliers corresponding to geometric conditions of contacts. A set of 1st-order differential equations governing rotational motions of each fingertip and the object and updating arc-length parameters should be accompanied with the Euler-Lagrange equations. Further more, nonholonomic constraints arising from twisting between the two normal axes to each tangent plane are rewritten into a set of Frenet-Serre equations with a geometrically given normal curvature and a motion-induced geodesic curvature.
Campbell, Kyle K; Braile, Thomas; Winker, Kevin
2016-01-01
The Philippine Islands are one of the most biologically diverse archipelagoes in the world. Current taxonomy, however, may underestimate levels of avian diversity and endemism in these islands. Although species limits can be difficult to determine among allopatric populations, quantitative methods for comparing phenotypic and genotypic data can provide useful metrics of divergence among populations and identify those that merit consideration for elevation to full species status. Using a conceptual approach that integrates genetic and phenotypic data, we compared populations among 48 species, estimating genetic divergence (p-distance) using the mtDNA marker ND2 and comparing plumage and morphometrics of museum study skins. Using conservative speciation thresholds, pairwise comparisons of genetic and phenotypic divergence suggested possible species-level divergences in more than half of the species studied (25 out of 48). In speciation process space, divergence routes were heterogeneous among taxa. Nearly all populations that surpassed high genotypic divergence thresholds were Passeriformes, and non-Passeriformes populations surpassed high phenotypic divergence thresholds more commonly than expected by chance. Overall, there was an apparent logarithmic increase in phenotypic divergence with respect to genetic divergence, suggesting the possibility that divergence among these lineages may initially be driven by divergent selection in this allopatric system. Also, genetic endemism was high among sampled islands. Higher taxonomy affected divergence in genotype and phenotype. Although broader lineage, genetic, phenotypic, and numeric sampling is needed to further explore heterogeneity among divergence processes and to accurately assess species-level diversity in these taxa, our results support the need for substantial taxonomic revisions among Philippine birds. The conservation implications are profound.
Geometric diffusion of quantum trajectories
Yang, Fan; Liu, Ren-Bao
2015-07-01
A quantum object can acquire a geometric phase (such as Berry phases and Aharonov-Bohm phases) when evolving along a path in a parameter space with non-trivial gauge structures. Inherent to quantum evolutions of wavepackets, quantum diffusion occurs along quantum trajectories. Here we show that quantum diffusion can also be geometric as characterized by the imaginary part of a geometric phase. The geometric quantum diffusion results from interference between different instantaneous eigenstate pathways which have different geometric phases during the adiabatic evolution. As a specific example, we study the quantum trajectories of optically excited electron-hole pairs in time-reversal symmetric insulators, driven by an elliptically polarized terahertz field. The imaginary geometric phase manifests itself as elliptical polarization in the terahertz sideband generation. The geometric quantum diffusion adds a new dimension to geometric phases and may have applications in many fields of physics, e.g., transport in topological insulators and novel electro-optical effects.
Brezinski, C
2012-01-01
Numerical analysis has witnessed many significant developments in the 20th century. This book brings together 16 papers dealing with historical developments, survey papers and papers on recent trends in selected areas of numerical analysis, such as: approximation and interpolation, solution of linear systems and eigenvalue problems, iterative methods, quadrature rules, solution of ordinary-, partial- and integral equations. The papers are reprinted from the 7-volume project of the Journal of Computational and Applied Mathematics on '/homepage/sac/cam/na2000/index.html<
International Nuclear Information System (INIS)
Zhurina, M.I.; Zatekin, V.V.; Popova, A.M.
1981-01-01
The collocation method of numerical solution of singular integral equations for partial scattering amplitudes in the three nucleon system using Tschebyscheff first kind polynomials as basis expansion functions is proposed. The selection of Tchebishev polynomials is due to the fact that the Fourier series on Tschebyscheff polynomials comerge much faster than, for instance the Taylor series and their convergence field is wider. Recurrent formulas for Tschebyscheff polynomials are most simple as compared with the corresponding formulas for other orthogonal polynomials and therefore most economical in the sence of count time. The Tschebyscheff polynomials are successfuly applied for integral equations solution in mathematical physics with singular nuclei. As example integral equations for amplitudes of the process of inelastic neutron scattering on deuteron are considered. The numerical solution method is demonstrated on the example of the separable Yamaguchi potential but this method can be simply generalized for other form separable potentials [ru
Geometric correlations and multifractals
International Nuclear Information System (INIS)
Amritkar, R.E.
1991-07-01
There are many situations where the usual statistical methods are not adequate to characterize correlations in the system. To characterize such situations we introduce mutual correlation dimensions which describe geometric correlations in the system. These dimensions allow us to distinguish between variables which are perfectly correlated with or without a phase lag, variables which are uncorrelated and variables which are partially correlated. We demonstrate the utility of our formalism by considering two examples from dynamical systems. The first example is about the loss of memory in chaotic signals and describes auto-correlations while the second example is about synchronization of chaotic signals and describes cross-correlations. (author). 19 refs, 6 figs
Ambrosetti, Antonio; Malchiodi, Andrea
2009-01-01
This volume contains lecture notes on some topics in geometric analysis, a growing mathematical subject which uses analytical techniques, mostly of partial differential equations, to treat problems in differential geometry and mathematical physics. The presentation of the material should be rather accessible to non-experts in the field, since the presentation is didactic in nature. The reader will be provided with a survey containing some of the most exciting topics in the field, with a series of techniques used to treat such problems.
Amasia, Mary; Kang, Seok-Won; Banerjee, Debjyoti; Madou, Marc
2013-01-01
A comprehensive study involving numerical analysis and experimental validation of temperature transients within a microchamber was performed for thermocycling operation in an integrated centrifugal microfluidic platform for polymerase chain reaction (PCR) amplification. Controlled heating and cooling of biological samples are essential processes in many sample preparation and detection steps for micro-total analysis systems. Specifically, the PCR process relies on highly controllable and uniform heating of nucleic acid samples for successful and efficient amplification. In these miniaturized systems, the heating process is often performed more rapidly, making the temperature control more difficult, and adding complexity to the integrated hardware system. To gain further insight into the complex temperature profiles within the PCR microchamber, numerical simulations using computational fluid dynamics and computational heat transfer were performed. The designed integrated centrifugal microfluidics platform utilizes thermoelectrics for ice-valving and thermocycling for PCR amplification. Embedded micro-thermocouples were used to record the static and dynamic thermal responses in the experiments. The data collected was subsequently used for computational validation of the numerical predictions for the system response during thermocycling, and these simulations were found to be in agreement with the experimental data to within ∼97%. When thermal contact resistance values were incorporated in the simulations, the numerical predictions were found to be in agreement with the experimental data to within ∼99.9%. This in-depth numerical modeling and experimental validation of a complex single-sided heating platform provide insights into hardware and system design for multi-layered polymer microfluidic systems. In addition, the biological capability along with the practical feasibility of the integrated system is demonstrated by successfully performing PCR amplification of
GEOMETRIC PROGRESSIONS ON ELLIPTIC CURVES.
Ciss, Abdoul Aziz; Moody, Dustin
2017-01-01
In this paper, we look at long geometric progressions on different model of elliptic curves, namely Weierstrass curves, Edwards and twisted Edwards curves, Huff curves and general quartics curves. By a geometric progression on an elliptic curve, we mean the existence of rational points on the curve whose x -coordinate (or y -coordinate) are in geometric progression. We find infinite families of twisted Edwards curves and Huff curves with geometric progressions of length 5, an infinite family of Weierstrass curves with 8 term progressions, as well as infinite families of quartic curves containing 10-term geometric progressions.
Discrete geometric structures for architecture
Pottmann, Helmut
2010-06-13
The emergence of freeform structures in contemporary architecture raises numerous challenging research problems, most of which are related to the actual fabrication and are a rich source of research topics in geometry and geometric computing. The talk will provide an overview of recent progress in this field, with a particular focus on discrete geometric structures. Most of these result from practical requirements on segmenting a freeform shape into planar panels and on the physical realization of supporting beams and nodes. A study of quadrilateral meshes with planar faces reveals beautiful relations to discrete differential geometry. In particular, we discuss meshes which discretize the network of principal curvature lines. Conical meshes are among these meshes; they possess conical offset meshes at a constant face/face distance, which in turn leads to a supporting beam layout with so-called torsion free nodes. This work can be generalized to a variety of multilayer structures and laid the ground for an adapted curvature theory for these meshes. There are also efforts on segmenting surfaces into planar hexagonal panels. Though these are less constrained than planar quadrilateral panels, this problem is still waiting for an elegant solution. Inspired by freeform designs in architecture which involve circles and spheres, we present a new kind of triangle mesh whose faces\\' in-circles form a packing, i.e., the in-circles of two triangles with a common edge have the same contact point on that edge. These "circle packing (CP) meshes" exhibit an aesthetic balance of shape and size of their faces. They are closely tied to sphere packings on surfaces and to various remarkable structures and patterns which are of interest in art, architecture, and design. CP meshes constitute a new link between architectural freeform design and computational conformal geometry. Recently, certain timber structures motivated us to study discrete patterns of geodesics on surfaces. This
Khabarov, Nikolay; Huggel, Christian; Obersteiner, Michael; Ramírez, Juan Manuel
2010-05-01
Mountain regions are typically characterized by rugged terrain which is susceptible to different types of landslides during high-intensity precipitation. Landslides account for billions of dollars of damage and many casualties, and are expected to increase in frequency in the future due to a projected increase of precipitation intensity. Early warning systems (EWS) are thought to be a primary tool for related disaster risk reduction and climate change adaptation to extreme climatic events and hydro-meteorological hazards, including landslides. An EWS for hazards such as landslides consist of different components, including environmental monitoring instruments (e.g. rainfall or flow sensors), physical or empirical process models to support decision-making (warnings, evacuation), data and voice communication, organization and logistics-related procedures, and population response. Considering this broad range, EWS are highly complex systems, and it is therefore difficult to understand the effect of the different components and changing conditions on the overall performance, ultimately being expressed as human lives saved or structural damage reduced. In this contribution we present a further development of our approach to assess a landslide EWS in an integral way, both at the system and component level. We utilize a numerical model using 6 hour rainfall data as basic input. A threshold function based on a rainfall-intensity/duration relation was applied as a decision criterion for evacuation. Damage to infrastructure and human lives was defined as a linear function of landslide magnitude, with the magnitude modelled using a power function of landslide frequency. Correct evacuation was assessed with a ‘true' reference rainfall dataset versus a dataset of artificially reduced quality imitating the observation system component. Performance of the EWS using these rainfall datasets was expressed in monetary terms (i.e. damage related to false and correct evacuation). We
Directory of Open Access Journals (Sweden)
Xiaojia Xiang
2015-01-01
Full Text Available The collocation method is extended to the special orthogonal group SO(3 with application to optimal attitude control (OAC of a rigid body. A left-invariant rigid-body attitude dynamical model on SO(3 is established. For the left invariance of the attitude configuration equation in body-fixed frame, a geometrically exact numerical method on SO(3, referred to as the geometric collocation method, is proposed by deriving the equivalent Lie algebra equation in so(3 of the left-invariant configuration equation. When compared with the general Gauss pseudo-spectral method, the explicit RKMK, and Lie group variational integrator having the same order and stepsize in numerical tests for evolving a free-floating rigid-body attitude dynamics, the proposed method is higher in accuracy, time performance, and structural conservativeness. In addition, the numerical method is applied to solve a constrained OAC problem on SO(3. The optimal control problem is transcribed into a nonlinear programming problem, in which the equivalent Lie algebra equation is being considered as the defect constraints instead of the configuration equation. The transcription method is coordinate-free and does not need chart switching or special handling of singularities. More importantly, with the numerical advantage of the geometric collocation method, the proposed OAC method may generate satisfying convergence rate.
Geometric modeling for computer aided design
Schwing, James L.
1993-01-01
Over the past several years, it has been the primary goal of this grant to design and implement software to be used in the conceptual design of aerospace vehicles. The work carried out under this grant was performed jointly with members of the Vehicle Analysis Branch (VAB) of NASA LaRC, Computer Sciences Corp., and Vigyan Corp. This has resulted in the development of several packages and design studies. Primary among these are the interactive geometric modeling tool, the Solid Modeling Aerospace Research Tool (smart), and the integration and execution tools provided by the Environment for Application Software Integration and Execution (EASIE). In addition, it is the purpose of the personnel of this grant to provide consultation in the areas of structural design, algorithm development, and software development and implementation, particularly in the areas of computer aided design, geometric surface representation, and parallel algorithms.
Energy Technology Data Exchange (ETDEWEB)
Goldberg, P.W.
1993-04-01
In this paper we consider the problem of learning the positions of spheres in metric spaces, given as data randomly drawn points classified according to whether they are internal or external to an unknown sphere. The particular metrics under consideration are geometrical shape metrics, and the results are intended to be applicable to the problem of learning to identify a shape from related shapes classified according to whether they resemble it visually. While it is typically NP-hard to locate a central point for a hypothesis sphere, we find that it is however often possible to obtain a non-spherical hypothesis which can accurately predict whether further random points lie within the unknown sphere. We exhibit algorithms which achieve this, and in the process indicate useful general techniques for computational learning. Finally we exhibit a natural shape metric and show that it defines a class of spheres not predictable in this sense, subject to standard cryptographic assumptions.
Simulating geometrically complex blast scenarios
Directory of Open Access Journals (Sweden)
Ian G. Cullis
2016-04-01
Full Text Available The effects of blast waves generated by energetic and non-energetic sources are of continuing interest to the ballistics research community. Modern conflicts are increasingly characterised by asymmetric urban warfare, with improvised explosive devices (IEDs often playing a dominant role on the one hand and an armed forces requirement for minimal collateral effects from their weapons on the other. These problems are characterised by disparate length- and time-scales and may also be governed by complex physics. There is thus an increasing need to be able to rapidly assess and accurately predict the effects of energetic blast in topologically complex scenarios. To this end, this paper presents a new QinetiQ-developed advanced computational package called EAGLE-Blast, which is capable of accurately resolving the generation, propagation and interaction of blast waves around geometrically complex shapes such as vehicles and buildings. After a brief description of the numerical methodology, various blast scenario simulations are described and the results compared with experimental data to demonstrate the validation of the scheme and its ability to describe these complex scenarios accurately and efficiently. The paper concludes with a brief discussion on the use of the code in supporting the development of algorithms for fast running engineering models.
Tang, H.; Sun, W.
2016-12-01
The theoretical computation of dislocation theory in a given earth model is necessary in the explanation of observations of the co- and post-seismic deformation of earthquakes. For this purpose, computation theories based on layered or pure half space [Okada, 1985; Okubo, 1992; Wang et al., 2006] and on spherically symmetric earth [Piersanti et al., 1995; Pollitz, 1997; Sabadini & Vermeersen, 1997; Wang, 1999] have been proposed. It is indicated that the compressibility, curvature and the continuous variation of the radial structure of Earth should be simultaneously taken into account for modern high precision displacement-based observations like GPS. Therefore, Tanaka et al. [2006; 2007] computed global displacement and gravity variation by combining the reciprocity theorem (RPT) [Okubo, 1993] and numerical inverse Laplace integration (NIL) instead of the normal mode method [Peltier, 1974]. Without using RPT, we follow the straightforward numerical integration of co-seismic deformation given by Sun et al. [1996] to present a straightforward numerical inverse Laplace integration method (SNIL). This method is used to compute the co- and post-seismic displacement of point dislocations buried in a spherically symmetric, self-gravitating viscoelastic and multilayered earth model and is easy to extended to the application of geoid and gravity. Comparing with pre-existing method, this method is relatively more straightforward and time-saving, mainly because we sum associated Legendre polynomials and dislocation love numbers before using Riemann-Merlin formula to implement SNIL.
McGee, Daniel Lee; Martinez-Planell, Rafael
2014-01-01
Tracing the path from a numerical Riemann sum approximating the area under a curve to a definite integral representing the precise area in various texts and online presentations, we found 3 semiotic registers that are used: the geometric register, the numerical register, and the symbolic register. The symbolic register had 3 representations: an…
Introduction to numerical analysis
Hildebrand, F B
1987-01-01
Well-known, respected introduction, updated to integrate concepts and procedures associated with computers. Computation, approximation, interpolation, numerical differentiation and integration, smoothing of data, other topics in lucid presentation. Includes 150 additional problems in this edition. Bibliography.
Geometric modeling in probability and statistics
Calin, Ovidiu
2014-01-01
This book covers topics of Informational Geometry, a field which deals with the differential geometric study of the manifold probability density functions. This is a field that is increasingly attracting the interest of researchers from many different areas of science, including mathematics, statistics, geometry, computer science, signal processing, physics and neuroscience. It is the authors’ hope that the present book will be a valuable reference for researchers and graduate students in one of the aforementioned fields. This textbook is a unified presentation of differential geometry and probability theory, and constitutes a text for a course directed at graduate or advanced undergraduate students interested in applications of differential geometry in probability and statistics. The book contains over 100 proposed exercises meant to help students deepen their understanding, and it is accompanied by software that is able to provide numerical computations of several information geometric objects. The reader...
Biryukov, Alexander; Degtyareva, Yana
2017-10-01
The probabilities of molecular quantum transitions induced by electromagnetic field are expressed as path integrals of a real alternating functional. We propose a new method for computing these integrals by means of recurrence relations. We apply this approach to description of the two-photon Rabi oscillations.
Cao, Xinhua; Xu, Xiaoyin; Voss, Stephan
2017-03-01
In this paper, we describe an enhanced DICOM Secondary Capture (SC) that integrates Image Quantification (IQ) results, Regions of Interest (ROIs), and Time Activity Curves (TACs) with screen shots by embedding extra medical imaging information into a standard DICOM header. A software toolkit of DICOM IQSC has been developed to implement the SC-centered information integration of quantitative analysis for routine practice of nuclear medicine. Primary experiments show that the DICOM IQSC method is simple and easy to implement seamlessly integrating post-processing workstations with PACS for archiving and retrieving IQ information. Additional DICOM IQSC applications in routine nuclear medicine and clinic research are also discussed.
Harmonic and geometric analysis
Citti, Giovanna; Pérez, Carlos; Sarti, Alessandro; Zhong, Xiao
2015-01-01
This book presents an expanded version of four series of lectures delivered by the authors at the CRM. Harmonic analysis, understood in a broad sense, has a very wide interplay with partial differential equations and in particular with the theory of quasiconformal mappings and its applications. Some areas in which real analysis has been extremely influential are PDE's and geometric analysis. Their foundations and subsequent developments made extensive use of the Calderón–Zygmund theory, especially the Lp inequalities for Calderón–Zygmund operators (Beurling transform and Riesz transform, among others) and the theory of Muckenhoupt weights. The first chapter is an application of harmonic analysis and the Heisenberg group to understanding human vision, while the second and third chapters cover some of the main topics on linear and multilinear harmonic analysis. The last serves as a comprehensive introduction to a deep result from De Giorgi, Moser and Nash on the regularity of elliptic partial differen...
Pelletier, J.D.; Mayer, L.; Pearthree, P.A.; House, P.K.; Demsey, K.A.; Klawon, J.K.; Vincent, K.R.
2005-01-01
Millions of people in the western United States live near the dynamic, distributary channel networks of alluvial fans where flood behavior is complex and poorly constrained. Here we test a new comprehensive approach to alluvial-fan flood hazard assessment that uses four complementary methods: two-dimensional raster-based hydraulic modeling, satellite-image change detection, fieldbased mapping of recent flood inundation, and surficial geologic mapping. Each of these methods provides spatial detail lacking in the standard method and each provides critical information for a comprehensive assessment. Our numerical model simultaneously solves the continuity equation and Manning's equation (Chow, 1959) using an implicit numerical method. It provides a robust numerical tool for predicting flood flows using the large, high-resolution Digital Elevation Models (DEMs) necessary to resolve the numerous small channels on the typical alluvial fan. Inundation extents and flow depths of historic floods can be reconstructed with the numerical model and validated against field- and satellite-based flood maps. A probabilistic flood hazard map can also be constructed by modeling multiple flood events with a range of specified discharges. This map can be used in conjunction with a surficial geologic map to further refine floodplain delineation on fans. To test the accuracy of the numerical model, we compared model predictions of flood inundation and flow depths against field- and satellite-based flood maps for two recent extreme events on the southern Tortolita and Harquahala piedmonts in Arizona. Model predictions match the field- and satellite-based maps closely. Probabilistic flood hazard maps based on the 10 yr, 100 yr, and maximum floods were also constructed for the study areas using stream gage records and paleoflood deposits. The resulting maps predict spatially complex flood hazards that strongly reflect small-scale topography and are consistent with surficial geology. In
Geometrical aspects of quantum spaces
International Nuclear Information System (INIS)
Ho, P.M.
1996-01-01
Various geometrical aspects of quantum spaces are presented showing the possibility of building physics on quantum spaces. In the first chapter the authors give the motivations for studying noncommutative geometry and also review the definition of a Hopf algebra and some general features of the differential geometry on quantum groups and quantum planes. In Chapter 2 and Chapter 3 the noncommutative version of differential calculus, integration and complex structure are established for the quantum sphere S 1 2 and the quantum complex projective space CP q (N), on which there are quantum group symmetries that are represented nonlinearly, and are respected by all the aforementioned structures. The braiding of S q 2 and CP q (N) is also described. In Chapter 4 the quantum projective geometry over the quantum projective space CP q (N) is developed. Collinearity conditions, coplanarity conditions, intersections and anharmonic ratios is described. In Chapter 5 an algebraic formulation of Reimannian geometry on quantum spaces is presented where Riemannian metric, distance, Laplacian, connection, and curvature have their quantum counterparts. This attempt is also extended to complex manifolds. Examples include the quantum sphere, the complex quantum projective space and the two-sheeted space. The quantum group of general coordinate transformations on some quantum spaces is also given
Geometric reasoning about assembly tools
Energy Technology Data Exchange (ETDEWEB)
Wilson, R.H.
1997-01-01
Planning for assembly requires reasoning about various tools used by humans, robots, or other automation to manipulate, attach, and test parts and subassemblies. This paper presents a general framework to represent and reason about geometric accessibility issues for a wide variety of such assembly tools. Central to the framework is a use volume encoding a minimum space that must be free in an assembly state to apply a given tool, and placement constraints on where that volume must be placed relative to the parts on which the tool acts. Determining whether a tool can be applied in a given assembly state is then reduced to an instance of the FINDPLACE problem. In addition, the author presents more efficient methods to integrate the framework into assembly planning. For tools that are applied either before or after their target parts are mated, one method pre-processes a single tool application for all possible states of assembly of a product in polynomial time, reducing all later state-tool queries to evaluations of a simple expression. For tools applied after their target parts are mated, a complementary method guarantees polynomial-time assembly planning. The author presents a wide variety of tools that can be described adequately using the approach, and surveys tool catalogs to determine coverage of standard tools. Finally, the author describes an implementation of the approach in an assembly planning system and experiments with a library of over one hundred manual and robotic tools and several complex assemblies.
Bonduel, M.; Bassier, M.; Vergauwen, M.; Pauwels, P.; Klein, R.
2017-11-01
The use of Building Information Modeling (BIM) for existing buildings based on point clouds is increasing. Standardized geometric quality assessment of the BIMs is needed to make them more reliable and thus reusable for future users. First, available literature on the subject is studied. Next, an initial proposal for a standardized geometric quality assessment is presented. Finally, this method is tested and evaluated with a case study. The number of specifications on BIM relating to existing buildings is limited. The Levels of Accuracy (LOA) specification of the USIBD provides definitions and suggestions regarding geometric model accuracy, but lacks a standardized assessment method. A deviation analysis is found to be dependent on (1) the used mathematical model, (2) the density of the point clouds and (3) the order of comparison. Results of the analysis can be graphical and numerical. An analysis on macro (building) and micro (BIM object) scale is necessary. On macro scale, the complete model is compared to the original point cloud and vice versa to get an overview of the general model quality. The graphical results show occluded zones and non-modeled objects respectively. Colored point clouds are derived from this analysis and integrated in the BIM. On micro scale, the relevant surface parts are extracted per BIM object and compared to the complete point cloud. Occluded zones are extracted based on a maximum deviation. What remains is classified according to the LOA specification. The numerical results are integrated in the BIM with the use of object parameters.
Geometric aspects of biological sequence comparison.
Stojmirović, Aleksandar; Yu, Yi-Kuo
2009-04-01
We introduce a geometric framework suitable for studying the relationships among biological sequences. In contrast to previous works, our formulation allows asymmetric distances (quasi-metrics), originating from uneven weighting of strings, which may induce non-trivial partial orders on sets of biosequences. The distances considered are more general than traditional generalized string edit distances. In particular, our framework enables non-trivial conversion between sequence similarities, both local and global, and distances. Our constructions apply to a wide class of scoring schemes and require much less restrictive gap penalties than the ones regularly used. Numerous examples are provided to illustrate the concepts introduced and their potential applications.
Gradient vector flow fast geometric active contours.
Paragios, Nikos; Mellina-Gottardo, Olivier; Ramesh, Visvanathan
2004-03-01
In this paper, we propose an edge-driven bidirectional geometric flow for boundary extraction. To this end, we combine the geodesic active contour flow and the gradient vector flow external force for snakes. The resulting motion equation is considered within a level set formulation, can deal with topological changes and important shape deformations. An efficient numerical schema is used for the flow implementation that exhibits robust behavior and has fast convergence rate. Promising results on real and synthetic images demonstrate the potentials of the flow.
Toroidal Precession as a Geometric Phase
Energy Technology Data Exchange (ETDEWEB)
J.W. Burby and H. Qin
2012-09-26
Toroidal precession is commonly understood as the orbit-averaged toroidal drift of guiding centers in axisymmetric and quasisymmetric configurations. We give a new, more natural description of precession as a geometric phase effect. In particular, we show that the precession angle arises as the holonomy of a guiding center's poloidal trajectory relative to a principal connection. The fact that this description is physically appropriate is borne out with new, manifestly coordinate-independent expressions for the precession angle that apply to all types of orbits in tokamaks and quasisymmetric stellarators alike. We then describe how these expressions may be fruitfully employed in numerical calculations of precession.
Hofmeister, Richard; Lemmen, Carsten; Nasermoaddeli, Hassan; Klingbeil, Knut; Wirtz, Kai
2015-04-01
Data and models for describing coastal systems span a diversity of disciplines, communities, ecosystems, regions and techniques. Previous attempts of unifying data exchange, coupling interfaces, or metadata information have not been successful. We introduce the new Modular System for Shelves and Coasts (MOSSCO, http://www.mossco.de), a novel coupling framework that enables the integration of a diverse array of models and data from different disciplines relating to coastal research. In the MOSSCO concept, the integrating framework imposes very few restrictions on contributed data or models; in fact, there is no distinction made between data and models. The few requirements are: (1) principle coupleability, i.e. access to I/O and timing information in submodels, which has recently been referred to as the Basic Model Interface (BMI) (2) open source/open data access and licencing and (3) communication of metadata, such as spatiotemporal information, naming conventions, and physical units. These requirements suffice to integrate different models and data sets into the MOSSCO infrastructure and subsequently built a modular integrated modeling tool that can span a diversity of processes and domains. We demonstrate how diverse coastal system constituents were integrated into this modular framework and how we deal with the diverging development of constituent data sets and models at external institutions. Finally, we show results from simulations with the fully coupled system using OGC WebServices in the WiMo geoportal (http://kofserver3.hzg.de/wimo), from where stakeholders can view the simulation results for further dissemination.
Geometric deviation modeling by kinematic matrix based on Lagrangian coordinate
Liu, Weidong; Hu, Yueming; Liu, Yu; Dai, Wanyi
2015-09-01
Typical representation of dimension and geometric accuracy is limited to the self-representation of dimension and geometric deviation based on geometry variation thinking, yet the interactivity affection of geometric variation and gesture variation of multi-rigid body is not included. In this paper, a kinematic matrix model based on Lagrangian coordinate is introduced, with the purpose of unified model for geometric variation and gesture variation and their interactive and integrated analysis. Kinematic model with joint, local base and movable base is built. The ideal feature of functional geometry is treated as the base body; the fitting feature of functional geometry is treated as the adjacent movable body; the local base of the kinematic model is fixed onto the ideal geometry, and the movable base of the kinematic model is fixed onto the fitting geometry. Furthermore, the geometric deviation is treated as relative location or rotation variation between the movable base and the local base, and it's expressed by the Lagrangian coordinate. Moreover, kinematic matrix based on Lagrangian coordinate for different types of geometry tolerance zones is constructed, and total freedom for each kinematic model is discussed. Finally, the Lagrangian coordinate library, kinematic matrix library for geometric deviation modeling is illustrated, and an example of block and piston fits is introduced. Dimension and geometric tolerances of the shaft and hole fitting feature are constructed by kinematic matrix and Lagrangian coordinate, and the results indicate that the proposed kinematic matrix is capable and robust in dimension and geometric tolerances modeling.
Effect of geometric scale on the extrudate swell of plastic micro-tubes
Ren, Zhong; Huang, Xingyuan
2018-01-01
In this study, the effect of geometric scale on the extrudate swell of plastic micro-tubes was numerically studied by using the finite element method. The four geometric models with same inner diameter but different wall thicknesses were used. Under the same boundary conditions, material parameters, and numerical algorithms, the extrudate swells and flow field distributions of two plastic micro-tubes were obtained. Study results show that the extrudate swell effect of plastic micro-tubes increase with the decreasing of geometric scale. Finally, the mechanisms of the geometric scale on the extrudate swell for the plastic micro-tubes were analyzed.
Directory of Open Access Journals (Sweden)
Pablo Dolado
2015-10-01
Full Text Available A novel technique of design of experiments applied to numerical simulations is proposed in this paper as a methodology for the sizing and design of thermal storage equipment integrated in any specific application. The technique is carried out through the response surfaces in order to limit the number of simulation runs required to achieve an appropriate solution. Thus, there are significant savings on the time spent on the design as well as a potential cost saving on the experimentation if similarity relationships between the prototype and the model are met. The technique is applied here to a previously developed and validated numerical model that simulates the thermal behavior of a phase change material-air heat exchanger. The incorporation of the thermal energy storage unit is analyzed in the case of a solar cooling application, improving the system coefficient of performance. The economic viability is mainly conditioned by the price of the macroencapsulated phase change material.
Fukushima, Toshio
2016-12-01
We present a method to integrate the gravitational field for general three-dimensional objects. By adopting the spherical polar coordinates centred at the evaluation point as the integration variables, we numerically compute the volume integral representation of the gravitational potential and of the acceleration vector. The variable transformation completely removes the algebraic singularities of the original integrals. The comparison with exact solutions reveals around 15 digits accuracy of the new method. Meanwhile, the six digit accuracy of the integrated gravitational field is realized by around 106 evaluations of the integrand per evaluation point, which costs at most a few seconds at a PC with Intel Core i7-4600U CPU running at 2.10 GHz clock. By using the new method, we show the gravitational field of a grand design spiral arm structure as an example. The computed gravitational field shows not only spiral shaped details but also a global feature composed of a thick oblate spheroid and a thin disc. The developed method is directly applicable to the electromagnetic field computation by means of Coulomb's law, the Biot-Savart law, and their retarded extensions. Sample FORTRAN 90 programs and test results are electronically available.
Downs, Nathan; Parisi, Alfio V.; Galligan, Linda; Turner, Joanna; Amar, Abdurazaq; King, Rachel; Ultra, Filipina; Butler, Harry
2016-01-01
A short series of practical classroom mathematics activities employing the use of a large and publicly accessible scientific data set are presented for use by students in years 9 and 10. The activities introduce and build understanding of integral calculus and trigonometric functions through the presentation of practical problem solving that…
Razali Hanipah, M.; Razul Razali, Akhtar
2017-10-01
Free-piston engine generator (FPEG) provides a novel method for electrical power generation in hybrid electric vehicle applications with scarcely reported prototype development and testing. This paper is looking into the motion control strategy for motoring the FPEG during starting. There are two motion profiles investigated namely, trapezoidal velocity and Scurve velocity. Both motion profiles were investigated numerically and the results have shown that the S-curve motion can only achieve 80% of the stroke when operated at the proposed motoring speed of 10Hz.
Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach
Arrieta, Jorge; Cartwright, Julian H.E.; Gouillart, Emmanuelle; Piro, Nicolas; Piro, Oreste; Tuval, Idan
2015-01-01
International audience; Mixing fluid in a container at low Reynolds number— in an inertialess environment—is not a trivial task. Reciprocating motions merely lead to cycles of mixing and unmixing, so continuous rotation, as used in many technological applications, would appear to be necessary. However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase. We show using journal-bearing flow as a model that such geometric mixing is a general tool...
Geometric inequalities for black holes
Energy Technology Data Exchange (ETDEWEB)
Dain, Sergio [Universidad Nacional de Cordoba (Argentina)
2013-07-01
Full text: A geometric inequality in General Relativity relates quantities that have both a physical interpretation and a geometrical definition. It is well known that the parameters that characterize the Kerr-Newman black hole satisfy several important geometric inequalities. Remarkably enough, some of these inequalities also hold for dynamical black holes. This kind of inequalities, which are valid in the dynamical and strong field regime, play an important role in the characterization of the gravitational collapse. They are closed related with the cosmic censorship conjecture. In this talk I will review recent results in this subject. (author)
Geometric inequalities for black holes
International Nuclear Information System (INIS)
Dain, Sergio
2013-01-01
Full text: A geometric inequality in General Relativity relates quantities that have both a physical interpretation and a geometrical definition. It is well known that the parameters that characterize the Kerr-Newman black hole satisfy several important geometric inequalities. Remarkably enough, some of these inequalities also hold for dynamical black holes. This kind of inequalities, which are valid in the dynamical and strong field regime, play an important role in the characterization of the gravitational collapse. They are closed related with the cosmic censorship conjecture. In this talk I will review recent results in this subject. (author)
Pisani, Lorenzo
2000-03-01
A new, simple estimate of the diffraction coefficients, to be used in a ray tracing calculation, is derived applying the stationary phase technique to the boundary wave integral. This approach is shown to be the last step (0-dimensions) of a dimensionality reduction procedure which begins with the Kirchhoff's integral method (2-dimensions) and proceeds with the boundary wave approach (1-dimension). While the reduction - from three to two - of the dimensionality, requires the physical optics approximation and the reduction from two to one holds only for perfectly conducting solids with flat faces and spherical or plane incident waves, no additional price is paid to pass from one to zero dimensions. The Zero-Dimensional (ZD) approach is validated through numerical comparison with higher dimensionality methods and analytical (exact) results in a number of test cases.
Sathyachandran, S. K.; Roy, D. P.; Boschetti, L.
2014-12-01
The Fire Radiative Power (FRP) [MW] is a measure of the rate of biomass combustion and can be retrieved from ground based and satellite observations using middle infra-red measurements. The temporal integral of FRP is the Fire Radiative Energy (FRE) [MJ] and is related linearly to the total biomass consumption and so pyrogenic emissions. Satellite derived biomass consumption and emissions estimates have been derived conventionally by computing the summed total FRP, or the average FRP (arithmetic average of FRP retrievals), over spatial geographic grids for fixed time periods. These two methods are prone to estimation bias, especially under irregular sampling conditions such as provided by polar-orbiting satellites, because the FRP can vary rapidly in space and time as a function of the fire behavior. Linear temporal integration of FRP taking into account when the FRP values were observed and using the trapezoidal rule for numerical integration has been suggested as an alternate FRE estimation method. In this study FRP data measured rapidly with a dual-band radiometer over eight prescribed fires are used to compute eight FRE values using the sum, mean and trapezoidal estimation approaches under a variety of simulated irregular sampling conditions. The estimated values are compared to biomass consumed measurements for each of the eight fires to provide insights into which method provides more accurate and precise biomass consumption estimates. The three methods are also applied to continental MODIS FRP data to study their differences using polar orbiting satellite data. The research findings indicate that trapezoidal FRP numerical integration provides the most reliable estimator.
Mobile Watermarking against Geometrical Distortions
Directory of Open Access Journals (Sweden)
Jing Zhang
2015-08-01
Full Text Available Mobile watermarking robust to geometrical distortions is still a great challenge. In mobile watermarking, efficient computation is necessary because mobile devices have very limited resources due to power consumption. In this paper, we propose a low-complexity geometrically resilient watermarking approach based on the optimal tradeoff circular harmonic function (OTCHF correlation filter and the minimum average correlation energy Mellin radial harmonic (MACE-MRH correlation filter. By the rotation, translation and scale tolerance properties of the two kinds of filter, the proposed watermark detector can be robust to geometrical attacks. The embedded watermark is weighted by a perceptual mask which matches very well with the properties of the human visual system. Before correlation, a whitening process is utilized to improve watermark detection reliability. Experimental results demonstrate that the proposed watermarking approach is computationally efficient and robust to geometrical distortions.
Saylor, Rick D.; Ford, Gregory D.
The integration of systems of ordinary differential equations (ODEs) that arise in atmospheric photochemistry is of significant concern to tropospheric and stratospheric chemistry modelers. As a consequence of the stiff nature of these ODE systems, their solution requires a large fraction of the total computational effort in three-dimensional chemical model simulations. Several integration techniques have been proposed and utilized over the years in an attempt to provide computationally efficient, yet accurate, solutions to chemical kinetics ODES. In this work, we present a comparison of some of these techniques and argue that valid comparisons of ODE solvers must take into account the trade-off between solution accuracy and computational efficiency. Misleading comparison results can be obtained by neglecting the fact that any ODE solution method can be made faster or slower by manipulation of the appropriate error tolerances or time steps. Comparisons among ODE solution techniques should therefore attempt to identify which technique can provide the most accurate solution with the least computational effort over the entire range of behavior of each technique. We present here a procedure by which ODE solver comparisons can achieve this goal. Using this methodology, we compare a variety of integration techniques, including methods proposed by Hesstvedt et al. (1978, Int. J. Chem. Kinet.10, 971-994), Gong and Cho (1993, Atmospheric Environment27A, 2147-2160), Young and Boris (1977, J. phys. Chem.81, 2424-2427) and Hindmarsh (1983, In Scientific Computing (edited by Stepleman R. S. et al.), pp. 55-64. North-Holland, Amsterdam). We find that Gear-type solvers such as the Livermore Solver for ordinary differential equations (LSODE) and the sparse-matrix version of LSODE (LSODES) provide the most accurate solution of our test problems with the least computational effort.
A geometric deformable model for echocardiographic image segmentation
Hang, X.; Greenberg, N. L.; Thomas, J. D.
2002-01-01
Gradient vector flow (GVF), an elegant external force for parametric deformable models, can capture object boundaries from both sides. A new geometric deformable model is proposed that combines GVF and the geodesic active contour model. The level set method is used as the numerical method of this model. The model is applied for echocardiographic image segmentation.
Energy Technology Data Exchange (ETDEWEB)
Saar, Martin O. [ETH Zurich (Switzerland); Univ. of Minnesota, Minneapolis, MN (United States); Seyfried, Jr., William E. [Univ. of Minnesota, Minneapolis, MN (United States); Longmire, Ellen K. [Univ. of Minnesota, Minneapolis, MN (United States)
2016-06-24
A total of 12 publications and 23 abstracts were produced as a result of this study. In particular, the compilation of a thermodynamic database utilizing consistent, current thermodynamic data is a major step toward accurately modeling multi-phase fluid interactions with solids. Existing databases designed for aqueous fluids did not mesh well with existing solid phase databases. Addition of a second liquid phase (CO2) magnifies the inconsistencies between aqueous and solid thermodynamic databases. Overall, the combination of high temperature and pressure lab studies (task 1), using a purpose built apparatus, and solid characterization (task 2), using XRCT and more developed technologies, allowed observation of dissolution and precipitation processes under CO2 reservoir conditions. These observations were combined with results from PIV experiments on multi-phase fluids (task 3) in typical flow path geometries. The results of the tasks 1, 2, and 3 were compiled and integrated into numerical models utilizing Lattice-Boltzmann simulations (task 4) to realistically model the physical processes and were ultimately folded into TOUGH2 code for reservoir scale modeling (task 5). Compilation of the thermodynamic database assisted comparisons to PIV experiments (Task 3) and greatly improved Lattice Boltzmann (Task 4) and TOUGH2 simulations (Task 5). PIV (Task 3) and experimental apparatus (Task 1) have identified problem areas in TOUGHREACT code. Additional lab experiments and coding work has been integrated into an improved numerical modeling code.
Barnard, Patrick L.; Foxgrover, Amy C.; Elias, Edwin P.L.; Erikson, Li H.; Hein, James R.; McGann, Mary; Mizell, Kira; Rosenbauer, Robert J.; Swarzenski, Peter W.; Takesue, Renee K.; Wong, Florence L.; Woodrow, Donald L.; Barnard, P.L.; Jaffee, B.E.; Schoellhamer, D.H.
2013-01-01
Over 150 million m3 of sand-sized sediment has disappeared from the central region of the San Francisco Bay Coastal System during the last half century. This enormous loss may reflect numerous anthropogenic influences, such as watershed damming, bay-fill development, aggregate mining, and dredging. The reduction in Bay sediment also appears to be linked to a reduction in sediment supply and recent widespread erosion of adjacent beaches, wetlands, and submarine environments. A unique, multi-faceted provenance study was performed to definitively establish the primary sources, sinks, and transport pathways of beach-sized sand in the region, thereby identifying the activities and processes that directly limit supply to the outer coast. This integrative program is based on comprehensive surficial sediment sampling of the San Francisco Bay Coastal System, including the seabed, Bay floor, area beaches, adjacent rock units, and major drainages. Analyses of sample morphometrics and biological composition (e.g., Foraminifera) were then integrated with a suite of tracers including 87Sr/86Sr and 143Nd/144Nd isotopes, rare earth elements, semi-quantitative X-ray diffraction mineralogy, and heavy minerals, and with process-based numerical modeling, in situ current measurements, and bedform asymmetry to robustly determine the provenance of beach-sized sand in the region.
Virgo, Simon; Ankit, Kumar; Nestler, Britta; Urai, Janos L.
2016-04-01
Crack-seal veins form in a complex interplay of coupled thermal, hydraulic, mechanical and chemical processes. Their formation and cyclic growth involves brittle fracturing and dilatancy, phases of increased fluid flow and the growth of crystals that fill the voids and reestablish the mechanical strength. Existing numerical models of vein formation focus on selected aspects of the coupled process. Until today, no model exists that is able to use a realistic representation of the fracturing AND sealing processes, simultaneously. To address this challenge, we propose the bidirectional coupling of two numerical methods that have proven themselves as very powerful to model the fundamental processes acting in crack-seal systems: Phase-field and the Discrete Element Method (DEM). The phase-field Method was recently successfully extended to model the precipitation of quartz crystals from an aqueous solution and applied to model the sealing of a vein over multiple opening events (Ankit et al., 2013; Ankit et al., 2015a; Ankit et al., 2015b). The advantage over former, purely kinematic approaches is that in phase-field, the crystal growth is modeled based on thermodynamic and kinetic principles. Different driving forces for microstructure evolution, such as chemical bulk free energy, interfacial energy, elastic strain energy and different transport processes, such as mass diffusion and advection, can be coupled and the effect on the evolution process can be studied in 3D. The Discrete Element Method was already used in several studies to model the fracturing of rocks and the incremental growth of veins by repeated fracturing (Virgo et al., 2013; Virgo et al., 2014). Materials in DEM are represented by volumes of packed spherical particles and the response to the material to stress is modeled by interaction of the particles with their nearest neighbours. For rocks, in 3D, the method provides a realistic brittle failure behaviour. Exchange Routines are being developed that
A geometric viewpoint on generalized hydrodynamics
Doyon, Benjamin; Spohn, Herbert; Yoshimura, Takato
2018-01-01
Generalized hydrodynamics (GHD) is a large-scale theory for the dynamics of many-body integrable systems. It consists of an infinite set of conservation laws for quasi-particles traveling with effective ("dressed") velocities that depend on the local state. We show that these equations can be recast into a geometric dynamical problem. They are conservation equations with state-independent quasi-particle velocities, in a space equipped with a family of metrics, parametrized by the quasi-particles' type and speed, that depend on the local state. In the classical hard rod or soliton gas picture, these metrics measure the free length of space as perceived by quasi-particles; in the quantum picture, they weigh space with the density of states available to them. Using this geometric construction, we find a general solution to the initial value problem of GHD, in terms of a set of integral equations where time appears explicitly. These integral equations are solvable by iteration and provide an extremely efficient solution algorithm for GHD.
Antenna with Dielectric Having Geometric Patterns
Dudley, Kenneth L. (Inventor); Elliott, Holly A. (Inventor); Cravey, Robin L. (Inventor); Connell, John W. (Inventor); Ghose, Sayata (Inventor); Watson, Kent A. (Inventor); Smith, Jr., Joseph G. (Inventor)
2013-01-01
An antenna includes a ground plane, a dielectric disposed on the ground plane, and an electrically-conductive radiator disposed on the dielectric. The dielectric includes at least one layer of a first dielectric material and a second dielectric material that collectively define a dielectric geometric pattern, which may comprise a fractal geometry. The radiator defines a radiator geometric pattern, and the dielectric geometric pattern is geometrically identical, or substantially geometrically identical, to the radiator geometric pattern.
de Rosnay, Patricia; Hólm, Elias; Bonavita, Massimo; English, Steve
2017-04-01
The European Centre for Medium-Range Weather Forecasts (ECMWF) system relies on an Earth System approach focusing on atmosphere, ocean, waves, land, and sea ice. Different data assimilation methods are used for the each component of the Earth System. A hybrid 4D-Var is used for the atmosphere, a simplified sea-surface temperature (SST) and sea ice analysis is used for medium-range forecasts and for the reanalyses (ERA-Interim and ERA5). The ECMWF land and atmosphere data assimilation systems are weakly coupled, using a coupled land-atmosphere background forecast and separate analyses for the atmosphere and for the surface (soil moisture and snow). Conventional and satellite observations that inform on the state of both subsystems are assimilated. They are located at the land-atmosphere interface and include two-metre temperature and relative humidity, snow depth, and soil moisture. In this presentation we present the land-atmosphere weakly coupled assimilation currently used at ECMWF for Numerical Weather Prediction (NWP) purpose. Perspectives of coupling enhancement using Ensemble Data Assimilaton (EDA) and EDA-based cross correlation estimates with coupling at the outer loop level of the atmospheric 4D-Var are discussed.
Rusyn, Ivan; Sedykh, Alexander; Guyton, Kathryn Z.; Tropsha, Alexander
2012-01-01
Quantitative structure-activity relationship (QSAR) models are widely used for in silico prediction of in vivo toxicity of drug candidates or environmental chemicals, adding value to candidate selection in drug development or in a search for less hazardous and more sustainable alternatives for chemicals in commerce. The development of traditional QSAR models is enabled by numerical descriptors representing the inherent chemical properties that can be easily defined for any number of molecules; however, traditional QSAR models often have limited predictive power due to the lack of data and complexity of in vivo endpoints. Although it has been indeed difficult to obtain experimentally derived toxicity data on a large number of chemicals in the past, the results of quantitative in vitro screening of thousands of environmental chemicals in hundreds of experimental systems are now available and continue to accumulate. In addition, publicly accessible toxicogenomics data collected on hundreds of chemicals provide another dimension of molecular information that is potentially useful for predictive toxicity modeling. These new characteristics of molecular bioactivity arising from short-term biological assays, i.e., in vitro screening and/or in vivo toxicogenomics data can now be exploited in combination with chemical structural information to generate hybrid QSAR–like quantitative models to predict human toxicity and carcinogenicity. Using several case studies, we illustrate the benefits of a hybrid modeling approach, namely improvements in the accuracy of models, enhanced interpretation of the most predictive features, and expanded applicability domain for wider chemical space coverage. PMID:22387746
Kim, Hanna; Xie, Linmao; Min, Ki-Bok; Bae, Seongho; Stephansson, Ove
2017-12-01
It is desirable to combine the stress measurement data produced by different methods to obtain a more reliable estimation of in situ stress. We present a regional case study of integrated in situ stress estimation by hydraulic fracturing, observations of borehole breakouts and drilling-induced fractures, and numerical modeling of a 1 km-deep borehole (EXP-1) in Pohang, South Korea. Prior to measuring the stress, World Stress Map (WSM) and modern field data in the Korean Peninsula are used to construct a best estimate stress model in this area. Then, new stress data from hydraulic fracturing and borehole observations is added to determine magnitude and orientation of horizontal stresses. Minimum horizontal principal stress is estimated from the shut-in pressure of the hydraulic fracturing measurement at a depth of about 700 m. The horizontal stress ratios ( S Hmax/ S hmin) derived from hydraulic fracturing, borehole breakout, and drilling-induced fractures are 1.4, 1.2, and 1.1-1.4, respectively, and the average orientations of the maximum horizontal stresses derived by field methods are N138°E, N122°E, and N136°E, respectively. The results of hydraulic fracturing and borehole observations are integrated with a result of numerical modeling to produce a final rock stress model. The results of the integration give in situ stress ratios of 1.3/1.0/0.8 ( S Hmax/ S V/ S hmin) with an average azimuth of S Hmax in the orientation range of N130°E-N136°E. It is found that the orientation of S Hmax is deviated by more than 40° clockwise compared to directions reported for the WSM in southeastern Korean peninsula.
Geometric curvature and phase of the Rabi model
Energy Technology Data Exchange (ETDEWEB)
Mao, Lijun; Huai, Sainan; Guo, Liping; Zhang, Yunbo, E-mail: ybzhang@sxu.edu.cn
2015-11-15
We study the geometric curvature and phase of the Rabi model. Under the rotating-wave approximation (RWA), we apply the gauge independent Berry curvature over a surface integral to calculate the Berry phase of the eigenstates for both single and two-qubit systems, which is found to be identical with the system of spin-1/2 particle in a magnetic field. We extend the idea to define a vacuum-induced geometric curvature when the system starts from an initial state with pure vacuum bosonic field. The induced geometric phase is related to the average photon number in a period which is possible to measure in the qubit–cavity system. We also calculate the geometric phase beyond the RWA and find an anomalous sudden change, which implies the breakdown of the adiabatic theorem and the Berry phases in an adiabatic cyclic evolution are ill-defined near the anti-crossing point in the spectrum.
Pizzati, Mattia; Cavozzi, Cristian; Magistroni, Corrado; Storti, Fabrizio
2016-04-01
Fracture density pattern predictions with low uncertainty is a fundamental issue for constraining fluid flow pathways in thrust-related anticlines in the frontal parts of thrust-and-fold belts and accretionary prisms, which can also provide plays for hydrocarbon exploration and development. Among the drivers that concur to determine the distribution of fractures in fold-and-thrust-belts, the complex kinematic pathways of folded structures play a key role. In areas with scarce and not reliable underground information, analogue modelling can provide effective support for developing and validating reliable hypotheses on structural architectures and their evolution. In this contribution, we propose a working method that combines analogue and numerical modelling. We deformed a sand-silicone multilayer to eventually produce a non-cylindrical thrust-related anticline at the wedge toe, which was our test geological structure at the reservoir scale. We cut 60 serial cross-sections through the central part of the deformed model to analyze faults and folds geometry using dedicated software (3D Move). The cross-sections were also used to reconstruct the 3D geometry of reference surfaces that compose the mechanical stratigraphy thanks to the use of the software GoCad. From the 3D model of the experimental anticline, by using 3D Move it was possible to calculate the cumulative stress and strain underwent by the deformed reference layers at the end of the deformation and also in incremental steps of fold growth. Based on these model outputs it was also possible to predict the orientation of three main fractures sets (joints and conjugate shear fractures) and their occurrence and density on model surfaces. The next step was the upscaling of the fracture network to the entire digital model volume, to create DFNs.
Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach.
Arrieta, Jorge; Cartwright, Julyan H E; Gouillart, Emmanuelle; Piro, Nicolas; Piro, Oreste; Tuval, Idan
2015-01-01
Mixing fluid in a container at low Reynolds number--in an inertialess environment--is not a trivial task. Reciprocating motions merely lead to cycles of mixing and unmixing, so continuous rotation, as used in many technological applications, would appear to be necessary. However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase. We show using journal-bearing flow as a model that such geometric mixing is a general tool for using deformable boundaries that return to the same position to mix fluid at low Reynolds number. We then simulate a biological example: we show that mixing in the stomach functions because of the "belly phase," peristaltic movement of the walls in a cyclical fashion introduces a geometric phase that avoids unmixing.
Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach.
Directory of Open Access Journals (Sweden)
Jorge Arrieta
Full Text Available Mixing fluid in a container at low Reynolds number--in an inertialess environment--is not a trivial task. Reciprocating motions merely lead to cycles of mixing and unmixing, so continuous rotation, as used in many technological applications, would appear to be necessary. However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase. We show using journal-bearing flow as a model that such geometric mixing is a general tool for using deformable boundaries that return to the same position to mix fluid at low Reynolds number. We then simulate a biological example: we show that mixing in the stomach functions because of the "belly phase," peristaltic movement of the walls in a cyclical fashion introduces a geometric phase that avoids unmixing.
Combining the multilevel fast multipole method with the uniform geometrical theory of diffraction
Directory of Open Access Journals (Sweden)
A. Tzoulis
2005-01-01
Full Text Available The presence of arbitrarily shaped and electrically large objects in the same environment leads to hybridization of the Method of Moments (MoM with the Uniform Geometrical Theory of Diffraction (UTD. The computation and memory complexity of the MoM solution is improved with the Multilevel Fast Multipole Method (MLFMM. By expanding the k-space integrals in spherical harmonics, further considerable amount of memory can be saved without compromising accuracy and numerical speed. However, until now MoM-UTD hybrid methods are restricted to conventional MoM formulations only with Electric Field Integral Equation (EFIE. In this contribution, a MLFMM-UTD hybridization for Combined Field Integral Equation (CFIE is proposed and applied within a hybrid Finite Element - Boundary Integral (FEBI technique. The MLFMM-UTD hybridization is performed at the translation procedure on the various levels of the MLFMM, using a far-field approximation of the corresponding translation operator. The formulation of this new hybrid technique is presented, as well as numerical results.
International Nuclear Information System (INIS)
Fota, C.
1996-12-01
This work is part of an evaluation of a high resolution time encoder implemented as a circular vernier. Two integrated technologies have been used, silicon CMOS and GaAs HEMT. After a short survey of the existing time encoding techniques, we propose a digital method using a circular time vernier built around two ring oscillators. We present the benefits of such a technique, a detailed analysis of the vernier, and simulation results. Technological spreads that are critical for such a time encoder have been measured on a silicon ship with 0.8 micron gate length CMOS technology. The achievable resolution is derived from the results. The frequencies dictated by the circular vernier architecture reach a few hundred Megahertz, the chip layout is thus critical, as showed from the measurements on a 0.3 micron GaAs HEMT chip. Measurements are compared with simulations for each chip. Several other circular vernier layouts are proposed in order to improve the results. A mathematical model of a calibration phase lock loop of the ring oscillators on a reference clock is also presented. (author)
Directory of Open Access Journals (Sweden)
Woo-Young Jung
2015-04-01
Full Text Available For the solution of geometrically nonlinear analysis of plates and shells, the formulation of a nonlinear nine-node refined first-order shear deformable element-based Lagrangian shell element is presented. Natural co-ordinate-based higher order transverse shear strains are used in present shell element. Using the assumed natural strain method with proper interpolation functions, the present shell element generates neither membrane nor shear locking behavior even when full integration is used in the formulation. Furthermore, a refined first-order shear deformation theory for thin and thick shells, which results in parabolic through-thickness distribution of the transverse shear strains from the formulation based on the third-order shear deformation theory, is proposed. This formulation eliminates the need for shear correction factors in the first-order theory. To avoid difficulties resulting from large increments of the rotations, a scheme of attached reference system is used for the expression of rotations of shell normal. Numerical examples demonstrate that the present element behaves reasonably satisfactorily either for the linear or for geometrically nonlinear analysis of thin and thick plates and shells with large displacement but small strain. Especially, the nonlinear results of slit annular plates with various loads provided the benchmark to test the accuracy of related numerical solutions.
Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach
Arrieta, Jorge; Cartwright, Julyan H. E.; Gouillart, Emmanuelle; Piro, Nicolas; Piro, Oreste; Tuval, Idan
2012-01-01
© 2015 Arrieta et al. Mixing fluid in a container at low Reynolds number - in an inertialess environment - is not a trivial task. Reciprocating motions merely lead to cycles of mixing and unmixing, so continuous rotation, as used in many technological applications, would appear to be necessary. However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase.We show using journal-bearing flow as a model that such geometric mixing is a general tool...
Numerical evolutions beyond our belief
de Almeida, Guilherme; Colégio Militar Associação Portuguesa de Astrônomos Amadores (APAA) Lisboa – Portugal
2014-01-01
The everyday life situations gave us a good enough training to deal with numerical evolutions operated by arithmetic progressions, so in this specific case we can make good numerical predictions. But our common sense is not usually prepared to deal with numbers that grow, or shrink, according to geometrical progressions. In the last cases, our intuition strongly fails, showing that our intuition is not always right. We also fail in comparing some other situations which we are not trained. Thi...
Theory and numerics for shape optimization in superconductivity
Energy Technology Data Exchange (ETDEWEB)
Heese, H.
2006-07-21
We consider a mathematical model for a thin superconducting film which is magnetically shielded by permanent magnets in order to improve the current carrying capability of the film. In a first part we study the behaviour of the magnetic field of the combined system, which is characterized via a boundary value problem for Laplace's equation for the quasi-scalar magnetic potential. In a second part we formulate and analyze a related geometric optimization problem that can be interpreted as a homogenization of the current distribution in the superconducting film by means of shape optimization for the magnet boundaries. We present a uniqueness and existence analysis for the boundary value problem based on boundary integral equations. The theoretical studies are complemented by a numerical approximation scheme for the potential, for which we prove exponential convergence rates under appropriate smoothness assumptions on the geometry. As central result for the geometric optimization problem we prove the differentiable dependence of the current distribution on the geometry, which also leads to an abstract existence result. Based on the differentiability result we derive two numerical schemes to realize the geometric optimization problem iteratively. The first approach relies on explicit parametrizations for the boundaries leading to a steepest descent scheme. The second approach uses level set methods which are based on an implicit boundary representation. The feasibility of both approaches is shown in a variety of examples. (orig.)
Directory of Open Access Journals (Sweden)
Costantino Masciopinto
2017-11-01
Full Text Available Aquifer over-exploitation may increase coastal seawater intrusion by reducing freshwater availability. Fractured subsurface formations commonly host important freshwater reservoirs along sea coasts. These water resources are particularly vulnerable to the contamination due to seawater infiltration occurring through rapid pathways via fractures. Modeling of density driven fluid flow in fractured aquifers is complex, as their hydrodynamics are controlled by interactions between preferential flow pathways, 3D interconnected fractures and rock-matrix porosity distribution. Moreover, physical heterogeneities produce highly localized water infiltrations that make the modeling of saltwater transport in such aquifers very challenging. The new approach described in this work provides a reliable hydrogeological model suitable to reproduce local advancements of the freshwater/saltwater wedge in coastal aquifers. The proposed model use flow simulation results to estimate water salinities in groundwater at a specific depth (1 m below water table by means of positions of the Ghyben-Herzberg saltwater/freshwater sharp interface along the coast. Measurements of salinity in 25 boreholes (i.e., salinity profiles have been used for the model calibration. The results provide the groundwater salinity map in freshwater/saltwater transition coastal zones of the Bari (Southern Italy fractured aquifer. Non-invasive geophysical measurements in groundwater, particularly into vertical 2D vertical cross-sections, were carried out by using the electrical resistivity tomography (ERT in order to validate the model results. The presented integrated approach is very easy to apply and gives very realistic salinity maps in heterogeneous aquifers, without simulating density driven water flow in fractures.
On numerical Bessel transformation
International Nuclear Information System (INIS)
Sommer, B.; Zabolitzky, J.G.
1979-01-01
The authors present a computer program to calculate the three dimensional Fourier or Bessel transforms and definite integrals with Bessel functions. Numerical integration of systems containing Bessel functions occurs in many physical problems, e.g. electromagnetic form factor of nuclei, all transitions involving multipole expansions at high momenta. Filon's integration rule is extended to spherical Bessel functions. The numerical error is of the order of the Simpson error term of the function which has to be transformed. Thus one gets a stable integral even at large arguments of the transformed function. (Auth.)
Analysing Geometric Obstacles. A Theorem on d-Elements
Directory of Open Access Journals (Sweden)
A. N. Bozhko
2017-01-01
Full Text Available The product geometry is a fundamental constructive property that has a strong impact on the basic design choices of the assembly process: the product assembly flotation and decomposition into assembly units. The assembly process must be mounted so that the previously set components and elements of technological system could not create geometric obstacles for the main and auxiliary working moves. The paper considers mathematical modelling methods of geometric constraints and restrictions in computer-aided design systems.Publications, about computer-aided design propose numerous varieties of the so-called direct modelling method for geometric obstacles. The principle of this method is to verify the intersection of the geometric model of a mobile object with a static fragment when the first moves along the chosen straight –line (most often trajectory.It turned out that even in the best version, the direct method is computationally very expensive for products of medium complexity, consisting of several dozen components. Therefore, it is important and urgent to determine the minimum number of geometric verifications, the results of which can be used to synthesize the correct design choices: the assembly flotation and product decomposition into assembly units.The paper proposes a theoretical-lattice formalization of the geometric obstacle of the product. It is shown that the aggregate of all constructive fragments that are assembled independently and do not contain geometric obstacles form a closed algebraic structure that is a lattice. A theorem on d-elements is proved. This theorem allows us to solve the problem of geometric obstacle by cost-conscious algebraic methods. The paper offers three ways for lattice generation: analysis of anti-chains "top-down", lattice reconstruction using a set of generative elements, and probabilistic conclusion based on the Bayesian networks of confidence.
Geometric procedures for civil engineers
Tonias, Elias C
2016-01-01
This book provides a multitude of geometric constructions usually encountered in civil engineering and surveying practice. A detailed geometric solution is provided to each construction as well as a step-by-step set of programming instructions for incorporation into a computing system. The volume is comprised of 12 chapters and appendices that may be grouped in three major parts: the first is intended for those who love geometry for its own sake and its evolution through the ages, in general, and, more specifically, with the introduction of the computer. The second section addresses geometric features used in the book and provides support procedures used by the constructions presented. The remaining chapters and the appendices contain the various constructions. The volume is ideal for engineering practitioners in civil and construction engineering and allied areas.
Geometric group theory an introduction
Löh, Clara
2017-01-01
Inspired by classical geometry, geometric group theory has in turn provided a variety of applications to geometry, topology, group theory, number theory and graph theory. This carefully written textbook provides a rigorous introduction to this rapidly evolving field whose methods have proven to be powerful tools in neighbouring fields such as geometric topology. Geometric group theory is the study of finitely generated groups via the geometry of their associated Cayley graphs. It turns out that the essence of the geometry of such groups is captured in the key notion of quasi-isometry, a large-scale version of isometry whose invariants include growth types, curvature conditions, boundary constructions, and amenability. This book covers the foundations of quasi-geometry of groups at an advanced undergraduate level. The subject is illustrated by many elementary examples, outlooks on applications, as well as an extensive collection of exercises.
International Nuclear Information System (INIS)
Egorov, Alexander A
2012-01-01
We consider theoretical and numerical methods for studying propagation and scattering of laser radiation of eigenmodes and non-eigenmodes in an irregular integrated-optical waveguide. Scattering of non-eigenmodes in an irregular integratedoptical waveguide is investigated for the first time. We present the calculated dispersion curves for TE and TM eigenmodes and TE non-eigenmodes. For the leaky TE 0 modes we plot the dependence of the complex dispersion relation and show the vertical complex profile of the field. The dependence of the scattered laser radiation field on the effective refractive index is obtained for the given parameters of the waveguide. We compare for the first time the calculated complex scattering diagram of laser radiation outside the waveguide layer in the plane, perpendicular to the plane of incidence, for the leaky and guided TE 0 modes.
Geometrical evaluation of the Maslov index
International Nuclear Information System (INIS)
Takahashi, Satoshi; Takatsuka, Kazuo
2004-01-01
A geometrical method to calculate the Maslov index, which is an important part of the quantum phase, is proposed. This method is particularly useful for the recently proposed amplitude-free quasicorrelation function approach for the quantization of chaos [K. Hotta and K. Takatsuka, J. Phys. A 36, 4785 (2003)]. In this theory the Maslov index is involved with no need to calculate the amplitude factor, which is usually obtained through integration of the stability matrix. Since this matrix constitutes the major origin of difficulty in semiclassical quantization of chaos and since its integration is time consuming, the present method, which avoids the stability matrix, should assist in opening a gate for practical semiclassical quantization of chaos in a large molecular system
Directory of Open Access Journals (Sweden)
Tetsuya Ishida
2018-03-01
Full Text Available In November 2011, the Japanese government resolved to build “Revival Roads” in the Tohoku region to accelerate the recovery from the Great East Japan Earthquake of March 2011. Because the Tohoku region experiences such cold and snowy weather in winter, complex degradation from a combination of frost damage, chloride attack from de-icing agents, alkali–silica reaction, cracking and fatigue is anticipated. Thus, to enhance the durability performance of road structures, particularly reinforced concrete (RC bridge decks, multiple countermeasures are proposed: a low water-to-cement ratio in the mix, mineral admixtures such as ground granulated blast furnace slag and/or fly ash to mitigate the risks of chloride attack and alkali–silica reaction, anticorrosion rebar and 6% entrained air for frost damage. It should be noted here that such high durability specifications may conversely increase the risk of early age cracking caused by temperature and shrinkage due to the large amounts of cement and the use of mineral admixtures. Against this background, this paper presents a numerical simulation of early age deformation and cracking of RC bridge decks with full 3D multiscale and multi-chemo-physical integrated analysis. First, a multiscale constitutive model of solidifying cementitious materials is briefly introduced based on systematic knowledge coupling microscopic thermodynamic phenomena and microscopic structural mechanics. With the aim to assess the early age thermal and shrinkage-induced cracks on real bridge deck, the study began with extensive model validations by applying the multiscale and multi-physical integrated analysis system to small specimens and mock-up RC bridge deck specimens. Then, through the application of the current computational system, factors that affect the generation and propagation of early age thermal and shrinkage-induced cracks are identified via experimental validation and full-scale numerical simulation on real
Geometric Langlands From Six Dimensions
Witten, Edward
2010-01-01
Geometric Langlands duality is usually formulated as a statement about Riemann surfaces, but it can be naturally understood as a consequence of electric-magnetic duality of four-dimensional gauge theory. This duality in turn is naturally understood as a consequence of the existence of a certain exotic supersymmetric conformal field theory in six dimensions. The same six-dimensional theory also gives a useful framework for understanding some recent mathematical results involving a counterpart of geometric Langlands duality for complex surfaces. (This article is based on a lecture at the Raoul Bott celebration, Montreal, June 2008.)
Geometric scaling as traveling waves
International Nuclear Information System (INIS)
Munier, S.; Peschanski, R.
2003-01-01
We show the relevance of the nonlinear Fisher and Kolmogorov-Petrovsky-Piscounov (KPP) equation to the problem of high energy evolution of the QCD amplitudes. We explain how the traveling wave solutions of this equation are related to geometric scaling, a phenomenon observed in deep-inelastic scattering experiments. Geometric scaling is for the first time shown to result from an exact solution of nonlinear QCD evolution equations. Using general results on the KPP equation, we compute the velocity of the wave front, which gives the full high energy dependence of the saturation scale
Murga, Alicia; Sano, Yusuke; Kawamoto, Yoichi; Ito, Kazuhide
2017-10-01
Mechanical and passive ventilation strategies directly impact indoor air quality. Passive ventilation has recently become widespread owing to its ability to reduce energy demand in buildings, such as the case of natural or cross ventilation. To understand the effect of natural ventilation on indoor environmental quality, outdoor-indoor flow paths need to be analyzed as functions of urban atmospheric conditions, topology of the built environment, and indoor conditions. Wind-driven natural ventilation (e.g., cross ventilation) can be calculated through the wind pressure coefficient distributions of outdoor wall surfaces and openings of a building, allowing the study of indoor air parameters and airborne contaminant concentrations. Variations in outside parameters will directly impact indoor air quality and residents' health. Numerical modeling can contribute to comprehend these various parameters because it allows full control of boundary conditions and sampling points. In this study, numerical weather prediction modeling was used to calculate wind profiles/distributions at the atmospheric scale, and computational fluid dynamics was used to model detailed urban and indoor flows, which were then integrated into a dynamic downscaling analysis to predict specific urban wind parameters from the atmospheric to built-environment scale. Wind velocity and contaminant concentration distributions inside a factory building were analyzed to assess the quality of the human working environment by using a computer simulated person. The impact of cross ventilation flows and its variations on local average contaminant concentration around a factory worker, and inhaled contaminant dose, were then discussed.
Dropwise Condensation Enhancement on Geometric Features
Zhao, Yajing; Preston, Daniel J.; Lu, Zhengmao; Wang, Evelyn N.
Dropwise condensation, which has been demonstrated to exhibit a 5-7X higher heat transfer coefficient compared with state-of-the-art filmwise condensation, contributes to energy savings in a wide range of applications such as desalination systems, steam cycles and dew harvesting. In order to enhance dropwise condensation performance, previous studies have investigated the effects of surface geometric features on droplet growth rates and found that bumps protruding from surfaces can effectively promote dropwise condensation. In this work, we show that while bumps on surfaces enable droplets to grow faster in some cases, there are also cases where bumps on surfaces actually degrade dropwise condensation. We numerically simulated and experimentally demonstrated that even the same surface geometric feature can exert completely opposite effects on dropwise condensation of water under two different working conditions (pure vapor vs. air vapor mixture). This phenomenon is explained by comparing the heat and mass transfer resistance of the surface structure to that of the vapor transport during dropwise condensation. We expect that the fundamental understanding developed in this study will provide useful guidelines for relevant condensation applications.
Constantinides, E. D.; Marhefka, R. J.
1994-01-01
A uniform geometrical optics (UGO) and an extended uniform geometrical theory of diffraction (EUTD) are developed for evaluating high frequency electromagnetic (EM) fields within transition regions associated with a two and three dimensional smooth caustic of reflected rays and a composite shadow boundary formed by the caustic termination or the confluence of the caustic with the reflection shadow boundary (RSB). The UGO is a uniform version of the classic geometrical optics (GO). It retains the simple ray optical expressions of classic GO and employs a new set of uniform reflection coefficients. The UGO also includes a uniform version of the complex GO ray field that exists on the dark side of the smooth caustic. The EUTD is an extension of the classic uniform geometrical theory of diffraction (UTD) and accounts for the non-ray optical behavior of the UGO reflected field near caustics by using a two-variable transition function in the expressions for the edge diffraction coefficients. It also uniformly recovers the classic UTD behavior of the edge diffracted field outside the composite shadow boundary transition region. The approach employed for constructing the UGO/EUTD solution is based on a spatial domain physical optics (PO) radiation integral representation for the fields which is then reduced using uniform asymptotic procedures. The UGO/EUTD analysis is also employed to investigate the far-zone RCS problem of plane wave scattering from two and three dimensional polynomial defined surfaces, and uniform reflection, zero-curvature, and edge diffraction coefficients are derived. Numerical results for the scattering and diffraction from cubic and fourth order polynomial strips are also shown and the UGO/EUTD solution is validated by comparison to an independent moment method (MM) solution. The UGO/EUTD solution is also compared with the classic GO/UTD solution. The failure of the classic techniques near caustics and composite shadow boundaries is clearly
Geometric methods for discrete dynamical systems
Easton, Robert W
1998-01-01
This book looks at dynamics as an iteration process where the output of a function is fed back as an input to determine the evolution of an initial state over time. The theory examines errors which arise from round-off in numerical simulations, from the inexactness of mathematical models used to describe physical processes, and from the effects of external controls. The author provides an introduction accessible to beginning graduate students and emphasizing geometric aspects of the theory. Conley''s ideas about rough orbits and chain-recurrence play a central role in the treatment. The book will be a useful reference for mathematicians, scientists, and engineers studying this field, and an ideal text for graduate courses in dynamical systems.
Random geometric graphs with general connection functions
Dettmann, Carl P.; Georgiou, Orestis
2016-03-01
In the original (1961) Gilbert model of random geometric graphs, nodes are placed according to a Poisson point process, and links formed between those within a fixed range. Motivated by wireless ad hoc networks "soft" or "probabilistic" connection models have recently been introduced, involving a "connection function" H (r ) that gives the probability that two nodes at distance r are linked (directly connect). In many applications (not only wireless networks), it is desirable that the graph is connected; that is, every node is linked to every other node in a multihop fashion. Here the connection probability of a dense network in a convex domain in two or three dimensions is expressed in terms of contributions from boundary components for a very general class of connection functions. It turns out that only a few quantities such as moments of the connection function appear. Good agreement is found with special cases from previous studies and with numerical simulations.
Point- and curve-based geometric conflation
López-Vázquez, C.
2013-01-01
Geometric conflation is the process undertaken to modify the coordinates of features in dataset A in order to match corresponding ones in dataset B. The overwhelming majority of the literature considers the use of points as features to define the transformation. In this article we present a procedure to consider one-dimensional curves also, which are commonly available as Global Navigation Satellite System (GNSS) tracks, routes, coastlines, and so on, in order to define the estimate of the displacements to be applied to each object in A. The procedure involves three steps, including the partial matching of corresponding curves, the computation of some analytical expression, and the addition of a correction term in order to satisfy basic cartographic rules. A numerical example is presented. © 2013 Copyright Taylor and Francis Group, LLC.
In Defence of Geometrical Algebra
Blasjo, V.N.E.
The geometrical algebra hypothesis was once the received interpretation of Greek mathematics. In recent decades, however, it has become anathema to many. I give a critical review of all arguments against it and offer a consistent rebuttal case against the modern consensus. Consequently, I find that
Geometric quantization and general relativity
International Nuclear Information System (INIS)
Souriau, J.-M.
1977-01-01
The purpose of geometric quantization is to give a rigorous mathematical content to the 'correspondence principle' between classical and quantum mechanics. The main tools are borrowed on one hand from differential geometry and topology (differential manifolds, differential forms, fiber bundles, homology and cohomology, homotopy), on the other hand from analysis (functions of positive type, infinite dimensional group representations, pseudo-differential operators). Some satisfactory results have been obtained in the study of dynamical systems, but some fundamental questions are still waiting for an answer. The 'geometric quantization of fields', where some further well known difficulties arise, is still in a preliminary stage. In particular, the geometric quantization on the gravitational field is still a mere project. The situation is even more uncertain due to the fact that there is no experimental evidence of any quantum gravitational effect which could give us a hint towards what we are supposed to look for. The first level of both Quantum Theory, and General Relativity describes passive matter: influence by the field without being a source of it (first quantization and equivalence principle respectively). In both cases this is only an approximation (matter is always a source). But this approximation turns out to be the least uncertain part of the description, because on one hand the first quantization avoids the problems of renormalization and on the other hand the equivalence principle does not imply any choice of field equations (it is known that one can modify Einstein equations at short distances without changing their geometrical properties). (Auth.)
Geometric scaling in exclusive processes
International Nuclear Information System (INIS)
Munier, S.; Wallon, S.
2003-01-01
We show that according to the present understanding of the energy evolution of the observables measured in deep-inelastic scattering, the photon-proton scattering amplitude has to exhibit geometric scaling at each impact parameter. We suggest a way to test this experimentally at HERA. A qualitative analysis based on published data is presented and discussed. (orig.)
Height and Tilt Geometric Texture
DEFF Research Database (Denmark)
Andersen, Vedrana; Desbrun, Mathieu; Bærentzen, Jakob Andreas
2009-01-01
compromise between functionality and simplicity: it can efficiently handle and process geometric texture too complex to be represented as a height field, without having recourse to full blown mesh editing algorithms. The height-and-tilt representation proposed here is fully intrinsic to the mesh, making...
Geometric phases and quantum computation
International Nuclear Information System (INIS)
Vedral, V.
2005-01-01
Full text: In my lectures I will talk about the notion of the geometric phase and explain its relevance for both fundamental quantum mechanics as well as quantum computation. The phase will be at first introduced via the idea of Pancharatnam which involves interference of three or more light beams. This notion will then be generalized to the evolving quantum systems. I will discuss both pure and mixed states as well as unitary and non-unitary evolutions. I will also show how the concept of the vacuum induced geometric phase arises in quantum optics. A simple measurement scheme involving a Mach Zehnder interferometer will be presented and will be used to illustrate all the concepts in the lecture. Finally, I will expose a simple generalization of the geometric phase to evolving degenerate states. This will be seen to lead to the possibility of universal quantum computation using geometric effects only. Moreover, this contains a promise of intrinsically fault tolerant quantum information processing, whose prospects will be outlined at the end of the lecture. (author)
Cartan's geometrical structure of supergravity
International Nuclear Information System (INIS)
Baaklini, N.S.
1977-06-01
The geometrical partnership of the vierbein and the spin-3/2 field in the structure of the supergravity Lagrangian is emphasized. Both fields are introduced as component of the same matrix differential form. The only local symmetry of the theory is SL(2,C)
International Nuclear Information System (INIS)
Klimkowski, Lukasz; Nagy, Stanislaw; Papiernik, Bartosz; Orlic, Bogdan; Kempka, Thomas
2015-01-01
Natural gas from the Zalecze gas field located in the Fore-Sudetic Monocline of the Southern Permian Basin has been produced since November 1973, and continuous gas production led to a decrease in the initial reservoir pressure from 151 bar to about 22 bar until 2010. We investigated a prospective enhanced gas recovery operation at the Zalecze gas field by coupled numerical hydro-mechanical simulations to account for the CO 2 storage capacity, trapping efficiency and mechanical integrity of the reservoir, cap-rock and regional faults. Dynamic flow simulations carried out indicate a CO 2 storage capacity of 106.6 Mt with a trapping efficiency of about 43% (45.8 Mt CO 2 ) established after 500 years of simulation. Two independent strategies on the assessment of mechanical integrity were followed by two different modeling groups resulting in the implementation of field- to regional-scale hydro-mechanical simulation models. The simulation results based on application of different constitutive laws for the lithological units show deviations of 31% to 93% for the calculated maximum vertical displacements at the reservoir top. Nevertheless, results of both simulation strategies indicate that fault reactivation generating potential leakage pathways from the reservoir to shallower units is very unlikely due to the low fault slip tendency (close to zero) in the Zechstein cap-rocks. Consequently, our simulation results also emphasise that the supra- and sub-saliferous fault systems at the Zalecze gas field are independent and very likely not hydraulically connected. Based on our simulation results derived from two independent modeling strategies with similar simulation results on fault and cap-rock integrity, we conclude that the investigated enhanced gas recovery scheme is feasible, with a negligibly low risk of relevant fault reactivation or formation fluid leakage through the Zechstein cap-rocks. (authors)
Efficient orbit integration by manifold correction methods.
Fukushima, Toshio
2005-12-01
Triggered by a desire to investigate, numerically, the planetary precession through a long-term numerical integration of the solar system, we developed a new formulation of numerical integration of orbital motion named manifold correct on methods. The main trick is to rigorously retain the consistency of physical relations, such as the orbital energy, the orbital angular momentum, or the Laplace integral, of a binary subsystem. This maintenance is done by applying a correction to the integrated variables at each integration step. Typical methods of correction are certain geometric transformations, such as spatial scaling and spatial rotation, which are commonly used in the comparison of reference frames, or mathematically reasonable operations, such as modularization of angle variables into the standard domain [-pi, pi). The form of the manifold correction methods finally evolved are the orbital longitude methods, which enable us to conduct an extremely precise integration of orbital motions. In unperturbed orbits, the integration errors are suppressed at the machine epsilon level for an indefinitely long period. In perturbed cases, on the other hand, the errors initially grow in proportion to the square root of time and then increase more rapidly, the onset of which depends on the type and magnitude of the perturbations. This feature is also realized for highly eccentric orbits by applying the same idea as used in KS-regularization. In particular, the introduction of time elements greatly enhances the performance of numerical integration of KS-regularized orbits, whether the scaling is applied or not.
A geometric framework for evaluating rare variant tests of association.
Liu, Keli; Fast, Shannon; Zawistowski, Matthew; Tintle, Nathan L
2013-05-01
The wave of next-generation sequencing data has arrived. However, many questions still remain about how to best analyze sequence data, particularly the contribution of rare genetic variants to human disease. Numerous statistical methods have been proposed to aggregate association signals across multiple rare variant sites in an effort to increase statistical power; however, the precise relation between the tests is often not well understood. We present a geometric representation for rare variant data in which rare allele counts in case and control samples are treated as vectors in Euclidean space. The geometric framework facilitates a rigorous classification of existing rare variant tests into two broad categories: tests for a difference in the lengths of the case and control vectors, and joint tests for a difference in either the lengths or angles of the two vectors. We demonstrate that genetic architecture of a trait, including the number and frequency of risk alleles, directly relates to the behavior of the length and joint tests. Hence, the geometric framework allows prediction of which tests will perform best under different disease models. Furthermore, the structure of the geometric framework immediately suggests additional classes and types of rare variant tests. We consider two general classes of tests which show robustness to noncausal and protective variants. The geometric framework introduces a novel and unique method to assess current rare variant methodology and provides guidelines for both applied and theoretical researchers. © 2013 Wiley Periodicals, Inc.
Earth Radii Used in Numerical Weather Models
2005-09-26
In the development of numerical atmospheric models , many simplifying assumptions are made. One of the simplifying assumptions is that the Earth can...geometric properties within or among spatial reference frames. This paper serves to document the values used for the Earth’s radius by several operational numerical atmospheric models for use in the SRM.
Measurement system and model for simultaneously measuring 6DOF geometric errors.
Zhao, Yuqiong; Zhang, Bin; Feng, Qibo
2017-09-04
A measurement system to simultaneously measure six degree-of-freedom (6DOF) geometric errors is proposed. The measurement method is based on a combination of mono-frequency laser interferometry and laser fiber collimation. A simpler and more integrated optical configuration is designed. To compensate for the measurement errors introduced by error crosstalk, element fabrication error, laser beam drift, and nonparallelism of two measurement beam, a unified measurement model, which can improve the measurement accuracy, is deduced and established using the ray-tracing method. A numerical simulation using the optical design software Zemax is conducted, and the results verify the correctness of the model. Several experiments are performed to demonstrate the feasibility and effectiveness of the proposed system and measurement model.
Second-Order Geometric Sliding Mode Attitude Observer with Application to Quadrotor on a Test Bench
Directory of Open Access Journals (Sweden)
Honglei An
2013-01-01
Full Text Available A sliding mode observer design framework is proposed based on the Lie group method of numerical integration on manifolds, and a Second-Order Geometric Sliding Mode Attitude Observer (SOGSMAO is designed for angular velocity estimation of quadrotor attitude. The algorithm constructs feedback in the angular velocity space and the space of equivalent Lie algebra of unit quaternion space, respectively. It avoids not only the complexity of constructing feedback in unit quaternion space but also the process of mandatory rescaling which is seen to deteriorate the accuracy of the angular velocity estimates during sliding. The performance of SOGSMAO is compared with traditional quaternion based sliding mode observer in which multiplicative quaternion correction is used and the results show that SOGSMAO gains better tracking performance. Then SOGSMAO is realized on a test bed and the effectiveness of the observer algorithm is verified by experimental studies.
DEFF Research Database (Denmark)
Eder, Martin Alexander; Bitsche, Robert
2015-01-01
section, that was inspired by a wind turbine blade, it is demonstrated that geometric nonlinear effects can induce an in-plane opening deformation in re-entrant corners that may decrease the fatigue life. The opening effect induces Mode-I stress intensity factors which exceed the threshold for fatigue...... crack growth at loads well below the load-carrying capacity of the beam. The findings in this paper are twofold: Firstly, the investigated analysis procedure can be integrated into the design process of wind turbine blade cross sections. Secondly, the proposed approach serves as a basis...... for computationally efficient numerical analysis approaches of structures that comprise complex geometry and anisotropic material behaviour – such as wind turbine rotor blades....
Doummar, J.; Kassem, A.; Gurdak, J. J.
2017-12-01
In the framework of a three-year USAID/NSF- funded PEER Science project, flow in a karst system in Lebanon (Assal Spring; discharge 0.2-2.5 m3/s yearly volume of 22-30 Mm3) dominated by snow and semi arid conditions was simulated using an integrated numerical model (Mike She 2016). The calibrated model (Nash-Sutcliffe coefficient of 0.77) is based on high resolution input data (2014-2017) and detailed catchment characterization. The approach is to assess the influence of various model parameters on recharge signals in the different hydrological karst compartments (Atmosphere, unsaturated zone, and saturated zone) based on an integrated numerical model. These parameters include precipitation intensity and magnitude, temperature, snow-melt parameters, in addition to karst specific spatially distributed features such as fast infiltration points, soil properties and thickness, topographical slopes, Epikarst and thickness of unsaturated zone, and hydraulic conductivity among others. Moreover, the model is currently simulated forward using various scenarios for future climate (Global Climate Models GCM; daily downscaled temperature and precipitation time series for Lebanon 2020-2045) in order to depict the flow rates expected in the future and the effect of climate change on hydrographs recession coefficients, discharge maxima and minima, and total spring discharge volume . Additionally, a sensitivity analysis of individual or coupled major parameters allows quantifying their impact on recharge or indirectly on the vulnerability of the system (soil thickness, soil and rock hydraulic conductivity appear to be amongst the highly sensitive parameters). This study particularly unravels the normalized single effect of rain magnitude and intensity, snow, and temperature change on the flow rate (e.g., a change of temperature of 3° on the catchment yields a Residual Mean Square Error RMSE of 0.15 m3/s in the spring discharge and a 16% error in the total annual volume with
DEFF Research Database (Denmark)
Emerek, Ruth
2004-01-01
Bidraget diskuterer de forskellige intergrationsopfattelse i Danmark - og hvad der kan forstås ved vellykket integration......Bidraget diskuterer de forskellige intergrationsopfattelse i Danmark - og hvad der kan forstås ved vellykket integration...
Geometrical methods in learning theory
International Nuclear Information System (INIS)
Burdet, G.; Combe, Ph.; Nencka, H.
2001-01-01
The methods of information theory provide natural approaches to learning algorithms in the case of stochastic formal neural networks. Most of the classical techniques are based on some extremization principle. A geometrical interpretation of the associated algorithms provides a powerful tool for understanding the learning process and its stability and offers a framework for discussing possible new learning rules. An illustration is given using sequential and parallel learning in the Boltzmann machine
Geometric Results for Compressible Magnetohydrodynamics
Arter, Wayne
2013-01-01
Recently, compressible magnetohydrodynamics (MHD) has been elegantly formulated in terms of Lie derivatives. This paper exploits the geometrical properties of the Lie bracket to give new insights into the properties of compressible MHD behaviour, both with and without feedback of the magnetic field on the flow. These results are expected to be useful for the solution of MHD equations in both tokamak fusion experiments and space plasmas.
Geometric monodromy - Semisimplicity and maximality
Cadoret, Anna; Hui, Chun Yin; Tamagawa, Akio
2017-01-01
Let X be a connected scheme, smooth and separated over an alge- braically closed field k of characteristic p ≥ 0, let f: Y → X be a smooth proper morphism and x a geometric point on X. We prove that the tensor invariants of bounded length ≤ d of π1(X; x) acting on the étale cohomology groups H*(Yx;
Shibata, Masaru
2016-01-01
This book is composed of two parts: First part describes basics in numerical relativity, that is, the formulations and methods for a solution of Einstein's equation and general relativistic matter field equations. This part will be helpful for beginners of numerical relativity who would like to understand the content of numerical relativity and its background. The second part focuses on the application of numerical relativity. A wide variety of scientific numerical results are introduced focusing in particular on the merger of binary neutron stars and black holes.
Riemannian geometry and geometric analysis
Jost, Jürgen
2017-01-01
This established reference work continues to provide its readers with a gateway to some of the most interesting developments in contemporary geometry. It offers insight into a wide range of topics, including fundamental concepts of Riemannian geometry, such as geodesics, connections and curvature; the basic models and tools of geometric analysis, such as harmonic functions, forms, mappings, eigenvalues, the Dirac operator and the heat flow method; as well as the most important variational principles of theoretical physics, such as Yang-Mills, Ginzburg-Landau or the nonlinear sigma model of quantum field theory. The present volume connects all these topics in a systematic geometric framework. At the same time, it equips the reader with the working tools of the field and enables her or him to delve into geometric research. The 7th edition has been systematically reorganized and updated. Almost no page has been left unchanged. It also includes new material, for instance on symplectic geometry, as well as the B...
Polar metals by geometric design
Kim, T. H.; Puggioni, D.; Yuan, Y.; Xie, L.; Zhou, H.; Campbell, N.; Ryan, P. J.; Choi, Y.; Kim, J.-W.; Patzner, J. R.; Ryu, S.; Podkaminer, J. P.; Irwin, J.; Ma, Y.; Fennie, C. J.; Rzchowski, M. S.; Pan, X. Q.; Gopalan, V.; Rondinelli, J. M.; Eom, C. B.
2016-05-01
Gauss’s law dictates that the net electric field inside a conductor in electrostatic equilibrium is zero by effective charge screening; free carriers within a metal eliminate internal dipoles that may arise owing to asymmetric charge distributions. Quantum physics supports this view, demonstrating that delocalized electrons make a static macroscopic polarization, an ill-defined quantity in metals—it is exceedingly unusual to find a polar metal that exhibits long-range ordered dipoles owing to cooperative atomic displacements aligned from dipolar interactions as in insulating phases. Here we describe the quantum mechanical design and experimental realization of room-temperature polar metals in thin-film ANiO3 perovskite nickelates using a strategy based on atomic-scale control of inversion-preserving (centric) displacements. We predict with ab initio calculations that cooperative polar A cation displacements are geometrically stabilized with a non-equilibrium amplitude and tilt pattern of the corner-connected NiO6 octahedra—the structural signatures of perovskites—owing to geometric constraints imposed by the underlying substrate. Heteroepitaxial thin-films grown on LaAlO3 (111) substrates fulfil the design principles. We achieve both a conducting polar monoclinic oxide that is inaccessible in compositionally identical films grown on (001) substrates, and observe a hidden, previously unreported, non-equilibrium structure in thin-film geometries. We expect that the geometric stabilization approach will provide novel avenues for realizing new multifunctional materials with unusual coexisting properties.
A new generalization of the Pareto–geometric distribution
Directory of Open Access Journals (Sweden)
M. Nassar
2013-07-01
Full Text Available In this paper we introduce a new distribution called the beta Pareto–geometric. We provide a comprehensive treatment of the mathematical properties of the proposed distribution and derive expressions for its moment generating function and the rth generalized moment. We discuss estimation of the parameters by maximum likelihood and obtain the information matrix that is easily numerically determined. We also demonstrate its usefulness on a real data set.
Geometrically unfitted finite element methods and applications
Burman, Erik; Larson, Mats; Olshanskii, Maxim
2017-01-01
This book provides a snapshot of the state of the art of the rapidly evolving field of integration of geometric data in finite element computations. The contributions to this volume, based on research presented at the UCL workshop on the topic in January 2016, include three review papers on core topics such as fictitious domain methods for elasticity, trace finite element methods for partial differential equations defined on surfaces, and Nitsche’s method for contact problems. Five chapters present original research articles on related theoretical topics, including Lagrange multiplier methods, interface problems, bulk-surface coupling, and approximation of partial differential equations on moving domains. Finally, two chapters discuss advanced applications such as crack propagation or flow in fractured poroelastic media. This is the first volume that provides a comprehensive overview of the field of unfitted finite element methods, including recent techniques such as cutFEM, traceFEM, ghost penalty, and aug...
International Nuclear Information System (INIS)
Furtado, W.; Isotani, S.; Antonini, R.; Blak, A.R.; Pontuschka, W.M.
1988-03-01
A method of data processing was developed and applied to the study of decay kinetics of interstitial atomic hydrogen (H 0 i ) 1 in X-irradiated a-Si:(H,O,N) 2 and natural beryl. A system of differential kinetic equations was constructed considering multiple possible reactions. the solutions were evaluated by Runge-Kutta's method of numerical integration. It was assumed that the H 0 i was produced by radiolytic irradiation of R-H type molecules and trapped at interstitial sites of both materials. The heating releases the H 0 which quickly is either retrapped, recombined with R-radical left in the matrix or combined with other H 0 atoms forming H 2 molecules. The parameters related to untrapping and recombination processes were found to obey Arrhenius law. On the other hand, the retrapping and H- 2 formation parameters were fit to a function proportional to T 1/2 - T 1/2 o , where at T 0 they vanish. (author) [pt
Raja, Muhammad Asif Zahoor; Zameer, Aneela; Khan, Aziz Ullah; Wazwaz, Abdul Majid
2016-01-01
In this study, a novel bio-inspired computing approach is developed to analyze the dynamics of nonlinear singular Thomas-Fermi equation (TFE) arising in potential and charge density models of an atom by exploiting the strength of finite difference scheme (FDS) for discretization and optimization through genetic algorithms (GAs) hybrid with sequential quadratic programming. The FDS procedures are used to transform the TFE differential equations into a system of nonlinear equations. A fitness function is constructed based on the residual error of constituent equations in the mean square sense and is formulated as the minimization problem. Optimization of parameters for the system is carried out with GAs, used as a tool for viable global search integrated with SQP algorithm for rapid refinement of the results. The design scheme is applied to solve TFE for five different scenarios by taking various step sizes and different input intervals. Comparison of the proposed results with the state of the art numerical and analytical solutions reveals that the worth of our scheme in terms of accuracy and convergence. The reliability and effectiveness of the proposed scheme are validated through consistently getting optimal values of statistical performance indices calculated for a sufficiently large number of independent runs to establish its significance.
Elmo, Davide; Stead, Doug
2010-02-01
Naturally fractured mine pillars provide an excellent example of the importance of accurately determining rock mass strength. Failure in slender pillars is predominantly controlled by naturally occurring discontinuities, their influence diminishing with increasing pillar width, with wider pillars failing through a combination of brittle and shearing processes. To accurately simulate this behaviour by numerical modelling, the current analysis incorporates a more realistic representation of the mechanical behaviour of discrete fracture systems. This involves realistic simulation and representation of fracture networks, either as individual entities or as a collective system of fracture sets, or a combination of both. By using an integrated finite element/discrete element-discrete fracture network approach it is possible to study the failure of rock masses in tension and compression, along both existing pre-existing fractures and through intact rock bridges, and incorporating complex kinematic mechanisms. The proposed modelling approach fully captures the anisotropic and inhomogeneous effects of natural jointing and is considered to be more realistic than methods relying solely on continuum or discontinuum representation. The paper concludes with a discussion on the development of synthetic rock mass properties, with the intention of providing a more robust link between rock mass strength and rock mass classification systems.
Geometric model from microscopic theory for nuclear absorption
John, Sarah; Townsend, Lawrence W.; Wilson, John W.; Tripathi, Ram K.
1993-01-01
A parameter-free geometric model for nuclear absorption is derived herein from microscopic theory. The expression for the absorption cross section in the eikonal approximation, taken in integral form, is separated into a geometric contribution that is described by an energy-dependent effective radius and two surface terms that cancel in an asymptotic series expansion. For collisions of light nuclei, an expression for the effective radius is derived from harmonic oscillator nuclear density functions. A direct extension to heavy nuclei with Woods-Saxon densities is made by identifying the equivalent half-density radius for the harmonic oscillator functions. Coulomb corrections are incorporated, and a simplified geometric form of the Bradt-Peters type is obtained. Results spanning the energy range from 1 MeV/nucleon to 1 GeV/nucleon are presented. Good agreement with experimental results is obtained.
Geometric model for nuclear absorption from microscopic theory
John, S.; Townsend, L. W.; Wilson, J. W.; Tripathi, R. K.
1993-01-01
A parameter-free geometric model for nuclear absorption is derived from microscopic theory. The expression for the absorption cross section in the eikonal approximation taken in integral form is separated into a geometric contribution, described by an energy-dependent effective radius, and two surface terms which are shown to cancel in an asymptotic series expansion. For collisions of light nuclei, an expression for the effective radius is derived using harmonic-oscillator nuclear density functions. A direct extension to heavy nuclei with Woods-Saxon densities is made by identifying the equivalent half density radius for the harmonic-oscillator functions. Coulomb corrections are incorporated and a simplified geometric form of the Bradt-Peters type obtained. Results spanning the energy range of 1 MeV/nucleon to 1 GeV/nucleon are presented. Good agreement with experimental results are obtained.
Geometrical determination of the constant of motion in General Relativity
International Nuclear Information System (INIS)
Catoni, F.; Cannata, R.; Zampetti, P.
2009-01-01
In recent time a theorem, due to E. Beltrami, through which the integration of the geodesic equations of a curved manifold is obtained by means of a merely geometric method, has been revisited. This way of dealing with the problem is well in accordance with the geometric spirit of the Theory of General Relativity. In this paper we show another relevant consequence of this method. Actually, the constants of the motion, introduced in this geometrical way that is completely independent of Newton theory, are related to the conservation laws for test particles in the Einstein theory. These conservation laws may be compared with the conservation laws of Newton. In particular, by the conservation of energy (E) and the L z component of angular momentum, the equivalence of the conservation laws for the Schwarzschild field is verified and the difference between Newton and Einstein theories for the rotating bodies (Kerr metric) is obtained in a straightforward way.
Effect of Computational Parameters on Springback Prediction by Numerical Simulation
Directory of Open Access Journals (Sweden)
Tomasz Trzepiecinski
2017-09-01
Full Text Available Elastic recovery of the material, called springback, is one of the problems in sheet metal forming of drawpieces, especially with a complex shape. The springback can be influenced by various technological, geometrical, and material parameters. In this paper the results of experimental testing and numerical study are presented. The experiments are conducted on DC04 steel sheets, commonly used in the automotive industry. The numerical analysis of V-die air bending tests is carried out with the finite element method (FEM-based ABAQUS/Standard 2016 program. A quadratic Hill anisotropic yield criterion is compared with an isotropic material described by the von Mises yield criterion. The effect of a number of integration points and integration rules on the springback amount and computation time is also considered. Two integration rules available in ABAQUS: the Gauss’ integration rule and Simpson’s integration rule are considered. The effect of sample orientation according to the sheet rolling direction and friction contact behaviour on the prediction of springback is also analysed. It is observed that the width of the sample bend in the V-bending test influences the stress-state in the cross-section of the sample. Different stress-states in the sample bend of the V-shaped die cause that the sheet undergoes springback in different planes. Friction contact phenomena slightly influences the springback behaviour.
Geometrization and Generalization of the Kowalevski Top
Dragović, Vladimir
2010-08-01
A new view on the Kowalevski top and the Kowalevski integration procedure is presented. For more than a century, the Kowalevski 1889 case, has attracted full attention of a wide community as the highlight of the classical theory of integrable systems. Despite hundreds of papers on the subject, the Kowalevski integration is still understood as a magic recipe, an unbelievable sequence of skillful tricks, unexpected identities and smart changes of variables. The novelty of our present approach is based on our four observations. The first one is that the so-called fundamental Kowalevski equation is an instance of a pencil equation of the theory of conics which leads us to a new geometric interpretation of the Kowalevski variables w, x 1, x 2 as the pencil parameter and the Darboux coordinates, respectively. The second is observation of the key algebraic property of the pencil equation which is followed by introduction and study of a new class of discriminantly separable polynomials. All steps of the Kowalevski integration procedure are now derived as easy and transparent logical consequences of our theory of discriminantly separable polynomials. The third observation connects the Kowalevski integration and the pencil equation with the theory of multi-valued groups. The Kowalevski change of variables is now recognized as an example of a two-valued group operation and its action. The final observation is surprising equivalence of the associativity of the two-valued group operation and its action to the n = 3 case of the Great Poncelet Theorem for pencils of conics.
Multiscale geometric modeling of macromolecules I: Cartesian representation
Xia, Kelin; Feng, Xin; Chen, Zhan; Tong, Yiying; Wei, Guo-Wei
2014-01-01
This paper focuses on the geometric modeling and computational algorithm development of biomolecular structures from two data sources: Protein Data Bank (PDB) and Electron Microscopy Data Bank (EMDB) in the Eulerian (or Cartesian) representation. Molecular surface (MS) contains non-smooth geometric singularities, such as cusps, tips and self-intersecting facets, which often lead to computational instabilities in molecular simulations, and violate the physical principle of surface free energy minimization. Variational multiscale surface definitions are proposed based on geometric flows and solvation analysis of biomolecular systems. Our approach leads to geometric and potential driven Laplace-Beltrami flows for biomolecular surface evolution and formation. The resulting surfaces are free of geometric singularities and minimize the total free energy of the biomolecular system. High order partial differential equation (PDE)-based nonlinear filters are employed for EMDB data processing. We show the efficacy of this approach in feature-preserving noise reduction. After the construction of protein multiresolution surfaces, we explore the analysis and characterization of surface morphology by using a variety of curvature definitions. Apart from the classical Gaussian curvature and mean curvature, maximum curvature, minimum curvature, shape index, and curvedness are also applied to macromolecular surface analysis for the first time. Our curvature analysis is uniquely coupled to the analysis of electrostatic surface potential, which is a by-product of our variational multiscale solvation models. As an expository investigation, we particularly emphasize the numerical algorithms and computational protocols for practical applications of the above multiscale geometric models. Such information may otherwise be scattered over the vast literature on this topic. Based on the curvature and electrostatic analysis from our multiresolution surfaces, we introduce a new concept, the
Geometric phase from dielectric matrix
International Nuclear Information System (INIS)
Banerjee, D.
2005-10-01
The dielectric property of the anisotropic optical medium is found by considering the polarized photon as two component spinor of spherical harmonics. The Geometric Phase of a polarized photon has been evaluated in two ways: the phase two-form of the dielectric matrix through a twist and the Pancharatnam phase (GP) by changing the angular momentum of the incident polarized photon over a closed triangular path on the extended Poincare sphere. The helicity in connection with the spin angular momentum of the chiral photon plays the key role in developing these phase holonomies. (author)
Field guide to geometrical optics
Greivenkamp, John E
2004-01-01
This Field Guide derives from the treatment of geometrical optics that has evolved from both the undergraduate and graduate programs at the Optical Sciences Center at the University of Arizona. The development is both rigorous and complete, and it features a consistent notation and sign convention. This volume covers Gaussian imagery, paraxial optics, first-order optical system design, system examples, illumination, chromatic effects, and an introduction to aberrations. The appendices provide supplemental material on radiometry and photometry, the human eye, and several other topics.
Geometric Computations On Indecisive Points
DEFF Research Database (Denmark)
Jørgensen, Allan Grønlund; Phillips, Jeff; Loffler, Maarten
2011-01-01
We study computing with indecisive point sets. Such points have spatial uncertainty where the true location is one of a finite number of possible locations. This data arises from probing distributions a few times or when the location is one of a few locations from a known database. In particular......, we study computing distributions of geometric functions such as the radius of the smallest enclosing ball and the diameter. Surprisingly, we can compute the distribution of the radius of the smallest enclosing ball exactly in polynomial time, but computing the same distribution for the diameter is #P...
Geometric Rationalization for Freeform Architecture
Jiang, Caigui
2016-06-20
The emergence of freeform architecture provides interesting geometric challenges with regards to the design and manufacturing of large-scale structures. To design these architectural structures, we have to consider two types of constraints. First, aesthetic constraints are important because the buildings have to be visually impressive. Sec- ond, functional constraints are important for the performance of a building and its e cient construction. This thesis contributes to the area of architectural geometry. Specifically, we are interested in the geometric rationalization of freeform architec- ture with the goal of combining aesthetic and functional constraints and construction requirements. Aesthetic requirements typically come from designers and architects. To obtain visually pleasing structures, they favor smoothness of the building shape, but also smoothness of the visible patterns on the surface. Functional requirements typically come from the engineers involved in the construction process. For exam- ple, covering freeform structures using planar panels is much cheaper than using non-planar ones. Further, constructed buildings have to be stable and should not collapse. In this thesis, we explore the geometric rationalization of freeform archi- tecture using four specific example problems inspired by real life applications. We achieve our results by developing optimization algorithms and a theoretical study of the underlying geometrical structure of the problems. The four example problems are the following: (1) The design of shading and lighting systems which are torsion-free structures with planar beams based on quad meshes. They satisfy the functionality requirements of preventing light from going inside a building as shad- ing systems or reflecting light into a building as lighting systems. (2) The Design of freeform honeycomb structures that are constructed based on hex-dominant meshes with a planar beam mounted along each edge. The beams intersect without
A history of geometrical methods
Coolidge, Julian Lowell
2013-01-01
Full and authoritative, this history of the techniques for dealing with geometric questions begins with synthetic geometry and its origins in Babylonian and Egyptian mathematics; reviews the contributions of China, Japan, India, and Greece; and discusses the non-Euclidean geometries. Subsequent sections cover algebraic geometry, starting with the precursors and advancing to the great awakening with Descartes; and differential geometry, from the early work of Huygens and Newton to projective and absolute differential geometry. The author's emphasis on proofs and notations, his comparisons betwe
Development of Multistep and Degenerate Variational Integrators for Applications in Plasma Physics
Ellison, Charles Leland
Geometric integrators yield high-fidelity numerical results by retaining conservation laws in the time advance. A particularly powerful class of geometric integrators is symplectic integrators, which are widely used in orbital mechanics and accelerator physics. An important application presently lacking symplectic integrators is the guiding center motion of magnetized particles represented by non-canonical coordinates. Because guiding center trajectories are foundational to many simulations of magnetically confined plasmas, geometric guiding center algorithms have high potential for impact. The motivation is compounded by the need to simulate long-pulse fusion devices, including ITER, and opportunities in high performance computing, including the use of petascale resources and beyond. This dissertation uses a systematic procedure for constructing geometric integrators --- known as variational integration --- to deliver new algorithms for guiding center trajectories and other plasma-relevant dynamical systems. These variational integrators are non-trivial because the Lagrangians of interest are degenerate - the Euler-Lagrange equations are first-order differential equations and the Legendre transform is not invertible. The first contribution of this dissertation is that variational integrators for degenerate Lagrangian systems are typically multistep methods. Multistep methods admit parasitic mode instabilities that can ruin the numerical results. These instabilities motivate the second major contribution: degenerate variational integrators. By replicating the degeneracy of the continuous system, degenerate variational integrators avoid parasitic mode instabilities. The new methods are therefore robust geometric integrators for degenerate Lagrangian systems. These developments in variational integration theory culminate in one-step degenerate variational integrators for non-canonical magnetic field line flow and guiding center dynamics. The guiding center integrator
Bright, William
In most languages encountered by linguists, the numerals, considered as a paradigmatic set, constitute a morpho-syntactic problem of only moderate complexity. The Indo-Aryan language family of North India, however, presents a curious contrast. The relatively regular numeral system of Sanskrit, as it has developed historically into the modern…
Wolter, A.; Gischig, V.; Stead, D.; Clague, J. J.
2016-06-01
We present an integrated approach to investigate the seismically triggered Madison Canyon landslide (volume = 20 Mm3), which killed 26 people in Montana, USA, in 1959. We created engineering geomorphological maps and conducted field surveys, long-range terrestrial digital photogrammetry, and preliminary 2D numerical modelling with the objective of determining the conditioning factors, mechanisms, movement behaviour, and evolution of the failure. We emphasise the importance of both endogenic (i.e. seismic) and exogenic (i.e. geomorphic) processes in conditioning the slope for failure and hypothesise a sequence of events based on the morphology of the deposit and seismic modelling. A section of the slope was slowly deforming before a magnitude-7.5 earthquake with an epicentre 30 km away triggered the catastrophic failure in August 1959. The failed rock mass rapidly fragmented as it descended the slope towards Madison River. Part of the mass remained relatively intact as it moved on a layer of pulverised debris. The main slide was followed by several debris slides, slumps, and rockfalls. The slide debris was extensively modified soon after the disaster by the US Army Corps of Engineers to provide a stable outflow channel from newly formed Earthquake Lake. Our modelling and observations show that the landslide occurred as a result of long-term damage of the slope induced by fluvial undercutting, erosion, weathering, and past seismicity, and due to the short-term triggering effect of the 1959 earthquake. Static models suggest the slope was stable prior to the 1959 earthquake; failure would have required a significant reduction in material strength. Preliminary dynamic models indicate that repeated seismic loading was a critical process for catastrophic failure. Although the ridge geometry and existing tension cracks in the initiation zone amplified ground motions, the most important factors in initiating failure were pre-existing discontinuities and seismically induced
Image understanding using geometric context
Zhang, Xiaochun; Liu, Chuancai
2017-07-01
A Gibbs Sampler based topic model for image annotation, which takes into account the interaction between visual geometric context and related topic, is presented. Most of the existing topic models for scene annotation use segmentation-based algorithm. However, topic models using segmentation algorithm alone sometimes can produce erroneous results when used to annotate real-life scene pictures. Therefore, our algorithm makes use of peaks of image surface instead of segmentation regions. Existing approaches use SIFT algorithm and treat the peaks as round blob features. In this paper, the peaks are treated as anisotropic blob features, which models low level visual elements more precisely. In order to better utilize visual features, our model not only takes into consideration visual codeword, but also considers influence of visual properties to topic formation, such as orientation, width, length and color. The basic idea is based on the assumption that different topics will produce distinct visual appearance, and different visual appearance is helpful to distinguish topics. During the learning stage, each topic will be associated with a set of distributions of visual properties, which depicts appearance of the topic. This paper considers more geometric properties, which will reduce topic uncertainty and learn the images better. Tested with Corel5K, SAIAPR-TC12 and Espgame100k Datasets, our method performs moderately better than some state of the arts methods.
Numerical evolutions beyond our belief
Directory of Open Access Journals (Sweden)
Guilherme de Almeida
2014-03-01
Full Text Available The everyday life situations gave us a good enough training to deal with numerical evolutions operated by arithmetic progressions, so in this specific case we can make good numerical predictions. But our common sense is not usually prepared to deal with numbers that grow, or shrink, according to geometrical progressions. In the last cases, our intuition strongly fails, showing that our intuition is not always right. We also fail in comparing some other situations which we are not trained. This article shows some of that limiting cases.
Geometric effects of ICMEs on geomagnetic storms
Cho, KyungSuk; Lee, Jae-Ok
2017-04-01
It has been known that the geomagnetic storm is occurred by the interaction between the Interplanetary Coronal Mass Ejection (ICME) and the Earth's magnetosphere; especially, the southward Bz component of ICME is thought as the main trigger. In this study, we investigate the relationship between Dst index and solar wind conditions; which are the southward Bz, electric field (VBz), and time integral of electric field as well as ICME parameters derived from toroidal fitting model in order to find what is main factor to the geomagnetic storm. We also inspect locations of Earth in ICMEs to understand the geometric effects of the Interplanetary Flux Ropes (IFRs) on the geomagnetic storms. Among 59 CDAW ICME lists, we select 30 IFR events that are available by the toroidal fitting model and classify them into two sub-groups: geomagnetic storms associated with the Magnetic Clouds (MCs) and the compression regions ahead of the MCs (sheath). The main results are as follows: (1) The time integral of electric field has a higher correlation coefficient (cc) with Dst index than the other parameters: cc=0.85 for 25 MC events and cc=0.99 for 5 sheath events. (2) The sheath associated intense storms (Dst ≤-100nT) having usually occur at flank regions of ICMEs while the MC associated intense storms occur regardless of the locations of the Earth in ICMEs. The strength of a geomagnetic storm strongly depends on electric field of IFR and durations of the IFR passages through the Earth.
Improved Object Proposals with Geometrical Features for Autonomous Driving
Directory of Open Access Journals (Sweden)
Yiliu Feng
2017-01-01
Full Text Available This paper aims at generating high-quality object proposals for object detection in autonomous driving. Most existing proposal generation methods are designed for the general object detection, which may not perform well in a particular scene. We propose several geometrical features suited for autonomous driving and integrate them into state-of-the-art general proposal generation methods. In particular, we formulate the integration as a feature fusion problem by fusing the geometrical features with existing proposal generation methods in a Bayesian framework. Experiments on the challenging KITTI benchmark demonstrate that our approach improves the existing methods significantly. Combined with a convolutional neural net detector, our approach achieves state-of-the-art performance on all three KITTI object classes.
Rational Geometrical Characters of Saddle Shape Cable Roof Supported by Tensioned Cables
Rocēns, K; Pakrastiņš, L; Serdjuks, D
1999-01-01
The saddle shape cable roof, which is supported by tension cables, is considered in the paper. The roof is kinematics invariable because of prestressing of rectangular (orthogonal) cable net The correlation between the main geometrical characters of the cable roof and weight of the cable net which is divided by the area covered by the cable roof, was ascertained by a numeral experiment. The main geometrical characters are the initial curvatures of stressing, suspension and tension cables and ...
Scott, L Ridgway
2011-01-01
Computational science is fundamentally changing how technological questions are addressed. The design of aircraft, automobiles, and even racing sailboats is now done by computational simulation. The mathematical foundation of this new approach is numerical analysis, which studies algorithms for computing expressions defined with real numbers. Emphasizing the theory behind the computation, this book provides a rigorous and self-contained introduction to numerical analysis and presents the advanced mathematics that underpin industrial software, including complete details that are missing from most textbooks. Using an inquiry-based learning approach, Numerical Analysis is written in a narrative style, provides historical background, and includes many of the proofs and technical details in exercises. Students will be able to go beyond an elementary understanding of numerical simulation and develop deep insights into the foundations of the subject. They will no longer have to accept the mathematical gaps that ex...
Geometrical charged-particle optics
Rose, Harald
2012-01-01
This second edition is an extended version of the first edition of Geometrical Charged-Particle Optics. The updated reference monograph is intended as a guide for researchers and graduate students who are seeking a comprehensive treatment of the design of instruments and beam-guiding systems of charged particles and their propagation in electromagnetic fields. Wave aspects are included in this edition for explaining electron holography, the Aharanov-Bohm effect and the resolution of electron microscopes limited by diffraction. Several methods for calculating the electromagnetic field are presented and procedures are outlined for calculating the properties of systems with arbitrarily curved axis. Detailed methods are presented for designing and optimizing special components such as aberration correctors, spectrometers, energy filters monochromators, ion traps, electron mirrors and cathode lenses. In particular, the optics of rotationally symmetric lenses, quadrupoles, and systems composed of these elements are...
Geometric Operators on Boolean Functions
DEFF Research Database (Denmark)
Frisvad, Jeppe Revall; Falster, Peter
In truth-functional propositional logic, any propositional formula represents a Boolean function (according to some valuation of the formula). We describe operators based on Decartes' concept of constructing coordinate systems, for translation of a propositional formula to the image of a Boolean...... function. With this image of a Boolean function corresponding to a propositional formula, we prove that the orthogonal projection operator leads to a theorem describing all rules of inference in propositional reasoning. In other words, we can capture all kinds of inference in propositional logic by means...... of a few geometric operators working on the images of Boolean functions. The operators we describe, arise from the niche area of array-based logic and have previously been tightly bound to an array-based representation of Boolean functions. We redefine the operators in an abstract form to make them...
Geometrical charged-particle optics
Rose, Harald H
2009-01-01
This reference monograph covers all theoretical aspects of modern geometrical charged-particle optics. It is intended as a guide for researchers, who are involved in the design of electron optical instruments and beam-guiding systems for charged particles, and as a tutorial for graduate students seeking a comprehensive treatment. Procedures for calculating the properties of systems with arbitrarily curved axes are outlined in detail and methods are discussed for designing and optimizing special components such as aberration correctors, spectrometers, energy filters, monochromators, ion traps, electron mirrors and cathode lenses. Also addressed is the design of novel electron optical components enabling sub-Angstroem spatial resolution and sub-0.1eV energy resolution. Relativistic motion and spin precession of the electron is treated in a concise way by employing a covariant five-dimensional procedure.
Geometric algebra in plasma electrodynamics
Resendes, D. P.; Resendes
2013-10-01
Geometric algebra (GA) is a recent broad mathematical framework incorporating synthetic and coordinate geometry, complex variables, quarternions, vector analysis, matrix algebra, spinors, tensors, and differential forms. It has been claimed to be a unified language for physics. GA is presented in the context of the Maxwell-Plasma system. In this formalism the divergence and curl differential operators are united in a single vector derivative, which is invertible, in the form of a first-order Green function. The four Maxwell equations can be combined into a single equation (for homogeneous and constant media) or into two equations involving the invertible vector derivative for more complex media. GA is applied to simple examples to illustrate the compactness of the notation and coordinate-free computations.
Li, Y.
2012-01-01
The geometrical statistics of fluid deformation are analyzed theoretically within the framework of the restricted Euler approximation, and numerically using direct numerical simulations. The restricted Euler analysis predicts that asymptotically a material line element becomes an eigenvector of the velocity gradient regardless its initial orientation. The asymptotic stretching rate equals the intermediate eigenvalue of the strain rate tensor. Analyses of numerical data show that the pressure ...
Cheng Min; Lu Yi Long; Yao Zhen Hua
2003-01-01
The principle of differential algebra is applied to analyse and calculate arbitrary order curvilinear-axis combined geometric-chromatic aberrations of electron optical systems. Expressions of differential algebraic form of high order combined aberrations are obtained and arbitrary order combined aberrations can be calculated numerically. As an example, a typical wide electron beam focusing system with curved optical axes named magnetic immersion lens has been studied. All the second-order and third-order combined geometric-chromatic aberrations of the lens have been calculated, and the patterns of the corresponding geometric aberrations and combined aberrations have been given as well.
Geometrical shock dynamics for magnetohydrodynamic fast shocks
Mostert, W.
2016-12-12
We describe a formulation of two-dimensional geometrical shock dynamics (GSD) suitable for ideal magnetohydrodynamic (MHD) fast shocks under magnetic fields of general strength and orientation. The resulting area–Mach-number–shock-angle relation is then incorporated into a numerical method using pseudospectral differentiation. The MHD-GSD model is verified by comparison with results from nonlinear finite-volume solution of the complete ideal MHD equations applied to a shock implosion flow in the presence of an oblique and spatially varying magnetic field ahead of the shock. Results from application of the MHD-GSD equations to the stability of fast MHD shocks in two dimensions are presented. It is shown that the time to formation of triple points for both perturbed MHD and gas-dynamic shocks increases as (Formula presented.), where (Formula presented.) is a measure of the initial Mach-number perturbation. Symmetry breaking in the MHD case is demonstrated. In cylindrical converging geometry, in the presence of an azimuthal field produced by a line current, the MHD shock behaves in the mean as in Pullin et al. (Phys. Fluids, vol. 26, 2014, 097103), but suffers a greater relative pressure fluctuation along the shock than the gas-dynamic shock. © 2016 Cambridge University Press
Geometric solitons of Hamiltonian flows on manifolds
Energy Technology Data Exchange (ETDEWEB)
Song, Chong, E-mail: songchong@xmu.edu.cn [School of Mathematical Sciences, Xiamen University, Xiamen 361005 (China); Sun, Xiaowei, E-mail: sunxw@cufe.edu.cn [School of Applied Mathematics, Central University of Finance and Economics, Beijing 100081 (China); Wang, Youde, E-mail: wyd@math.ac.cn [Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190 (China)
2013-12-15
It is well-known that the LIE (Locally Induction Equation) admit soliton-type solutions and same soliton solutions arise from different and apparently irrelevant physical models. By comparing the solitons of LIE and Killing magnetic geodesics, we observe that these solitons are essentially decided by two families of isometries of the domain and the target space, respectively. With this insight, we propose the new concept of geometric solitons of Hamiltonian flows on manifolds, such as geometric Schrödinger flows and KdV flows for maps. Moreover, we give several examples of geometric solitons of the Schrödinger flow and geometric KdV flow, including magnetic curves as geometric Schrödinger solitons and explicit geometric KdV solitons on surfaces of revolution.
Geometric decomposition of the conformation tensor in viscoelastic turbulence
Hameduddin, Ismail; Meneveau, Charles; Zaki, Tamer A.; Gayme, Dennice F.
2018-05-01
This work introduces a mathematical approach to analysing the polymer dynamics in turbulent viscoelastic flows that uses a new geometric decomposition of the conformation tensor, along with associated scalar measures of the polymer fluctuations. The approach circumvents an inherent difficulty in traditional Reynolds decompositions of the conformation tensor: the fluctuating tensor fields are not positive-definite and so do not retain the physical meaning of the tensor. The geometric decomposition of the conformation tensor yields both mean and fluctuating tensor fields that are positive-definite. The fluctuating tensor in the present decomposition has a clear physical interpretation as a polymer deformation relative to the mean configuration. Scalar measures of this fluctuating conformation tensor are developed based on the non-Euclidean geometry of the set of positive-definite tensors. Drag-reduced viscoelastic turbulent channel flow is then used an example case study. The conformation tensor field, obtained using direct numerical simulations, is analysed using the proposed framework.
A geometric approach for quadrotor trajectory tracking control
Shi, Xiao-Ning; Zhang, Yong-An; Zhou, Di
2015-11-01
This paper investigates the trajectory tracking problem for quadrotor with attitude finite-time convergence via geometric approach. First, a global geometric dynamic description is presented on the special Euclidean group (SE(3)), and the trajectory tracking control is decomposed into two cascaded tracking control loops: the position tracking control loop and the attitude tracking control loop. Then, based on the fact that the attitude tracking loop is a fast loop, a finite-time controller based on the exponential coordinate is proposed to speed up the response rate of the attitude control loop, so that the artificial singularity and redundancy can be avoided. In addition, a backstepping controller is designed for the position tracking loop to construct the thrust magnitude control input for the position dynamics and the reference rotation matrix for the attitude tracking loop. Finally, the numerical simulation results are presented to demonstrate the effectiveness of this trajectory tracking strategy.
Topology-optimized metasurfaces: impact of initial geometric layout.
Yang, Jianji; Fan, Jonathan A
2017-08-15
Topology optimization is a powerful iterative inverse design technique in metasurface engineering and can transform an initial layout into a high-performance device. With this method, devices are optimized within a local design phase space, making the identification of suitable initial geometries essential. In this Letter, we examine the impact of initial geometric layout on the performance of large-angle (75 deg) topology-optimized metagrating deflectors. We find that when conventional metasurface designs based on dielectric nanoposts are used as initial layouts for topology optimization, the final devices have efficiencies around 65%. In contrast, when random initial layouts are used, the final devices have ultra-high efficiencies that can reach 94%. Our numerical experiments suggest that device topologies based on conventional metasurface designs may not be suitable to produce ultra-high-efficiency, large-angle metasurfaces. Rather, initial geometric layouts with non-trivial topologies and shapes are required.
Geometric Analogue of Holographic Reduced Representation
Aerts, Diederik; Czachor, Marek; De Moor, Bart
2007-01-01
Holographic reduced representations (HRR) are based on superpositions of convolution-bound $n$-tuples, but the $n$-tuples cannot be regarded as vectors since the formalism is basis dependent. This is why HRR cannot be associated with geometric structures. Replacing convolutions by geometric products one arrives at reduced representations analogous to HRR but interpretable in terms of geometry. Variable bindings occurring in both HRR and its geometric analogue mathematically correspond to two ...
Guide to Geometric Algebra in Practice
Dorst, Leo
2011-01-01
This highly practical "Guide to Geometric Algebra in Practice" reviews algebraic techniques for geometrical problems in computer science and engineering, and the relationships between them. The topics covered range from powerful new theoretical developments, to successful applications, and the development of new software and hardware tools. This title: provides hands-on review exercises throughout the book, together with helpful chapter summaries; presents a concise introductory tutorial to conformal geometric algebra (CGA) in the appendices; examines the application of CGA for the d
Geometrical and Graphical Solutions of Quadratic Equations.
Hornsby, E. John, Jr.
1990-01-01
Presented are several geometrical and graphical methods of solving quadratic equations. Discussed are Greek origins, Carlyle's method, von Staudt's method, fixed graph methods and imaginary solutions. (CW)
Geometric Aspects of Iterated Matrix Multiplication
DEFF Research Database (Denmark)
Gesmundo, Fulvio
2016-01-01
This paper studies geometric properties of the Iterated Matrix Multiplication polynomial and the hypersurface that it defines. We focus on geometric aspects that may be relevant for complexity theory such as the symmetry group of the polynomial, the dual variety and the Jacobian loci of the hyper......This paper studies geometric properties of the Iterated Matrix Multiplication polynomial and the hypersurface that it defines. We focus on geometric aspects that may be relevant for complexity theory such as the symmetry group of the polynomial, the dual variety and the Jacobian loci...
DEFF Research Database (Denmark)
Olwig, Karen Fog
2011-01-01
, while the countries have adopted disparate policies and ideologies, differences in the actual treatment and attitudes towards immigrants and refugees in everyday life are less clear, due to parallel integration programmes based on strong similarities in the welfare systems and in cultural notions...
Optimization of porthole die geometrical variables by Taguchi method
Gagliardi, F.; Ciancio, C.; Ambrogio, G.; Filice, L.
2017-10-01
Porthole die extrusion is commonly used to manufacture hollow profiles made of lightweight alloys for numerous industrial applications. The reliability of extruded parts is affected strongly by the quality of the longitudinal and transversal seam welds. According to that, the die geometry must be designed correctly and the process parameters must be selected properly to achieve the desired product quality. In this study, numerical 3D simulations have been created and run to investigate the role of various geometrical variables on punch load and maximum pressure inside the welding chamber. These are important outputs to take into account affecting, respectively, the necessary capacity of the extrusion press and the quality of the welding lines. The Taguchi technique has been used to reduce the number of the required numerical simulations necessary for considering the influence of twelve different geometric variables. Moreover, the Analysis of variance (ANOVA) has been implemented to individually analyze the effect of each input parameter on the two responses. Then, the methodology has been utilized to determine the optimal process configuration individually optimizing the two investigated process outputs. Finally, the responses of the optimized parameters have been verified through finite element simulations approximating the predicted value closely. This study shows the feasibility of the Taguchi technique for predicting performance, optimization and therefore for improving the design of a porthole extrusion process.
Information geometric methods for complexity
Felice, Domenico; Cafaro, Carlo; Mancini, Stefano
2018-03-01
Research on the use of information geometry (IG) in modern physics has witnessed significant advances recently. In this review article, we report on the utilization of IG methods to define measures of complexity in both classical and, whenever available, quantum physical settings. A paradigmatic example of a dramatic change in complexity is given by phase transitions (PTs). Hence, we review both global and local aspects of PTs described in terms of the scalar curvature of the parameter manifold and the components of the metric tensor, respectively. We also report on the behavior of geodesic paths on the parameter manifold used to gain insight into the dynamics of PTs. Going further, we survey measures of complexity arising in the geometric framework. In particular, we quantify complexity of networks in terms of the Riemannian volume of the parameter space of a statistical manifold associated with a given network. We are also concerned with complexity measures that account for the interactions of a given number of parts of a system that cannot be described in terms of a smaller number of parts of the system. Finally, we investigate complexity measures of entropic motion on curved statistical manifolds that arise from a probabilistic description of physical systems in the presence of limited information. The Kullback-Leibler divergence, the distance to an exponential family and volumes of curved parameter manifolds, are examples of essential IG notions exploited in our discussion of complexity. We conclude by discussing strengths, limits, and possible future applications of IG methods to the physics of complexity.
Generalized Geometric Quantum Speed Limits
Pires, Diego Paiva; Cianciaruso, Marco; Céleri, Lucas C.; Adesso, Gerardo; Soares-Pinto, Diogo O.
2016-04-01
The attempt to gain a theoretical understanding of the concept of time in quantum mechanics has triggered significant progress towards the search for faster and more efficient quantum technologies. One of such advances consists in the interpretation of the time-energy uncertainty relations as lower bounds for the minimal evolution time between two distinguishable states of a quantum system, also known as quantum speed limits. We investigate how the nonuniqueness of a bona fide measure of distinguishability defined on the quantum-state space affects the quantum speed limits and can be exploited in order to derive improved bounds. Specifically, we establish an infinite family of quantum speed limits valid for unitary and nonunitary evolutions, based on an elegant information geometric formalism. Our work unifies and generalizes existing results on quantum speed limits and provides instances of novel bounds that are tighter than any established one based on the conventional quantum Fisher information. We illustrate our findings with relevant examples, demonstrating the importance of choosing different information metrics for open system dynamics, as well as clarifying the roles of classical populations versus quantum coherences, in the determination and saturation of the speed limits. Our results can find applications in the optimization and control of quantum technologies such as quantum computation and metrology, and might provide new insights in fundamental investigations of quantum thermodynamics.
Generalized Geometric Quantum Speed Limits
Directory of Open Access Journals (Sweden)
Diego Paiva Pires
2016-06-01
Full Text Available The attempt to gain a theoretical understanding of the concept of time in quantum mechanics has triggered significant progress towards the search for faster and more efficient quantum technologies. One of such advances consists in the interpretation of the time-energy uncertainty relations as lower bounds for the minimal evolution time between two distinguishable states of a quantum system, also known as quantum speed limits. We investigate how the nonuniqueness of a bona fide measure of distinguishability defined on the quantum-state space affects the quantum speed limits and can be exploited in order to derive improved bounds. Specifically, we establish an infinite family of quantum speed limits valid for unitary and nonunitary evolutions, based on an elegant information geometric formalism. Our work unifies and generalizes existing results on quantum speed limits and provides instances of novel bounds that are tighter than any established one based on the conventional quantum Fisher information. We illustrate our findings with relevant examples, demonstrating the importance of choosing different information metrics for open system dynamics, as well as clarifying the roles of classical populations versus quantum coherences, in the determination and saturation of the speed limits. Our results can find applications in the optimization and control of quantum technologies such as quantum computation and metrology, and might provide new insights in fundamental investigations of quantum thermodynamics.
Geometric Phase Generated Optical Illusion.
Yue, Fuyong; Zang, Xiaofei; Wen, Dandan; Li, Zile; Zhang, Chunmei; Liu, Huigang; Gerardot, Brian D; Wang, Wei; Zheng, Guoxing; Chen, Xianzhong
2017-09-12
An optical illusion, such as "Rubin's vase", is caused by the information gathered by the eye, which is processed in the brain to give a perception that does not tally with a physical measurement of the stimulus source. Metasurfaces are metamaterials of reduced dimensionality which have opened up new avenues for flat optics. The recent advancement in spin-controlled metasurface holograms has attracted considerate attention, providing a new method to realize optical illusions. We propose and experimentally demonstrate a metasurface device to generate an optical illusion. The metasurface device is designed to display two asymmetrically distributed off-axis images of "Rubin faces" with high fidelity, high efficiency and broadband operation that are interchangeable by controlling the helicity of the incident light. Upon the illumination of a linearly polarized light beam, the optical illusion of a 'vase' is perceived. Our result provides an intuitive demonstration of the figure-ground distinction that our brains make during the visual perception. The alliance between geometric metasurface and the optical illusion opens a pathway for new applications related to encryption, optical patterning, and information processing.
Geometric aspects of ordering phenomena
Cugliandolo, Leticia F.
2017-01-01
A macroscopic system prepared in a disordered phase and quenched across a second-order phase transition into an ordered phase undergoes a coarsening process whereby it orders locally in one of the equilibrium states. The study of the evolution of the morphology of the ordered structures in two dimensions has recently unveiled two interesting and generic features. On the one hand, the dynamics first approach a critical percolating state via the growth of a new lengthscale and satisfying scaling properties with respect to it. The time needed to reach the critical percolating state diverges with the system size, though more weakly than the equilibration time. On the other hand, once the critical percolating structures established, the geometrical and statistical properties at larger scales than the one established by the usual dynamic growing length remain the ones of critical percolation. These observations are common to different microscopic dynamics (single spin flip, local and non-local spin exchange, voter) in pure or weakly disordered systems. We discuss these results and we refer to the relevant publications for details. xml:lang="fr"
Baker, John G.
2009-01-01
Recent advances in numerical relativity have fueled an explosion of progress in understanding the predictions of Einstein's theory of gravity, General Relativity, for the strong field dynamics, the gravitational radiation wave forms, and consequently the state of the remnant produced from the merger of compact binary objects. I will review recent results from the field, focusing on mergers of two black holes.
Austerity and geometric structure of field theories
International Nuclear Information System (INIS)
Kheyfets, A.
1986-01-01
The relation between the austerity idea and the geometric structure of the three basic field theories - electrodynamics, Yang-Mills theory, and general relativity - is studied. One of the most significant manifestations of the austerity idea in field theories is thought to be expressed by the boundary of a boundary principle (BBP). The BBP says that almost all content of the field theories can be deduced from the topological identity of delta dot produced with delta = 0 used twice, at the 1-2-3-dimensional level (providing the homogeneous field equations), and at the 2-3-4-dimensional level (providing the conservation laws for the source currents). There are some difficulties in this line of thought due to the apparent lack of universality in application of the BBP to the three basic modern field theories above. This dissertation: (a) analyzes the difficulties by means of algebraic topology, integration theory, and modern differential geometry based on the concepts of principal bundles and Ehresmann connections: (b) extends the BBP to the unified Kaluza-Klein theory; (c) reformulates the inhomogeneous field equations and the BBP in terms of E. Cartan moment of rotation, in the way universal for the three theories and compatible with the original austerity idea; and (d) underlines the important role of the soldering structure on spacetime, and indicates that the future development of the austerity idea would involve the generalized theories
Geometric phases in discrete dynamical systems
Energy Technology Data Exchange (ETDEWEB)
Cartwright, Julyan H.E., E-mail: julyan.cartwright@csic.es [Instituto Andaluz de Ciencias de la Tierra, CSIC–Universidad de Granada, E-18100 Armilla, Granada (Spain); Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071 Granada (Spain); Piro, Nicolas, E-mail: nicolas.piro@epfl.ch [École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne (Switzerland); Piro, Oreste, E-mail: piro@imedea.uib-csic.es [Departamento de Física, Universitat de les Illes Balears, E-07122 Palma de Mallorca (Spain); Tuval, Idan, E-mail: ituval@imedea.uib-csic.es [Mediterranean Institute for Advanced Studies, CSIC–Universitat de les Illes Balears, E-07190 Mallorca (Spain)
2016-10-14
In order to study the behaviour of discrete dynamical systems under adiabatic cyclic variations of their parameters, we consider discrete versions of adiabatically-rotated rotators. Parallelling the studies in continuous systems, we generalize the concept of geometric phase to discrete dynamics and investigate its presence in these rotators. For the rotated sine circle map, we demonstrate an analytical relationship between the geometric phase and the rotation number of the system. For the discrete version of the rotated rotator considered by Berry, the rotated standard map, we further explore this connection as well as the role of the geometric phase at the onset of chaos. Further into the chaotic regime, we show that the geometric phase is also related to the diffusive behaviour of the dynamical variables and the Lyapunov exponent. - Highlights: • We extend the concept of geometric phase to maps. • For the rotated sine circle map, we demonstrate an analytical relationship between the geometric phase and the rotation number. • For the rotated standard map, we explore the role of the geometric phase at the onset of chaos. • We show that the geometric phase is related to the diffusive behaviour of the dynamical variables and the Lyapunov exponent.
A geometric characterization of arithmetic varieties
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
The main result is the characterization of arithmetically defined divisors in the plane as geometrically rigid divisors in the plane. Keywords. Equisingular; geometrically rigid. 1. Introduction. This paper is an attempt to generalize a result of Belyi (see [1]). Theorem (Belyi). Let C be a smooth projective curve over an algebraic ...
Early Sex Differences in Weighting Geometric Cues
Lourenco, Stella F.; Addy, Dede; Huttenlocher, Janellen; Fabian, Lydia
2011-01-01
When geometric and non-geometric information are both available for specifying location, men have been shown to rely more heavily on geometry compared to women. To shed insight on the nature and developmental origins of this sex difference, we examined how 18- to 24-month-olds represented the geometry of a surrounding (rectangular) space when…
Geometric Growing Patterns: What's the Rule?
Hourigan, Mairéad; Leavy, Aisling
2015-01-01
While within a geometric repeating pattern, there is an identifiable core which is made up of objects that repeat in a predictable manner, a geometric growing pattern (also called visual or pictorial growing patterns in other curricula) "is a pattern that is made from a sequence of figures [or objects] that change from one term to the next in…
Geometric Control of Patterned Linear Systems
Hamilton, Sarah C
2012-01-01
This monograph is aiming at researchers of systems control, especially those interested in multiagent systems, distributed and decentralized control, and structured systems. The book assumes no prior background in geometric control theory; however, a first year graduate course in linear control systems is desirable. Since not all control researchers today are exposed to geometric control theory, the book also adopts a tutorial style by way of examples that illustrate the geometric and abstract algebra concepts used in linear geometric control. In addition, the matrix calculations required for the studied control synthesis problems of linear multivariable control are illustrated via a set of running design examples. As such, some of the design examples are of higher dimension than one may typically see in a text; this is so that all the geometric features of the design problem are illuminated.
Geometric distortion correction for sinusoidally scanned images
International Nuclear Information System (INIS)
Xu, Lijun; Tian, Xiangrui; Li, Xiaolu; Shang, Guangyi; Yao, Junen
2011-01-01
A method for correcting the geometric distortion of sinusoidally scanned images was proposed. The generation mechanism of the geometric distortion in sinusoidally scanned images was analyzed. Based on the relationship between the coordinates of uniformly scanned points and those of sinusoidally scanned points, a transformation formula was obtained for correcting the geometric distortion when the sampling rate was a constant. By comparing the forward method with the inverse method, a hybrid method for correcting the geometric distortion of sinusoidally scanned images was proposed. This method takes advantage of both the forward and inverse methods and was proven to be better than either of them in terms of peak signal-to-noise ratio (PSNR). The time consumed by the hybrid method was between the other two. When a higher PSNR is desired, the hybrid method is recommended if time permits. In addition, it is a universal approach to the correction of geometric distortion of the images scanned in the sinusoidal mode
Geometrical Inverse Preconditioning for Symmetric Positive Definite Matrices
Directory of Open Access Journals (Sweden)
Jean-Paul Chehab
2016-07-01
Full Text Available We focus on inverse preconditioners based on minimizing F ( X = 1 − cos ( X A , I , where X A is the preconditioned matrix and A is symmetric and positive definite. We present and analyze gradient-type methods to minimize F ( X on a suitable compact set. For this, we use the geometrical properties of the non-polyhedral cone of symmetric and positive definite matrices, and also the special properties of F ( X on the feasible set. Preliminary and encouraging numerical results are also presented in which dense and sparse approximations are included.
Directory of Open Access Journals (Sweden)
Erokhin V.V.
2017-12-01
Full Text Available The article deals with methods for the implementation of a geometric problem in CNC machines using digital differential analyzers. The advantages and disadvantages of the implementation of interpolation in CNC systems by various methods are considered, special attention is paid to the general methods of digital differential analyzers in the implementation of the interpolation of the movement of the working organs of the machine tool. Interpolation methods are analyzed in which the Euler method is used for numerical integration, based on the expansion of the function in a Taylor series with discarding the highest (second and higher degrees of expansion. The mathematical formalization of the construction of complex curves is shown by the methods of digital differential analyzers - plane curves of the second order, such as parabola, hyperbola, ellipse.
Nakamura, T
1993-01-01
In GR13 we heard many reports on recent. progress as well as future plans of detection of gravitational waves. According to these reports (see the report of the workshop on the detection of gravitational waves by Paik in this volume), it is highly probable that the sensitivity of detectors such as laser interferometers and ultra low temperature resonant bars will reach the level of h ~ 10—21 by 1998. in this level we may expect the detection of the gravitational waves from astrophysical sources such as coalescing binary neutron stars once a year or so. Therefore the progress in numerical relativity is urgently required to predict the wave pattern and amplitude of the gravitational waves from realistic astrophysical sources. The time left for numerical relativists is only six years or so although there are so many difﬁculties in principle as well as in practice.
Image-Based Geometric Modeling and Mesh Generation
2013-01-01
As a new interdisciplinary research area, “image-based geometric modeling and mesh generation” integrates image processing, geometric modeling and mesh generation with finite element method (FEM) to solve problems in computational biomedicine, materials sciences and engineering. It is well known that FEM is currently well-developed and efficient, but mesh generation for complex geometries (e.g., the human body) still takes about 80% of the total analysis time and is the major obstacle to reduce the total computation time. It is mainly because none of the traditional approaches is sufficient to effectively construct finite element meshes for arbitrarily complicated domains, and generally a great deal of manual interaction is involved in mesh generation. This contributed volume, the first for such an interdisciplinary topic, collects the latest research by experts in this area. These papers cover a broad range of topics, including medical imaging, image alignment and segmentation, image-to-mesh conversion,...
Geometric singularities and spectra of Landau-Ginzburg models
International Nuclear Information System (INIS)
Greene, B.R.; Roan, S.S.; Yau, S.T.
1991-01-01
Some mathematical and physical aspects of superconformal string compactification in weighted projective space are discussed. In particular, we recast the path integral argument establishing the connection between Landau-Ginsburg conformal theories and Calabi-Yau string compactification in a geometric framework. We then prove that the naive expression for the vanishing of the first Chern class for a complete intersection (adopted from the smooth case) is sufficient to ensure that the resulting variety, which is generically singular, can be resolved to a smooth Calabi-Yau space. This justifies much analysis which has recently been expended on the study of Landau-Ginzburg models. Furthermore, we derive some simple formulae for the determination of the Witten index in these theories which are complementary to those derived using semiclassical reasoning by Vafa. Finally, we also comment on the possible geometrical significance of unorbifolded Landau-Ginzburg theories. (orig.)
Material and geometric nonlinear analysis of reinforced concrete frames
Directory of Open Access Journals (Sweden)
E. Parente Jr
Full Text Available The analysis of reinforced concrete structures until failure requires the consideration of geometric and material nonlinearities. However, nonlinear analysis is much more complex and costly than linear analysis. In order to obtain a computationally efficient approach to nonlinear analysis of reinforced concrete structures, this work presents the formulation of a nonlinear plane frame element. Geometric nonlinearity is considered using the co-rotational approach and material nonlinearity is included using appropriate constitutive relations for concrete and steel. The integration of stress resultants and tangent constitutive matrix is carried out by the automatic subdivision of the cross-section and the application of the Gauss quadrature in each subdivision. The formulation and computational implementation are validated using experimental results available in the literature. Excellent results were obtained.
An algebraic geometric approach to separation of variables
Schöbel, Konrad
2015-01-01
Konrad Schöbel aims to lay the foundations for a consequent algebraic geometric treatment of variable separation, which is one of the oldest and most powerful methods to construct exact solutions for the fundamental equations in classical and quantum physics. The present work reveals a surprising algebraic geometric structure behind the famous list of separation coordinates, bringing together a great range of mathematics and mathematical physics, from the late 19th century theory of separation of variables to modern moduli space theory, Stasheff polytopes and operads. "I am particularly impressed by his mastery of a variety of techniques and his ability to show clearly how they interact to produce his results.” (Jim Stasheff) Contents The Foundation: The Algebraic Integrability Conditions The Proof of Concept: A Complete Solution for the 3-Sphere The Generalisation: A Solution for Spheres of Arbitrary Dimension The Perspectives: Applications and Generalisations Target Groups Scientists in the fie...
Directory of Open Access Journals (Sweden)
Chaolang Hu
2012-01-01
Full Text Available In order to increase productivity, it is important to study the performance of a hydraulically fractured well producing at constant wellbore pressure. This paper constructs a new productivity formula, which is obtained by solving a weakly singular integral equation of the first kind, for an infinite-conductivity hydraulically fractured well producing at constant pressure. And the two key components of this paper are a weakly singular integral equation of the first kind and a steady-state productivity formula. A new midrectangle algorithm and a Galerkin method are presented in order to solve the weakly singular integral equation. The numerical results of these two methods are in accordance with each other. And then the solutions of the weakly singular integral equation are utilized for the productivity formula of hydraulic fractured wells producing at constant pressure, which provide fast analytical tools to evaluate production performance of infinite-conductivity fractured wells. The paper also shows equipotential threads, which are generated from the numerical results, with different fluid potential values. These threads can be approximately taken as a family of ellipses whose focuses are the two endpoints of the fracture, which is in accordance with the regular assumption in Kuchuk and Brigham, 1979.
A geometrical model for DNA organization in bacteria.
Directory of Open Access Journals (Sweden)
Mathias Buenemann
Full Text Available Recent experimental studies have revealed that bacteria, such as C. crescentus, show a remarkable spatial ordering of their chromosome. A strong linear correlation has been found between the position of genes on the chromosomal map and their spatial position in the cellular volume. We show that this correlation can be explained by a purely geometrical model. Namely, self-avoidance of DNA, specific positioning of one or few DNA loci (such as origin or terminus together with the action of DNA compaction proteins (that organize the chromosome into topological domains are sufficient to get a linear arrangement of the chromosome along the cell axis. We develop a Monte-Carlo method that allows us to test our model numerically and to analyze the dependence of the spatial ordering on various physiologically relevant parameters. We show that the proposed geometrical ordering mechanism is robust and universal (i.e. does not depend on specific bacterial details. The geometrical mechanism should work in all bacteria that have compacted chromosomes with spatially fixed regions. We use our model to make specific and experimentally testable predictions about the spatial arrangement of the chromosome in mutants of C. crescentus and the growth-stage dependent ordering in E. coli.
Interstitial integrals in the multiple-scattering model
International Nuclear Information System (INIS)
Swanson, J.R.; Dill, D.
1982-01-01
We present an efficient method for the evaluation of integrals involving multiple-scattering wave functions over the interstitial region. Transformation of the multicenter interstitial wave functions to a single center representation followed by a geometric projection reduces the integrals to products of analytic angular integrals and numerical radial integrals. The projection function, which has the value 1 in the interstitial region and 0 elsewhere, has a closed-form partial-wave expansion. The method is tested by comparing its results with exact normalization and dipole integrals; the differences are 2% at worst and typically less than 1%. By providing an efficient means of calculating Coulomb integrals, the method allows treatment of electron correlations using a multiple scattering basis set
Method of locating related items in a geometric space for data mining
Hendrickson, Bruce A.
1999-01-01
A method for locating related items in a geometric space transforms relationships among items to geometric locations. The method locates items in the geometric space so that the distance between items corresponds to the degree of relatedness. The method facilitates communication of the structure of the relationships among the items. The method is especially beneficial for communicating databases with many items, and with non-regular relationship patterns. Examples of such databases include databases containing items such as scientific papers or patents, related by citations or keywords. A computer system adapted for practice of the present invention can include a processor, a storage subsystem, a display device, and computer software to direct the location and display of the entities. The method comprises assigning numeric values as a measure of similarity between each pairing of items. A matrix is constructed, based on the numeric values. The eigenvectors and eigenvalues of the matrix are determined. Each item is located in the geometric space at coordinates determined from the eigenvectors and eigenvalues. Proper construction of the matrix and proper determination of coordinates from eigenvectors can ensure that distance between items in the geometric space is representative of the numeric value measure of the items' similarity.
Energy Technology Data Exchange (ETDEWEB)
Chen, Zhaoting; Wang, Rong Hui; Chen, Li; Dong, Chung Uang [School of Civil Engineering and Transportation, South China University of Technology, Guangzhou (China)
2016-08-15
This article investigated the strongly nonlinear free vibration of four edges simply supported stiffened plates with geometric imperfections. The von Karman nonlinear strain-displacement relationships are applied. The nonlinear vibration of stiffened plate is reduced to a one-degree-of-freedom nonlinear system by assuming mode shapes. The Multiple scales Lindstedt-Poincare method (MSLP) and Modified Lindstedt-Poincare method (MLP) are used to solve the governing equations of vibration. Numerical examples for stiffened plates with different initial geometric imperfections are presented in order to discuss the influences to the strongly nonlinear free vibration of the stiffened plate. The results showed that: the frequency ratio reduced as the initial geometric imperfections of plate increased, which showed that the increase of the initial geometric imperfections of plate can lead to the decrease of nonlinear effect; by comparing the results calculated by MSLP method, using MS method to study strongly nonlinear vibration can lead to serious mistakes.
4th Italian-Japanese workshop on Geometric Properties for Parabolic and Elliptic PDE’s
Ishige, Kazuhiro; Nitsch, Carlo; Salani, Paolo
2016-01-01
This book collects recent research papers by respected specialists in the field. It presents advances in the field of geometric properties for parabolic and elliptic partial differential equations, an area that has always attracted great attention. It settles the basic issues (existence, uniqueness, stability and regularity of solutions of initial/boundary value problems) before focusing on the topological and/or geometric aspects. These topics interact with many other areas of research and rely on a wide range of mathematical tools and techniques, both analytic and geometric. The Italian and Japanese mathematical schools have a long history of research on PDEs and have numerous active groups collaborating in the study of the geometric properties of their solutions. .
Wei, Jyh-Da; Tsai, Ming-Hung; Lee, Gen-Cher; Huang, Jeng-Hung; Lee, Der-Tsai
2009-01-01
Algorithm visualization is a unique research topic that integrates engineering skills such as computer graphics, system programming, database management, computer networks, etc., to facilitate algorithmic researchers in testing their ideas, demonstrating new findings, and teaching algorithm design in the classroom. Within the broad applications of algorithm visualization, there still remain performance issues that deserve further research, e.g., system portability, collaboration capability, and animation effect in 3D environments. Using modern technologies of Java programming, we develop an algorithm visualization and debugging system, dubbed GeoBuilder, for geometric computing. The GeoBuilder system features Java's promising portability, engagement of collaboration in algorithm development, and automatic camera positioning for tracking 3D geometric objects. In this paper, we describe the design of the GeoBuilder system and demonstrate its applications.
A Geometrical View of Higgs Effective Theory
CERN. Geneva
2016-01-01
A geometric formulation of Higgs Effective Field Theory (HEFT) is presented. Experimental observables are given in terms of geometric invariants of the scalar sigma model sector such as the curvature of the scalar field manifold M. We show how the curvature can be measured experimentally via Higgs cross-sections, W_L scattering, and the S parameter. The one-loop action of HEFT is given in terms of geometric invariants of M. The distinction between the Standard Model (SM) and HEFT is whether M is flat or curved, with the curvature a signal of the scale of new physics.
Geometrical formulation of the conformal Ward identity
International Nuclear Information System (INIS)
Kachkachi, M.
2002-08-01
In this paper we use deep ideas in complex geometry that proved to be very powerful in unveiling the Polyakov measure on the moduli space of Riemann surfaces and lead to obtain the partition function of perturbative string theory for 2, 3, 4 loops. Indeed, a geometrical interpretation of the conformal Ward identity in two dimensional conformal field theory is proposed: the conformal anomaly is interpreted as a deformation of the complex structure of the basic Riemann surface. This point of view is in line with the modern trend of geometric quantizations that are based on deformations of classical structures. Then, we solve the conformal Ward identity by using this geometrical formalism. (author)
Geometrical analysis of the interacting boson model
International Nuclear Information System (INIS)
Dieperink, A.E.L.
1983-01-01
The Interacting Boson Model is considered, in relation with geometrical models and the application of mean field techniques to algebraic models, in three lectures. In the first, several methods are reviewed to establish a connection between the algebraic formulation of collective nuclear properties in terms of the group SU(6) and the geometric approach. In the second lecture the geometric interpretation of new degrees of freedom that arise in the neutron-proton IBA is discussed, and in the third one some further applications of algebraic techniques to the calculation of static and dynamic collective properties are presented. (U.K.)
Lectures on geometrical properties of nuclei
International Nuclear Information System (INIS)
Myers, W.D.
1975-11-01
Material concerning the geometrical properties of nuclei is drawn from a number of different sources. The leptodermous nature of nuclear density distributions and potential wells is used to draw together the various geometrical properties of these systems and to provide a unified means for their description. Extensive use is made of expansions of radial properties in terms of the surface diffuseness. A strong case is made for the use of convolution as a geometrical ansatz for generating diffuse surface distributions because of the number of simplifications that arise which are of practical importance. 7 figures
Stock price prediction using geometric Brownian motion
Farida Agustini, W.; Restu Affianti, Ika; Putri, Endah RM
2018-03-01
Geometric Brownian motion is a mathematical model for predicting the future price of stock. The phase that done before stock price prediction is determine stock expected price formulation and determine the confidence level of 95%. On stock price prediction using geometric Brownian Motion model, the algorithm starts from calculating the value of return, followed by estimating value of volatility and drift, obtain the stock price forecast, calculating the forecast MAPE, calculating the stock expected price and calculating the confidence level of 95%. Based on the research, the output analysis shows that geometric Brownian motion model is the prediction technique with high rate of accuracy. It is proven with forecast MAPE value ≤ 20%.
DEFF Research Database (Denmark)
Kim, Oleksiy S.; Meincke, Peter; Breinbjerg, Olav
2007-01-01
The problem of electromagnetic scattering by composite metallic and dielectric objects is solved using the coupled volume-surface integral equation (VSIE). The method of moments (MoM) based on higher-order hierarchical Legendre basis functions and higher-order curvilinear geometrical elements...... with the analytical Mie series solution. Scattering by more complex metal-dielectric objects are also considered to compare the presented technique with other numerical methods....
Integrated investigation approach for determining mechanical properties of poly-silicon membranes
Brueckner, J.; Dehe, A.; Auerswald, E.; Dudek, R.; Michel, B.; Rzepka, S.
2014-01-01
A methodology is presented for determining mechanical properties of free-standing thin films such as poly-silicon membranes. The integrated investigation approach comprises test structure development, mechanical testing, and numerical simulation. All membrane test structures developed and manufactured consist of the same material but have different stiffness due to variations in the geometric design. The mechanical tests apply microscopic loads utilizing a nanoindentation tool. Young's modulu...
Geometric continuum mechanics and induced beam theories
R Eugster, Simon
2015-01-01
This research monograph discusses novel approaches to geometric continuum mechanics and introduces beams as constraint continuous bodies. In the coordinate free and metric independent geometric formulation of continuum mechanics as well as for beam theories, the principle of virtual work serves as the fundamental principle of mechanics. Based on the perception of analytical mechanics that forces of a mechanical system are defined as dual quantities to the kinematical description, the virtual work approach is a systematic way to treat arbitrary mechanical systems. Whereas this methodology is very convenient to formulate induced beam theories, it is essential in geometric continuum mechanics when the assumptions on the physical space are relaxed and the space is modeled as a smooth manifold. The book addresses researcher and graduate students in engineering and mathematics interested in recent developments of a geometric formulation of continuum mechanics and a hierarchical development of induced beam theories.
Transition curves for highway geometric design
Kobryń, Andrzej
2017-01-01
This book provides concise descriptions of the various solutions of transition curves, which can be used in geometric design of roads and highways. It presents mathematical methods and curvature functions for defining transition curves. .
5th Dagstuhl Seminar on Geometric Modelling
Brunnett, Guido; Farin, Gerald; Goldman, Ron
2004-01-01
In 19 articles presented by leading experts in the field of geometric modelling the state-of-the-art on representing, modeling, and analyzing curves, surfaces as well as other 3-dimensional geometry is given. The range of applications include CAD/CAM-systems, computer graphics, scientific visualization, virtual reality, simulation and medical imaging. The content of this book is based on selected lectures given at a workshop held at IBFI Schloss Dagstuhl, Germany. Topics treated are: – curve and surface modelling – non-manifold modelling in CAD – multiresolution analysis of complex geometric models – surface reconstruction – variational design – computational geometry of curves and surfaces – 3D meshing – geometric modelling for scientific visualization – geometric models for biomedical applications
Geometric symmetries in superfluid vortex dynamics
Kozik, Evgeny; Svistunov, Boris
2010-10-01
Dynamics of quantized vortex lines in a superfluid feature symmetries associated with the geometric character of the complex-valued field, w(z)=x(z)+iy(z) , describing the instant shape of the line. Along with a natural set of Noether’s constants of motion, which—apart from their rather specific expressions in terms of w(z) —are nothing but components of the total linear and angular momenta of the fluid, the geometric symmetry brings about crucial consequences for kinetics of distortion waves on the vortex lines, the Kelvin waves. It is the geometric symmetry that renders Kelvin-wave cascade local in the wave-number space. Similar considerations apply to other systems with purely geometric degrees of freedom.
Geometric U-folds in four dimensions
Lazaroiu, C. I.; Shahbazi, C. S.
2018-01-01
We describe a general construction of geometric U-folds compatible with a non-trivial extension of the global formulation of four-dimensional extended supergravity on a differentiable spin manifold. The topology of geometric U-folds depends on certain flat fiber bundles which encode how supergravity fields are globally glued together. We show that smooth non-trivial U-folds of this type can exist only in theories where both the scalar and space-time manifolds have non-trivial fundamental group and in addition the scalar map of the solution is homotopically non-trivial. Consistency with string theory requires smooth geometric U-folds to be glued using subgroups of the effective discrete U-duality group, implying that the fundamental group of the scalar manifold of such solutions must be a subgroup of the latter. We construct simple examples of geometric U-folds in a generalization of the axion-dilaton model of \
Directory of Open Access Journals (Sweden)
Oscar E Ruiz
2006-06-01
Full Text Available Geometric Reasoning ability is central to many applications in CAD/CAM/CAPP environments. An increasing demand exists for Geometric Reasoning systems which evaluate the feasibility of virtual scenes speciﬁed by geometric relations. Thus, the Geometric Constraint Satisfaction or Scene Feasibility (GCS/SF problem consists of a basic scenario containing geometric entities, whose context is used to propose constraining relations among still undeﬁned entities. If the constraint speciﬁcation is consistent, the answer of the problem is one of ﬁnitely or inﬁnitely many solution scenarios satisfying the prescribed constraints. Otherwise, a diagnostic of inconsistency is expected. The three main approaches used for this problem are numerical, procedural or operational and mathematical. Numerical and procedural approaches answer only part of the problem, and are not complete in the sense that a failure to provide an answer does not preclude the existence of one. The mathematical approach previously presented by the authors describes the problem using a set of polynomial equations. The common roots to this set of polynomials characterizes the solution space for such a problem. That work presents the use of Groebner basis techniques for verifying the consistency of the constraints. It also integrates subgroups of the Special Euclidean Group of Displacements SE(3 in the problem formulation to exploit the structure implied by geometric relations. Although theoretically sound, these techniques require large amounts of computing resources. This work proposes Divide-and-Conquer techniques applied to local GCS/SF subproblems to identify strongly constrained clusters of geometric entities. The identiﬁcation and preprocessing of these clusters generally reduces the eﬀort required in solving the overall problem. Cluster identiﬁcation can be related to identifying short cycles in the Spatial Constraint graph for the GCS/SF problem. Their preprocessing
Mechanisms of geometrical seismic attenuation
Directory of Open Access Journals (Sweden)
Igor B. Morozov
2011-07-01
Full Text Available In several recent reports, we have explained the frequency dependence of the apparent seismic quality-factor (Q observed in many studies according to the effects of geometrical attenuation, which was defined as the zero-frequency limit of the temporal attenuation coefficient. In particular, geometrical attenuation was found to be positive for most waves traveling within the lithosphere. Here, we present three theoretical models that illustrate the origin of this geometrical attenuation, and we investigate the causes of its preferential positive values. In addition, we discuss the physical basis and limitations of both the conventional and new attenuation models. For waves in media with slowly varying properties, geometrical attenuation is caused by variations in the wavefront curvature, which can be both positive (for defocusing and negative (for focusing. In media with velocity/density contrasts, incoherent reflectivity leads to geometrical-attenuation coefficients which are proportional to the mean squared reflectivity and are always positive. For «coherent» reflectivity, the geometrical attenuation is approximately zero, and the attenuation process can be described according to the concept of «scattering Q». However, the true meaning of this parameter is in describing the mean reflectivity within the medium, and not that of the traditional resonator quality factor known in mechanics. The general conclusion from these models is that non-zero and often positive levels of geometrical attenuation are common in realistic, heterogeneous media, both observationally and theoretically. When transformed into the conventional Q-factor form, this positive geometrical attenuation leads to Q values that quickly increase with frequency. These predictions show that the positive frequency-dependent Q observed in many datasets might represent artifacts of the transformations of the attenuation coefficients into Q.
Numerical Algorithm for Delta of Asian Option
Directory of Open Access Journals (Sweden)
Boxiang Zhang
2015-01-01
Full Text Available We study the numerical solution of the Greeks of Asian options. In particular, we derive a close form solution of Δ of Asian geometric option and use this analytical form as a control to numerically calculate Δ of Asian arithmetic option, which is known to have no explicit close form solution. We implement our proposed numerical method and compare the standard error with other classical variance reduction methods. Our method provides an efficient solution to the hedging strategy with Asian options.
Hopman, AHN; Smedts, F; Dignef, W; Ummelen, M; Sonke, G; Mravunac, M; Vooijs, GP; Speel, EJM; Ramaekers, FCS
Cervical intraepithelial neoplasia (CIN I, II, and III) and cases of CIN III associated with micro-invasive cervical carcinoma (CIN III & mCA) were analysed for evidence of episomal or integrated human papillomavirus (HPV) 16/18 DNA by fluorescence in situ hybridization (FISH). In parallel,
Hopman, A.H.N.; Smedts, F.; Dignef, W.; Ummelen, M.; Sonke, G.S.; Mravunac, M.; Vooijs, G.P.; Speel, E.J.; Ramaekers, F.C.S.
2004-01-01
Cervical intraepithelial neoplasia (CIN I, II, and III) and cases of CIN III associated with micro-invasive cervical carcinoma (CIN III & mCA) were analysed for evidence of episomal or integrated human papillomavirus (HPV) 16/18 DNA by fluorescence in situ hybridization (FISH). In parallel,
Geometric Phase of the Gyromotion for Charged Particles in a Time-dependent Magnetic Field
International Nuclear Information System (INIS)
Liu, Jian; Qin, Hong
2011-01-01
We study the dynamics of the gyrophase of a charged particle in a magnetic field which is uniform in space but changes slowly with time. As the magnetic field evolves slowly with time, the changing of the gyrophase is composed of two parts. The rst part is the dynamical phase, which is the time integral of the instantaneous gyrofrequency. The second part, called geometric gyrophase, is more interesting, and it is an example of the geometric phase which has found many important applications in different branches of physics. If the magnetic field returns to the initial value after a loop in the parameter space, then the geometric gyrophase equals the solid angle spanned by the loop in the parameter space. This classical geometric gyrophase is compared with the geometric phase (the Berry phase) of the spin wave function of an electron placed in the same adiabatically changing magnetic field. Even though gyromotion is not the classical counterpart of the quantum spin, the similarities between the geometric phases of the two cases nevertheless reveal the similar geometric nature of the different physics laws governing these two physics phenomena.
A numerical performance assessment of a commercial cardiopulmonary by-pass blood heat exchanger.
Consolo, Filippo; Fiore, Gianfranco B; Pelosi, Alessandra; Reggiani, Stefano; Redaelli, Alberto
2015-06-01
We developed a numerical model, based on multi-physics computational fluid dynamics (CFD) simulations, to assist the design process of a plastic hollow-fiber bundle blood heat exchanger (BHE) integrated within the INSPIRE(TM), a blood oxygenator (OXY) for cardiopulmonary by-pass procedures, recently released by Sorin Group Italia. In a comparative study, we analyzed five different geometrical design solutions of the BHE module. Quantitative geometrical-dependent parameters providing a comprehensive evaluation of both the hemo- and thermo-dynamics performance of the device were extracted to identify the best-performing prototypical solution. A convenient design configuration was identified, characterized by (i) a uniform blood flow pattern within the fiber bundle, preventing blood flow shunting and the onset of stagnation/recirculation areas and/or high velocity pathways, (ii) an enhanced blood heating efficiency, and (iii) a reduced blood pressure drop. The selected design configuration was then prototyped and tested to experimentally characterize the device performance. Experimental results confirmed numerical predictions, proving the effectiveness of CFD modeling as a reliable tool for in silico identification of suitable working conditions of blood handling medical devices. Notably, the numerical approach limited the need for extensive prototyping, thus reducing the corresponding machinery costs and time-to-market. Copyright © 2015 IPEM. Published by Elsevier Ltd. All rights reserved.
Kuznetsov, G. V.; Strizhak, P. A.
2014-01-01
A model of the heat-and-mass transfer in the neighborhood of a finely atomized water drop moving through the high-temperature products of combustion of materials has been developed for numerical analysis of the macroscopic mechanisms of movement of such a drop in a mixture of combustion products and water vapor with account for the complex of interrelated physical processes and phase transitions taking place in this case. The influence of the convection on the integral characteristics of the evaporation of the indicated drop was analyzed and the sizes of its "temperature" and "concentration" wakes were estimated. The conditions under which the integral characteristics of the evaporation of this drop can be calculated in the diffusion approximation were determined.
Numerical simulation of electrochemical desalination
Hlushkou, D.; Knust, K. N.; Crooks, R. M.; Tallarek, U.
2016-05-01
We present an effective numerical approach to simulate electrochemically mediated desalination of seawater. This new membraneless, energy efficient desalination method relies on the oxidation of chloride ions, which generates an ion depletion zone and local electric field gradient near the junction of a microchannel branch to redirect sea salt into the brine stream, consequently producing desalted water. The proposed numerical model is based on resolution of the 3D coupled Navier-Stokes, Nernst-Planck, and Poisson equations at non-uniform spatial grids. The model is implemented as a parallel code and can be employed to simulate mass-charge transport coupled with surface or volume reactions in 3D systems showing an arbitrarily complex geometrical configuration.
Chin, Jeffrey C.; Csank, Jeffrey T.
2016-01-01
The Tool for Turbine Engine Closed-Loop Transient Analysis (TTECTrA ver2) is a control design tool thatenables preliminary estimation of transient performance for models without requiring a full nonlinear controller to bedesigned. The program is compatible with subsonic engine models implemented in the MATLAB/Simulink (TheMathworks, Inc.) environment and Numerical Propulsion System Simulation (NPSS) framework. At a specified flightcondition, TTECTrA will design a closed-loop controller meeting user-defined requirements in a semi or fully automatedfashion. Multiple specifications may be provided, in which case TTECTrA will design one controller for each, producing acollection of controllers in a single run. Each resulting controller contains a setpoint map, a schedule of setpointcontroller gains, and limiters; all contributing to transient characteristics. The goal of the program is to providesteady-state engine designers with more immediate feedback on the transient engine performance earlier in the design cycle.
DEFF Research Database (Denmark)
Pang, Kar Mun; Karvounis, Nikolas; Walther, Jens Honore
2016-01-01
skeletal model are close to those produced by the larger and more comprehensive chemical mechanisms, apart from those at the low pressure condition. The current study also demonstrates that the variation of averaged soot volume fraction with respect to the change of combustion chamber pressure captured...... using the revised soot model agrees reasonably well with the measurements in terms of peak values. The numerical model is subsequently applied to investigate the flame development, soot/nitrogen monoxide formation and heat transfer in a two-stroke, low-speed uniflow-scavenged marine diesel engine......% higher compared to that when only convective heat loss is considered. The averaged nitrogen monoxide concentration is 7.7% lower when both convective and soot radiative heat losses are accounted for but the net soot mass production is less sensitive to soot radiation. A sensitivity study reveals...
Introduction to Dynamical Systems and Geometric Mechanics
Maruskin, Jared M.
2012-01-01
Introduction to Dynamical Systems and Geometric Mechanics provides a comprehensive tour of two fields that are intimately entwined: dynamical systems is the study of the behavior of physical systems that may be described by a set of nonlinear first-order ordinary differential equations in Euclidean space, whereas geometric mechanics explores similar systems that instead evolve on differentiable manifolds. In the study of geometric mechanics, however, additional geometric structures are often present, since such systems arise from the laws of nature that govern the motions of particles, bodies, and even galaxies. In the first part of the text, we discuss linearization and stability of trajectories and fixed points, invariant manifold theory, periodic orbits, PoincarÃ© maps, Floquet theory, the PoincarÃ©-Bendixson theorem, bifurcations, and chaos. The second part of the text begins with a self-contained chapter on differential geometry that introduces notions of manifolds, mappings, vector fields, the Jacobi-Lie bracket, and differential forms. The final chapters cover Lagrangian and Hamiltonian mechanics from a modern geometric perspective, mechanics on Lie groups, and nonholonomic mechanics via both moving frames and fiber bundle decompositions. The text can be reasonably digested in a single-semester introductory graduate-level course. Each chapter concludes with an application that can serve as a springboard project for further investigation or in-class discussion.
Directory of Open Access Journals (Sweden)
Vysokomorny Vladimir S.
2016-01-01
Full Text Available The mathematical model of heat and mass transfer processes with phase transition is developed. It allows analyzing of integral characteristics for the condenser setup of independent power-supply plant with the organic Rankine cycle. Different kinds of organic liquids can be used as a coolant and working substance. The temperatures of the working liquid at the condenser outlet under different values of outside air temperature are determined. The comparative analysis of the utilization efficiency of different cooling systems and organic coolants is carried out.
Directory of Open Access Journals (Sweden)
Olga V. Vysokomornaya
2015-01-01
Full Text Available The mathematical model of heat and mass transfer processes with phase transition is developed. It allows analysis of integral characteristics for the condenser setup of independent power-supply plant with the organic Rankine cycle. Different kinds of organic liquids can be used as a coolant and working substance. The temperatures of the working liquid at the condenser outlet under different values of outside air temperature are determined. The comparative analysis of the utilization efficiency of different cooling systems and organic coolants is carried out.
Neaux, Dimitri; Guy, Franck; Gilissen, Emmanuel; Coudyzer, Walter; Vignaud, Patrick; Ducrocq, Stéphane
2013-01-01
The organization of the bony face is complex, its morphology being influenced in part by the rest of the cranium. Characterizing the facial morphological variation and craniofacial covariation patterns in extant hominids is fundamental to the understanding of their evolutionary history. Numerous studies on hominid facial shape have proposed hypotheses concerning the relationship between the anterior facial shape, facial block orientation and basicranial flexion. In this study we test these hypotheses in a sample of adult specimens belonging to three extant hominid genera (Homo, Pan and Gorilla). Intraspecific variation and covariation patterns are analyzed using geometric morphometric methods and multivariate statistics, such as partial least squared on three-dimensional landmarks coordinates. Our results indicate significant intraspecific covariation between facial shape, facial block orientation and basicranial flexion. Hominids share similar characteristics in the relationship between anterior facial shape and facial block orientation. Modern humans exhibit a specific pattern in the covariation between anterior facial shape and basicranial flexion. This peculiar feature underscores the role of modern humans' highly-flexed basicranium in the overall integration of the cranium. Furthermore, our results are consistent with the hypothesis of a relationship between the reduction of the value of the cranial base angle and a downward rotation of the facial block in modern humans, and to a lesser extent in chimpanzees.
Quantum three-body reaction dynamics including the geometric phase effect
International Nuclear Information System (INIS)
Wu, Y.S.M.
1992-01-01
Accurate quantum mechanical reactive scattering calculations within the framework of symmetrized hyperspherical coordinate techniques are presented for several processes involving collisions of an electron with a hydrogen atom and an atom with a diatomic molecule in three-dimensional space, and the collinear collision of an atom with a diatomic molecule. In addition to the interest of the processes themselves, the results are compared with previous experimental and theoretical results in such a way as to provide tests of the general usefulness of the methods used. The general theory for the calculation of accurate differential cross sections in the reactive collision of an atom with a diatomic molecule including the geometric phase effect in three-dimensional space is described. This methodology has permitted, for the first time, the calculation of integral and differential cross sections over a significantly larger range of collision energies (up to 2.6 eV total energy) than previously possible for the system H + H 2 . The authors present numerical solutions of the quantum mechanical streamlines of probability current density for collinear atom-diatom reactions. It is used to study the barrier height dependence of dynamics on the Cl + HCl reaction
Nodal free geometric phases: Concept and application to geometric quantum computation
International Nuclear Information System (INIS)
Ericsson, Marie; Kult, David; Sjoeqvist, Erik; Aberg, Johan
2008-01-01
Nodal free geometric phases are the eigenvalues of the final member of a parallel transporting family of unitary operators. These phases are gauge invariant, always well defined, and can be measured interferometrically. Nodal free geometric phases can be used to construct various types of quantum phase gates
Estimating motors from a variety of geometric data in 3D conformal geometric algebra
Valkenburg, R.; Dorst, L.; Dorst, L.; Lasenby, J.
2011-01-01
The motion rotors, or motors, are used to model Euclidean motion in 3D conformal geometric algebra. In this chapter we present a technique for estimating the motor which best transforms one set of noisy geometric objects onto another. The technique reduces to an eigenrotator problem and has some
International Nuclear Information System (INIS)
Bodvarsson, G.S.; Lippmann, M.J.
1980-01-01
The computer program CCC (conduction-convection-consolidation), developed at Lawrence Berkeley Laboratory, solves numerically the heat and mass flow equations for a fully saturated medium, and computes one-dimensional consolidation of the simulated systems. The model employs the Integrated Finite Difference Method (IFDM) in discretizing the saturated medium and formulating the governing equations. The sets of equations are solved either by an iterative solution technique (old version) or an efficient sparse solver (new version). The deformation of the medium is calculated using the one-dimensional consolidation theory of Terzaghi. In this paper, the numerical code is described, validation examples given and areas of application discussed. Several example problems involving flow through fractured media are also presented
Zhang, Wei-Guo; Li, Zhe; Liu, Yong-Jun
2018-01-01
In this paper, we study the pricing problem of the continuously monitored fixed and floating strike geometric Asian power options in a mixed fractional Brownian motion environment. First, we derive both closed-form solutions and mixed fractional partial differential equations for fixed and floating strike geometric Asian power options based on delta-hedging strategy and partial differential equation method. Second, we present the lower and upper bounds of the prices of fixed and floating strike geometric Asian power options under the assumption that both risk-free interest rate and volatility are interval numbers. Finally, numerical studies are performed to illustrate the performance of our proposed pricing model.
Geometric function theory in higher dimension
2017-01-01
The book collects the most relevant outcomes from the INdAM Workshop “Geometric Function Theory in Higher Dimension” held in Cortona on September 5-9, 2016. The Workshop was mainly devoted to discussions of basic open problems in the area, and this volume follows the same line. In particular, it offers a selection of original contributions on Loewner theory in one and higher dimensions, semigroups theory, iteration theory and related topics. Written by experts in geometric function theory in one and several complex variables, it focuses on new research frontiers in this area and on challenging open problems. The book is intended for graduate students and researchers working in complex analysis, several complex variables and geometric function theory.
Geometrical factors in the perception of sacredness
DEFF Research Database (Denmark)
Costa, Marco; Bonetti, Leonardo
2016-01-01
in geometrical figures differing in shape, verticality, size, and symmetry. Verticality, symmetry, and convexity were found to be important factors in the perception of sacredness. In the second test, participants had to mark the point inside geometrical surfaces that was perceived as most sacred, dominant......Geometrical and environmental factors in the perception of sacredness, dominance, and attractiveness were assessed by 137 participants in five tests. In the first test, a two-alternative forced-choice paradigm was used to test the perception of sacredness, dominance, and attractiveness......, and attractive. The top and the center areas were associated with sacredness, dominance, and attractiveness. In the third test, peaks and elevated regions in landscapes were evaluated as more sacred, dominant, and attractive than valley regions. In the fourth test, three figures sharing the same area...