Discrete integrable systems and deformations of associative algebras

International Nuclear Information System (INIS)

Konopelchenko, B G

2009-01-01

Interrelations between discrete deformations of the structure constants for associative algebras and discrete integrable systems are reviewed. Theory of deformations for associative algebras is presented. Closed left ideal generated by the elements representing the multiplication table plays a central role in this theory. Deformations of the structure constants are generated by the deformation driving algebra and governed by the central system of equations. It is demonstrated that many discrete equations such as discrete Boussinesq equation, discrete WDVV equation, discrete Schwarzian KP and BKP equations, discrete Hirota-Miwa equations for KP and BKP hierarchies are particular realizations of the central system. An interaction between the theories of discrete integrable systems and discrete deformations of associative algebras is reciprocal and fruitful. An interpretation of the Menelaus relation (discrete Schwarzian KP equation), discrete Hirota-Miwa equation for KP hierarchy, consistency around the cube as the associativity conditions and the concept of gauge equivalence, for instance, between the Menelaus and KP configurations are particular examples.

Integrable discretization s of derivative nonlinear Schroedinger equations

International Nuclear Information System (INIS)

Tsuchida, Takayuki

2002-01-01

We propose integrable discretizations of derivative nonlinear Schroedinger (DNLS) equations such as the Kaup-Newell equation, the Chen-Lee-Liu equation and the Gerdjikov-Ivanov equation by constructing Lax pairs. The discrete DNLS systems admit the reduction of complex conjugation between two dependent variables and possess bi-Hamiltonian structure. Through transformations of variables and reductions, we obtain novel integrable discretizations of the nonlinear Schroedinger (NLS), modified KdV (mKdV), mixed NLS, matrix NLS, matrix KdV, matrix mKdV, coupled NLS, coupled Hirota, coupled Sasa-Satsuma and Burgers equations. We also discuss integrable discretizations of the sine-Gordon equation, the massive Thirring model and their generalizations. (author)

An integrable semi-discretization of the Boussinesq equation

Energy Technology Data Exchange (ETDEWEB)

Zhang, Yingnan, E-mail: ynzhang@njnu.edu.cn [Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, Jiangsu (China); Tian, Lixin, E-mail: tianlixin@njnu.edu.cn [Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, Jiangsu (China); Nonlinear Scientific Research Center, Jiangsu University, Zhenjiang, Jiangsu (China)

2016-10-23

Highlights: • A new integrable semi-discretization of the Boussinesq equation is present. • A Bäcklund transformation and a Lax pair for the differential-difference system is derived by using Hirota's bilinear method. • The soliton solutions of 'good' Boussinesq equation and numerical algorithms are investigated. - Abstract: In this paper, we present an integrable semi-discretization of the Boussinesq equation. Different from other discrete analogues, we discretize the ‘time’ variable and get an integrable differential-difference system. Under a standard limitation, the differential-difference system converges to the continuous Boussinesq equation such that the discrete system can be used to design numerical algorithms. Using Hirota's bilinear method, we find a Bäcklund transformation and a Lax pair of the differential-difference system. For the case of ‘good’ Boussinesq equation, we investigate the soliton solutions of its discrete analogue and design numerical algorithms. We find an effective way to reduce the phase shift caused by the discretization. The numerical results coincide with our analysis.

Discrete integrable systems and hodograph transformations arising from motions of discrete plane curves

International Nuclear Information System (INIS)

Feng Baofeng; Maruno, Ken-ichi; Inoguchi, Jun-ichi; Kajiwara, Kenji; Ohta, Yasuhiro

2011-01-01

We consider integrable discretizations of some soliton equations associated with the motions of plane curves: the Wadati-Konno-Ichikawa elastic beam equation, the complex Dym equation and the short pulse equation. They are related to the modified KdV or the sine-Gordon equations by the hodograph transformations. Based on the observation that the hodograph transformations are regarded as the Euler-Lagrange transformations of the curve motions, we construct the discrete analogues of the hodograph transformations, which yield integrable discretizations of those soliton equations. (paper)

A hierarchy of Liouville integrable discrete Hamiltonian equations

Energy Technology Data Exchange (ETDEWEB)

Xu Xixiang [College of Science, Shandong University of Science and Technology, Qingdao 266510 (China)], E-mail: xixiang_xu@yahoo.com.cn

2008-05-12

Based on a discrete four-by-four matrix spectral problem, a hierarchy of Lax integrable lattice equations with two potentials is derived. Two Hamiltonian forms are constructed for each lattice equation in the resulting hierarchy by means of the discrete variational identity. A strong symmetry operator of the resulting hierarchy is given. Finally, it is shown that the resulting lattice equations are all Liouville integrable discrete Hamiltonian systems.

A Baecklund transformation between two integrable discrete hungry systems

International Nuclear Information System (INIS)

Fukuda, Akiko; Yamamoto, Yusaku; Iwasaki, Masashi; Ishiwata, Emiko; Nakamura, Yoshimasa

2011-01-01

The discrete hungry Toda (dhToda) equation and the discrete hungry Lotka-Volterra (dhLV) system are known as integrable discrete hungry systems. In this Letter, through finding the LR transformations associated with the dhToda equation and the dhLV system, we present a Baecklund transformation between these integrable systems.

A Baecklund transformation between two integrable discrete hungry systems

Energy Technology Data Exchange (ETDEWEB)

Fukuda, Akiko, E-mail: j1409704@ed.kagu.tus.ac.j [Department of Mathematical Information Science, Graduate School of Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan); Yamamoto, Yusaku [Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501 (Japan); Iwasaki, Masashi [Department of Informatics and Environmental Science, Kyoto Prefectural University, 1-5, Nakaragi-cho, Shimogamo, Sakyo-ku, Kyoto 606-8522 (Japan); Ishiwata, Emiko [Department of Mathematical Information Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan); Nakamura, Yoshimasa [Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501 (Japan)

2011-01-17

The discrete hungry Toda (dhToda) equation and the discrete hungry Lotka-Volterra (dhLV) system are known as integrable discrete hungry systems. In this Letter, through finding the LR transformations associated with the dhToda equation and the dhLV system, we present a Baecklund transformation between these integrable systems.

Smooth surfaces from bilinear patches: Discrete affine minimal surfaces

KAUST Repository

Kä ferbö ck, Florian; Pottmann, Helmut

2013-01-01

Motivated by applications in freeform architecture, we study surfaces which are composed of smoothly joined bilinear patches. These surfaces turn out to be discrete versions of negatively curved affine minimal surfaces and share many properties

Integral and discrete inequalities and their applications

CERN Document Server

Qin, Yuming

2016-01-01

This book focuses on one- and multi-dimensional linear integral and discrete Gronwall-Bellman type inequalities. It provides a useful collection and systematic presentation of known and new results, as well as many applications to differential (ODE and PDE), difference, and integral equations. With this work the author fills a gap in the literature on inequalities, offering an ideal source for researchers in these topics. The present volume is part 1 of the author’s two-volume work on inequalities. Integral and discrete inequalities are a very important tool in classical analysis and play a crucial role in establishing the well-posedness of the related equations, i.e., differential, difference and integral equations.

Integrals of Motion for Discrete-Time Optimal Control Problems

OpenAIRE

Torres, Delfim F. M.

2003-01-01

We obtain a discrete time analog of E. Noether's theorem in Optimal Control, asserting that integrals of motion associated to the discrete time Pontryagin Maximum Principle can be computed from the quasi-invariance properties of the discrete time Lagrangian and discrete time control system. As corollaries, results for first-order and higher-order discrete problems of the calculus of variations are obtained.

Discrete Painlevé equations: an integrability paradigm

International Nuclear Information System (INIS)

Grammaticos, B; Ramani, A

2014-01-01

In this paper we present a review of results on discrete Painlevé equations. We begin with an introduction which serves as a refresher on the continuous Painlevé equations. Next, in the first, main part of the paper, we introduce the discrete Painlevé equations, the various methods for their derivation, and their properties as well as their classification scheme. Along the way we present a brief summary of the two major discrete integrability detectors and of Quispel–Roberts–Thompson mapping, which plays a primordial role in the derivation of discrete Painlevé equations. The second part of the paper is more technical and focuses on the presentation of new results on what are called asymmetric discrete Painlevé equations. (comment)

A curvature theory for discrete surfaces based on mesh parallelity

KAUST Repository

Bobenko, Alexander Ivanovich

2009-12-18

We consider a general theory of curvatures of discrete surfaces equipped with edgewise parallel Gauss images, and where mean and Gaussian curvatures of faces are derived from the faces\\' areas and mixed areas. Remarkably these notions are capable of unifying notable previously defined classes of surfaces, such as discrete isothermic minimal surfaces and surfaces of constant mean curvature. We discuss various types of natural Gauss images, the existence of principal curvatures, constant curvature surfaces, Christoffel duality, Koenigs nets, contact element nets, s-isothermic nets, and interesting special cases such as discrete Delaunay surfaces derived from elliptic billiards. © 2009 Springer-Verlag.

Causal Dynamics of Discrete Surfaces

Directory of Open Access Journals (Sweden)

Pablo Arrighi

2014-03-01

Full Text Available We formalize the intuitive idea of a labelled discrete surface which evolves in time, subject to two natural constraints: the evolution does not propagate information too fast; and it acts everywhere the same.

Smooth surfaces from bilinear patches: Discrete affine minimal surfaces

KAUST Repository

Käferböck, Florian

2013-06-01

Motivated by applications in freeform architecture, we study surfaces which are composed of smoothly joined bilinear patches. These surfaces turn out to be discrete versions of negatively curved affine minimal surfaces and share many properties with their classical smooth counterparts. We present computational design approaches and study special cases which should be interesting for the architectural application. 2013 Elsevier B.V.

Lax Pairs for Discrete Integrable Equations via Darboux Transformations

International Nuclear Information System (INIS)

Cao Ce-Wen; Zhang Guang-Yao

2012-01-01

A method is developed to construct discrete Lax pairs using Darboux transformations. More kinds of Lax pairs are found for some newly appeared discrete integrable equations, including the H1, the special H3 and the Q1 models in the Adler—Bobenko—Suris list and the closely related discrete and semi-discrete pKdV, pMKdV, SG and Liouville equations. (general)

On Generating Discrete Integrable Systems via Lie Algebras and Commutator Equations

International Nuclear Information System (INIS)

Zhang Yu-Feng; Tam, Honwah

2016-01-01

In the paper, we introduce the Lie algebras and the commutator equations to rewrite the Tu-d scheme for generating discrete integrable systems regularly. By the approach the various loop algebras of the Lie algebra A_1 are defined so that the well-known Toda hierarchy and a novel discrete integrable system are obtained, respectively. A reduction of the later hierarchy is just right the famous Ablowitz–Ladik hierarchy. Finally, via two different enlarging Lie algebras of the Lie algebra A_1, we derive two resulting differential-difference integrable couplings of the Toda hierarchy, of course, they are all various discrete expanding integrable models of the Toda hierarchy. When the introduced spectral matrices are higher degrees, the way presented in the paper is more convenient to generate discrete integrable equations than the Tu-d scheme by using the software Maple. (paper)

On the complete integrability of the discrete Nahm equations

International Nuclear Information System (INIS)

Murray, M.K.

2000-01-01

The discrete Nahm equations, a system of matrix valued difference equations, arose in the work of Braam and Austin on half-integral mass hyperbolic monopoles. We show that the discrete Nahm equations are completely integrable in a natural sense: to any solution we can associate a spectral curve and a holomorphic line-bundle over the spectral curve, such that the discrete-time DN evolution corresponds to walking in the Jacobian of the spectral curve in a straight line through the line-bundle with steps of a fixed size. Some of the implications for hyperbolic monopoles are also discussed. (orig.)

Discrete exterior calculus discretization of incompressible Navier–Stokes equations over surface simplicial meshes

KAUST Repository

Mohamed, Mamdouh S.

2016-02-11

A conservative discretization of incompressible Navier–Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.

Discrete exterior calculus discretization of incompressible Navier-Stokes equations over surface simplicial meshes

Science.gov (United States)

Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

2016-05-01

A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.

Integrable semi-discretizations of the reduced Ostrovsky equation

International Nuclear Information System (INIS)

Feng, Bao-Feng; Maruno, Ken-ichi; Ohta, Yasuhiro

2015-01-01

Based on our previous work on the reduced Ostrovsky equation (J. Phys. A: Math. Theor. 45 355203), we construct its integrable semi-discretizations. Since the reduced Ostrovsky equation admits two alternative representations, one being its original form, the other the differentiated form (the short wave limit of the Degasperis–Procesi equation) two semi-discrete analogues of the reduced Ostrovsky equation are constructed possessing the same N-loop soliton solution. The relationship between these two versions of semi-discretizations is also clarified. (paper)

Integrable discretizations of the (2+1)-dimensional sinh-Gordon equation

International Nuclear Information System (INIS)

Hu, Xing-Biao; Yu, Guo-Fu

2007-01-01

In this paper, we propose two semi-discrete equations and one fully discrete equation and study them by Hirota's bilinear method. These equations have continuum limits into a system which admits the (2+1)-dimensional generalization of the sinh-Gordon equation. As a result, two integrable semi-discrete versions and one fully discrete version for the sinh-Gordon equation are found. Baecklund transformations, nonlinear superposition formulae, determinant solution and Lax pairs for these discrete versions are presented

Integrated two-section discrete mode laser

NARCIS (Netherlands)

Anandarajah, P.M.; Latkowski, S.; Browning, C.; Zhou, R.; O'Carroll, J.; Phelan, R.; Kelly, B.; O'Gorman, J.; Barry, L.P.

2012-01-01

The authors present the design and characterization of a novel integrated two-section discrete mode index patterned diode laser source. The two slotted regions etched into the laser ridge waveguide are formed in the same fabrication step as the ridge, thus avoiding the requirement for complex

An integrable (2+1)-dimensional Toda equation with two discrete variables

International Nuclear Information System (INIS)

Cao Cewen; Cao Jianli

2007-01-01

An integrable (2+1)-dimensional Toda equation with two discrete variables is presented from the compatible condition of a Lax triad composed of the ZS-AKNS (Zakharov, Shabat; Ablowitz, Kaup, Newell, Segur) eigenvalue problem and two discrete spectral problems. Through the nonlinearization technique, the Lax triad is transformed into a Hamiltonian system and two symplectic maps, respectively, which are integrable in the Liouville sense, sharing the same set of integrals, functionally independent and involutive with each other. In the Jacobi variety of the associated algebraic curve, both the continuous and the discrete flows are straightened out by the Abel-Jacobi coordinates, and are integrated by quadratures. An explicit algebraic-geometric solution in the original variable is obtained by the Riemann-Jacobi inversion

Effects of image charges, interfacial charge discreteness, and surface roughness on the zeta potential of spherical electric double layers.

Science.gov (United States)

Gan, Zecheng; Xing, Xiangjun; Xu, Zhenli

2012-07-21

We investigate the effects of image charges, interfacial charge discreteness, and surface roughness on spherical electric double layer structures in electrolyte solutions with divalent counterions in the setting of the primitive model. By using Monte Carlo simulations and the image charge method, the zeta potential profile and the integrated charge distribution function are computed for varying surface charge strengths and salt concentrations. Systematic comparisons were carried out between three distinct models for interfacial charges: (1) SURF1 with uniform surface charges, (2) SURF2 with discrete point charges on the interface, and (3) SURF3 with discrete interfacial charges and finite excluded volume. By comparing the integrated charge distribution function and the zeta potential profile, we argue that the potential at the distance of one ion diameter from the macroion surface is a suitable location to define the zeta potential. In SURF2 model, we find that image charge effects strongly enhance charge inversion for monovalent interfacial charges, and strongly suppress charge inversion for multivalent interfacial charges. For SURF3, the image charge effect becomes much smaller. Finally, with image charges in action, we find that excluded volumes (in SURF3) suppress charge inversion for monovalent interfacial charges and enhance charge inversion for multivalent interfacial charges. Overall, our results demonstrate that all these aspects, i.e., image charges, interfacial charge discreteness, their excluding volumes, have significant impacts on zeta potentials of electric double layers.

Irreducibility and co-primeness as an integrability criterion for discrete equations

International Nuclear Information System (INIS)

Kanki, Masataka; Mada, Jun; Mase, Takafumi; Tokihiro, Tetsuji

2014-01-01

We study the Laurent property, the irreducibility and co-primeness of discrete integrable and non-integrable equations. First we study a discrete integrable equation related to the Somos-4 sequence, and also a non-integrable equation as a comparison. We prove that the conditions of irreducibility and co-primeness hold only in the integrable case. Next, we generalize our previous results on the singularities of the discrete Korteweg–de Vries (dKdV) equation. In our previous paper (Kanki et al 2014 J. Phys. A: Math. Theor. 47 065201) we described the singularity confinement test (one of the integrability criteria) using the Laurent property, and the irreducibility, and co-primeness of the terms in the bilinear dKdV equation, in which we only considered simplified boundary conditions. This restriction was needed to obtain simple (monomial) relations between the bilinear form and the nonlinear form of the dKdV equation. In this paper, we prove the co-primeness of the terms in the nonlinear dKdV equation for general initial conditions and boundary conditions, by using the localization of Laurent rings and the interchange of the axes. We assert that co-primeness of the terms can be used as a new integrability criterion, which is a mathematical re-interpretation of the confinement of singularities in the case of discrete equations. (paper)

On various integrable discretizations of a general two-component Volterra system

International Nuclear Information System (INIS)

Babalic, Corina N; Carstea, A S

2013-01-01

We present two integrable discretizations of a general differential–difference bicomponent Volterra system. The results are obtained by discretizing directly the corresponding Hirota bilinear equations in two different ways. Multisoliton solutions are presented together with a new discrete form of Lotka–Volterra equation obtained by an alternative bilinearization. (paper)

A Family of Integrable Rational Semi-Discrete Systems and Its Reduction

International Nuclear Information System (INIS)

Xu Xixiang

2010-01-01

Within framework of zero curvature representation theory, a family of integrahle rational semi-discrete systems is derived from a matrix spectral problem. The Hamiltonian forms of obtained semi-discrete systems are constructed by means of the discrete trace identity. The Liouville integrability for the obtained family is demonstrated. In the end, a reduced family of obtained semi-discrete systems and its Hamiltonian form are worked out. (general)

Critical bifurcation surfaces of 3D discrete dynamics

Directory of Open Access Journals (Sweden)

Michael Sonis

2000-01-01

Full Text Available This paper deals with the analytical representation of bifurcations of each 3D discrete dynamics depending on the set of bifurcation parameters. The procedure of bifurcation analysis proposed in this paper represents the 3D elaboration and specification of the general algorithm of the n-dimensional linear bifurcation analysis proposed by the author earlier. It is proven that 3D domain of asymptotic stability (attraction of the fixed point for a given 3D discrete dynamics is bounded by three critical bifurcation surfaces: the divergence, flip and flutter surfaces. The analytical construction of these surfaces is achieved with the help of classical Routh–Hurvitz conditions of asymptotic stability. As an application the adjustment process proposed by T. Puu for the Cournot oligopoly model is considered in detail.

Advances in discrete differential geometry

CERN Document Server

2016-01-01

This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, ...

New block matrix spectral problem and Hamiltonian structure of the discrete integrable coupling system

Energy Technology Data Exchange (ETDEWEB)

Yu Fajun [College of Maths and Systematic Science, Shenyang Normal University, Shenyang 110034 (China)], E-mail: yufajun888@163.com

2008-06-09

In [W.X. Ma, J. Phys. A: Math. Theor. 40 (2007) 15055], Prof. Ma gave a beautiful result (a discrete variational identity). In this Letter, based on a discrete block matrix spectral problem, a new hierarchy of Lax integrable lattice equations with four potentials is derived. By using of the discrete variational identity, we obtain Hamiltonian structure of the discrete soliton equation hierarchy. Finally, an integrable coupling system of the soliton equation hierarchy and its Hamiltonian structure are obtained through the discrete variational identity.

New block matrix spectral problem and Hamiltonian structure of the discrete integrable coupling system

International Nuclear Information System (INIS)

Yu Fajun

2008-01-01

In [W.X. Ma, J. Phys. A: Math. Theor. 40 (2007) 15055], Prof. Ma gave a beautiful result (a discrete variational identity). In this Letter, based on a discrete block matrix spectral problem, a new hierarchy of Lax integrable lattice equations with four potentials is derived. By using of the discrete variational identity, we obtain Hamiltonian structure of the discrete soliton equation hierarchy. Finally, an integrable coupling system of the soliton equation hierarchy and its Hamiltonian structure are obtained through the discrete variational identity

Constructing New Discrete Integrable Coupling System for Soliton Equation by Kronecker Product

International Nuclear Information System (INIS)

Yu Fajun; Zhang Hongqing

2008-01-01

It is shown that the Kronecker product can be applied to constructing new discrete integrable coupling system of soliton equation hierarchy in this paper. A direct application to the fractional cubic Volterra lattice spectral problem leads to a novel integrable coupling system of soliton equation hierarchy. It is also indicated that the study of discrete integrable couplings by using the Kronecker product is an efficient and straightforward method. This method can be used generally

On Darboux-integrable semi-discrete chains

International Nuclear Information System (INIS)

Habibullin, Ismagil; Sakieva, Alfia; Zheltukhina, Natalya

2010-01-01

A differential-difference equation d/dx t (n+1,x) = f(x,t(n,x),t(n+1,x),d/dx t (n,x)) with unknown t(n, x) depending on the continuous and discrete variables x and n is studied. We call an equation of such kind Darboux integrable if there exist two functions (called integrals) F and I of a finite number of dynamical variables such that D x F = 0 and DI = I, where D x is the operator of total differentiation with respect to x and D is the shift operator: Dp(n) = p(n + 1). It is proved that the integrals can be brought to some canonical form. A method of construction of an explicit formula for a general solution to Darboux-integrable chains is discussed and such solutions are found for a class of chains.

Two hierarchies of integrable lattice equations associated with a discrete matrix spectral problem

International Nuclear Information System (INIS)

Li Xinyue; Xu Xixiang; Zhao Qiulan

2008-01-01

Two hierarchies of nonlinear integrable positive and negative lattice models are derived from a discrete spectral problem. The two lattice hierarchies are proved to have discrete zero curvature representations associated with a discrete spectral problem, which also shows that the positive and negative hierarchies correspond to positive and negative power expansions of Lax operators with respect to the spectral parameter, respectively. Moreover, the integrable lattice models in the positive hierarchy are of polynomial type, and the integrable lattice models in the negative hierarchy are of rational type. Further, we construct infinite conservation laws of the positive hierarchy, then, the integrable coupling systems of the positive hierarchy are derived from enlarging Lax pair

An Integrable Discrete Generalized Nonlinear Schrödinger Equation and Its Reductions

International Nuclear Information System (INIS)

Li Hong-Min; Li Yu-Qi; Chen Yong

2014-01-01

An integrable discrete system obtained by the algebraization of the difference operator is studied. The system is named discrete generalized nonlinear Schrödinger (GNLS) equation, which can be reduced to classical discrete nonlinear Schrödinger (NLS) equation. Furthermore, all of the linear reductions for the discrete GNLS equation are given through the theory of circulant matrices and the discrete NLS equation is obtained by one of the reductions. At the same time, the recursion operator and symmetries of continuous GNLS equation are successfully recovered by its corresponding discrete ones. (general)

Integrable discretizations and self-adaptive moving mesh method for a coupled short pulse equation

International Nuclear Information System (INIS)

Feng, Bao-Feng; Chen, Junchao; Chen, Yong; Maruno, Ken-ichi; Ohta, Yasuhiro

2015-01-01

In the present paper, integrable semi-discrete and fully discrete analogues of a coupled short pulse (CSP) equation are constructed. The key to the construction are the bilinear forms and determinant structure of the solutions of the CSP equation. We also construct N-soliton solutions for the semi-discrete and fully discrete analogues of the CSP equations in the form of Casorati determinants. In the continuous limit, we show that the fully discrete CSP equation converges to the semi-discrete CSP equation, then further to the continuous CSP equation. Moreover, the integrable semi-discretization of the CSP equation is used as a self-adaptive moving mesh method for numerical simulations. The numerical results agree with the analytical results very well. (paper)

On a discrete version of the CP 1 sigma model and surfaces immersed in R3

International Nuclear Information System (INIS)

Grundland, A M; Levi, D; Martina, L

2003-01-01

We present a discretization of the CP 1 sigma model. We show that the discrete CP 1 sigma model is described by a nonlinear partial second-order difference equation with rational nonlinearity. To derive discrete surfaces immersed in three-dimensional Euclidean space a 'complex' lattice is introduced. The so-obtained surfaces are characterized in terms of the quadrilateral cross-ratio of four surface points. In this way we prove that all surfaces associated with the discrete CP 1 sigma model are of constant mean curvature. An explicit example of such discrete surfaces is constructed

A Calderón multiplicative preconditioner for coupled surface-volume electric field integral equations

KAUST Repository

Bagci, Hakan

2010-08-01

A well-conditioned coupled set of surface (S) and volume (V) electric field integral equations (S-EFIE and V-EFIE) for analyzing wave interactions with densely discretized composite structures is presented. Whereas the V-EFIE operator is well-posed even when applied to densely discretized volumes, a classically formulated S-EFIE operator is ill-posed when applied to densely discretized surfaces. This renders the discretized coupled S-EFIE and V-EFIE system ill-conditioned, and its iterative solution inefficient or even impossible. The proposed scheme regularizes the coupled set of S-EFIE and V-EFIE using a Calderón multiplicative preconditioner (CMP)-based technique. The resulting scheme enables the efficient analysis of electromagnetic interactions with composite structures containing fine/subwavelength geometric features. Numerical examples demonstrate the efficiency of the proposed scheme. © 2006 IEEE.

Discretely Integrated Condition Event (DICE) Simulation for Pharmacoeconomics.

Science.gov (United States)

Caro, J Jaime

2016-07-01

Several decision-analytic modeling techniques are in use for pharmacoeconomic analyses. Discretely integrated condition event (DICE) simulation is proposed as a unifying approach that has been deliberately designed to meet the modeling requirements in a straightforward transparent way, without forcing assumptions (e.g., only one transition per cycle) or unnecessary complexity. At the core of DICE are conditions that represent aspects that persist over time. They have levels that can change and many may coexist. Events reflect instantaneous occurrences that may modify some conditions or the timing of other events. The conditions are discretely integrated with events by updating their levels at those times. Profiles of determinant values allow for differences among patients in the predictors of the disease course. Any number of valuations (e.g., utility, cost, willingness-to-pay) of conditions and events can be applied concurrently in a single run. A DICE model is conveniently specified in a series of tables that follow a consistent format and the simulation can be implemented fully in MS Excel, facilitating review and validation. DICE incorporates both state-transition (Markov) models and non-resource-constrained discrete event simulation in a single formulation; it can be executed as a cohort or a microsimulation; and deterministically or stochastically.

Integrable discretizations for the short-wave model of the Camassa-Holm equation

International Nuclear Information System (INIS)

Feng Baofeng; Maruno, Ken-ichi; Ohta, Yasuhiro

2010-01-01

The link between the short-wave model of the Camassa-Holm equation (SCHE) and bilinear equations of the two-dimensional Toda lattice equation is clarified. The parametric form of the N-cuspon solution of the SCHE in Casorati determinant is then given. Based on the above finding, integrable semi-discrete and full-discrete analogues of the SCHE are constructed. The determinant solutions of both semi-discrete and fully discrete analogues of the SCHE are also presented.

On the Complete Integrability of Nonlinear Dynamical Systems on Discrete Manifolds within the Gradient-Holonomic Approach

International Nuclear Information System (INIS)

Prykarpatsky, Yarema A.; Bogolubov, Nikolai N. Jr.; Prykarpatsky, Anatoliy K.; Samoylenko, Valeriy H.

2010-12-01

A gradient-holonomic approach for the Lax type integrability analysis of differential-discrete dynamical systems is devised. The asymptotical solutions to the related Lax equation are studied and the related gradient identity is stated. The integrability of a discrete nonlinear Schroedinger type dynamical system is treated in detail. The integrability of a generalized Riemann type discrete hydrodynamical system is discussed. (author)

A discrete history of the Lorentzian path integral

NARCIS (Netherlands)

Loll, R.

2003-01-01

In these lecture notes, I describe the motivation behind a recent formulation of a non-perturbative gravitational path integral for Lorentzian (instead of the usual Euclidean) space-times, and give a pedagogical introduction to its main features. At the regularized, discrete level this approach

Effect of the surface charge discretization on electric double layers: a Monte Carlo simulation study.

Science.gov (United States)

Madurga, Sergio; Martín-Molina, Alberto; Vilaseca, Eudald; Mas, Francesc; Quesada-Pérez, Manuel

2007-06-21

The structure of the electric double layer in contact with discrete and continuously charged planar surfaces is studied within the framework of the primitive model through Monte Carlo simulations. Three different discretization models are considered together with the case of uniform distribution. The effect of discreteness is analyzed in terms of charge density profiles. For point surface groups, a complete equivalence with the situation of uniformly distributed charge is found if profiles are exclusively analyzed as a function of the distance to the charged surface. However, some differences are observed moving parallel to the surface. Significant discrepancies with approaches that do not account for discreteness are reported if charge sites of finite size placed on the surface are considered.

A class of conservative Hamiltonians with exactly integrable discrete two-dimensional parametric maps

International Nuclear Information System (INIS)

Dikande, Alain M; Njumbe, E Epie

2010-01-01

A class of discrete conservative Hamiltonians with completely integrable two-dimensional (2D) mappings is constructed whose generic models are three families of non-integrable discrete Hamiltonians with on-site potentials whose double-well shapes vary. Unlike the discrete 2D mappings associated with the generic models, which all display pitchfork bifurcations towards randomly pinned states with chaotic features, for the derived models the pitchfork bifurcation leads to fixed points always surrounded by periodic trajectories. A nonlinear stability analysis reveals a finite crossover on the bifurcation line at which the pitchfork transition takes the maps from regular real periodic trajectories towards a regime dominated by a cluster of periodic point trajectories representing the allowed real solutions. The rich variety of structures displayed by the new class of discrete maps, combined with their complete integrability, offer rich perspectives for theoretical modelling of a wide class of systems undergoing structural instabilities without noticeable chaotic precursors.

A semi-discrete integrable multi-component coherently coupled nonlinear Schrödinger system

International Nuclear Information System (INIS)

Zhao, Hai-qiong; Yuan, Jinyun

2016-01-01

A new integrable semi-discrete version is proposed for the multi-component coherently coupled nonlinear Schrödinger equation. The integrability of the semi-discrete system is confirmed by existence of Lax pair and infinite number of conservation laws. With the aid of gauge transformations, explicit formulas for N -fold Darboux transformations are derived whereby some physically important solutions of the system are presented. Furthermore, the theory of the semi-discrete system including Lax pair, Darboux transformations, exact solutions and infinite number of conservation laws are shown for their continuous counterparts in the continuous limit. (paper)

On the mixed discretization of the time domain magnetic field integral equation

KAUST Repository

Ulku, Huseyin Arda

2012-09-01

Time domain magnetic field integral equation (MFIE) is discretized using divergence-conforming Rao-Wilton-Glisson (RWG) and curl-conforming Buffa-Christiansen (BC) functions as spatial basis and testing functions, respectively. The resulting mixed discretization scheme, unlike the classical scheme which uses RWG functions as both basis and testing functions, is proper: Testing functions belong to dual space of the basis functions. Numerical results demonstrate that the marching on-in-time (MOT) solution of the mixed discretized MFIE yields more accurate results than that of classically discretized MFIE. © 2012 IEEE.

Connection between Fourier coefficient and Discretized Cartesian path integration

International Nuclear Information System (INIS)

Coalson, R.D.

1986-01-01

The relationship between so-called Discretized and Fourier coefficient formulations of Cartesian path integration is examined. In particular, an intimate connection between the two is established by rewriting the Discretized formulation in a manifestly Fourier-like way. This leads to improved understanding of both the limit behavior and the convergence properties of computational prescriptions based on the two formalisms. The performance of various prescriptions is compared with regard to calculation of on-diagonal statistical density matrix elements for a number of prototypical 1-d potentials. A consistent convergence order among these prescriptions is established

Iterative discrete ordinates solution of the equation for surface-reflected radiance

Science.gov (United States)

Radkevich, Alexander

2017-11-01

This paper presents a new method of numerical solution of the integral equation for the radiance reflected from an anisotropic surface. The equation relates the radiance at the surface level with BRDF and solutions of the standard radiative transfer problems for a slab with no reflection on its surfaces. It is also shown that the kernel of the equation satisfies the condition of the existence of a unique solution and the convergence of the successive approximations to that solution. The developed method features two basic steps: discretization on a 2D quadrature, and solving the resulting system of algebraic equations with successive over-relaxation method based on the Gauss-Seidel iterative process. Presented numerical examples show good coincidence between the surface-reflected radiance obtained with DISORT and the proposed method. Analysis of contributions of the direct and diffuse (but not yet reflected) parts of the downward radiance to the total solution is performed. Together, they represent a very good initial guess for the iterative process. This fact ensures fast convergence. The numerical evidence is given that the fastest convergence occurs with the relaxation parameter of 1 (no relaxation). An integral equation for BRDF is derived as inversion of the original equation. The potential of this new equation for BRDF retrievals is analyzed. The approach is found not viable as the BRDF equation appears to be an ill-posed problem, and it requires knowledge the surface-reflected radiance on the entire domain of both Sun and viewing zenith angles.

A Calderón multiplicative preconditioner for coupled surface-volume electric field integral equations

KAUST Repository

Bagci, Hakan; Andriulli, Francesco P.; Cools, Kristof; Olyslager, Femke; Michielssen, Eric

2010-01-01

A well-conditioned coupled set of surface (S) and volume (V) electric field integral equations (S-EFIE and V-EFIE) for analyzing wave interactions with densely discretized composite structures is presented. Whereas the V-EFIE operator is well

Discrete nodal integral transport-theory method for multidimensional reactor physics and shielding calculations

International Nuclear Information System (INIS)

Lawrence, R.D.; Dorning, J.J.

1980-01-01

A coarse-mesh discrete nodal integral transport theory method has been developed for the efficient numerical solution of multidimensional transport problems of interest in reactor physics and shielding applications. The method, which is the discrete transport theory analogue and logical extension of the nodal Green's function method previously developed for multidimensional neutron diffusion problems, utilizes the same transverse integration procedure to reduce the multidimensional equations to coupled one-dimensional equations. This is followed by the conversion of the differential equations to local, one-dimensional, in-node integral equations by integrating back along neutron flight paths. One-dimensional and two-dimensional transport theory test problems have been systematically studied to verify the superior computational efficiency of the new method

Three semi-direct sum Lie algebras and three discrete integrable couplings associated with the modified K dV lattice equation

International Nuclear Information System (INIS)

Yu Zhang; Zhang Yufeng

2009-01-01

Three semi-direct sum Lie algebras are constructed, which is an efficient and new way to obtain discrete integrable couplings. As its applications, three discrete integrable couplings associated with the modified K dV lattice equation are worked out. The approach can be used to produce other discrete integrable couplings of the discrete hierarchies of soliton equations.

Discretization of the induced-charge boundary integral equation.

Science.gov (United States)

Bardhan, Jaydeep P; Eisenberg, Robert S; Gillespie, Dirk

2009-07-01

Boundary-element methods (BEMs) for solving integral equations numerically have been used in many fields to compute the induced charges at dielectric boundaries. In this paper, we consider a more accurate implementation of BEM in the context of ions in aqueous solution near proteins, but our results are applicable more generally. The ions that modulate protein function are often within a few angstroms of the protein, which leads to the significant accumulation of polarization charge at the protein-solvent interface. Computing the induced charge accurately and quickly poses a numerical challenge in solving a popular integral equation using BEM. In particular, the accuracy of simulations can depend strongly on seemingly minor details of how the entries of the BEM matrix are calculated. We demonstrate that when the dielectric interface is discretized into flat tiles, the qualocation method of Tausch [IEEE Trans Comput.-Comput.-Aided Des. 20, 1398 (2001)] to compute the BEM matrix elements is always more accurate than the traditional centroid-collocation method. Qualocation is not more expensive to implement than collocation and can save significant computational time by reducing the number of boundary elements needed to discretize the dielectric interfaces.

Discretization of the induced-charge boundary integral equation.

Energy Technology Data Exchange (ETDEWEB)

Bardhan, J. P.; Eisenberg, R. S.; Gillespie, D.; Rush Univ. Medical Center

2009-07-01

Boundary-element methods (BEMs) for solving integral equations numerically have been used in many fields to compute the induced charges at dielectric boundaries. In this paper, we consider a more accurate implementation of BEM in the context of ions in aqueous solution near proteins, but our results are applicable more generally. The ions that modulate protein function are often within a few angstroms of the protein, which leads to the significant accumulation of polarization charge at the protein-solvent interface. Computing the induced charge accurately and quickly poses a numerical challenge in solving a popular integral equation using BEM. In particular, the accuracy of simulations can depend strongly on seemingly minor details of how the entries of the BEM matrix are calculated. We demonstrate that when the dielectric interface is discretized into flat tiles, the qualocation method of Tausch et al. [IEEE Trans Comput.-Comput.-Aided Des. 20, 1398 (2001)] to compute the BEM matrix elements is always more accurate than the traditional centroid-collocation method. Qualocation is not more expensive to implement than collocation and can save significant computational time by reducing the number of boundary elements needed to discretize the dielectric interfaces.

On the axiomatization of some classes of discrete universal integrals

Czech Academy of Sciences Publication Activity Database

Klement, E.P.; Mesiar, Radko

2012-01-01

Roč. 28, č. 1 (2012), s. 13-18 ISSN 0950-7051 R&D Projects: GA ČR GAP402/11/0378 Institutional research plan: CEZ:AV0Z10750506 Keywords : Comonotone modularity * Copula * Universal integral Subject RIV: BA - General Mathematics Impact factor: 4.104, year: 2012 http://library.utia.cas.cz/separaty/2012/E/mesiar-on the axiomatization of some classes of discrete universal integrals. pdf

Effect of the surface charge discretization on electric double layers. A Monte Carlo simulation study

OpenAIRE

Madurga Díez, Sergio; Martín-Molina, Alberto; Vilaseca i Font, Eudald; Mas i Pujadas, Francesc; Quesada-Pérez, Manuel

2007-01-01

The structure of the electric double layer in contact with discrete and continuously charged planar surfaces is studied within the framework of the primitive model through Monte Carlo simulations. Three different discretization models are considered together with the case of uniform distribution. The effect of discreteness is analyzed in terms of charge density profiles. For point surface groups,a complete equivalence with the situation of uniformly distributed charge is found if profiles are...

Matrix integral solutions to the discrete KP hierarchy and its Pfaffianized version

International Nuclear Information System (INIS)

Lafortune, Stéphane; Li, Chun-Xia

2016-01-01

Matrix integrals used in random matrix theory for the study of eigenvalues of Hermitian ensembles have been shown to provide τ -functions for several hierarchies of integrable equations. In this article, we extend this relation by showing that such integrals can also provide τ -functions for the discrete KP hierarchy and a coupled version of the same hierarchy obtained through the process of Pfaffianization. To do so, we consider the first equation of the discrete KP hierarchy, the Hirota–Miwa equation. We write the Wronskian determinant solutions to the Hirota–Miwa equation and consider a particular form of matrix integrals, which we show is an example of those Wronskian solutions. The argument is then generalized to the whole hierarchy. A similar strategy is used for the Pfaffianized version of the hierarchy except that in that case, the solutions are written in terms of Pfaffians rather than determinants. (paper)

On discrete 2D integrable equations of higher order

International Nuclear Information System (INIS)

Adler, V E; Postnikov, V V

2014-01-01

We study two-dimensional discrete integrable equations of order 1 with respect to one independent variable and m with respect to another one. A generalization of the multidimensional consistency property is proposed for this type of equations. The examples are related to the Bäcklund–Darboux transformations for the lattice equations of Bogoyavlensky type. (paper)

Integrated simulation of continuous-scale and discrete-scale radiative transfer in metal foams

Science.gov (United States)

Xia, Xin-Lin; Li, Yang; Sun, Chuang; Ai, Qing; Tan, He-Ping

2018-06-01

A novel integrated simulation of radiative transfer in metal foams is presented. It integrates the continuous-scale simulation with the direct discrete-scale simulation in a single computational domain. It relies on the coupling of the real discrete-scale foam geometry with the equivalent continuous-scale medium through a specially defined scale-coupled zone. This zone holds continuous but nonhomogeneous volumetric radiative properties. The scale-coupled approach is compared to the traditional continuous-scale approach using volumetric radiative properties in the equivalent participating medium and to the direct discrete-scale approach employing the real 3D foam geometry obtained by computed tomography. All the analyses are based on geometrical optics. The Monte Carlo ray-tracing procedure is used for computations of the absorbed radiative fluxes and the apparent radiative behaviors of metal foams. The results obtained by the three approaches are in tenable agreement. The scale-coupled approach is fully validated in calculating the apparent radiative behaviors of metal foams composed of very absorbing to very reflective struts and that composed of very rough to very smooth struts. This new approach leads to a reduction in computational time by approximately one order of magnitude compared to the direct discrete-scale approach. Meanwhile, it can offer information on the local geometry-dependent feature and at the same time the equivalent feature in an integrated simulation. This new approach is promising to combine the advantages of the continuous-scale approach (rapid calculations) and direct discrete-scale approach (accurate prediction of local radiative quantities).

Comparison of discrete Hodge star operators for surfaces

KAUST Repository

Mohamed, Mamdouh S.

2016-05-10

We investigate the performance of various discrete Hodge star operators for discrete exterior calculus (DEC) using circumcentric and barycentric dual meshes. The performance is evaluated through the DEC solution of Darcy and incompressible Navier–Stokes flows over surfaces. While the circumcentric Hodge operators may be favorable due to their diagonal structure, the barycentric (geometric) and the Galerkin Hodge operators have the advantage of admitting arbitrary simplicial meshes. Numerical experiments reveal that the barycentric and the Galerkin Hodge operators retain the numerical convergence order attained through the circumcentric (diagonal) Hodge operators. Furthermore, when the barycentric or the Galerkin Hodge operators are employed, a super-convergence behavior is observed for the incompressible flow solution over unstructured simplicial surface meshes generated by successive subdivision of coarser meshes. Insofar as the computational cost is concerned, the Darcy flow solutions exhibit a moderate increase in the solution time when using the barycentric or the Galerkin Hodge operators due to a modest decrease in the linear system sparsity. On the other hand, for the incompressible flow simulations, both the solution time and the linear system sparsity do not change for either the circumcentric or the barycentric and the Galerkin Hodge operators.

A systematic method for constructing time discretizations of integrable lattice systems: local equations of motion

International Nuclear Information System (INIS)

Tsuchida, Takayuki

2010-01-01

We propose a new method for discretizing the time variable in integrable lattice systems while maintaining the locality of the equations of motion. The method is based on the zero-curvature (Lax pair) representation and the lowest-order 'conservation laws'. In contrast to the pioneering work of Ablowitz and Ladik, our method allows the auxiliary dependent variables appearing in the stage of time discretization to be expressed locally in terms of the original dependent variables. The time-discretized lattice systems have the same set of conserved quantities and the same structures of the solutions as the continuous-time lattice systems; only the time evolution of the parameters in the solutions that correspond to the angle variables is discretized. The effectiveness of our method is illustrated using examples such as the Toda lattice, the Volterra lattice, the modified Volterra lattice, the Ablowitz-Ladik lattice (an integrable semi-discrete nonlinear Schroedinger system) and the lattice Heisenberg ferromagnet model. For the modified Volterra lattice, we also present its ultradiscrete analogue.

Commutativity of the source generation procedure and integrable semi-discretizations: the two-dimensional Leznov lattice

International Nuclear Information System (INIS)

Hu Juan; Yu Guofu; Tam, Hon-Wah

2012-01-01

The source generation procedure (SGP) is applied to a y-directional discrete version and an x-directional discrete version of the Leznov lattice. Consequently, a y-discrete Leznov lattice equation with self-consistent sources (y-discrete Leznov ESCS) and an x-discrete Leznov ESCS are presented. Also utilizing the SGP, a new type of Leznov lattice equation with self-consistent sources (new Leznov ESCS) is derived. It is interesting that the two semi-discrete Leznov ESCS produced constitute a y-discretization for the Leznov ESCS given by Wang et al (2007 J. Phys. A: Math. Theor. 40 12691) and an x-discretization for the new Leznov ESCS, respectively. This means that the commutativity of SGP and integrable semi-discretizations is valid for the two-dimensional Leznov lattice equation. (paper)

A curvature theory for discrete surfaces based on mesh parallelity

KAUST Repository

Bobenko, Alexander Ivanovich; Pottmann, Helmut; Wallner, Johannes

2009-01-01

We consider a general theory of curvatures of discrete surfaces equipped with edgewise parallel Gauss images, and where mean and Gaussian curvatures of faces are derived from the faces' areas and mixed areas. Remarkably these notions are capable

Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations

KAUST Repository

Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

2017-01-01

A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy

The Integration of Continuous and Discrete Latent Variable Models: Potential Problems and Promising Opportunities

Science.gov (United States)

Bauer, Daniel J.; Curran, Patrick J.

2004-01-01

Structural equation mixture modeling (SEMM) integrates continuous and discrete latent variable models. Drawing on prior research on the relationships between continuous and discrete latent variable models, the authors identify 3 conditions that may lead to the estimation of spurious latent classes in SEMM: misspecification of the structural model,…

Prediction of Nanoparticle and Colloid Attachment on Unfavorable Mineral Surfaces Using Representative Discrete Heterogeneity.

Science.gov (United States)

Trauscht, Jacob; Pazmino, Eddy; Johnson, William P

2015-09-01

Despite several decades of research there currently exists no mechanistic theory to predict colloid attachment in porous media under environmental conditions where colloid-collector repulsion exists (unfavorable conditions for attachment). It has long been inferred that nano- to microscale surface heterogeneity (herein called discrete heterogeneity) drives colloid attachment under unfavorable conditions. Incorporating discrete heterogeneity into colloid-collector interaction calculations in particle trajectory simulations predicts colloid attachment under unfavorable conditions. As yet, discrete heterogeneity cannot be independently measured by spectroscopic or other approaches in ways directly relevant to colloid-surface interaction. This, combined with the fact that a given discrete heterogeneity representation will interact differently with differently sized colloids as well as different ionic strengths for a given sized colloid, suggests a strategy to back out representative discrete heterogeneity by a comparison of simulations to experiments performed across a range of colloid size, solution IS, and fluid velocity. This has recently been performed for interaction of carboxylate-modified polystyrene latex (CML) microsphere attachment to soda lime glass at pH 6.7 with NaCl electrolyte. However, extension to other surfaces, pH values, and electrolytes is needed. For this reason, the attachment of CML (0.25, 1.1, and 2.0 μm diameters) from aqueous suspension onto a variety of unfavorable mineral surfaces (soda lime glass, muscovite, and albite) was examined for pH values of 6.7 and 8.0), fluid velocities (1.71 × 10(-3) and 5.94 × 10(-3) m s(-1)), IS (6.0 and 20 mM), and electrolytes (NaCl, CaSO4, and multivalent mixtures). The resulting representative heterogeneities (heterodomain size and surface coverage, where heterodomain refers to nano- to microscale attractive domains) yielded colloid attachment predictions that were compared to predictions from existing

Infinitely many conservation laws for two integrable lattice hierarchies associated with a new discrete Schroedinger spectral problem

International Nuclear Information System (INIS)

Zhu, Zuo-nong; Tam, Hon-Wah; Ding, Qing

2003-01-01

In this Letter, by means of considering matrix form of a new Schroedinger discrete spectral operator equation, and constructing opportune time evolution equations, and using discrete zero curvature representation, two discrete integrable lattice hierarchies proposed by Boiti et al. [J. Phys. A: Math. Gen. 36 (2003) 139] are re-derived. From the matrix Lax representations, we demonstrate the existence of infinitely many conservation laws for the two lattice hierarchies and give the corresponding conserved densities and the associated fluxes by means of formulae. Thus their integrability is further confirmed. Specially we obtain the infinitely many conservation laws for a new discrete version of the KdV equation. A connection between the conservation laws of the discrete KdV equation and the ones of the KdV equation is discussed by two examples

Discrete Surface Evolution and Mesh Deformation for Aircraft Icing Applications

Science.gov (United States)

Thompson, David; Tong, Xiaoling; Arnoldus, Qiuhan; Collins, Eric; McLaurin, David; Luke, Edward; Bidwell, Colin S.

2013-01-01

Robust, automated mesh generation for problems with deforming geometries, such as ice accreting on aerodynamic surfaces, remains a challenging problem. Here we describe a technique to deform a discrete surface as it evolves due to the accretion of ice. The surface evolution algorithm is based on a smoothed, face-offsetting approach. We also describe a fast algebraic technique to propagate the computed surface deformations into the surrounding volume mesh while maintaining geometric mesh quality. Preliminary results presented here demonstrate the ecacy of the approach for a sphere with a prescribed accretion rate, a rime ice accretion, and a more complex glaze ice accretion.

A two-component generalization of the reduced Ostrovsky equation and its integrable semi-discrete analogue

International Nuclear Information System (INIS)

Feng, Bao-Feng; Maruno, Ken-ichi; Ohta, Yasuhiro

2017-01-01

In the present paper, we propose a two-component generalization of the reduced Ostrovsky (Vakhnenko) equation, whose differential form can be viewed as the short-wave limit of a two-component Degasperis–Procesi (DP) equation. They are integrable due to the existence of Lax pairs. Moreover, we have shown that the two-component reduced Ostrovsky equation can be reduced from an extended BKP hierarchy with negative flow through a pseudo 3-reduction and a hodograph (reciprocal) transform. As a by-product, its bilinear form and N -soliton solution in terms of pfaffians are presented. One- and two-soliton solutions are provided and analyzed. In the second part of the paper, we start with a modified BKP hierarchy, which is a Bäcklund transformation of the above extended BKP hierarchy, an integrable semi-discrete analogue of the two-component reduced Ostrovsky equation is constructed by defining an appropriate discrete hodograph transform and dependent variable transformations. In particular, the backward difference form of above semi-discrete two-component reduced Ostrovsky equation gives rise to the integrable semi-discretization of the short wave limit of a two-component DP equation. Their N -soliton solutions in terms of pffafians are also provided. (paper)

On the mixed discretization of the time domain magnetic field integral equation

KAUST Repository

Ulku, Huseyin Arda; Bogaert, Ignace; Cools, Kristof; Andriulli, Francesco P.; Bagci, Hakan

2012-01-01

Time domain magnetic field integral equation (MFIE) is discretized using divergence-conforming Rao-Wilton-Glisson (RWG) and curl-conforming Buffa-Christiansen (BC) functions as spatial basis and testing functions, respectively. The resulting mixed

The choice of optimal Discrete Interaction Approximation to the kinetic integral for ocean waves

Directory of Open Access Journals (Sweden)

V. G. Polnikov

2003-01-01

Full Text Available A lot of discrete configurations for the four-wave nonlinear interaction processes have been calculated and tested by the method proposed earlier in the frame of the concept of Fast Discrete Interaction Approximation to the Hasselmann's kinetic integral (Polnikov and Farina, 2002. It was found that there are several simple configurations, which are more efficient than the one proposed originally in Hasselmann et al. (1985. Finally, the optimal multiple Discrete Interaction Approximation (DIA to the kinetic integral for deep-water waves was found. Wave spectrum features have been intercompared for a number of different configurations of DIA, applied to a long-time solution of kinetic equation. On the basis of this intercomparison the better efficiency of the configurations proposed was confirmed. Certain recommendations were given for implementation of new approximations to the wave forecast practice.

Development of discrete gas kinetic scheme for simulation of 3D viscous incompressible and compressible flows

Science.gov (United States)

Yang, L. M.; Shu, C.; Wang, Y.; Sun, Y.

2016-08-01

The sphere function-based gas kinetic scheme (GKS), which was presented by Shu and his coworkers [23] for simulation of inviscid compressible flows, is extended to simulate 3D viscous incompressible and compressible flows in this work. Firstly, we use certain discrete points to represent the spherical surface in the phase velocity space. Then, integrals along the spherical surface for conservation forms of moments, which are needed to recover 3D Navier-Stokes equations, are approximated by integral quadrature. The basic requirement is that these conservation forms of moments can be exactly satisfied by weighted summation of distribution functions at discrete points. It was found that the integral quadrature by eight discrete points on the spherical surface, which forms the D3Q8 discrete velocity model, can exactly match the integral. In this way, the conservative variables and numerical fluxes can be computed by weighted summation of distribution functions at eight discrete points. That is, the application of complicated formulations resultant from integrals can be replaced by a simple solution process. Several numerical examples including laminar flat plate boundary layer, 3D lid-driven cavity flow, steady flow through a 90° bending square duct, transonic flow around DPW-W1 wing and supersonic flow around NACA0012 airfoil are chosen to validate the proposed scheme. Numerical results demonstrate that the present scheme can provide reasonable numerical results for 3D viscous flows.

Integrated information in discrete dynamical systems: motivation and theoretical framework.

Directory of Open Access Journals (Sweden)

David Balduzzi

2008-06-01

Full Text Available This paper introduces a time- and state-dependent measure of integrated information, phi, which captures the repertoire of causal states available to a system as a whole. Specifically, phi quantifies how much information is generated (uncertainty is reduced when a system enters a particular state through causal interactions among its elements, above and beyond the information generated independently by its parts. Such mathematical characterization is motivated by the observation that integrated information captures two key phenomenological properties of consciousness: (i there is a large repertoire of conscious experiences so that, when one particular experience occurs, it generates a large amount of information by ruling out all the others; and (ii this information is integrated, in that each experience appears as a whole that cannot be decomposed into independent parts. This paper extends previous work on stationary systems and applies integrated information to discrete networks as a function of their dynamics and causal architecture. An analysis of basic examples indicates the following: (i phi varies depending on the state entered by a network, being higher if active and inactive elements are balanced and lower if the network is inactive or hyperactive. (ii phi varies for systems with identical or similar surface dynamics depending on the underlying causal architecture, being low for systems that merely copy or replay activity states. (iii phi varies as a function of network architecture. High phi values can be obtained by architectures that conjoin functional specialization with functional integration. Strictly modular and homogeneous systems cannot generate high phi because the former lack integration, whereas the latter lack information. Feedforward and lattice architectures are capable of generating high phi but are inefficient. (iv In Hopfield networks, phi is low for attractor states and neutral states, but increases if the networks

Integrated information in discrete dynamical systems: motivation and theoretical framework.

Science.gov (United States)

Balduzzi, David; Tononi, Giulio

2008-06-13

This paper introduces a time- and state-dependent measure of integrated information, phi, which captures the repertoire of causal states available to a system as a whole. Specifically, phi quantifies how much information is generated (uncertainty is reduced) when a system enters a particular state through causal interactions among its elements, above and beyond the information generated independently by its parts. Such mathematical characterization is motivated by the observation that integrated information captures two key phenomenological properties of consciousness: (i) there is a large repertoire of conscious experiences so that, when one particular experience occurs, it generates a large amount of information by ruling out all the others; and (ii) this information is integrated, in that each experience appears as a whole that cannot be decomposed into independent parts. This paper extends previous work on stationary systems and applies integrated information to discrete networks as a function of their dynamics and causal architecture. An analysis of basic examples indicates the following: (i) phi varies depending on the state entered by a network, being higher if active and inactive elements are balanced and lower if the network is inactive or hyperactive. (ii) phi varies for systems with identical or similar surface dynamics depending on the underlying causal architecture, being low for systems that merely copy or replay activity states. (iii) phi varies as a function of network architecture. High phi values can be obtained by architectures that conjoin functional specialization with functional integration. Strictly modular and homogeneous systems cannot generate high phi because the former lack integration, whereas the latter lack information. Feedforward and lattice architectures are capable of generating high phi but are inefficient. (iv) In Hopfield networks, phi is low for attractor states and neutral states, but increases if the networks are optimized

Shifts of integration variable within four- and N-dimensional Feynman integrals

International Nuclear Information System (INIS)

Elias, V.; McKeon, G.; Mann, R.B.

1983-01-01

We resolve inconsistencies between integration in four dimensions, where shifts of integration variable may lead to surface terms, and dimensional regularization, where no surface terms accompany such shifts, by showing that surface terms arise only for discrete values of the dimension parameter. General formulas for variable-of-integration shifts within N-dimensional Feynman integrals are presented, and the VVA triangle anomaly is interpreted as a manifestation of surface terms occurring in exactly four dimensions

Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations

KAUST Repository

Mohamed, Mamdouh S.

2017-05-23

A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy otherwise. The mimetic character of many of the DEC operators provides exact conservation of both mass and vorticity, in addition to superior kinetic energy conservation. The employment of barycentric Hodge star allows the discretization to admit arbitrary simplicial meshes. The discretization scheme is presented along with various numerical test cases demonstrating its main characteristics.

Chaotic properties between the nonintegrable discrete nonlinear Schroedinger equation and a nonintegrable discrete Heisenberg model

International Nuclear Information System (INIS)

Ding Qing

2007-01-01

We prove that the integrable-nonintegrable discrete nonlinear Schroedinger equation (AL-DNLS) introduced by Cai, Bishop and Gronbech-Jensen (Phys. Rev. Lett. 72 591(1994)) is the discrete gauge equivalent to an integrable-nonintegrable discrete Heisenberg model from the geometric point of view. Then we study whether the transmission and bifurcation properties of the AL-DNLS equation are preserved under the action of discrete gauge transformations. Our results reveal that the transmission property of the AL-DNLS equation is completely preserved and the bifurcation property is conditionally preserved to those of the integrable-nonintegrable discrete Heisenberg model

Discrete mKdV and discrete sine-Gordon flows on discrete space curves

International Nuclear Information System (INIS)

Inoguchi, Jun-ichi; Kajiwara, Kenji; Matsuura, Nozomu; Ohta, Yasuhiro

2014-01-01

In this paper, we consider the discrete deformation of the discrete space curves with constant torsion described by the discrete mKdV or the discrete sine-Gordon equations, and show that it is formulated as the torsion-preserving equidistant deformation on the osculating plane which satisfies the isoperimetric condition. The curve is reconstructed from the deformation data by using the Sym–Tafel formula. The isoperimetric equidistant deformation of the space curves does not preserve the torsion in general. However, it is possible to construct the torsion-preserving deformation by tuning the deformation parameters. Further, it is also possible to make an arbitrary choice of the deformation described by the discrete mKdV equation or by the discrete sine-Gordon equation at each step. We finally show that the discrete deformation of discrete space curves yields the discrete K-surfaces. (paper)

Path integral measure and triangulation independence in discrete gravity

Science.gov (United States)

Dittrich, Bianca; Steinhaus, Sebastian

2012-02-01

A path integral measure for gravity should also preserve the fundamental symmetry of general relativity, which is diffeomorphism symmetry. In previous work, we argued that a successful implementation of this symmetry into discrete quantum gravity models would imply discretization independence. We therefore consider the requirement of triangulation independence for the measure in (linearized) Regge calculus, which is a discrete model for quantum gravity, appearing in the semi-classical limit of spin foam models. To this end we develop a technique to evaluate the linearized Regge action associated to Pachner moves in 3D and 4D and show that it has a simple, factorized structure. We succeed in finding a local measure for 3D (linearized) Regge calculus that leads to triangulation independence. This measure factor coincides with the asymptotics of the Ponzano Regge Model, a 3D spin foam model for gravity. We furthermore discuss to which extent one can find a triangulation independent measure for 4D Regge calculus and how such a measure would be related to a quantum model for 4D flat space. To this end, we also determine the dependence of classical Regge calculus on the choice of triangulation in 3D and 4D.

Discrete exterior calculus discretization of incompressible Navier–Stokes equations over surface simplicial meshes

KAUST Repository

Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

2016-01-01

A conservative discretization of incompressible Navier–Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a

Discrete impurity band from surface danging bonds in nitrogen and phosphorus doped SiC nanowires

Science.gov (United States)

Li, Yan-Jing; Li, Shu-Long; Gong, Pei; Li, Ya-Lin; Cao, Mao-Sheng; Fang, Xiao-Yong

2018-04-01

The electronic structure and optical properties of the nitrogen and phosphorus doped silicon carbide nanowires (SiCNWs) are investigated using first-principle calculations based on density functional theory. The results show doping can change the type of the band gap and improve the conductivity. However, the doped SiCNWs form a discrete impurity levels at the Fermi energy, and the dispersion degree decreases with the diameter increasing. In order to reveal the root of this phenomenon, we hydrogenated the doped SiCNWs, found that the surface dangling bonds were saturated, and the discrete impurity levels are degeneracy, which indicates that the discrete impurity band of the doped SiCNWs is derived from the dangling bonds. The surface passivation can degenerate the impurity levels. Therefore, both doping and surface passivation can better improve the photoelectric properties of the SiCNWs. The result can provide additional candidates in producing nano-optoelectronic devices.

Equilibrium and response properties of the integrate-and-fire neuron in discrete time

Directory of Open Access Journals (Sweden)

Moritz Helias

2010-01-01

Full Text Available The integrate-and-fire neuron with exponential postsynaptic potentials is a frequently employed model to study neural networks. Simulations in discrete time still have highest performance at moderate numerical errors, which makes them first choice for long-term simulations of plastic networks. Here we extend the population density approach to investigate how the equilibrium and response properties of the leaky integrate-and-fire neuron are affected by time discretization. We present a novel analytical treatment of the boundary condition at threshold, taking both discretization of time and finite synaptic weights into account. We uncover an increased membrane potential density just below threshold as the decisive property that explains the deviations found between simulations and the classical diffusion approximation. Temporal discretization and finite synaptic weights both contribute to this effect. Our treatment improves the standard formula to calculate the neuron’s equilibrium firing rate. Direct solution of the Markov process describing the evolution of the membrane potential density confirms our analysis and yields a method to calculate the firing rate exactly. Knowing the shape of the membrane potential distribution near threshold enables us to devise the transient response properties of the neuron model to synaptic input. We find a pronounced non-linear fast response component that has not been described by the prevailing continuous time theory for Gaussian white noise input.

Hamiltonian structures and integrability for a discrete coupled KdV-type equation hierarchy

International Nuclear Information System (INIS)

Zhao Haiqiong; Zhu Zuonong; Zhang Jingli

2011-01-01

Coupled Korteweg-de Vries (KdV) systems have many important physical applications. By considering a 4 × 4 spectral problem, we derive a discrete coupled KdV-type equation hierarchy. Our hierarchy includes the coupled Volterra system proposed by Lou et al. (e-print arXiv: 0711.0420) as the first member which is a discrete version of the coupled KdV equation. We also investigate the integrability in the Liouville sense and the multi-Hamiltonian structures for the obtained hierarchy. (authors)

Current in heavy-current planar diode with discrete emission surface

International Nuclear Information System (INIS)

Belomyttsev, S.Ya.; Korovin, S.D.; Pegel', I.V

1999-01-01

Dependence of current in a high-current planar diode on the size of emission centres was studied. Essential effect of emission surface microstructure on the current value in the planar diode was demonstrated. It was determined that if the distance between the emitter essentially exceeded their size then current dependence on the ratio of size to the value of the diode gap was an exponential function with 3/2 index. Current dependence on voltage obeyed the exponential law with 3/2 index up to higher voltage values in the planar diode with discrete emission surface in contrast to the case of a planar diode with homogeneous emission surface [ru

Resonance and web structure in discrete soliton systems: the two-dimensional Toda lattice and its fully discrete and ultra-discrete analogues

International Nuclear Information System (INIS)

Maruno, Ken-ichi; Biondini, Gino

2004-01-01

We present a class of solutions of the two-dimensional Toda lattice equation, its fully discrete analogue and its ultra-discrete limit. These solutions demonstrate the existence of soliton resonance and web-like structure in discrete integrable systems such as differential-difference equations, difference equations and cellular automata (ultra-discrete equations)

Optimization and Quantization in Gradient Symbol Systems: A Framework for Integrating the Continuous and the Discrete in Cognition

Science.gov (United States)

Smolensky, Paul; Goldrick, Matthew; Mathis, Donald

2014-01-01

Mental representations have continuous as well as discrete, combinatorial properties. For example, while predominantly discrete, phonological representations also vary continuously; this is reflected by gradient effects in instrumental studies of speech production. Can an integrated theoretical framework address both aspects of structure? The…

A Discrete Spectral Problem and Related Hierarchy of Discrete Hamiltonian Lattice Equations

International Nuclear Information System (INIS)

Xu Xixiang; Cao Weili

2007-01-01

Staring from a discrete matrix spectral problem, a hierarchy of lattice soliton equations is presented though discrete zero curvature representation. The resulting lattice soliton equations possess non-local Lax pairs. The Hamiltonian structures are established for the resulting hierarchy by the discrete trace identity. Liouville integrability of resulting hierarchy is demonstrated.

Constructing irregular surfaces to enclose macromolecular complexes for mesoscale modeling using the discrete surface charge optimization (DISCO) algorithm.

Science.gov (United States)

Zhang, Qing; Beard, Daniel A; Schlick, Tamar

2003-12-01

Salt-mediated electrostatics interactions play an essential role in biomolecular structures and dynamics. Because macromolecular systems modeled at atomic resolution contain thousands of solute atoms, the electrostatic computations constitute an expensive part of the force and energy calculations. Implicit solvent models are one way to simplify the model and associated calculations, but they are generally used in combination with standard atomic models for the solute. To approximate electrostatics interactions in models on the polymer level (e.g., supercoiled DNA) that are simulated over long times (e.g., milliseconds) using Brownian dynamics, Beard and Schlick have developed the DiSCO (Discrete Surface Charge Optimization) algorithm. DiSCO represents a macromolecular complex by a few hundred discrete charges on a surface enclosing the system modeled by the Debye-Hückel (screened Coulombic) approximation to the Poisson-Boltzmann equation, and treats the salt solution as continuum solvation. DiSCO can represent the nucleosome core particle (>12,000 atoms), for example, by 353 discrete surface charges distributed on the surfaces of a large disk for the nucleosome core particle and a slender cylinder for the histone tail; the charges are optimized with respect to the Poisson-Boltzmann solution for the electric field, yielding a approximately 5.5% residual. Because regular surfaces enclosing macromolecules are not sufficiently general and may be suboptimal for certain systems, we develop a general method to construct irregular models tailored to the geometry of macromolecules. We also compare charge optimization based on both the electric field and electrostatic potential refinement. Results indicate that irregular surfaces can lead to a more accurate approximation (lower residuals), and the refinement in terms of the electric field is more robust. We also show that surface smoothing for irregular models is important, that the charge optimization (by the TNPACK

Darboux and binary Darboux transformations for discrete integrable systems I. Discrete potential KdV equation

International Nuclear Information System (INIS)

Shi, Ying; Zhang, Da-jun; Nimmo, Jonathan J C

2014-01-01

The Hirota–Miwa equation can be written in ‘nonlinear’ form in two ways: the discrete KP equation and, by using a compatible continuous variable, the discrete potential KP equation. For both systems, we consider the Darboux and binary Darboux transformations, expressed in terms of the continuous variable, and obtain exact solutions in Wronskian and Grammian form. We discuss reductions of both systems to the discrete KdV and discrete potential KdV equation, respectively, and exploit this connection to find the Darboux and binary Darboux transformations and exact solutions of these equations. (paper)

Discrete Curvature Theories and Applications

KAUST Repository

Sun, Xiang

2016-08-25

Discrete Di erential Geometry (DDG) concerns discrete counterparts of notions and methods in di erential geometry. This thesis deals with a core subject in DDG, discrete curvature theories on various types of polyhedral surfaces that are practically important for free-form architecture, sunlight-redirecting shading systems, and face recognition. Modeled as polyhedral surfaces, the shapes of free-form structures may have to satisfy di erent geometric or physical constraints. We study a combination of geometry and physics { the discrete surfaces that can stand on their own, as well as having proper shapes for the manufacture. These proper shapes, known as circular and conical meshes, are closely related to discrete principal curvatures. We study curvature theories that make such surfaces possible. Shading systems of freeform building skins are new types of energy-saving structures that can re-direct the sunlight. From these systems, discrete line congruences across polyhedral surfaces can be abstracted. We develop a new curvature theory for polyhedral surfaces equipped with normal congruences { a particular type of congruences de ned by linear interpolation of vertex normals. The main results are a discussion of various de nitions of normality, a detailed study of the geometry of such congruences, and a concept of curvatures and shape operators associated with the faces of a triangle mesh. These curvatures are compatible with both normal congruences and the Steiner formula. In addition to architecture, we consider the role of discrete curvatures in face recognition. We use geometric measure theory to introduce the notion of asymptotic cones associated with a singular subspace of a Riemannian manifold, which is an extension of the classical notion of asymptotic directions. We get a simple expression of these cones for polyhedral surfaces, as well as convergence and approximation theorems. We use the asymptotic cones as facial descriptors and demonstrate the

Time step rescaling recovers continuous-time dynamical properties for discrete-time Langevin integration of nonequilibrium systems.

Science.gov (United States)

Sivak, David A; Chodera, John D; Crooks, Gavin E

2014-06-19

When simulating molecular systems using deterministic equations of motion (e.g., Newtonian dynamics), such equations are generally numerically integrated according to a well-developed set of algorithms that share commonly agreed-upon desirable properties. However, for stochastic equations of motion (e.g., Langevin dynamics), there is still broad disagreement over which integration algorithms are most appropriate. While multiple desiderata have been proposed throughout the literature, consensus on which criteria are important is absent, and no published integration scheme satisfies all desiderata simultaneously. Additional nontrivial complications stem from simulating systems driven out of equilibrium using existing stochastic integration schemes in conjunction with recently developed nonequilibrium fluctuation theorems. Here, we examine a family of discrete time integration schemes for Langevin dynamics, assessing how each member satisfies a variety of desiderata that have been enumerated in prior efforts to construct suitable Langevin integrators. We show that the incorporation of a novel time step rescaling in the deterministic updates of position and velocity can correct a number of dynamical defects in these integrators. Finally, we identify a particular splitting (related to the velocity Verlet discretization) that has essentially universally appropriate properties for the simulation of Langevin dynamics for molecular systems in equilibrium, nonequilibrium, and path sampling contexts.

Counterion release from a discretely charged surface in an electrolyte: Monte Carlo simulation study

International Nuclear Information System (INIS)

Hernández-Contreras, M

2015-01-01

Monte Carlo simulations allowed us to determine the amount of released electric charges from a discretely charged surface in 1:1 aqueous electrolyte solution as a function of surface charge density. Within the restricted primitive model and for a fixed concentration of 0.1 M bulk electrolyte in solution, there is an increase in the number of released counterions per unit surface area as the strength of the surface charge is enhanced. A similar behaviour of the number of released counterions was also found through the use of mean field and liquid theory methods

Six-component semi-discrete integrable nonlinear Schrödinger system

Science.gov (United States)

Vakhnenko, Oleksiy O.

2018-01-01

We suggest the six-component integrable nonlinear system on a quasi-one-dimensional lattice. Due to its symmetrical form, the general system permits a number of reductions; one of which treated as the semi-discrete integrable nonlinear Schrödinger system on a lattice with three structural elements in the unit cell is considered in considerable details. Besides six truly independent basic field variables, the system is characterized by four concomitant fields whose background values produce three additional types of inter-site resonant interactions between the basic fields. As a result, the system dynamics becomes associated with the highly nonstandard form of Poisson structure. The elementary Poisson brackets between all field variables are calculated and presented explicitly. The richness of system dynamics is demonstrated on the multi-component soliton solution written in terms of properly parameterized soliton characteristics.

Direct linearizing transform for three-dimensional discrete integrable systems: the lattice AKP, BKP and CKP equations.

Science.gov (United States)

Fu, Wei; Nijhoff, Frank W

2017-07-01

A unified framework is presented for the solution structure of three-dimensional discrete integrable systems, including the lattice AKP, BKP and CKP equations. This is done through the so-called direct linearizing transform, which establishes a general class of integral transforms between solutions. As a particular application, novel soliton-type solutions for the lattice CKP equation are obtained.

Comparison of discrete Hodge star operators for surfaces

KAUST Repository

Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

2016-01-01

We investigate the performance of various discrete Hodge star operators for discrete exterior calculus (DEC) using circumcentric and barycentric dual meshes. The performance is evaluated through the DEC solution of Darcy and incompressible Navier

Geometric discretization of the multidimensional Dirac delta distribution - Application to the Poisson equation with singular source terms

Science.gov (United States)

Egan, Raphael; Gibou, Frédéric

2017-10-01

We present a discretization method for the multidimensional Dirac distribution. We show its applicability in the context of integration problems, and for discretizing Dirac-distributed source terms in Poisson equations with constant or variable diffusion coefficients. The discretization is cell-based and can thus be applied in a straightforward fashion to Quadtree/Octree grids. The method produces second-order accurate results for integration. Superlinear convergence is observed when it is used to model Dirac-distributed source terms in Poisson equations: the observed order of convergence is 2 or slightly smaller. The method is consistent with the discretization of Dirac delta distribution for codimension one surfaces presented in [1,2]. We present Quadtree/Octree construction procedures to preserve convergence and present various numerical examples, including multi-scale problems that are intractable with uniform grids.

Humans can integrate feedback of discrete events in their sensorimotor control of a robotic hand.

Science.gov (United States)

Cipriani, Christian; Segil, Jacob L; Clemente, Francesco; ff Weir, Richard F; Edin, Benoni

2014-11-01

Providing functionally effective sensory feedback to users of prosthetics is a largely unsolved challenge. Traditional solutions require high band-widths for providing feedback for the control of manipulation and yet have been largely unsuccessful. In this study, we have explored a strategy that relies on temporally discrete sensory feedback that is technically simple to provide. According to the Discrete Event-driven Sensory feedback Control (DESC) policy, motor tasks in humans are organized in phases delimited by means of sensory encoded discrete mechanical events. To explore the applicability of DESC for control, we designed a paradigm in which healthy humans operated an artificial robot hand to lift and replace an instrumented object, a task that can readily be learned and mastered under visual control. Assuming that the central nervous system of humans naturally organizes motor tasks based on a strategy akin to DESC, we delivered short-lasting vibrotactile feedback related to events that are known to forcefully affect progression of the grasp-lift-and-hold task. After training, we determined whether the artificial feedback had been integrated with the sensorimotor control by introducing short delays and we indeed observed that the participants significantly delayed subsequent phases of the task. This study thus gives support to the DESC policy hypothesis. Moreover, it demonstrates that humans can integrate temporally discrete sensory feedback while controlling an artificial hand and invites further studies in which inexpensive, noninvasive technology could be used in clever ways to provide physiologically appropriate sensory feedback in upper limb prosthetics with much lower band-width requirements than with traditional solutions.

On Discrete Killing Vector Fields and Patterns on Surfaces

KAUST Repository

Ben-Chen, Mirela

2010-09-21

Symmetry is one of the most important properties of a shape, unifying form and function. It encodes semantic information on one hand, and affects the shape\\'s aesthetic value on the other. Symmetry comes in many flavors, amongst the most interesting being intrinsic symmetry, which is defined only in terms of the intrinsic geometry of the shape. Continuous intrinsic symmetries can be represented using infinitesimal rigid transformations, which are given as tangent vector fields on the surface - known as Killing Vector Fields. As exact symmetries are quite rare, especially when considering noisy sampled surfaces, we propose a method for relaxing the exact symmetry constraint to allow for approximate symmetries and approximate Killing Vector Fields, and show how to discretize these concepts for generating such vector fields on a triangulated mesh. We discuss the properties of approximate Killing Vector Fields, and propose an application to utilize them for texture and geometry synthesis. Journal compilation © 2010 The Eurographics Association and Blackwell Publishing Ltd.

A high-order method for the integration of the Galerkin semi-discretized nuclear reactor kinetics equations

International Nuclear Information System (INIS)

Vargas, L.

1988-01-01

The numerical approximate solution of the space-time nuclear reactor kinetics equation is investigated using a finite-element discretization of the space variable and a high order integration scheme for the resulting semi-discretized parabolic equation. The Galerkin method with spatial piecewise polynomial Lagrange basis functions are used to obtained a continuous time semi-discretized form of the space-time reactor kinetics equation. A temporal discretization is then carried out with a numerical scheme based on the Iterated Defect Correction (IDC) method using piecewise quadratic polynomials or exponential functions. The kinetics equations are thus solved with in a general finite element framework with respect to space as well as time variables in which the order of convergence of the spatial and temporal discretizations is consistently high. A computer code GALFEM/IDC is developed, to implement the numerical schemes described above. This issued to solve a one space dimensional benchmark problem. The results of the numerical experiments confirm the theoretical arguments and show that the convergence is very fast and the overall procedure is quite efficient. This is due to the good asymptotic properties of the numerical scheme which is of third order in the time interval

The selection of a mode of urban transportation: Integrating psychological variables to discrete choice models

International Nuclear Information System (INIS)

Cordoba Maquilon, Jorge E; Gonzalez Calderon, Carlos A; Posada Henao, John J

2011-01-01

A study using revealed preference surveys and psychological tests was conducted. Key psychological variables of behavior involved in the choice of transportation mode in a population sample of the Metropolitan Area of the Valle de Aburra were detected. The experiment used the random utility theory for discrete choice models and reasoned action in order to assess beliefs. This was used as a tool for analysis of the psychological variables using the sixteen personality factor questionnaire (16PF test). In addition to the revealed preference surveys, two other surveys were carried out: one with socio-economic characteristics and the other with latent indicators. This methodology allows for an integration of discrete choice models and latent variables. The integration makes the model operational and quantifies the unobservable psychological variables. The most relevant result obtained was that anxiety affects the choice of urban transportation mode and shows that physiological alterations, as well as problems in perception and beliefs, can affect the decision-making process.

Numerical convergence of discrete exterior calculus on arbitrary surface meshes

KAUST Repository

Mohamed, Mamdouh S.

2018-02-13

Discrete exterior calculus (DEC) is a structure-preserving numerical framework for partial differential equations solution, particularly suitable for simplicial meshes. A longstanding and widespread assumption has been that DEC requires special (Delaunay) triangulations, which complicated the mesh generation process especially for curved surfaces. This paper presents numerical evidence demonstrating that this restriction is unnecessary. Convergence experiments are carried out for various physical problems using both Delaunay and non-Delaunay triangulations. Signed diagonal definition for the key DEC operator (Hodge star) is adopted. The errors converge as expected for all considered meshes and experiments. This relieves the DEC paradigm from unnecessary triangulation limitation.

Discrete integration of continuous Kalman filtering equations for time invariant second-order structural systems

Science.gov (United States)

Park, K. C.; Belvin, W. Keith

1990-01-01

A general form for the first-order representation of the continuous second-order linear structural-dynamics equations is introduced to derive a corresponding form of first-order continuous Kalman filtering equations. Time integration of the resulting equations is carried out via a set of linear multistep integration formulas. It is shown that a judicious combined selection of computational paths and the undetermined matrices introduced in the general form of the first-order linear structural systems leads to a class of second-order discrete Kalman filtering equations involving only symmetric sparse N x N solution matrices.

Automated vehicle guidance using discrete reference markers. [road surface steering techniques

Science.gov (United States)

Johnston, A. R.; Assefi, T.; Lai, J. Y.

1979-01-01

Techniques for providing steering control for an automated vehicle using discrete reference markers fixed to the road surface are investigated analytically. Either optical or magnetic approaches can be used for the sensor, which generates a measurement of the lateral offset of the vehicle path at each marker to form the basic data for steering control. Possible mechanizations of sensor and controller are outlined. Techniques for handling certain anomalous conditions, such as a missing marker, or loss of acquisition, and special maneuvers, such as u-turns and switching, are briefly discussed. A general analysis of the vehicle dynamics and the discrete control system is presented using the state variable formulation. Noise in both the sensor measurement and in the steering servo are accounted for. An optimal controller is simulated on a general purpose computer, and the resulting plots of vehicle path are presented. Parameters representing a small multipassenger tram were selected, and the simulation runs show response to an erroneous sensor measurement and acquisition following large initial path errors.

Integrated Surface Dataset (Global)

Data.gov (United States)

National Oceanic and Atmospheric Administration, Department of Commerce — The Integrated Surface (ISD) Dataset (ISD) is composed of worldwide surface weather observations from over 35,000 stations, though the best spatial coverage is...

Numerical Evaluation of the "Dual-Kernel Counter-flow" Matric Convolution Integral that Arises in Discrete/Continuous (D/C) Control Theory

Science.gov (United States)

Nixon, Douglas D.

2009-01-01

Discrete/Continuous (D/C) control theory is a new generalized theory of discrete-time control that expands the concept of conventional (exact) discrete-time control to create a framework for design and implementation of discretetime control systems that include a continuous-time command function generator so that actuator commands need not be constant between control decisions, but can be more generally defined and implemented as functions that vary with time across sample period. Because the plant/control system construct contains two linear subsystems arranged in tandem, a novel dual-kernel counter-flow convolution integral appears in the formulation. As part of the D/C system design and implementation process, numerical evaluation of that integral over the sample period is required. Three fundamentally different evaluation methods and associated algorithms are derived for the constant-coefficient case. Numerical results are matched against three available examples that have closed-form solutions.

Metriplectic Gyrokinetics and Discretization Methods for the Landau Collision Integral

Science.gov (United States)

Hirvijoki, Eero; Burby, Joshua W.; Kraus, Michael

2017-10-01

We present two important results for the kinetic theory and numerical simulation of warm plasmas: 1) We provide a metriplectic formulation of collisional electrostatic gyrokinetics that is fully consistent with the First and Second Laws of Thermodynamics. 2) We provide a metriplectic temporal and velocity-space discretization for the particle phase-space Landau collision integral that satisfies the conservation of energy, momentum, and particle densities to machine precision, as well as guarantees the existence of numerical H-theorem. The properties are demonstrated algebraically. These two result have important implications: 1) Numerical methods addressing the Vlasov-Maxwell-Landau system of equations, or its reduced gyrokinetic versions, should start from a metriplectic formulation to preserve the fundamental physical principles also at the discrete level. 2) The plasma physics community should search for a metriplectic reduction theory that would serve a similar purpose as the existing Lagrangian and Hamiltonian reduction theories do in gyrokinetics. The discovery of metriplectic formulation of collisional electrostatic gyrokinetics is strong evidence in favor of such theory and, if uncovered, the theory would be invaluable in constructing reduced plasma models. Supported by U.S. DOE Contract Nos. DE-AC02-09-CH11466 (EH) and DE-AC05-06OR23100 (JWB) and by European Union's Horizon 2020 research and innovation Grant No. 708124 (MK).

Variational discretization of the nonequilibrium thermodynamics of simple systems

Science.gov (United States)

Gay-Balmaz, François; Yoshimura, Hiroaki

2018-04-01

In this paper, we develop variational integrators for the nonequilibrium thermodynamics of simple closed systems. These integrators are obtained by a discretization of the Lagrangian variational formulation of nonequilibrium thermodynamics developed in (Gay-Balmaz and Yoshimura 2017a J. Geom. Phys. part I 111 169–93 Gay-Balmaz and Yoshimura 2017b J. Geom. Phys. part II 111 194–212) and thus extend the variational integrators of Lagrangian mechanics, to include irreversible processes. In the continuous setting, we derive the structure preserving property of the flow of such systems. This property is an extension of the symplectic property of the flow of the Euler–Lagrange equations. In the discrete setting, we show that the discrete flow solution of our numerical scheme verifies a discrete version of this property. We also present the regularity conditions which ensure the existence of the discrete flow. We finally illustrate our discrete variational schemes with the implementation of an example of a simple and closed system.

Solving Hammerstein Type Integral Equation by New Discrete Adomian Decomposition Methods

Directory of Open Access Journals (Sweden)

Huda O. Bakodah

2013-01-01

Full Text Available New discrete Adomian decomposition methods are presented by using some identified Clenshaw-Curtis quadrature rules. We investigate two mixed quadrature rules one of precision five and the other of precision seven. The first rule is formed by using the Fejér second rule of precision three and Simpson rule of precision three, while the second rule is formed by using the Fejér second rule of precision five and the Boole rule of precision five. Our methods were applied to a nonlinear integral equation of the Hammerstein type and some examples are given to illustrate the validity of our methods.

Evolution equation of Lie-type for finite deformations, time-discrete integration, and incremental methods

Czech Academy of Sciences Publication Activity Database

Fiala, Zdeněk

2015-01-01

Roč. 226, č. 1 (2015), s. 17-35 ISSN 0001-5970 R&D Projects: GA ČR(CZ) GA103/09/2101 Institutional support: RVO:68378297 Keywords : solid mechanics * finite deformations * evolution equation of Lie-type * time-discrete integration Subject RIV: BA - General Mathematics OBOR OECD: Statistics and probability Impact factor: 1.694, year: 2015 http://link.springer.com/article/10.1007%2Fs00707-014-1162-9#page-1

Optimization and quantization in gradient symbol systems: a framework for integrating the continuous and the discrete in cognition.

Science.gov (United States)

Smolensky, Paul; Goldrick, Matthew; Mathis, Donald

2014-08-01

Mental representations have continuous as well as discrete, combinatorial properties. For example, while predominantly discrete, phonological representations also vary continuously; this is reflected by gradient effects in instrumental studies of speech production. Can an integrated theoretical framework address both aspects of structure? The framework we introduce here, Gradient Symbol Processing, characterizes the emergence of grammatical macrostructure from the Parallel Distributed Processing microstructure (McClelland, Rumelhart, & The PDP Research Group, 1986) of language processing. The mental representations that emerge, Distributed Symbol Systems, have both combinatorial and gradient structure. They are processed through Subsymbolic Optimization-Quantization, in which an optimization process favoring representations that satisfy well-formedness constraints operates in parallel with a distributed quantization process favoring discrete symbolic structures. We apply a particular instantiation of this framework, λ-Diffusion Theory, to phonological production. Simulations of the resulting model suggest that Gradient Symbol Processing offers a way to unify accounts of grammatical competence with both discrete and continuous patterns in language performance. Copyright © 2013 Cognitive Science Society, Inc.

QUALITY THROUGH INTEGRATION OF PRODUCTION AND SHOP FLOOR MANAGEMENT BY DISCRETE EVENT SIMULATION

Directory of Open Access Journals (Sweden)

Zoran Mirović

2007-06-01

Full Text Available With the intention to integrate strategic and tactical decision making and develop the capability of plans and schedules reconfiguration and synchronization in a very short cycle time many firms have proceeded to the adoption of ERP and Advanced Planning and Scheduling (APS technologies. The final goal is a purposeful scheduling system that guide in the right direction the current, high priority needs of the shop floor while remaining consistent with long-term production plans. The difference, and the power, of Discrete-Event Simulation (DES is its ability to mimic dynamic manufacturing systems, consisting of complex structures, and many heterogeneous interacting components. This paper describes such an integrated system (ERP/APS/DES and draw attention to the essential role of simulation based scheduling within it.

Solitonlike solutions of the generalized discrete nonlinear Schrödinger equation

DEFF Research Database (Denmark)

Rasmussen, Kim; Henning, D.; Gabriel, H.

1996-01-01

We investigate the solution properties oi. a generalized discrete nonlinear Schrodinger equation describing a nonlinear lattice chain. The generalized equation interpolates between the integrable discrete Ablowitz-Ladik equation and the nonintegrable discrete Schrodinger equation. Special interes...... nonlinear Schrodinger equation. In this way eve are able to construct coherent solitonlike structures of profile determined by the map parameters.......We investigate the solution properties oi. a generalized discrete nonlinear Schrodinger equation describing a nonlinear lattice chain. The generalized equation interpolates between the integrable discrete Ablowitz-Ladik equation and the nonintegrable discrete Schrodinger equation. Special interest...

Discrete density of states

International Nuclear Information System (INIS)

Aydin, Alhun; Sisman, Altug

2016-01-01

By considering the quantum-mechanically minimum allowable energy interval, we exactly count number of states (NOS) and introduce discrete density of states (DOS) concept for a particle in a box for various dimensions. Expressions for bounded and unbounded continua are analytically recovered from discrete ones. Even though substantial fluctuations prevail in discrete DOS, they're almost completely flattened out after summation or integration operation. It's seen that relative errors of analytical expressions of bounded/unbounded continua rapidly decrease for high NOS values (weak confinement or high energy conditions), while the proposed analytical expressions based on Weyl's conjecture always preserve their lower error characteristic. - Highlights: • Discrete density of states considering minimum energy difference is proposed. • Analytical DOS and NOS formulas based on Weyl conjecture are given. • Discrete DOS and NOS functions are examined for various dimensions. • Relative errors of analytical formulas are much better than the conventional ones.

Preparing the generalized Harvey–Shack rough surface scattering method for use with the discrete ordinates method

DEFF Research Database (Denmark)

Johansen, Villads Egede

2015-01-01

The paper shows how to implement the generalized Harvey–Shack (GHS) method for isotropic rough surfaces discretized in a polar coordinate system and approximated using Fourier series. This is particularly relevant for the use of the GHS method as a boundary condition for radiative transfer proble...

Solving discrete zero point problems

NARCIS (Netherlands)

van der Laan, G.; Talman, A.J.J.; Yang, Z.F.

2004-01-01

In this paper an algorithm is proposed to .nd a discrete zero point of a function on the collection of integral points in the n-dimensional Euclidean space IRn.Starting with a given integral point, the algorithm generates a .nite sequence of adjacent integral simplices of varying dimension and

On reductions of the discrete Kadomtsev-Petviashvili-type equations

Science.gov (United States)

Fu, Wei; Nijhoff, Frank W.

2017-12-01

The reduction by restricting the spectral parameters k and k\\prime on a generic algebraic curve of degree N is performed for the discrete AKP, BKP and CKP equations, respectively. A variety of two-dimensional discrete integrable systems possessing a more general solution structure arise from the reduction, and in each case a unified formula for the generic positive integer N≥slant 2 is given to express the corresponding reduced integrable lattice equations. The obtained extended two-dimensional lattice models give rise to many important integrable partial difference equations as special degenerations. Some new integrable lattice models such as the discrete Sawada-Kotera, Kaup-Kupershmidt and Hirota-Satsuma equations in extended form are given as examples within the framework.

Lung ventilation injures areas with discrete alveolar flooding, in a surface tension-dependent fashion.

Science.gov (United States)

Wu, You; Kharge, Angana Banerjee; Perlman, Carrie E

2014-10-01

With proteinaceous-liquid flooding of discrete alveoli, a model of the edema pattern in the acute respiratory distress syndrome, lung inflation over expands aerated alveoli adjacent to flooded alveoli. Theoretical considerations suggest that the overexpansion may be proportional to surface tension, T. Yet recent evidence indicates proteinaceous edema liquid may not elevate T. Thus whether the overexpansion is injurious is not known. Here, working in the isolated, perfused rat lung, we quantify fluorescence movement from the vasculature to the alveolar liquid phase as a measure of overdistension injury to the alveolar-capillary barrier. We label the perfusate with fluorescence; micropuncture a surface alveolus and instill a controlled volume of nonfluorescent liquid to obtain a micropunctured-but-aerated region (control group) or a region with discrete alveolar flooding; image the region at a constant transpulmonary pressure of 5 cmH2O; apply five ventilation cycles with a positive end-expiratory pressure of 0-20 cmH2O and tidal volume of 6 or 12 ml/kg; return the lung to a constant transpulmonary pressure of 5 cmH2O; and image for an additional 10 min. In aerated areas, ventilation is not injurious. With discrete alveolar flooding, all ventilation protocols cause sustained injury. Greater positive end-expiratory pressure or tidal volume increases injury. Furthermore, we determine T and find injury increases with T. Inclusion of either plasma proteins or Survanta in the flooding liquid does not alter T or injury. Inclusion of 2.7-10% albumin and 1% Survanta together, however, lowers T and injury. Contrary to expectation, albumin inclusion in our model facilitates exogenous surfactant activity. Copyright © 2014 the American Physiological Society.

Discrete convolution-operators and radioactive disintegration. [Numerical solution

Energy Technology Data Exchange (ETDEWEB)

Kalla, S L; VALENTINUZZI, M E [UNIVERSIDAD NACIONAL DE TUCUMAN (ARGENTINA). FACULTAD DE CIENCIAS EXACTAS Y TECNOLOGIA

1975-08-01

The basic concepts of discrete convolution and discrete convolution-operators are briefly described. Then, using the discrete convolution - operators, the differential equations associated with the process of radioactive disintegration are numerically solved. The importance of the method is emphasized to solve numerically, differential and integral equations.

Generation of a quantum integrable class of discrete-time or relativistic periodic Toda chains

International Nuclear Information System (INIS)

Kundu, Anjan

1994-01-01

A new integrable class of quantum models representing a family of different discrete-time or relativistic generalisations of the periodic Toda chain (TC), including that of a recently proposed classical model close to TC [Lett. Math. Phys. 29 (1993) 165] is presented. All such models are shown to be obtainable from a single ancestor model at different realisations of the underlying quantised algebra. As a consequence the 2x2 Lax operators and the associated quantum R-matrices for these models are easily derived ensuring their quantum integrability. It is shown that the functional Bethe ansatz developed for the quantum TC is trivially generalised to achieve separation of variables also for the present models. ((orig.))

Time Domain Surface Integral Equation Solvers for Quantum Corrected Electromagnetic Analysis of Plasmonic Nanostructures

KAUST Repository

Uysal, Ismail Enes

2016-10-01

Plasmonic structures are utilized in many applications ranging from bio-medicine to solar energy generation and transfer. Numerical schemes capable of solving equations of classical electrodynamics have been the method of choice for characterizing scattering properties of such structures. However, as dimensions of these plasmonic structures reduce to nanometer scale, quantum mechanical effects start to appear. These effects cannot be accurately modeled by available classical numerical methods. One of these quantum effects is the tunneling, which is observed when two structures are located within a sub-nanometer distance of each other. At these small distances electrons “jump" from one structure to another and introduce a path for electric current to flow. Classical equations of electrodynamics and the schemes used for solving them do not account for this additional current path. This limitation can be lifted by introducing an auxiliary tunnel with material properties obtained using quantum models and applying a classical solver to the structures connected by this auxiliary tunnel. Early work on this topic focused on quantum models that are generated using a simple one-dimensional wave function to find the tunneling probability and assume a simple Drude model for the permittivity of the tunnel. These tunnel models are then used together with a classical frequency domain solver. In this thesis, a time domain surface integral equation solver for quantum corrected analysis of transient plasmonic interactions is proposed. This solver has several advantages: (i) As opposed to frequency domain solvers, it provides results at a broad band of frequencies with a single simulation. (ii) As opposed to differential equation solvers, it only discretizes surfaces (reducing number of unknowns), enforces the radiation condition implicitly (increasing the accuracy), and allows for time step selection independent of spatial discretization (increasing efficiency). The quantum model

Discrete density of states

Energy Technology Data Exchange (ETDEWEB)

Aydin, Alhun; Sisman, Altug, E-mail: sismanal@itu.edu.tr

2016-03-22

By considering the quantum-mechanically minimum allowable energy interval, we exactly count number of states (NOS) and introduce discrete density of states (DOS) concept for a particle in a box for various dimensions. Expressions for bounded and unbounded continua are analytically recovered from discrete ones. Even though substantial fluctuations prevail in discrete DOS, they're almost completely flattened out after summation or integration operation. It's seen that relative errors of analytical expressions of bounded/unbounded continua rapidly decrease for high NOS values (weak confinement or high energy conditions), while the proposed analytical expressions based on Weyl's conjecture always preserve their lower error characteristic. - Highlights: • Discrete density of states considering minimum energy difference is proposed. • Analytical DOS and NOS formulas based on Weyl conjecture are given. • Discrete DOS and NOS functions are examined for various dimensions. • Relative errors of analytical formulas are much better than the conventional ones.

Universal discrete Fourier optics RF photonic integrated circuit architecture.

Science.gov (United States)

Hall, Trevor J; Hasan, Mehedi

2016-04-04

This paper describes a coherent electro-optic circuit architecture that generates a frequency comb consisting of N spatially separated orders using a generalised Mach-Zenhder interferometer (MZI) with its N × 1 combiner replaced by an optical N × N Discrete Fourier Transform (DFT). Advantage may be taken of the tight optical path-length control, component and circuit symmetries and emerging trimming algorithms offered by photonic integration in any platform that offers linear electro-optic phase modulation such as LiNbO3, silicon, III-V or hybrid technology. The circuit architecture subsumes all MZI-based RF photonic circuit architectures in the prior art given an appropriate choice of output port(s) and dimension N although the principal application envisaged is phase correlated subcarrier generation for all optical orthogonal frequency division multiplexing. A transfer matrix approach is used to model the operation of the architecture. The predictions of the model are validated by simulations performed using an industry standard software tool. Implementation is found to be practical.

Interactions of Soliton Waves for a Generalized Discrete KdV Equation

International Nuclear Information System (INIS)

Zhou Tong; Zhu Zuo-Nong

2017-01-01

It is well known that soliton interactions in discrete integrable systems often possess new properties which are different from the continuous integrable systems, e.g., we found that there are such discrete solitons in a semidiscrete integrable system (the time variable is continuous and the space one is discrete) that the shorter solitary waves travel faster than the taller ones. Very recently, this kind of soliton was also observed in a full discrete generalized KdV system (the both of time and space variables are discrete) introduced by Kanki et al. In this paper, for the generalized discrete KdV (gdKdV) equation, we describe its richer structures of one-soliton solutions. The interactions of two-soliton waves to the gdKdV equation are studied. Some new features of the soliton interactions are proposed by rigorous theoretical analysis. (paper)

Quantum Riemann surfaces. Pt. 2; The discrete series

Energy Technology Data Exchange (ETDEWEB)

Klimek, S. (Dept. of Mathematics, IUPUI, Indianapolis, IN (United States)); Lesniewski, A. (Dept. of Physics, Harvard Univ., Cambridge, MA (United States))

1992-02-01

We continue our study of noncommutative deformations of two-dimensional hyperbolic manifolds which we initiated in Part I. We construct a sequence of C{sup *}-algebras which are quantizations of a compact Riemann surface of genus g corresponding to special values of the Planck constant. These algebras are direct integrals of finite-dimensional C{sup *}-algebras. (orig.).

Finite-dimensional reductions of the discrete Toda chain

International Nuclear Information System (INIS)

Kazakova, T G

2004-01-01

The problem of construction of integrable boundary conditions for the discrete Toda chain is considered. The restricted chains for properly chosen closure conditions are reduced to the well-known discrete Painleve equations dP III , dP V , dP VI . Lax representations for these discrete Painleve equations are found

Integrated Surface/subsurface flow modeling in PFLOTRAN

Energy Technology Data Exchange (ETDEWEB)

Painter, Scott L [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

2016-10-01

Understanding soil water, groundwater, and shallow surface water dynamics as an integrated hydrological system is critical for understanding the Earth’s critical zone, the thin outer layer at our planet’s surface where vegetation, soil, rock, and gases interact to regulate the environment. Computational tools that take this view of soil moisture and shallow surface flows as a single integrated system are typically referred to as integrated surface/subsurface hydrology models. We extend the open-source, highly parallel, subsurface flow and reactive transport simulator PFLOTRAN to accommodate surface flows. In contrast to most previous implementations, we do not represent a distinct surface system. Instead, the vertical gradient in hydraulic head at the land surface is neglected, which allows the surface flow system to be eliminated and incorporated directly into the subsurface system. This tight coupling approach leads to a robust capability and also greatly simplifies implementation in existing subsurface simulators such as PFLOTRAN. Successful comparisons to independent numerical solutions build confidence in the approximation and implementation. Example simulations of the Walker Branch and East Fork Poplar Creek watersheds near Oak Ridge, Tennessee demonstrate the robustness of the approach in geometrically complex applications. The lack of a robust integrated surface/subsurface hydrology capability had been a barrier to PFLOTRAN’s use in critical zone studies. This work addresses that capability gap, thus enabling PFLOTRAN as a community platform for building integrated models of the critical zone.

The Predominance Of Integrative Tests Over Discrete Point Tests In Evaluating The Medical Students' General English Knowledge

Directory of Open Access Journals (Sweden)

maryam Heydarpour Meymeh

2009-03-01

Full Text Available Background and purpose: Multiple choice tests are the most common type of tests used in evaluating the general English knowledge of the students in most medical universities, however the efficacy of these tests are not examined precisely. Wecompare and examine the integrative tests and discrete point tests as measures of the English language knowledge of medical students.Methods: Three tests were given to 60 undergraduate physiotherapy and Audiology students in their second year of study (after passing their general English course. They were divided into 2 groups.The first test for both groups was an integrative test, writing. The second test was a multiple - choice test 0.(prepositions for group one and a multiple - choice test of tensesfor group two. The same items which were mostfi-equently used wrongly in thefirst test were used in the items of the second test. A third test, a TOEFL, was given to the subjects in order to estimate the correlation between this test and tests one and two.Results: The students performed better in the second test, discrete point test rather than the first which was an integrative test. The same grammatical mistakes in the composition were used correctly in the multiple choice tests by the students.Conclusion:Our findings show that student perform better in non-productive rather than productive test. Since being competent English language user is an expected outcome of university language courses it seems warranted to switch to integrative tests as a measure of English language competency.Keywords: INTEGRATIVE TESTS, ENGLISH LANGUAGE FOR MEDICINE, ACADEMIC ENGLISH

Exterior difference systems and invariance properties of discrete mechanics

International Nuclear Information System (INIS)

Xie Zheng; Xie Duanqiang; Li Hongbo

2008-01-01

Invariance properties describe the fundamental physical laws in discrete mechanics. Can those properties be described in a geometric way? We investigate an exterior difference system called the discrete Euler-Lagrange system, whose solution has one-to-one correspondence with solutions of discrete Euler-Lagrange equations, and use it to define the first integrals. The preservation of the discrete symplectic form along the discrete Hamilton phase flows and the discrete Noether's theorem is also described in the language of difference forms

Discrete Chebyshev nets and a universal permutability theorem

International Nuclear Information System (INIS)

Schief, W K

2007-01-01

The Pohlmeyer-Lund-Regge system which was set down independently in the contexts of Lagrangian field theories and the relativistic motion of a string and which played a key role in the development of a geometric interpretation of soliton theory is known to appear in a variety of important guises such as the vectorial Lund-Regge equation, the O(4) nonlinear σ-model and the SU(2) chiral model. Here, it is demonstrated that these avatars may be discretized in such a manner that both integrability and equivalence are preserved. The corresponding discretization procedure is geometric and algebraic in nature and based on discrete Chebyshev nets and generalized discrete Lelieuvre formulae. In connection with the derivation of associated Baecklund transformations, it is shown that a generalized discrete Lund-Regge equation may be interpreted as a universal permutability theorem for integrable equations which admit commuting matrix Darboux transformations acting on su(2) linear representations. Three-dimensional coordinate systems and lattices of 'Lund-Regge' type related to particular continuous and discrete Zakharov-Manakov systems are obtained as a by-product of this analysis

On an integrable discretization of the modified Korteweg-de Vries equation

Science.gov (United States)

Suris, Yuri B.

1997-02-01

We find time discretizations for the two “second flows” of the Ablowitz-Ladik hierachy. These discretizations are described by local equations of motion, as opposed to the previously known ones, due to Taha and Ablowitz. Certain superpositions of our maps allow a one-field reduction and serve therefore as valid space-time discretizations of the modified Korteweg-de Vries equation. We expect the performance of these discretizations to be much better then that of the Taha-Ablowitz scheme. The way of finding interpolating Hamiltonians for our maps is also indicated, as well as the solution of an initial value problem in terms of matrix factorizations.

Discrete bipolar universal integrals

Czech Academy of Sciences Publication Activity Database

Greco, S.; Mesiar, Radko; Rindone, F.

2014-01-01

Roč. 252, č. 1 (2014), s. 55-65 ISSN 0165-0114 R&D Projects: GA ČR GAP402/11/0378 Institutional support: RVO:67985556 Keywords : bipolar integral * universal integral * Choquet integral Subject RIV: BA - General Mathematics Impact factor: 1.986, year: 2014 http://library.utia.cas.cz/separaty/2014/E/mesiar-0432224.pdf

Two-dimensional parasitic capacitance extraction for integrated circuit with dual discrete geometric methods

International Nuclear Information System (INIS)

Ren Dan; Ren Zhuoxiang; Qu Hui; Xu Xiaoyu

2015-01-01

Capacitance extraction is one of the key issues in integrated circuits and also a typical electrostatic problem. The dual discrete geometric method (DGM) is investigated to provide relative solutions in two-dimensional unstructured mesh space. The energy complementary characteristic and quick field energy computation thereof based on it are emphasized. Contrastive analysis between the dual finite element methods and the dual DGMs are presented both from theoretical derivation and through case studies. The DGM, taking the scalar potential as unknown on dual interlocked meshes, with simple form and good accuracy, is expected to be one of the mainstreaming methods in associated areas. (paper)

Observations of discrete energy loss effects in spectra of positrons reflected from solid surfaces

International Nuclear Information System (INIS)

Dale, J.M.; Hulett, L.D.; Pendyala, S.

1980-01-01

Surfaces of tungsten and silicon have been bombarded with monoenergetic beams of positrons and electrons. Spectra of reflected particles show energy loss tails with discrete peaks at kinetic energies about 15 eV lower than that of the elastic peaks. In the higher energy loss range for tungsten, positron spectra show fine structure that is not apparent in the electron spectra. This suggests that the positrons are losing energy through mechanisms different from that of the electrons

Painleve test and discrete Boltzmann equations

International Nuclear Information System (INIS)

Euler, N.; Steeb, W.H.

1989-01-01

The Painleve test for various discrete Boltzmann equations is performed. The connection with integrability is discussed. Furthermore the Lie symmetry vector fields are derived and group-theoretical reduction of the discrete Boltzmann equations to ordinary differentiable equations is performed. Lie Backlund transformations are gained by performing the Painleve analysis for the ordinary differential equations. 16 refs

Lax pairs for ultra-discrete Painleve cellular automata

International Nuclear Information System (INIS)

Joshi, N; Nijhoff, F W; Ormerod, C

2004-01-01

Ultra-discrete versions of the discrete Painleve equations are well known. However, evidence for their integrability has so far been restricted. In this letter, we show that their Lax pairs can be constructed and, furthermore, that compatibility conditions of the result yield the ultra-discrete Painleve equation. For conciseness, we restrict our attention to a new d-P III . (letter to the editor)

Discrete microfluidics based on aluminum nitride surface acoustic wave devices

OpenAIRE

Zhou, J.; Pang, H.F.; Garcia-Gancedo, L.; Iborra, E.; Clement, M.; De Miguel-Ramos, M.; Jin, H.; Luo, J.K.; Smith, S.; Dong, S.R.; Wang, D.M.; Fu, Y.Q.

2015-01-01

To date, most surface acoustic wave (SAW) devices have been made from bulk piezoelectric materials, such as quartz, lithium niobate or lithium tantalite. These bulk materials are brittle, less easily integrated with electronics for control and signal processing, and difficult to realize multiple wave modes or apply complex electrode designs. Using thin film SAWs makes it convenient to integrate microelectronics and multiple sensing or microfluidics techniques into a lab-on-a-chip with low cos...

About several classes of bi-orthogonal polynomials and discrete integrable systems

International Nuclear Information System (INIS)

Chang, Xiang-Ke; Chen, Xiao-Min; Hu, Xing-Biao; Tam, Hon-Wah

2015-01-01

By introducing some special bi-orthogonal polynomials, we derive the so-called discrete hungry quotient-difference (dhQD) algorithm and a system related to the QD-type discrete hungry Lotka–Volterra (QD-type dhLV) system, together with their Lax pairs. These two known equations can be regarded as extensions of the QD algorithm. When this idea is applied to a higher analogue of the discrete-time Toda (HADT) equation and the quotient–quotient-difference (QQD) scheme proposed by Spicer, Nijhoff and van der Kamp, two extended systems are constructed. We call these systems the hungry forms of the higher analogue discrete-time Toda (hHADT) equation and the quotient-quotient-difference (hQQD) scheme, respectively. In addition, the corresponding Lax pairs are provided. (paper)

Positivity for Convective Semi-discretizations

KAUST Repository

Fekete, Imre

2017-04-19

We propose a technique for investigating stability properties like positivity and forward invariance of an interval for method-of-lines discretizations, and apply the technique to study positivity preservation for a class of TVD semi-discretizations of 1D scalar hyperbolic conservation laws. This technique is a generalization of the approach suggested in Khalsaraei (J Comput Appl Math 235(1): 137–143, 2010). We give more relaxed conditions on the time-step for positivity preservation for slope-limited semi-discretizations integrated in time with explicit Runge–Kutta methods. We show that the step-size restrictions derived are sharp in a certain sense, and that many higher-order explicit Runge–Kutta methods, including the classical 4th-order method and all non-confluent methods with a negative Butcher coefficient, cannot generally maintain positivity for these semi-discretizations under any positive step size. We also apply the proposed technique to centered finite difference discretizations of scalar hyperbolic and parabolic problems.

Discrete Routh reduction

International Nuclear Information System (INIS)

Jalnapurkar, Sameer M; Leok, Melvin; Marsden, Jerrold E; West, Matthew

2006-01-01

This paper develops the theory of Abelian Routh reduction for discrete mechanical systems and applies it to the variational integration of mechanical systems with Abelian symmetry. The reduction of variational Runge-Kutta discretizations is considered, as well as the extent to which symmetry reduction and discretization commute. These reduced methods allow the direct simulation of dynamical features such as relative equilibria and relative periodic orbits that can be obscured or difficult to identify in the unreduced dynamics. The methods are demonstrated for the dynamics of an Earth orbiting satellite with a non-spherical J 2 correction, as well as the double spherical pendulum. The J 2 problem is interesting because in the unreduced picture, geometric phases inherent in the model and those due to numerical discretization can be hard to distinguish, but this issue does not appear in the reduced algorithm, where one can directly observe interesting dynamical structures in the reduced phase space (the cotangent bundle of shape space), in which the geometric phases have been removed. The main feature of the double spherical pendulum example is that it has a non-trivial magnetic term in its reduced symplectic form. Our method is still efficient as it can directly handle the essential non-canonical nature of the symplectic structure. In contrast, a traditional symplectic method for canonical systems could require repeated coordinate changes if one is evoking Darboux' theorem to transform the symplectic structure into canonical form, thereby incurring additional computational cost. Our method allows one to design reduced symplectic integrators in a natural way, despite the non-canonical nature of the symplectic structure

Extended discrete-ordinate method considering full polarization state

International Nuclear Information System (INIS)

Box, Michael A.; Qin Yi

2006-01-01

This paper presents an extension to the standard discrete-ordinate method (DOM) to consider generalized sources including: beam sources which can be placed at any (vertical) position and illuminate in any direction, thermal emission from the atmosphere and angularly distributed sources which illuminate from a surface as continuous functions of zenith and azimuth angles. As special cases, the thermal emission from the surface and deep space can be implemented as angularly distributed sources. Analytical-particular solutions for all source types are derived using the infinite medium Green's function. Radiation field zenith angle interpolation using source function integration is developed for all source types. The development considers the full state of polarization, including the sources (as applicable) and the (BRDF) surface, but the development can be reduced easily to scalar problems and is ready to be implemented in a single set of code for both scalar and vector radiative transfer computation

Discrete gauge symmetries in discrete MSSM-like orientifolds

International Nuclear Information System (INIS)

Ibáñez, L.E.; Schellekens, A.N.; Uranga, A.M.

2012-01-01

Motivated by the necessity of discrete Z N symmetries in the MSSM to insure baryon stability, we study the origin of discrete gauge symmetries from open string sector U(1)'s in orientifolds based on rational conformal field theory. By means of an explicit construction, we find an integral basis for the couplings of axions and U(1) factors for all simple current MIPFs and orientifolds of all 168 Gepner models, a total of 32 990 distinct cases. We discuss how the presence of discrete symmetries surviving as a subgroup of broken U(1)'s can be derived using this basis. We apply this procedure to models with MSSM chiral spectrum, concretely to all known U(3)×U(2)×U(1)×U(1) and U(3)×Sp(2)×U(1)×U(1) configurations with chiral bi-fundamentals, but no chiral tensors, as well as some SU(5) GUT models. We find examples of models with Z 2 (R-parity) and Z 3 symmetries that forbid certain B and/or L violating MSSM couplings. Their presence is however relatively rare, at the level of a few percent of all cases.

An optimized surface plasmon photovoltaic structure using energy transfer between discrete nano-particles.

Science.gov (United States)

Lin, Albert; Fu, Sze-Ming; Chung, Yen-Kai; Lai, Shih-Yun; Tseng, Chi-Wei

2013-01-14

Surface plasmon enhancement has been proposed as a way to achieve higher absorption for thin-film photovoltaics, where surface plasmon polariton(SPP) and localized surface plasmon (LSP) are shown to provide dense near field and far field light scattering. Here it is shown that controlled far-field light scattering can be achieved using successive coupling between surface plasmonic (SP) nano-particles. Through genetic algorithm (GA) optimization, energy transfer between discrete nano-particles (ETDNP) is identified, which enhances solar cell efficiency. The optimized energy transfer structure acts like lumped-element transmission line and can properly alter the direction of photon flow. Increased in-plane component of wavevector is thus achieved and photon path length is extended. In addition, Wood-Rayleigh anomaly, at which transmission minimum occurs, is avoided through GA optimization. Optimized energy transfer structure provides 46.95% improvement over baseline planar cell. It achieves larger angular scattering capability compared to conventional surface plasmon polariton back reflector structure and index-guided structure due to SP energy transfer through mode coupling. Via SP mediated energy transfer, an alternative way to control the light flow inside thin-film is proposed, which can be more efficient than conventional index-guided mode using total internal reflection (TIR).

Calculating and controlling the error of discrete representations of Pareto surfaces in convex multi-criteria optimization.

Science.gov (United States)

Craft, David

2010-10-01

A discrete set of points and their convex combinations can serve as a sparse representation of the Pareto surface in multiple objective convex optimization. We develop a method to evaluate the quality of such a representation, and show by example that in multiple objective radiotherapy planning, the number of Pareto optimal solutions needed to represent Pareto surfaces of up to five dimensions grows at most linearly with the number of objectives. The method described is also applicable to the representation of convex sets. Copyright © 2009 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

Extended discrete-ordinate method considering full polarization state

Energy Technology Data Exchange (ETDEWEB)

Box, Michael A. [School of Physics, University of New South Wales (Australia)]. E-mail: m.box@unsw.edu.au; Qin Yi [School of Physics, University of New South Wales (Australia)]. E-mail: yi.qin@csiro.au

2006-01-15

This paper presents an extension to the standard discrete-ordinate method (DOM) to consider generalized sources including: beam sources which can be placed at any (vertical) position and illuminate in any direction, thermal emission from the atmosphere and angularly distributed sources which illuminate from a surface as continuous functions of zenith and azimuth angles. As special cases, the thermal emission from the surface and deep space can be implemented as angularly distributed sources. Analytical-particular solutions for all source types are derived using the infinite medium Green's function. Radiation field zenith angle interpolation using source function integration is developed for all source types. The development considers the full state of polarization, including the sources (as applicable) and the (BRDF) surface, but the development can be reduced easily to scalar problems and is ready to be implemented in a single set of code for both scalar and vector radiative transfer computation.

AN ACCURATE ORBITAL INTEGRATOR FOR THE RESTRICTED THREE-BODY PROBLEM AS A SPECIAL CASE OF THE DISCRETE-TIME GENERAL THREE-BODY PROBLEM

International Nuclear Information System (INIS)

Minesaki, Yukitaka

2013-01-01

For the restricted three-body problem, we propose an accurate orbital integration scheme that retains all conserved quantities of the two-body problem with two primaries and approximately preserves the Jacobi integral. The scheme is obtained by taking the limit as mass approaches zero in the discrete-time general three-body problem. For a long time interval, the proposed scheme precisely reproduces various periodic orbits that cannot be accurately computed by other generic integrators

On organizing principles of discrete differential geometry. Geometry of spheres

International Nuclear Information System (INIS)

Bobenko, Alexander I; Suris, Yury B

2007-01-01

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

Exact analysis of discrete data

CERN Document Server

Hirji, Karim F

2005-01-01

Researchers in fields ranging from biology and medicine to the social sciences, law, and economics regularly encounter variables that are discrete or categorical in nature. While there is no dearth of books on the analysis and interpretation of such data, these generally focus on large sample methods. When sample sizes are not large or the data are otherwise sparse, exact methods--methods not based on asymptotic theory--are more accurate and therefore preferable.This book introduces the statistical theory, analysis methods, and computation techniques for exact analysis of discrete data. After reviewing the relevant discrete distributions, the author develops the exact methods from the ground up in a conceptually integrated manner. The topics covered range from univariate discrete data analysis, a single and several 2 x 2 tables, a single and several 2 x K tables, incidence density and inverse sampling designs, unmatched and matched case -control studies, paired binary and trinomial response models, and Markov...

Bianchi surfaces: integrability in an arbitrary parametrization

International Nuclear Information System (INIS)

Nieszporski, Maciej; Sym, Antoni

2009-01-01

We discuss integrability of normal field equations of arbitrarily parametrized Bianchi surfaces. A geometric definition of the Bianchi surfaces is presented as well as the Baecklund transformation for the normal field equations in an arbitrarily chosen surface parametrization.

Discrete-continuous analysis of optimal equipment replacement

OpenAIRE

YATSENKO, Yuri; HRITONENKO, Natali

2008-01-01

In Operations Research, the equipment replacement process is usually modeled in discrete time. The optimal replacement strategies are found from discrete (or integer) programming problems, well known for their analytic and computational complexity. An alternative approach is represented by continuous-time vintage capital models that explicitly involve the equipment lifetime and are described by nonlinear integral equations. Then the optimal replacement is determined via the opt...

Nonlinear integrodifferential equations as discrete systems

Science.gov (United States)

Tamizhmani, K. M.; Satsuma, J.; Grammaticos, B.; Ramani, A.

1999-06-01

We analyse a class of integrodifferential equations of the `intermediate long wave' (ILW) type. We show that these equations can be formally interpreted as discrete, differential-difference systems. This allows us to link equations of this type with previous results of ours involving differential-delay equations and, on the basis of this, propose new integrable equations of ILW type. Finally, we extend this approach to pure difference equations and propose ILW forms for the discrete lattice KdV equation.

Modeling and Inversion of Magnetic Anomalies Caused by Sediment–Basement Interface Using Three-Dimensional Cauchy-Type Integrals

DEFF Research Database (Denmark)

Cai, Hongzhu; Zhdanov, Michael

2014-01-01

This letter introduces a new method for the modeling and inversion of magnetic anomalies caused by crystalline basements. The method is based on the 3-D Cauchy-type integral representation of the magnetic field. Traditional methods use volume integrals over the domains occupied by anomalous...... is particularly significant in solving problems of the modeling and inversion of magnetic data for the depth to the basement. In this letter, a novel method is proposed, which only requires discretizing the magnetic contrast surface for modeling and inversion. We demonstrate the method using several synthetic...... susceptibility and on the prismatic representation of the volumes with an anomalous susceptibility distribution. Such discretization is computationally expensive, particularly in 3-D cases. The technique of Cauchy-type integrals makes it possible to represent the magnetic field as surface integrals, which...

Discrete gradients in discrete classical mechanics

International Nuclear Information System (INIS)

Renna, L.

1987-01-01

A simple model of discrete classical mechanics is given where, starting from the continuous Hamilton equations, discrete equations of motion are established together with a proper discrete gradient definition. The conservation laws of the total discrete momentum, angular momentum, and energy are demonstrated

Effects of Macroion Geometry and Charge Discretization in Charge Reversal

OpenAIRE

Mukherjee, Arup K.

2008-01-01

The effects of discrete macroion surface charge distribution and valences of these surface charges and counterions on charge reversal have been studied for macroions of three different geometries and compared with those of continuous surface charge distributions. The geometry of the macroion has been observed to play an important role in overcharging in these cases. The interplay of valences of discrete microions and counterions have noticeable effects on overcharging efficiency. For some val...

High-order solution methods for grey discrete ordinates thermal radiative transfer

Energy Technology Data Exchange (ETDEWEB)

Maginot, Peter G., E-mail: maginot1@llnl.gov [Lawrence Livermore National Laboratory, Livermore, CA 94551 (United States); Ragusa, Jean C., E-mail: jean.ragusa@tamu.edu [Department of Nuclear Engineering, Texas A& M University, College Station, TX 77843 (United States); Morel, Jim E., E-mail: morel@tamu.edu [Department of Nuclear Engineering, Texas A& M University, College Station, TX 77843 (United States)

2016-12-15

This work presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation is accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.

The inverse problem of the calculus of variations for discrete systems

Science.gov (United States)

Barbero-Liñán, María; Farré Puiggalí, Marta; Ferraro, Sebastián; Martín de Diego, David

2018-05-01

We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also provide a transition between the discrete and the continuous problems and propose variationality as an interesting geometric property to take into account in the design and computer simulation of numerical integrators for constrained systems. For instance, nonholonomic mechanics is generally non variational but some special cases admit an alternative variational description. We apply some standard nonholonomic integrators to such an example to study which ones conserve this property.

Transient analysis of electromagnetic wave interactions on plasmonic nanostructures using a surface integral equation solver

KAUST Repository

Uysal, Ismail Enes

2016-08-09

Transient electromagnetic interactions on plasmonic nanostructures are analyzed by solving the Poggio-Miller-Chan-Harrington-Wu-Tsai (PMCHWT) surface integral equation (SIE). Equivalent (unknown) electric and magnetic current densities, which are introduced on the surfaces of the nanostructures, are expanded using Rao-Wilton-Glisson and polynomial basis functions in space and time, respectively. Inserting this expansion into the PMCHWT-SIE and Galerkin testing the resulting equation at discrete times yield a system of equations that is solved for the current expansion coefficients by a marching on-in-time (MOT) scheme. The resulting MOT-PMCHWT-SIE solver calls for computation of additional convolutions between the temporal basis function and the plasmonic medium\\'s permittivity and Green function. This computation is carried out with almost no additional cost and without changing the computational complexity of the solver. Time-domain samples of the permittivity and the Green function required by these convolutions are obtained from their frequency-domain samples using a fast relaxed vector fitting algorithm. Numerical results demonstrate the accuracy and applicability of the proposed MOT-PMCHWT solver. © 2016 Optical Society of America.

Simulations of incompressible Navier Stokes equations on curved surfaces using discrete exterior calculus

Science.gov (United States)

Samtaney, Ravi; Mohamed, Mamdouh; Hirani, Anil

2015-11-01

We present examples of numerical solutions of incompressible flow on 2D curved domains. The Navier-Stokes equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. A conservative discretization of Navier-Stokes equations on simplicial meshes is developed based on discrete exterior calculus (DEC). The discretization is then carried out by substituting the corresponding discrete operators based on the DEC framework. By construction, the method is conservative in that both the discrete divergence and circulation are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step. Numerical examples include Taylor vortices on a sphere, Stuart vortices on a sphere, and flow past a cylinder on domains with varying curvature. Supported by the KAUST Office of Competitive Research Funds under Award No. URF/1/1401-01.

Response-surface models for deterministic effects of localized irradiation of the skin by discrete {beta}/{gamma} -emitting sources

Energy Technology Data Exchange (ETDEWEB)

Scott, B.R.

1995-12-01

Individuals who work at nuclear reactor facilities can be at risk for deterministic effects in the skin from exposure to discrete {Beta}- and {gamma}-emitting ({Beta}{gamma}E) sources (e.g., {Beta}{gamma}E hot particles) on the skin or clothing. Deterministic effects are non-cancer effects that have a threshold and increase in severity as dose increases (e.g., ulcer in skin). Hot {Beta}{gamma}E particles are {sup 60}Co- or nuclear fuel-derived particles with diameters > 10 {mu}m and < 3 mm and contain at least 3.7 kBq (0.1 {mu}Ci) of radioactivity. For such {Beta}{gamma}E sources on the skin, it is the beta component of the dose that is most important. To develop exposure limitation systems that adequately control exposure of workers to discrete {Beta}{gamma}E sources, models are needed for systems that adequately control exposure of workers to discrete {Beta}{gamma}E sources, models are needed for evaluating the risk of deterministic effects of localized {Beta} irradiation of the skin. The purpose of this study was to develop dose-rate and irradiated-area dependent, response-surface models for evaluating risks of significant deterministic effects of localized irradiation of the skin by discrete {Beta}{gamma}E sources and to use modeling results to recommend approaches to limiting occupational exposure to such sources. The significance of the research results as follows: (1) response-surface models are now available for evaluating the risk of specific deterministic effects of localized irradiation of the skin; (2) modeling results have been used to recommend approaches to limiting occupational exposure of workers to {Beta} radiation from {Beta}{gamma}E sources on the skin or on clothing; and (3) the generic irradiated-volume, weighting-factor approach to limiting exposure can be applied to other organs including the eye, the ear, and organs of the respiratory or gastrointestinal tract and can be used for both deterministic and stochastic effects.

Response-surface models for deterministic effects of localized irradiation of the skin by discrete β/γ -emitting sources

International Nuclear Information System (INIS)

Scott, B.R.

1995-01-01

Individuals who work at nuclear reactor facilities can be at risk for deterministic effects in the skin from exposure to discrete Β- and γ-emitting (ΒγE) sources (e.g., ΒγE hot particles) on the skin or clothing. Deterministic effects are non-cancer effects that have a threshold and increase in severity as dose increases (e.g., ulcer in skin). Hot ΒγE particles are 60 Co- or nuclear fuel-derived particles with diameters > 10 μm and < 3 mm and contain at least 3.7 kBq (0.1 μCi) of radioactivity. For such ΒγE sources on the skin, it is the beta component of the dose that is most important. To develop exposure limitation systems that adequately control exposure of workers to discrete ΒγE sources, models are needed for systems that adequately control exposure of workers to discrete ΒγE sources, models are needed for evaluating the risk of deterministic effects of localized Β irradiation of the skin. The purpose of this study was to develop dose-rate and irradiated-area dependent, response-surface models for evaluating risks of significant deterministic effects of localized irradiation of the skin by discrete ΒγE sources and to use modeling results to recommend approaches to limiting occupational exposure to such sources. The significance of the research results as follows: (1) response-surface models are now available for evaluating the risk of specific deterministic effects of localized irradiation of the skin; (2) modeling results have been used to recommend approaches to limiting occupational exposure of workers to Β radiation from ΒγE sources on the skin or on clothing; and (3) the generic irradiated-volume, weighting-factor approach to limiting exposure can be applied to other organs including the eye, the ear, and organs of the respiratory or gastrointestinal tract and can be used for both deterministic and stochastic effects

The (2+1)-dimensional nonisospectral relativistic Toda hierarchy related to the generalized discrete Painleve hierarchy

International Nuclear Information System (INIS)

Zhu Zuonong

2007-01-01

In this paper, we will concentrate on the topic of integrable discrete hierarchies in 2+1 dimensions, and their connection with discrete Painleve hierarchies. By considering a (2+1)-dimensional nonisospectral discrete linear problem, two new (2+1)-dimensional nonisospectral integrable lattice hierarchies-the 2+1 nonisospectral relativistic Toda lattice hierarchy and the 2+1 nonisospectral negative relativistic Toda lattice hierarchy-are constructed. It is shown that the reductions of the two new 2+1 nonisospectral lattice hierarchies lead to the (2+1)-dimensional nonisospectral Volterra lattice hierarchy and the (2+1)-dimensional nonisospectral negative Volterra lattice hierarchy. We also obtain two new (1+1)-dimensional nonisospectral integrable lattice hierarchies and two new ordinary difference hierarchies which are direct reductions of the two 2+1 nonisospectral integrable lattice hierarchies. One of the two difference hierarchies yields our previously obtained generalized discrete first Painleve (dP I ) hierarchy and another one yields a generalized alternative discrete second Painleve (alt-dP II ) hierarchy

Integrated biomechanical and topographical surface characterization (IBTSC)

Energy Technology Data Exchange (ETDEWEB)

Löberg, Johanna, E-mail: Johanna.Loberg@dentsply.com [Dentsply Implants, Box 14, SE-431 21 Mölndal (Sweden); Mattisson, Ingela [Dentsply Implants, Box 14, SE-431 21 Mölndal (Sweden); Ahlberg, Elisabet [Department of Chemistry and Molecular Biology, University of Gothenburg, SE-41296 Gothenburg (Sweden)

2014-01-30

In an attempt to reduce the need for animal studies in dental implant applications, a new model has been developed which combines well-known surface characterization methods with theoretical biomechanical calculations. The model has been named integrated biomechanical and topographical surface characterization (IBTSC), and gives a comprehensive description of the surface topography and the ability of the surface to induce retention strength with bone. IBTSC comprises determination of 3D-surface roughness parameters by using 3D-scanning electron microscopy (3D-SEM) and atomic force microscopy (AFM), and calculation of the ability of different surface topographies to induce retention strength in bone by using the local model. Inherent in this integrated approach is the use of a length scale analysis, which makes it possible to separate different size levels of surface features. The IBTSC concept is tested on surfaces with different level of hierarchy, induced by mechanical as well as chemical treatment. Sequential treatment with oxalic and hydrofluoric acid results in precipitated nano-sized features that increase the surface roughness and the surface slope on the sub-micro and nano levels. This surface shows the highest calculated shear strength using the local model. The validity, robustness and applicability of the IBTSC concept are demonstrated and discussed.

A collection of integrable systems of the Toda type in continuous and discrete time, with 2x2 Lax representations

OpenAIRE

Suris, Yuri B.

1997-01-01

A fairly complete list of Toda-like integrable lattice systems, both in the continuous and discrete time, is given. For each system the Newtonian, Lagrangian and Hamiltonian formulations are presented, as well as the 2x2 Lax representation and r-matrix structure. The material is given in the "no comment" style, in particular, all proofs are omitted.

On Discrete Killing Vector Fields and Patterns on Surfaces

KAUST Repository

Ben-Chen, Mirela; Butscher, Adrian; Solomon, Justin; Guibas, Leonidas

2010-01-01

, and show how to discretize these concepts for generating such vector fields on a triangulated mesh. We discuss the properties of approximate Killing Vector Fields, and propose an application to utilize them for texture and geometry synthesis. Journal

Group-theoretical aspects of the discrete sine-Gordon equation

International Nuclear Information System (INIS)

Orfanidis, S.J.

1980-01-01

The group-theoretical interpretation of the sine-Gordon equation in terms of connection forms on fiber bundles is extended to the discrete case. Solutions of the discrete sine-Gordon equation induce surfaces on a lattice in the SU(2) group space. The inverse scattering representation, expressing the parallel transport of fibers, is implemented by means of finite rotations. Discrete Baecklund transformations are realized as gauge transformations. The three-dimensional inverse scattering representation is used to derive a discrete nonlinear sigma model, and the corresponding Baecklund transformation and Pohlmeyer's R transformation are constructed

Numerical solution of boundary-integral equations for molecular electrostatics.

Science.gov (United States)

Bardhan, Jaydeep P

2009-03-07

Numerous molecular processes, such as ion permeation through channel proteins, are governed by relatively small changes in energetics. As a result, theoretical investigations of these processes require accurate numerical methods. In the present paper, we evaluate the accuracy of two approaches to simulating boundary-integral equations for continuum models of the electrostatics of solvation. The analysis emphasizes boundary-element method simulations of the integral-equation formulation known as the apparent-surface-charge (ASC) method or polarizable-continuum model (PCM). In many numerical implementations of the ASC/PCM model, one forces the integral equation to be satisfied exactly at a set of discrete points on the boundary. We demonstrate in this paper that this approach to discretization, known as point collocation, is significantly less accurate than an alternative approach known as qualocation. Furthermore, the qualocation method offers this improvement in accuracy without increasing simulation time. Numerical examples demonstrate that electrostatic part of the solvation free energy, when calculated using the collocation and qualocation methods, can differ significantly; for a polypeptide, the answers can differ by as much as 10 kcal/mol (approximately 4% of the total electrostatic contribution to solvation). The applicability of the qualocation discretization to other integral-equation formulations is also discussed, and two equivalences between integral-equation methods are derived.

Manifestly gauge invariant discretizations of the Schrödinger equation

International Nuclear Information System (INIS)

Halvorsen, Tore Gunnar; Kvaal, Simen

2012-01-01

Grid-based discretizations of the time dependent Schrödinger equation coupled to an external magnetic field are converted to manifest gauge invariant discretizations. This is done using generalizations of ideas used in classical lattice gauge theory, and the process defined is applicable to a large class of discretized differential operators. In particular, popular discretizations such as pseudospectral discretizations using the fast Fourier transform can be transformed to gauge invariant schemes. Also generic gauge invariant versions of generic time integration methods are considered, enabling completely gauge invariant calculations of the time dependent Schrödinger equation. Numerical examples illuminating the differences between a gauge invariant discretization and conventional discretization procedures are also presented. -- Highlights: ► We investigate the Schrödinger equation coupled to an external magnetic field. ► Any grid-based discretization is made trivially gauge invariant. ► An extension of classical lattice gauge theory.

Domain Discretization and Circle Packings

DEFF Research Database (Denmark)

Dias, Kealey

A circle packing is a configuration of circles which are tangent with one another in a prescribed pattern determined by a combinatorial triangulation, where the configuration fills a planar domain or a two-dimensional surface. The vertices in the triangulation correspond to centers of circles...... to domain discretization problems such as triangulation and unstructured mesh generation techniques. We wish to ask ourselves the question: given a cloud of points in the plane (we restrict ourselves to planar domains), is it possible to construct a circle packing preserving the positions of the vertices...... and constrained meshes having predefined vertices as constraints. A standard method of two-dimensional mesh generation involves conformal mapping of the surface or domain to standardized shapes, such as a disk. Since circle packing is a new technique for constructing discrete conformal mappings, it is possible...

Search Parameter Optimization for Discrete, Bayesian, and Continuous Search Algorithms

Science.gov (United States)

2017-09-01

NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA THESIS SEARCH PARAMETER OPTIMIZATION FOR DISCRETE , BAYESIAN, AND CONTINUOUS SEARCH ALGORITHMS by...to 09-22-2017 4. TITLE AND SUBTITLE SEARCH PARAMETER OPTIMIZATION FOR DISCRETE , BAYESIAN, AND CON- TINUOUS SEARCH ALGORITHMS 5. FUNDING NUMBERS 6...simple search and rescue acts to prosecuting aerial/surface/submersible targets on mission. This research looks at varying the known discrete and

Quadratic Term Structure Models in Discrete Time

OpenAIRE

Marco Realdon

2006-01-01

This paper extends the results on quadratic term structure models in continuos time to the discrete time setting. The continuos time setting can be seen as a special case of the discrete time one. Recursive closed form solutions for zero coupon bonds are provided even in the presence of multiple correlated underlying factors. Pricing bond options requires simple integration. Model parameters may well be time dependent without scuppering such tractability. Model estimation does not require a r...

On the influence of spatial discretization in LWR steady state and burnup calculations with HELIOS 1.9

International Nuclear Information System (INIS)

Merk, B.; Weiss, F. P.

2009-01-01

Cell and burnup calculations are fundamental to all deterministic static and transient 3D full core calculations for different operational states of the reactor. The spatial discretization used for the cell and burnup calculations influences significantly the results of full integral transport solutions. The influence of the discretization on k inf is shown for the steady state case and the influence on the neutron spectrum is analyzed. Moreover, the differences in k inf are presented for different spatial discretization strategies in the burnup calculation of Uranium Oxide (UOX) fuel. The resulting different flux distributions cause significant changes in the isotopic densities. The influence of the discretization strategies on the calculation of homogenized few group cross-sections is investigated. This detailed discretization study demonstrates the need for sufficiently fine discretization to produce reliable and accurate results when using integral transport methods. In contrast to the currently used discretization schemes, refined discretization is especially important in the moderator region of the unit cell to reproduce the influence on the thermal neutron spectrum. Additionally, the need for sufficient discretization affects the idea of full core calculations based on integral transport methods since it has to be discussed whether it is worth to do full core calculations with reduced discretization when facing this strong discretization effect. The computer resources required for full core calculations with fine discretization are currently not available. (authors)

Sub-discretized surface model with application to contact mechanics in multi-body simulation

Energy Technology Data Exchange (ETDEWEB)

Johnson, S; Williams, J

2008-02-28

The mechanics of contact between rough and imperfectly spherical adhesive powder grains are often complicated by a variety of factors, including several which vary over sub-grain length scales. These include several traction factors that vary spatially over the surface of the individual grains, including high energy electron and acceptor sites (electrostatic), hydrophobic and hydrophilic sites (electrostatic and capillary), surface energy (general adhesion), geometry (van der Waals and mechanical), and elasto-plastic deformation (mechanical). For mechanical deformation and reaction, coupled motions, such as twisting with bending and sliding, as well as surface roughness add an asymmetry to the contact force which invalidates assumptions for popular models of contact, such as the Hertzian and its derivatives, for the non-adhesive case, and the JKR and DMT models for adhesive contacts. Though several contact laws have been offered to ameliorate these drawbacks, they are often constrained to particular loading paths (most often normal loading) and are relatively complicated for computational implementation. This paper offers a simple and general computational method for augmenting contact law predictions in multi-body simulations through characterization of the contact surfaces using a hierarchically-defined surface sub-discretization. For the case of adhesive contact between powder grains in low stress regimes, this technique can allow a variety of existing contact laws to be resolved across scales, allowing for moments and torques about the contact area as well as normal and tangential tractions to be resolved. This is especially useful for multi-body simulation applications where the modeler desires statistical distributions and calibration for parameters in contact laws commonly used for resolving near-surface contact mechanics. The approach is verified against analytical results for the case of rough, elastic spheres.

Degree distribution in discrete case

International Nuclear Information System (INIS)

Wang, Li-Na; Chen, Bin; Yan, Zai-Zai

2011-01-01

Vertex degree of many network models and real-life networks is limited to non-negative integer. By means of measure and integral, the relation of the degree distribution and the cumulative degree distribution in discrete case is analyzed. The degree distribution, obtained by the differential of its cumulative, is only suitable for continuous case or discrete case with constant degree change. When degree change is not a constant but proportional to degree itself, power-law degree distribution and its cumulative have the same exponent and the mean value is finite for power-law exponent greater than 1. -- Highlights: → Degree change is the crux for using the cumulative degree distribution method. → It suits for discrete case with constant degree change. → If degree change is proportional to degree, power-law degree distribution and its cumulative have the same exponent. → In addition, the mean value is finite for power-law exponent greater than 1.

Numerical convergence of discrete exterior calculus on arbitrary surface meshes

KAUST Repository

Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

2018-01-01

Discrete exterior calculus (DEC) is a structure-preserving numerical framework for partial differential equations solution, particularly suitable for simplicial meshes. A longstanding and widespread assumption has been that DEC requires special

Simulation of time-dependent free-surface Navier-Stokes flows

International Nuclear Information System (INIS)

Muldowney, G.P.

1989-01-01

Two numerical methods for simulation of time-dependent free-surface Navier-Stokes flows are developed. Both techniques are based on semi-implicit time advancement of the momentum equations, integral formulation of the spatial problem at each timestep, and spectral-element discretization to solve the resulting integral equation. Central to each algorithm is a boundary-specific solution step which permits the spatial treatment in two dimensions to be performed in O(N 3 ) operations per timestep despite the presence of deforming geometry. The first approach is a domain-integral formulation involving integrals over the entire flow domain of kernel functions which arise in time-differencing the Navier-Stokes equations. The second is a particular-solution formulation which replaces domain integration with an iterative scheme to generate particular velocity and pressure fields on individual elements, followed by a patching step to produce a particular solution continuous over the full domain. Two of the most difficult aspects of viscous free-surface flow simulations, namely time-dependent geometry and nontrivial boundary conditions, are well accommodated by these integral equation techniques. In addition the methods offer spectral accuracy in space and admit arbitrarily high-order discretization in time. For large-scale computations and/or long-term time advancement the domain-integral algorithm must be executed on a supercomputer to deliver results in reasonable processing time. A detailed simulation of gas liquid flow with full resolution of the free phase boundary requires approximately five CPU hours at 80 megaflops

Integrating Continuous-Time and Discrete-Event Concepts in Process Modelling, Simulation and Control

NARCIS (Netherlands)

Beek, van D.A.; Gordijn, S.H.F.; Rooda, J.E.; Ertas, A.

1995-01-01

Currently, modelling of systems in the process industry requires the use of different specification languages for the specification of the discrete-event and continuous-time subsystems. In this way, models are restricted to individual subsystems of either a continuous-time or discrete-event nature.

High order three part split symplectic integrators: Efficient techniques for the long time simulation of the disordered discrete nonlinear Schrödinger equation

Energy Technology Data Exchange (ETDEWEB)

Skokos, Ch., E-mail: haris.skokos@uct.ac.za [Physics Department, Aristotle University of Thessaloniki, GR-54124 Thessaloniki (Greece); Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701 (South Africa); Gerlach, E. [Lohrmann Observatory, Technical University Dresden, D-01062 Dresden (Germany); Bodyfelt, J.D., E-mail: J.Bodyfelt@massey.ac.nz [Centre for Theoretical Chemistry and Physics, The New Zealand Institute for Advanced Study, Massey University, Albany, Private Bag 102904, North Shore City, Auckland 0745 (New Zealand); Papamikos, G. [School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, CT2 7NF (United Kingdom); Eggl, S. [IMCCE, Observatoire de Paris, 77 Avenue Denfert-Rochereau, F-75014 Paris (France)

2014-05-01

While symplectic integration methods based on operator splitting are well established in many branches of science, high order methods for Hamiltonian systems that split in more than two parts have not been studied in great detail. Here, we present several high order symplectic integrators for Hamiltonian systems that can be split in exactly three integrable parts. We apply these techniques, as a practical case, for the integration of the disordered, discrete nonlinear Schrödinger equation (DDNLS) and compare their efficiencies. Three part split algorithms provide effective means to numerically study the asymptotic behavior of wave packet spreading in the DDNLS – a hotly debated subject in current scientific literature.

High order three part split symplectic integrators: Efficient techniques for the long time simulation of the disordered discrete nonlinear Schrödinger equation

International Nuclear Information System (INIS)

Skokos, Ch.; Gerlach, E.; Bodyfelt, J.D.; Papamikos, G.; Eggl, S.

2014-01-01

While symplectic integration methods based on operator splitting are well established in many branches of science, high order methods for Hamiltonian systems that split in more than two parts have not been studied in great detail. Here, we present several high order symplectic integrators for Hamiltonian systems that can be split in exactly three integrable parts. We apply these techniques, as a practical case, for the integration of the disordered, discrete nonlinear Schrödinger equation (DDNLS) and compare their efficiencies. Three part split algorithms provide effective means to numerically study the asymptotic behavior of wave packet spreading in the DDNLS – a hotly debated subject in current scientific literature.

Discrete Ordinates Approximations to the First- and Second-Order Radiation Transport Equations

International Nuclear Information System (INIS)

FAN, WESLEY C.; DRUMM, CLIFTON R.; POWELL, JENNIFER L. email wcfan@sandia.gov

2002-01-01

The conventional discrete ordinates approximation to the Boltzmann transport equation can be described in a matrix form. Specifically, the within-group scattering integral can be represented by three components: a moment-to-discrete matrix, a scattering cross-section matrix and a discrete-to-moment matrix. Using and extending these entities, we derive and summarize the matrix representations of the second-order transport equations

Discrete Ordinates Approximations to the First- and Second-Order Radiation Transport Equations

CERN Document Server

Fan, W C; Powell, J L

2002-01-01

The conventional discrete ordinates approximation to the Boltzmann transport equation can be described in a matrix form. Specifically, the within-group scattering integral can be represented by three components: a moment-to-discrete matrix, a scattering cross-section matrix and a discrete-to-moment matrix. Using and extending these entities, we derive and summarize the matrix representations of the second-order transport equations.

Comment on 'Conservative discretizations of the Kepler motion'

International Nuclear Information System (INIS)

Cieslinski, Jan L

2010-01-01

We show that the exact integrator for the classical Kepler motion, recently found by Kozlov (2007 J. Phys. A: Math. Theor. 40 4529-39), can be derived in a simple natural way, using a well-known exact discretization of the harmonic oscillator. We also draw attention to important earlier references, where the exact discretization of the four-dimensional isotropic harmonic oscillator has been applied to the perturbed Kepler problem. (comments and replies)

An integrable coupling family of Merola-Ragnisco-Tu lattice systems, its Hamiltonian structure and related nonisospectral integrable lattice family

Energy Technology Data Exchange (ETDEWEB)

Xu Xixiang, E-mail: xu_xixiang@hotmail.co [College of Science, Shandong University of Science and Technology, Qingdao, 266510 (China)

2010-01-04

An integrable coupling family of Merola-Ragnisco-Tu lattice systems is derived from a four-by-four matrix spectral problem. The Hamiltonian structure of the resulting integrable coupling family is established by the discrete variational identity. Each lattice system in the resulting integrable coupling family is proved to be integrable discrete Hamiltonian system in Liouville sense. Ultimately, a nonisospectral integrable lattice family associated with the resulting integrable lattice family is constructed through discrete zero curvature representation.

An integrable coupling family of Merola-Ragnisco-Tu lattice systems, its Hamiltonian structure and related nonisospectral integrable lattice family

International Nuclear Information System (INIS)

Xu Xixiang

2010-01-01

An integrable coupling family of Merola-Ragnisco-Tu lattice systems is derived from a four-by-four matrix spectral problem. The Hamiltonian structure of the resulting integrable coupling family is established by the discrete variational identity. Each lattice system in the resulting integrable coupling family is proved to be integrable discrete Hamiltonian system in Liouville sense. Ultimately, a nonisospectral integrable lattice family associated with the resulting integrable lattice family is constructed through discrete zero curvature representation.

Developing an integrated digitizing and display surface

Science.gov (United States)

Hipple, James D.; Wedding, Daniel K.; Wedding, Donald K., Sr.

1995-04-01

The development of an integrated digitizing and display surface, which utilizes touch entry and flat panel display (FPD) technology, is a significant hardware advance in the field of geographic information systems (GIS). Inherent qualities of the FPD, notably the ac gas plasma display, makes such a marriage inevitable. Large diagonal sizes, high resolution color, screen flatness, and monitor thickness are desirable features of an integrated digitizing and display surface. Recently, the GIS literature has addressed a need for such an innovation. The development of graphics displays based on sophisticated technologies include `photorealistic' (or high definition) imaging at resolutions of 2048 X 2048 or greater, palates of 16.7 million colors, formats greater than 30 inches diagonal, and integrated touch entry. In this paper, there is an evaluation of FPDs and data input technologies in the development of such a product.

Discrete coupled derivative nonlinear Schroedinger equations and their quasi-periodic solutions

International Nuclear Information System (INIS)

Geng Xianguo; Su Ting

2007-01-01

A hierarchy of nonlinear differential-difference equations associated with a discrete isospectral problem is proposed, in which a typical differential-difference equation is a discrete coupled derivative nonlinear Schroedinger equation. With the help of the nonlinearization of the Lax pairs, the hierarchy of nonlinear differential-difference equations is decomposed into a new integrable symplectic map and a class of finite-dimensional integrable Hamiltonian systems. Based on the theory of algebraic curve, the Abel-Jacobi coordinates are introduced to straighten out the corresponding flows, from which quasi-periodic solutions for these differential-difference equations are obtained resorting to the Riemann-theta functions. Moreover, a (2+1)-dimensional discrete coupled derivative nonlinear Schroedinger equation is proposed and its quasi-periodic solutions are derived

A parallel algorithm for solving the integral form of the discrete ordinates equations

International Nuclear Information System (INIS)

Zerr, R. J.; Azmy, Y. Y.

2009-01-01

The integral form of the discrete ordinates equations involves a system of equations that has a large, dense coefficient matrix. The serial construction methodology is presented and properties that affect the execution times to construct and solve the system are evaluated. Two approaches for massively parallel implementation of the solution algorithm are proposed and the current results of one of these are presented. The system of equations May be solved using two parallel solvers-block Jacobi and conjugate gradient. Results indicate that both methods can reduce overall wall-clock time for execution. The conjugate gradient solver exhibits better performance to compete with the traditional source iteration technique in terms of execution time and scalability. The parallel conjugate gradient method is synchronous, hence it does not increase the number of iterations for convergence compared to serial execution, and the efficiency of the algorithm demonstrates an apparent asymptotic decline. (authors)

Hyperdeterminants as integrable discrete systems

International Nuclear Information System (INIS)

Tsarev, Sergey P; Wolf, Thomas

2009-01-01

We give the basic definitions and some theoretical results about hyperdeterminants, introduced by A Cayley in 1845. We prove integrability (understood as 4D consistency) of a nonlinear difference equation defined by the 2 x 2 x 2-hyperdeterminant. This result gives rise to the following hypothesis: the difference equations defined by hyperdeterminants of any size are integrable. We show that this hypothesis already fails in the case of the 2 x 2 x 2 x 2-hyperdeterminant.

Hyperdeterminants as integrable discrete systems

Energy Technology Data Exchange (ETDEWEB)

Tsarev, Sergey P [Institute of Space and Information Technologies, Siberian Federal University, Svobodnyi Avenue, 79, 660041, Krasnoyarsk (Russian Federation); Wolf, Thomas [Department of Mathematics, Brock University, 500 Glenridge Avenue, St Catharines, Ontario L2S 3A1 (Canada)], E-mail: sptsarev@mail.ru, E-mail: twolf@brocku.ca

2009-10-30

We give the basic definitions and some theoretical results about hyperdeterminants, introduced by A Cayley in 1845. We prove integrability (understood as 4D consistency) of a nonlinear difference equation defined by the 2 x 2 x 2-hyperdeterminant. This result gives rise to the following hypothesis: the difference equations defined by hyperdeterminants of any size are integrable. We show that this hypothesis already fails in the case of the 2 x 2 x 2 x 2-hyperdeterminant.

Collective Robotic Assembly of Discrete Lattice Elements (CRADLE)

Data.gov (United States)

National Aeronautics and Space Administration — CRADLE seeks to address this need through a novel application of an integrated robot-structure-material system based on discrete lattice construction using task...

Optimum DMOS cell doping profiles for high-voltage discrete and integrated device technologies

Science.gov (United States)

Shenai, Krishna

1992-05-01

It is shown that the implantation and activation sequences of B and As result in significant variations in the contact resistance and p-base sheet resistance beneath the n+-source diffusion of a DMOSFET cell. For identical process parameters, the contact resistance of As-doped n+ silicon was significantly improved when high-dose B was implanted due to higher As surface concentration. The SUPREM III process modeling results were found to be in qualitative agreement with the measured spreading resistance profiles and the discrepancies could be attributed to larger high-temperature diffusion constants used in SUPREM III and the coupled As-B diffusion/activation effects that are not accounted for in process modeling. The experimental results are discussed within the framework of fabricating high-performance DMOSFET cells and CMOS high-voltage devices on the same chip for discrete and smart-power applications.

Surface free energy for systems with integrable boundary conditions

International Nuclear Information System (INIS)

Goehmann, Frank; Bortz, Michael; Frahm, Holger

2005-01-01

The surface free energy is the difference between the free energies for a system with open boundary conditions and the same system with periodic boundary conditions. We use the quantum transfer matrix formalism to express the surface free energy in the thermodynamic limit of systems with integrable boundary conditions as a matrix element of certain projection operators. Specializing to the XXZ spin-1/2 chain we introduce a novel 'finite temperature boundary operator' which characterizes the thermodynamical properties of surfaces related to integrable boundary conditions

SITE-94. Discrete-feature modelling of the Aespoe site: 2. Development of the integrated site-scale model

International Nuclear Information System (INIS)

Geier, J.E.

1996-12-01

A 3-dimensional, discrete-feature hydrological model is developed. The model integrates structural and hydrologic data for the Aespoe site, on scales ranging from semi regional fracture zones to individual fractures in the vicinity of the nuclear waste canisters. Hydrologic properties of the large-scale structures are initially estimated from cross-hole hydrologic test data, and automatically calibrated by numerical simulation of network flow, and comparison with undisturbed heads and observed drawdown in selected cross-hole tests. The calibrated model is combined with a separately derived fracture network model, to yield the integrated model. This model is partly validated by simulation of transient responses to a long-term pumping test and a convergent tracer test, based on the LPT2 experiment at Aespoe. The integrated model predicts that discharge from the SITE-94 repository is predominantly via fracture zones along the eastern shore of Aespoe. Similar discharge loci are produced by numerous model variants that explore uncertainty with regard to effective semi regional boundary conditions, hydrologic properties of the site-scale structures, and alternative structural/hydrological interpretations. 32 refs

SITE-94. Discrete-feature modelling of the Aespoe site: 2. Development of the integrated site-scale model

Energy Technology Data Exchange (ETDEWEB)

Geier, J.E. [Golder Associates AB, Uppsala (Sweden)

1996-12-01

A 3-dimensional, discrete-feature hydrological model is developed. The model integrates structural and hydrologic data for the Aespoe site, on scales ranging from semi regional fracture zones to individual fractures in the vicinity of the nuclear waste canisters. Hydrologic properties of the large-scale structures are initially estimated from cross-hole hydrologic test data, and automatically calibrated by numerical simulation of network flow, and comparison with undisturbed heads and observed drawdown in selected cross-hole tests. The calibrated model is combined with a separately derived fracture network model, to yield the integrated model. This model is partly validated by simulation of transient responses to a long-term pumping test and a convergent tracer test, based on the LPT2 experiment at Aespoe. The integrated model predicts that discharge from the SITE-94 repository is predominantly via fracture zones along the eastern shore of Aespoe. Similar discharge loci are produced by numerous model variants that explore uncertainty with regard to effective semi regional boundary conditions, hydrologic properties of the site-scale structures, and alternative structural/hydrological interpretations. 32 refs.

Application of Terrestrial Laser Scanner with an Integrated Thermal Camera in Non-Destructive Evaluation of Concrete Surface of Hydrotechnical Objects

Science.gov (United States)

Kaczmarek, Łukasz Dominik; Dobak, Paweł Józef; Kiełbasiński, Kamil

2017-12-01

The authors present possible applications of thermal data as an additional source of information on an object's behaviour during the technical assessment of the condition of a concrete surface. For the study one of the most recent propositions introduced by Zoller + Fröhlich company was used, which is an integration of a thermal camera with a terrestrial laser scanner. This solution enables an acquisition of geometric and spectral data on the surveyed object and also provides information on the surface's temperature in the selected points. A section of the dam's downstream concrete wall was selected as the subject of the study for which a number of scans were carried out and a number of thermal images were taken at different times of the day. The obtained thermal data was confronted with the acquired spectral information for the specified points. This made it possible to carry out broader analysis of the surface and an inspection of the revealed fissure. The thermal analysis of said fissure indicated that the temperature changes within it are slower, which may affect the way the concrete works and may require further elaboration by the appropriate experts. Through the integration of a thermal camera with a terrestrial laser scanner one can not only analyse changes of temperature in the discretely selected points but on the whole surface as well. Moreover, it is also possible to accurately determine the range and the area of the change affecting the surface. The authors note the limitations of the presented solution like, inter alia, the resolution of the thermal camera.

Quantum circuit dynamics via path integrals: Is there a classical action for discrete-time paths?

Science.gov (United States)

Penney, Mark D.; Enshan Koh, Dax; Spekkens, Robert W.

2017-07-01

It is straightforward to compute the transition amplitudes of a quantum circuit using the sum-over-paths methodology when the gates in the circuit are balanced, where a balanced gate is one for which all non-zero transition amplitudes are of equal magnitude. Here we consider the question of whether, for such circuits, the relative phases of different discrete-time paths through the configuration space can be defined in terms of a classical action, as they are for continuous-time paths. We show how to do so for certain kinds of quantum circuits, namely, Clifford circuits where the elementary systems are continuous-variable systems or discrete systems of odd-prime dimension. These types of circuit are distinguished by having phase-space representations that serve to define their classical counterparts. For discrete systems, the phase-space coordinates are also discrete variables. We show that for each gate in the generating set, one can associate a symplectomorphism on the phase-space and to each of these one can associate a generating function, defined on two copies of the configuration space. For discrete systems, the latter association is achieved using tools from algebraic geometry. Finally, we show that if the action functional for a discrete-time path through a sequence of gates is defined using the sum of the corresponding generating functions, then it yields the correct relative phases for the path-sum expression. These results are likely to be relevant for quantizing physical theories where time is fundamentally discrete, characterizing the classical limit of discrete-time quantum dynamics, and proving complexity results for quantum circuits.

Covariant path integrals on hyperbolic surfaces

Science.gov (United States)

Schaefer, Joe

1997-11-01

DeWitt's covariant formulation of path integration [B. De Witt, "Dynamical theory in curved spaces. I. A review of the classical and quantum action principles," Rev. Mod. Phys. 29, 377-397 (1957)] has two practical advantages over the traditional methods of "lattice approximations;" there is no ordering problem, and classical symmetries are manifestly preserved at the quantum level. Applying the spectral theorem for unbounded self-adjoint operators, we provide a rigorous proof of the convergence of certain path integrals on Riemann surfaces of constant curvature -1. The Pauli-DeWitt curvature correction term arises, as in DeWitt's work. Introducing a Fuchsian group Γ of the first kind, and a continuous, bounded, Γ-automorphic potential V, we obtain a Feynman-Kac formula for the automorphic Schrödinger equation on the Riemann surface ΓH. We analyze the Wick rotation and prove the strong convergence of the so-called Feynman maps [K. D. Elworthy, Path Integration on Manifolds, Mathematical Aspects of Superspace, edited by Seifert, Clarke, and Rosenblum (Reidel, Boston, 1983), pp. 47-90] on a dense set of states. Finally, we give a new proof of some results in C. Grosche and F. Steiner, "The path integral on the Poincare upper half plane and for Liouville quantum mechanics," Phys. Lett. A 123, 319-328 (1987).

Strongly asymmetric discrete Painlevé equations: The additive case

Energy Technology Data Exchange (ETDEWEB)

Grammaticos, B. [IMNC, Université Paris VII and XI, CNRS, UMR 8165, Bât. 440, 91406 Orsay (France); Ramani, A. [Centre de Physique Théorique, Ecole Polytechnique, CNRS, 91128 Palaiseau (France); Tamizhmani, K. M. [Department of Mathematics, Pondicherry University, Kalapet, 605014 Puducherry (India); Tamizhmani, T. [Avvaiyar Government College for Women, 609602 Karaikal (India); Satsuma, J. [Department of Physics and Mathematics, Aoyama Gakuin University, 5-10-1 Fuchinobe, Chuo-ku, Sagamihara-shi 252-5258 (Japan)

2014-05-15

We examine a class of discrete Painlevé equations which present a strong asymmetry. These equations can be written as a system of two equations, the right-hand-sides of which do not have the same functional form. We limit here our investigation to two canonical families of the Quispel-Roberts-Thompson (QRT) classification both of which lead to difference equations. Several new integrable discrete systems are identified.

Spaces of fractional quotients, discrete operators, and their applications. II

International Nuclear Information System (INIS)

Lifanov, I K; Poltavskii, L N

1999-01-01

The theory of discrete operators in spaces of fractional quotients is developed. A theorem on the stability of discrete operators under smooth perturbations is proved. On this basis, using special quadrature formulae of rectangular kind, the convergence of approximate solutions of hypersingular integral equations to their exact solutions is demonstrated and a mathematical substantiation of the method of closed discrete vortex frameworks is obtained. The same line of argument is also applied to difference equations arising in the solution of the homogeneous Dirichlet problem for a general second-order elliptic equation with variable coefficients

Digital and discrete geometry theory and algorithms

CERN Document Server

Chen, Li

2014-01-01

This book provides comprehensive coverage of the modern methods for geometric problems in the computing sciences. It also covers concurrent topics in data sciences including geometric processing, manifold learning, Google search, cloud data, and R-tree for wireless networks and BigData.The author investigates digital geometry and its related constructive methods in discrete geometry, offering detailed methods and algorithms. The book is divided into five sections: basic geometry; digital curves, surfaces and manifolds; discretely represented objects; geometric computation and processing; and a

Discrete Mathematics

DEFF Research Database (Denmark)

Sørensen, John Aasted

2011-01-01

The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics......; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...

Discrete breathers in Bose–Einstein condensates

International Nuclear Information System (INIS)

Franzosi, Roberto; Politi, Antonio; Livi, Roberto; Oppo, Gian-Luca

2011-01-01

Discrete breathers, originally introduced in the context of biopolymers and coupled nonlinear oscillators, are also localized modes of excitation of Bose–Einstein condensates (BEC) in periodic potentials such as those generated by counter-propagating laser beams in an optical lattice. Static and dynamical properties of breather states are analysed in the discrete nonlinear Schrödinger equation that is derived in the limit of deep potential wells, tight-binding and the superfluid regime of the condensate. Static and mobile breathers can be formed by progressive re-shaping of initial Gaussian wave-packets or by transporting atomic density towards dissipative boundaries of the lattice. Static breathers generated via boundary dissipations are determined via a transfer-matrix approach and discussed in the two analytic limits of highly localized and very broad profiles. Mobile breathers that move across the lattice are well approximated by modified analytical expressions derived from integrable models with two independent parameters: the core-phase gradient and the peak amplitude. Finally, possible experimental realizations of discrete breathers in BEC in optical lattices are discussed in the presence of residual harmonic trapping and in interferometry configurations suitable to investigate discrete breathers' interactions. (invited article)

Compatible Spatial Discretizations for Partial Differential Equations

Energy Technology Data Exchange (ETDEWEB)

Arnold, Douglas, N, ed.

2004-11-25

From May 11--15, 2004, the Institute for Mathematics and its Applications held a hot topics workshop on Compatible Spatial Discretizations for Partial Differential Equations. The numerical solution of partial differential equations (PDE) is a fundamental task in science and engineering. The goal of the workshop was to bring together a spectrum of scientists at the forefront of the research in the numerical solution of PDEs to discuss compatible spatial discretizations. We define compatible spatial discretizations as those that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum principles. A wide variety of discretization methods applied across a wide range of scientific and engineering applications have been designed to or found to inherit or mimic intrinsic spatial structure and reproduce fundamental properties of the solution of the continuous PDE model at the finite dimensional level. A profusion of such methods and concepts relevant to understanding them have been developed and explored: mixed finite element methods, mimetic finite differences, support operator methods, control volume methods, discrete differential forms, Whitney forms, conservative differencing, discrete Hodge operators, discrete Helmholtz decomposition, finite integration techniques, staggered grid and dual grid methods, etc. This workshop seeks to foster communication among the diverse groups of researchers designing, applying, and studying such methods as well as researchers involved in practical solution of large scale problems that may benefit from advancements in such discretizations; to help elucidate the relations between the different methods and concepts; and to generally advance our understanding in the area of compatible spatial discretization methods for PDE. Particular points of emphasis included: + Identification of intrinsic properties of PDE models that are critical for the fidelity of numerical

Quantum circuit dynamics via path integrals: Is there a classical action for discrete-time paths?

International Nuclear Information System (INIS)

Penney, Mark D; Koh, Dax Enshan; Spekkens, Robert W

2017-01-01

It is straightforward to compute the transition amplitudes of a quantum circuit using the sum-over-paths methodology when the gates in the circuit are balanced, where a balanced gate is one for which all non-zero transition amplitudes are of equal magnitude. Here we consider the question of whether, for such circuits, the relative phases of different discrete-time paths through the configuration space can be defined in terms of a classical action, as they are for continuous-time paths. We show how to do so for certain kinds of quantum circuits, namely, Clifford circuits where the elementary systems are continuous-variable systems or discrete systems of odd-prime dimension. These types of circuit are distinguished by having phase-space representations that serve to define their classical counterparts. For discrete systems, the phase-space coordinates are also discrete variables. We show that for each gate in the generating set, one can associate a symplectomorphism on the phase-space and to each of these one can associate a generating function, defined on two copies of the configuration space. For discrete systems, the latter association is achieved using tools from algebraic geometry. Finally, we show that if the action functional for a discrete-time path through a sequence of gates is defined using the sum of the corresponding generating functions, then it yields the correct relative phases for the path-sum expression. These results are likely to be relevant for quantizing physical theories where time is fundamentally discrete, characterizing the classical limit of discrete-time quantum dynamics, and proving complexity results for quantum circuits. (paper)

Study on the methodology for hydrogeological site descriptive modelling by discrete fracture networks

International Nuclear Information System (INIS)

Tanaka, Tatsuya; Ando, Kenichi; Hashimoto, Shuuji; Saegusa, Hiromitsu; Takeuchi, Shinji; Amano, Kenji

2007-01-01

This study aims to establish comprehensive techniques for site descriptive modelling considering the hydraulic heterogeneity due to the Water Conducting Features in fractured rocks. The WCFs was defined by the interpretation and integration of geological and hydrogeological data obtained from the deep borehole investigation campaign in the Mizunami URL project and Regional Hydrogeological Study. As a result of surface based investigation phase, the block-scale hydrogeological descriptive model was generated using hydraulic discrete fracture networks. Uncertainties and remaining issues associated with the assumption in interpreting the data and its modelling were addressed in a systematic way. (author)

Baecklund transformations for discrete Painleve equations: Discrete PII-PV

International Nuclear Information System (INIS)

Sakka, A.; Mugan, U.

2006-01-01

Transformation properties of discrete Painleve equations are investigated by using an algorithmic method. This method yields explicit transformations which relates the solutions of discrete Painleve equations, discrete P II -P V , with different values of parameters. The particular solutions which are expressible in terms of the discrete analogue of the classical special functions of discrete Painleve equations can also be obtained from these transformations

A multi-resolution approach to heat kernels on discrete surfaces

KAUST Repository

Vaxman, Amir; Ben-Chen, Mirela; Gotsman, Craig

2010-01-01

process - limits this type of analysis to 3D models of modest resolution. We show how to use the unique properties of the heat kernel of a discrete two dimensional manifold to overcome these limitations. Combining a multi-resolution approach with a novel

Electromagnetic Modeling, Optimization and Uncertainty Quantification for Antenna and Radar Systems Surfaces Scattering and Energy Absorption

Science.gov (United States)

2017-03-06

the various solution domains. The WGF method does not require any discretizations except for the actual junction/launching/termination regions. 3 (a...which amount to discrete finite-differencing of the Green functions) can be used to produce arbitrary (user-prescribed) algebraic convergence order...order Nystrom integral-equation method for surface scattering problems, Numer. Math . 124, 603–645 (2013). [25] Bruno, O. P. and Kunyansky, L., A fast

Integrable mappings via rational elliptic surfaces

International Nuclear Information System (INIS)

Tsuda, Teruhisa

2004-01-01

We present a geometric description of the QRT map (which is an integrable mapping introduced by Quispel, Roberts and Thompson) in terms of the addition formula of a rational elliptic surface. By this formulation, we classify all the cases when the QRT map is periodic; and show that its period is 2, 3, 4, 5 or 6. A generalization of the QRT map which acts birationally on a pencil of K3 surfaces, or Calabi-Yau manifolds, is also presented

How to discretize differential systems in a systematic way

International Nuclear Information System (INIS)

Murata, M; Satsuma, J; Ramani, A; Grammaticos, B

2010-01-01

We present a systematic approach to the construction of discrete analogues for differential systems. Our method is tailored to first-order differential equations and relies on a formal linearization, followed by a Pade-like rational approximation of an exponential evolution operator. We apply our method to a host of systems for which there exist discretization results obtained by what we call the 'intuitive' method and compare the discretizations obtained. A discussion of our method as compared to one of the Mickens is also presented. Finally we apply our method to a system of coupled Riccati equations with emphasis on the preservation of the integrable character of the differential system.

Ray effects in the discrete-ordinate solution for surface radiation exchange

Energy Technology Data Exchange (ETDEWEB)

Liou, B T [Dept. of Mechanical Engineering, National Cheng Kung Univ., Tainan (Taiwan, Province of China); Wu, C Y [Dept. of Mechanical Engineering, National Cheng Kung Univ., Tainan (Taiwan, Province of China)

1997-04-01

A study of the application of the discrete-ordinate method (DOM) with remedy for the ray effects to the solution of surface radiation exchange is presented in this paper. The remedy for the ray effects is achieved by dividing the radiative intensity into the attenuated incident and the medium emitting components. To demonstrate the application of the technique, this work considers radiative heat transfer in a two-dimensional cylindrical enclosure filled with a nearly transparent medium. The results obtained by the present DOM are in excellent agreement with those by the radiosity/irradiation method. (orig.). With 4 figs., 3 tabs. [Deutsch] In der Arbeit wird ein Weg aufgezeigt, wie die Stoerstrahlungseffekte bei Anwendung der Methode der diskreten Ordinaten auf die Berechnung des Energietausches zwischen Oberflaechenstrahlern vermieden werden koennen. Dies laesst sich durch Aufspaltung der Strahlungsintensitaet in die abgeschwaechte einfallende und die vom Medium emittierte Komponente erreichen. Als Beispiel fuer die Anwendung dieses Verfahrens dient der Waermeaustausch durch Strahlung in einem zweidimensionalen zylindrischen Behaeltnis, das mit einem nahezu transparenten Medium befuellt ist. Die mit der modifizierten Methode erhaltenen Ergebnisse stimmen ausgezeichnet mit jenen nach dem klassischen Brutto-Verfahren ueberein. (orig.)

Discrete Bat Algorithm for Optimal Problem of Permutation Flow Shop Scheduling

Science.gov (United States)

Luo, Qifang; Zhou, Yongquan; Xie, Jian; Ma, Mingzhi; Li, Liangliang

2014-01-01

A discrete bat algorithm (DBA) is proposed for optimal permutation flow shop scheduling problem (PFSP). Firstly, the discrete bat algorithm is constructed based on the idea of basic bat algorithm, which divide whole scheduling problem into many subscheduling problems and then NEH heuristic be introduced to solve subscheduling problem. Secondly, some subsequences are operated with certain probability in the pulse emission and loudness phases. An intensive virtual population neighborhood search is integrated into the discrete bat algorithm to further improve the performance. Finally, the experimental results show the suitability and efficiency of the present discrete bat algorithm for optimal permutation flow shop scheduling problem. PMID:25243220

Discrete bat algorithm for optimal problem of permutation flow shop scheduling.

Science.gov (United States)

Luo, Qifang; Zhou, Yongquan; Xie, Jian; Ma, Mingzhi; Li, Liangliang

2014-01-01

A discrete bat algorithm (DBA) is proposed for optimal permutation flow shop scheduling problem (PFSP). Firstly, the discrete bat algorithm is constructed based on the idea of basic bat algorithm, which divide whole scheduling problem into many subscheduling problems and then NEH heuristic be introduced to solve subscheduling problem. Secondly, some subsequences are operated with certain probability in the pulse emission and loudness phases. An intensive virtual population neighborhood search is integrated into the discrete bat algorithm to further improve the performance. Finally, the experimental results show the suitability and efficiency of the present discrete bat algorithm for optimal permutation flow shop scheduling problem.

Effects of Discrete Charge Clustering in Simulations of Charged Interfaces.

Science.gov (United States)

Grime, John M A; Khan, Malek O

2010-10-12

A system of counterions between charged surfaces is investigated, with the surfaces represented by uniform charged planes and three different arrangements of discrete surface charges - an equispaced grid and two different clustered arrangements. The behaviors of a series of systems with identical net surface charge density are examined, with particular emphasis placed on the long ranged corrections via the method of "charged slabs" and the effects of the simulation cell size. Marked differences are observed in counterion distributions and the osmotic pressure dependent on the particular representation of the charged surfaces; the uniformly charged surfaces and equispaced grids of discrete charge behave in a broadly similar manner, but the clustered systems display a pronounced decrease in osmotic pressure as the simulation size is increased. The influence of the long ranged correction is shown to be minimal for all but the very smallest of system sizes.

Covariant path integrals on hyperbolic surfaces

International Nuclear Information System (INIS)

Schaefer, J.

1997-01-01

DeWitt close-quote s covariant formulation of path integration [B. De Witt, open-quotes Dynamical theory in curved spaces. I. A review of the classical and quantum action principles,close quotes Rev. Mod. Phys. 29, 377 endash 397 (1957)] has two practical advantages over the traditional methods of open-quotes lattice approximations;close quotes there is no ordering problem, and classical symmetries are manifestly preserved at the quantum level. Applying the spectral theorem for unbounded self-adjoint operators, we provide a rigorous proof of the convergence of certain path integrals on Riemann surfaces of constant curvature -1. The Pauli endash DeWitt curvature correction term arises, as in DeWitt close-quote s work. Introducing a Fuchsian group Γ of the first kind, and a continuous, bounded, Γ-automorphic potential V, we obtain a Feynman endash Kac formula for the automorphic Schroedinger equation on the Riemann surface Γ backslash H. We analyze the Wick rotation and prove the strong convergence of the so-called Feynman maps [K. D. Elworthy, Path Integration on Manifolds, Mathematical Aspects of Superspace, edited by Seifert, Clarke, and Rosenblum (Reidel, Boston, 1983), pp. 47 endash 90] on a dense set of states. Finally, we give a new proof of some results in C. Grosche and F. Steiner, open-quotes The path integral on the Poincare upper half plane and for Liouville quantum mechanics,close quotes Phys. Lett. A 123, 319 endash 328 (1987). copyright 1997 American Institute of Physics

Discrete geometric structures for architecture

KAUST Repository

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

A spectral approach for discrete dislocation dynamics simulations of nanoindentation

Science.gov (United States)

Bertin, Nicolas; Glavas, Vedran; Datta, Dibakar; Cai, Wei

2018-07-01

We present a spectral approach to perform nanoindentation simulations using three-dimensional nodal discrete dislocation dynamics. The method relies on a two step approach. First, the contact problem between an indenter of arbitrary shape and an isotropic elastic half-space is solved using a spectral iterative algorithm, and the contact pressure is fully determined on the half-space surface. The contact pressure is then used as a boundary condition of the spectral solver to determine the resulting stress field produced in the simulation volume. In both stages, the mechanical fields are decomposed into Fourier modes and are efficiently computed using fast Fourier transforms. To further improve the computational efficiency, the method is coupled with a subcycling integrator and a special approach is devised to approximate the displacement field associated with surface steps. As a benchmark, the method is used to compute the response of an elastic half-space using different types of indenter. An example of a dislocation dynamics nanoindentation simulation with complex initial microstructure is presented.

Discretization analysis of bifurcation based nonlinear amplifiers

Science.gov (United States)

Feldkord, Sven; Reit, Marco; Mathis, Wolfgang

2017-09-01

Recently, for modeling biological amplification processes, nonlinear amplifiers based on the supercritical Andronov-Hopf bifurcation have been widely analyzed analytically. For technical realizations, digital systems have become the most relevant systems in signal processing applications. The underlying continuous-time systems are transferred to the discrete-time domain using numerical integration methods. Within this contribution, effects on the qualitative behavior of the Andronov-Hopf bifurcation based systems concerning numerical integration methods are analyzed. It is shown exemplarily that explicit Runge-Kutta methods transform the truncated normalform equation of the Andronov-Hopf bifurcation into the normalform equation of the Neimark-Sacker bifurcation. Dependent on the order of the integration method, higher order terms are added during this transformation.A rescaled normalform equation of the Neimark-Sacker bifurcation is introduced that allows a parametric design of a discrete-time system which corresponds to the rescaled Andronov-Hopf system. This system approximates the characteristics of the rescaled Hopf-type amplifier for a large range of parameters. The natural frequency and the peak amplitude are preserved for every set of parameters. The Neimark-Sacker bifurcation based systems avoid large computational effort that would be caused by applying higher order integration methods to the continuous-time normalform equations.

Effect of different machining processes on the tool surface integrity and fatigue life

Energy Technology Data Exchange (ETDEWEB)

Cao, Chuan Liang [College of Mechanical and Electrical Engineering, Nanchang University, Nanchang (China); Zhang, Xianglin [School of Materials Science and Engineering, Huazhong University of Science and Technology, Wuhan (China)

2016-08-15

Ultra-precision grinding, wire-cut electro discharge machining and lapping are often used to machine the tools in fine blanking industry. And the surface integrity from these machining processes causes great concerns in the research field. To study the effect of processing surface integrity on the fine blanking tool life, the surface integrity of different tool materials under different processing conditions and its influence on fatigue life were thoroughly analyzed in the present study. The result shows that the surface integrity of different materials was quite different on the same processing condition. For the same tool material, the surface integrity on varying processing conditions was quite different too and deeply influenced the fatigue life.

Template-Guided Self-Assembly of Discrete Optoplasmonic Molecules and Extended Optoplasmonic Arrays

Directory of Open Access Journals (Sweden)

Reinhard Björn M.

2015-01-01

Full Text Available The integration of metallic and dielectric building blocks into optoplasmonic structures creates new electromagnetic systems in which plasmonic and photonic modes can interact in the near-, intermediate- and farfield. The morphology-dependent electromagnetic coupling between the different building blocks in these hybrid structures provides a multitude of opportunities for controlling electromagnetic fields in both spatial and frequency domain as well as for engineering the phase landscape and the local density of optical states. Control over any of these properties requires, however, rational fabrication approaches for well-defined metal-dielectric hybrid structures. Template-guided self-assembly is a versatile fabrication method capable of integrating metallic and dielectric components into discrete optoplasmonic structures, arrays, or metasurfaces. The structural flexibility provided by the approach is illustrated by two representative implementations of optoplasmonic materials discussed in this review. In optoplasmonic atoms or molecules optical microcavities (OMs serve as whispering gallery mode resonators that provide a discrete photonic mode spectrum to interact with plasmonic nanostructures contained in the evanescent fields of the OMs. In extended hetero-nanoparticle arrays in-plane scattered light induces geometry-dependent photonic resonances that mix with the localized surface plasmon resonances of the metal nanoparticles.We characterize the fundamental electromagnetic working principles underlying both optoplasmonic approaches and review the fabrication strategies implemented to realize them.

A Note on Discrete Mathematics and Calculus.

Science.gov (United States)

O'Reilly, Thomas J.

1987-01-01

Much of the current literature on the topic of discrete mathematics and calculus during the first two years of an undergraduate mathematics curriculum is cited. A relationship between the recursive integration formulas and recursively defined polynomials is described. A Pascal program is included. (Author/RH)

Solving very large scattering problems using a parallel PWTD-enhanced surface integral equation solver

KAUST Repository

Liu, Yang

2013-07-01

The computational complexity and memory requirements of multilevel plane wave time domain (PWTD)-accelerated marching-on-in-time (MOT)-based surface integral equation (SIE) solvers scale as O(NtNs(log 2)Ns) and O(Ns 1.5); here N t and Ns denote numbers of temporal and spatial basis functions discretizing the current [Shanker et al., IEEE Trans. Antennas Propag., 51, 628-641, 2003]. In the past, serial versions of these solvers have been successfully applied to the analysis of scattering from perfect electrically conducting as well as homogeneous penetrable targets involving up to Ns ≈ 0.5 × 106 and Nt ≈ 10 3. To solve larger problems, parallel PWTD-enhanced MOT solvers are called for. Even though a simple parallelization strategy was demonstrated in the context of electromagnetic compatibility analysis [M. Lu et al., in Proc. IEEE Int. Symp. AP-S, 4, 4212-4215, 2004], by and large, progress in this area has been slow. The lack of progress can be attributed wholesale to difficulties associated with the construction of a scalable PWTD kernel. © 2013 IEEE.

How to detect integrability in cellular automata

International Nuclear Information System (INIS)

Joshi, N; Lafortune, S

2005-01-01

Ultra-discrete equations are generalized cellular automata in the sense that the dependent (and independent) variables take only integer values. We present a new method for identifying integrable ultra-discrete equations which is the equivalent of the singularity confinement property for difference equations and the Painleve property for differential equations. Using this criterion, we find integrable ultra-discrete equations which include the ultra-discrete Painleve equations. (letter to the editor)

Discrete variational Hamiltonian mechanics

International Nuclear Information System (INIS)

Lall, S; West, M

2006-01-01

The main contribution of this paper is to present a canonical choice of a Hamiltonian theory corresponding to the theory of discrete Lagrangian mechanics. We make use of Lagrange duality and follow a path parallel to that used for construction of the Pontryagin principle in optimal control theory. We use duality results regarding sensitivity and separability to show the relationship between generating functions and symplectic integrators. We also discuss connections to optimal control theory and numerical algorithms

Discrete Approaches to Quantum Gravity in Four Dimensions

Directory of Open Access Journals (Sweden)

Loll Renate

1998-01-01

Full Text Available The construction of a consistent theory of quantum gravity is a problem in theoretical physics that has so far defied all attempts at resolution. One ansatz to try to obtain a non-trivial quantum theory proceeds via a discretization of space-time and the Einstein action. I review here three major areas of research: gauge-theoretic approaches, both in a path-integral and a Hamiltonian formulation; quantum Regge calculus; and the method of dynamical triangulations, confining attention to work that is strictly four-dimensional, strictly discrete, and strictly quantum in nature.

A Numerical Study of Quantization-Based Integrators

Directory of Open Access Journals (Sweden)

Barros Fernando

2014-01-01

Full Text Available Adaptive step size solvers are nowadays considered fundamental to achieve efficient ODE integration. While, traditionally, ODE solvers have been designed based on discrete time machines, new approaches based on discrete event systems have been proposed. Quantization provides an efficient integration technique based on signal threshold crossing, leading to independent and modular solvers communicating through discrete events. These solvers can benefit from the large body of knowledge on discrete event simulation techniques, like parallelization, to obtain efficient numerical integration. In this paper we introduce new solvers based on quantization and adaptive sampling techniques. Preliminary numerical results comparing these solvers are presented.

Integrable Seven-Point Discrete Equations and Second-Order Evolution Chains

Science.gov (United States)

Adler, V. E.

2018-04-01

We consider differential-difference equations defining continuous symmetries for discrete equations on a triangular lattice. We show that a certain combination of continuous flows can be represented as a secondorder scalar evolution chain. We illustrate the general construction with a set of examples including an analogue of the elliptic Yamilov chain.

Optimizing integrated airport surface and terminal airspace operations under uncertainty

Science.gov (United States)

Bosson, Christabelle S.

In airports and surrounding terminal airspaces, the integration of surface, arrival and departure scheduling and routing have the potential to improve the operations efficiency. Moreover, because both the airport surface and the terminal airspace are often altered by random perturbations, the consideration of uncertainty in flight schedules is crucial to improve the design of robust flight schedules. Previous research mainly focused on independently solving arrival scheduling problems, departure scheduling problems and surface management scheduling problems and most of the developed models are deterministic. This dissertation presents an alternate method to model the integrated operations by using a machine job-shop scheduling formulation. A multistage stochastic programming approach is chosen to formulate the problem in the presence of uncertainty and candidate solutions are obtained by solving sample average approximation problems with finite sample size. The developed mixed-integer-linear-programming algorithm-based scheduler is capable of computing optimal aircraft schedules and routings that reflect the integration of air and ground operations. The assembled methodology is applied to a Los Angeles case study. To show the benefits of integrated operations over First-Come-First-Served, a preliminary proof-of-concept is conducted for a set of fourteen aircraft evolving under deterministic conditions in a model of the Los Angeles International Airport surface and surrounding terminal areas. Using historical data, a representative 30-minute traffic schedule and aircraft mix scenario is constructed. The results of the Los Angeles application show that the integration of air and ground operations and the use of a time-based separation strategy enable both significant surface and air time savings. The solution computed by the optimization provides a more efficient routing and scheduling than the First-Come-First-Served solution. Additionally, a data driven analysis is

Numerical computation of discrete differential scattering cross sections for Monte Carlo charged particle transport

International Nuclear Information System (INIS)

Walsh, Jonathan A.; Palmer, Todd S.; Urbatsch, Todd J.

2015-01-01

Highlights: • Generation of discrete differential scattering angle and energy loss cross sections. • Gauss–Radau quadrature utilizing numerically computed cross section moments. • Development of a charged particle transport capability in the Milagro IMC code. • Integration of cross section generation and charged particle transport capabilities. - Abstract: We investigate a method for numerically generating discrete scattering cross sections for use in charged particle transport simulations. We describe the cross section generation procedure and compare it to existing methods used to obtain discrete cross sections. The numerical approach presented here is generalized to allow greater flexibility in choosing a cross section model from which to derive discrete values. Cross section data computed with this method compare favorably with discrete data generated with an existing method. Additionally, a charged particle transport capability is demonstrated in the time-dependent Implicit Monte Carlo radiative transfer code, Milagro. We verify the implementation of charged particle transport in Milagro with analytic test problems and we compare calculated electron depth–dose profiles with another particle transport code that has a validated electron transport capability. Finally, we investigate the integration of the new discrete cross section generation method with the charged particle transport capability in Milagro.

Using Discrete Event Simulation to Model Integrated Commodities Consumption for a Launch Campaign of the Space Launch System

Science.gov (United States)

Leonard, Daniel; Parsons, Jeremy W.; Cates, Grant

2014-01-01

In May 2013, NASA's GSDO Program requested a study to develop a discrete event simulation (DES) model that analyzes the launch campaign process of the Space Launch System (SLS) from an integrated commodities perspective. The scope of the study includes launch countdown and scrub turnaround and focuses on four core launch commodities: hydrogen, oxygen, nitrogen, and helium. Previously, the commodities were only analyzed individually and deterministically for their launch support capability, but this study was the first to integrate them to examine the impact of their interactions on a launch campaign as well as the effects of process variability on commodity availability. The study produced a validated DES model with Rockwell Arena that showed that Kennedy Space Center's ground systems were capable of supporting a 48-hour scrub turnaround for the SLS. The model will be maintained and updated to provide commodity consumption analysis of future ground system and SLS configurations.

Adaptive Fuzzy Integral Sliding-Mode Regulator for Induction Motor Using Nonlinear Sliding Surface

OpenAIRE

Yong-Kun Lu

2015-01-01

An adaptive fuzzy integral sliding-mode controller using nonlinear sliding surface is designed for the speed regulator of a field-oriented induction motor drive in this paper. Combining the conventional integral sliding surface with fractional-order integral, a nonlinear sliding surface is proposed for the integral sliding-mode speed control, which can overcome the windup problem and the convergence speed problem. An adaptive fuzzy control term is utilized to approximate the uncertainty. The ...

An isogeometric boundary element method for electromagnetic scattering with compatible B-spline discretizations

Science.gov (United States)

Simpson, R. N.; Liu, Z.; Vázquez, R.; Evans, J. A.

2018-06-01

We outline the construction of compatible B-splines on 3D surfaces that satisfy the continuity requirements for electromagnetic scattering analysis with the boundary element method (method of moments). Our approach makes use of Non-Uniform Rational B-splines to represent model geometry and compatible B-splines to approximate the surface current, and adopts the isogeometric concept in which the basis for analysis is taken directly from CAD (geometry) data. The approach allows for high-order approximations and crucially provides a direct link with CAD data structures that allows for efficient design workflows. After outlining the construction of div- and curl-conforming B-splines defined over 3D surfaces we describe their use with the electric and magnetic field integral equations using a Galerkin formulation. We use Bézier extraction to accelerate the computation of NURBS and B-spline terms and employ H-matrices to provide accelerated computations and memory reduction for the dense matrices that result from the boundary integral discretization. The method is verified using the well known Mie scattering problem posed over a perfectly electrically conducting sphere and the classic NASA almond problem. Finally, we demonstrate the ability of the approach to handle models with complex geometry directly from CAD without mesh generation.

Long-time behaviour of discretizations of the simple pendulum equation

Energy Technology Data Exchange (ETDEWEB)

Cieslinski, Jan L [Uniwersytet w Bialymstoku, Wydzial Fizyki, ul. Lipowa 41, 15-424 Bialystok (Poland); Ratkiewicz, Boguslaw [Doctoral Studies, Wydzial Fizyki, Uniwersytet Adama Mickiewicza, Poznan (Poland)], E-mail: janek@alpha.uwb.edu.pl, E-mail: bograt@poczta.onet.pl

2009-03-13

We compare several discretizations of the simple pendulum equation in a series of numerical experiments. The stress is put on the long-time behaviour. The chosen numerical schemes are either symplectic maps or integrable (energy-preserving) maps, or both. Therefore, they preserve qualitative features of solutions (such as periodicity). We describe characteristic periodic time dependences of numerical estimates of the period and the amplitude, and explain them as systematic numerical by-effects produced by any method. Finally, we propose a new numerical scheme which is a modification of the discrete gradient method. This modified discrete gradient method preserves (almost exactly) the period of small oscillations for any time step.

Long-time behaviour of discretizations of the simple pendulum equation

International Nuclear Information System (INIS)

Cieslinski, Jan L; Ratkiewicz, Boguslaw

2009-01-01

We compare several discretizations of the simple pendulum equation in a series of numerical experiments. The stress is put on the long-time behaviour. The chosen numerical schemes are either symplectic maps or integrable (energy-preserving) maps, or both. Therefore, they preserve qualitative features of solutions (such as periodicity). We describe characteristic periodic time dependences of numerical estimates of the period and the amplitude, and explain them as systematic numerical by-effects produced by any method. Finally, we propose a new numerical scheme which is a modification of the discrete gradient method. This modified discrete gradient method preserves (almost exactly) the period of small oscillations for any time step

Mimetic discretization methods

CERN Document Server

Castillo, Jose E

2013-01-01

To help solve physical and engineering problems, mimetic or compatible algebraic discretization methods employ discrete constructs to mimic the continuous identities and theorems found in vector calculus. Mimetic Discretization Methods focuses on the recent mimetic discretization method co-developed by the first author. Based on the Castillo-Grone operators, this simple mimetic discretization method is invariably valid for spatial dimensions no greater than three. The book also presents a numerical method for obtaining corresponding discrete operators that mimic the continuum differential and

Self-Assembly of Discrete Metal Complexes in Aqueous Solution via Block Copolypeptide Amphiphiles

Directory of Open Access Journals (Sweden)

Timothy J. Deming

2013-01-01

Full Text Available The integration of discrete metal complexes has been attracting significant interest due to the potential of these materials for soft metal-metal interactions and supramolecular assembly. Additionally, block copolypeptide amphiphiles have been investigated concerning their capacity for self-assembly into structures such as nanoparticles, nanosheets and nanofibers. In this study, we combined these two concepts by investigating the self-assembly of discrete metal complexes in aqueous solution using block copolypeptides. Normally, discrete metal complexes such as [Au(CN2]−, when molecularly dispersed in water, cannot interact with one another. Our results demonstrated, however, that the addition of block copolypeptide amphiphiles such as K183L19 to [Au(CN2]− solutions induced one-dimensional integration of the discrete metal complex, resulting in photoluminescence originating from multinuclear complexes with metal-metal interactions. Transmission electron microscopy (TEM showed a fibrous nanostructure with lengths and widths of approximately 100 and 20 nm, respectively, which grew to form advanced nanoarchitectures, including those resembling the weave patterns of Waraji (traditional Japanese straw sandals. This concept of combining block copolypeptide amphiphiles with discrete coordination compounds allows the design of flexible and functional supramolecular coordination systems in water.

Integrable boundary conditions and modified Lax equations

International Nuclear Information System (INIS)

Avan, Jean; Doikou, Anastasia

2008-01-01

We consider integrable boundary conditions for both discrete and continuum classical integrable models. Local integrals of motion generated by the corresponding 'transfer' matrices give rise to time evolution equations for the initial Lax operator. We systematically identify the modified Lax pairs for both discrete and continuum boundary integrable models, depending on the classical r-matrix and the boundary matrix

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.

Integral-preserving integrators

International Nuclear Information System (INIS)

McLaren, D I; Quispel, G R W

2004-01-01

Ordinary differential equations having a first integral may be solved numerically using one of several methods, with the integral preserved to machine accuracy. One such method is the discrete gradient method. It is shown here that the order of the method can be bootstrapped repeatedly to higher orders of accuracy. The method is illustrated using the Henon-Heiles system. (letter to the editor)

Integrated system of production information processing for surface mines

Energy Technology Data Exchange (ETDEWEB)

Li, K.; Wang, S.; Zeng, Z.; Wei, J.; Ren, Z. [China University of Mining and Technology, Xuzhou (China). Dept of Mining Engineering

2000-09-01

Based on the concept of geological statistic, mathematical program, condition simulation, system engineering, and the features and duties of each main department in surface mine production, an integrated system for surface mine production information was studied systematically and developed by using the technology of data warehousing, CAD, object-oriented and system integration, which leads to the systematizing and automating of the information management, data processing, optimization computing and plotting. In this paper, its overall object, system design, structure and functions and some key techniques were described. 2 refs., 3 figs.

Digital Resonant Controller based on Modified Tustin Discretization Method

Directory of Open Access Journals (Sweden)

STOJIC, D.

2016-11-01

Full Text Available Resonant controllers are used in power converter voltage and current control due to their simplicity and accuracy. However, digital implementation of resonant controllers introduces problems related to zero and pole mapping from the continuous to the discrete time domain. Namely, some discretization methods introduce significant errors in the digital controller resonant frequency, resulting in the loss of the asymptotic AC reference tracking, especially at high resonant frequencies. The delay compensation typical for resonant controllers can also be compromised. Based on the existing analysis, it can be concluded that the Tustin discretization with frequency prewarping represents a preferable choice from the point of view of the resonant frequency accuracy. However, this discretization method has a shortcoming in applications that require real-time frequency adaptation, since complex trigonometric evaluation is required for each frequency change. In order to overcome this problem, in this paper the modified Tustin discretization method is proposed based on the Taylor series approximation of the frequency prewarping function. By comparing the novel discretization method with commonly used two-integrator-based proportional-resonant (PR digital controllers, it is shown that the resulting digital controller resonant frequency and time delay compensation errors are significantly reduced for the novel controller.

Surface-Enhanced Raman Spectroscopy Integrated Centrifugal Microfluidics Platform

DEFF Research Database (Denmark)

Durucan, Onur

This PhD thesis demonstrates (i) centrifugal microfluidics disc platform integrated with Au capped nanopillar (NP) substrates for surface-enhanced Raman spectroscopy (SERS) based sensing, and (ii) novel sample analysis concepts achieved by synergistical combination of sensing techniques and minia......This PhD thesis demonstrates (i) centrifugal microfluidics disc platform integrated with Au capped nanopillar (NP) substrates for surface-enhanced Raman spectroscopy (SERS) based sensing, and (ii) novel sample analysis concepts achieved by synergistical combination of sensing techniques...... dense array of NP structures. Furthermore, the wicking assisted nanofiltration procedure was accomplished in centrifugal microfluidics platform and as a result additional sample purification was achieved through the centrifugation process. In this way, the Au coated NP substrate was utilized...

Application of Terrestrial Laser Scanner with an Integrated Thermal Camera in Non-Destructive Evaluation of Concrete Surface of Hydrotechnical Objects

Directory of Open Access Journals (Sweden)

Kowalska Maria

2017-12-01

Full Text Available The authors present possible applications of thermal data as an additional source of information on an object’s behaviour during the technical assessment of the condition of a concrete surface. For the study one of the most recent propositions introduced by Zoller + Fröhlich company was used, which is an integration of a thermal camera with a terrestrial laser scanner. This solution enables an acquisition of geometric and spectral data on the surveyed object and also provides information on the surface’s temperature in the selected points. A section of the dam’s downstream concrete wall was selected as the subject of the study for which a number of scans were carried out and a number of thermal images were taken at different times of the day. The obtained thermal data was confronted with the acquired spectral information for the specified points. This made it possible to carry out broader analysis of the surface and an inspection of the revealed fissure. The thermal analysis of said fissure indicated that the temperature changes within it are slower, which may affect the way the concrete works and may require further elaboration by the appropriate experts. Through the integration of a thermal camera with a terrestrial laser scanner one can not only analyse changes of temperature in the discretely selected points but on the whole surface as well. Moreover, it is also possible to accurately determine the range and the area of the change affecting the surface. The authors note the limitations of the presented solution like, inter alia, the resolution of the thermal camera.

Surface Design Based on Discrete Conformal Transformations

Science.gov (United States)

Duque, Carlos; Santangelo, Christian; Vouga, Etienne

Conformal transformations are angle-preserving maps from one domain to another. Although angles are preserved, the lengths between arbitrary points are not generally conserved. As a consequence there is always a given amount of distortion associated to any conformal map. Different uses of such transformations can be found in various fields, but have been used by us to program non-uniformly swellable gel sheets to buckle into prescribed three dimensional shapes. In this work we apply circle packings as a kind of discrete conformal map in order to find conformal maps from the sphere to the plane that can be used as nearly uniform swelling patterns to program non-Euclidean sheets to buckle into spheres. We explore the possibility of tuning the area distortion to fit the experimental range of minimum and maximum swelling by modifying the boundary of the planar domain through the introduction of different cutting schemes.

Continuous versus discrete structures II -- Discrete Hamiltonian systems and Helmholtz conditions

OpenAIRE

Cresson, Jacky; Pierret, Frédéric

2015-01-01

We define discrete Hamiltonian systems in the framework of discrete embeddings. An explicit comparison with previous attempts is given. We then solve the discrete Helmholtz's inverse problem for the discrete calculus of variation in the Hamiltonian setting. Several applications are discussed.

A continuous-time/discrete-time mixed audio-band sigma delta ADC

International Nuclear Information System (INIS)

Liu Yan; Hua Siliang; Wang Donghui; Hou Chaohuan

2011-01-01

This paper introduces a mixed continuous-time/discrete-time, single-loop, fourth-order, 4-bit audio-band sigma delta ADC that combines the benefits of continuous-time and discrete-time circuits, while mitigating the challenges associated with continuous-time design. Measurement results show that the peak SNR of this ADC reaches 100 dB and the total power consumption is less than 30 mW. (semiconductor integrated circuits)

A multidimensionally consistent version of Hirota’s discrete KdV equation

International Nuclear Information System (INIS)

Atkinson, James

2012-01-01

A multidimensionally consistent generalization of Hirota’s discrete KdV equation is proposed, it is a quad equation defined by a polynomial that is quadratic in each variable. Soliton solutions and interpretation of the model as superposition principle are given. It is discussed how an important property of the defining polynomial, a factorization of discriminants, appears also in the few other known discrete integrable multi-quadratic models. (fast track communication)

Discrete Mathematics

DEFF Research Database (Denmark)

Sørensen, John Aasted

2011-01-01

; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics...... to new problems. Relations and functions: Define a product set; define and apply equivalence relations; construct and apply functions. Apply these concepts to new problems. Natural numbers and induction: Define the natural numbers; apply the principle of induction to verify a selection of properties...

Digital Discretion

DEFF Research Database (Denmark)

Busch, Peter Andre; Zinner Henriksen, Helle

2018-01-01

discretion is suggested to reduce this footprint by influencing or replacing their discretionary practices using ICT. What is less researched is whether digital discretion can cause changes in public policy outcomes, and under what conditions such changes can occur. Using the concept of public service values......This study reviews 44 peer-reviewed articles on digital discretion published in the period from 1998 to January 2017. Street-level bureaucrats have traditionally had a wide ability to exercise discretion stirring debate since they can add their personal footprint on public policies. Digital......, we suggest that digital discretion can strengthen ethical and democratic values but weaken professional and relational values. Furthermore, we conclude that contextual factors such as considerations made by policy makers on the macro-level and the degree of professionalization of street...

Integrable systems twistors, loop groups, and Riemann surfaces

CERN Document Server

Hitchin, NJ; Ward, RS

2013-01-01

This textbook is designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors. The book has its origins in a series of lecture courses given by the authors, all of whom are internationally known mathematicians and renowned expositors. It is written in an accessible and informal style, and fills a gap in the existing literature. The introduction by Nigel Hitchin addresses the meaning of integrability: how do werecognize an integrable system? His own contribution then develops connections with algebraic geometry, and inclu

Discrete symmetries in the MSSM

Energy Technology Data Exchange (ETDEWEB)

Schieren, Roland

2010-12-02

The use of discrete symmetries, especially abelian ones, in physics beyond the standard model of particle physics is discussed. A method is developed how a general, abelian, discrete symmetry can be obtained via spontaneous symmetry breaking. In addition, anomalies are treated in the path integral approach with special attention to anomaly cancellation via the Green-Schwarz mechanism. All this is applied to the minimal supersymmetric standard model. A unique Z{sup R}{sub 4} symmetry is discovered which solves the {mu}-problem as well as problems with proton decay and allows to embed the standard model gauge group into a simple group, i.e. the Z{sup R}{sub 4} is compatible with grand unification. Also the flavor problem in the context of minimal flavor violation is addressed. Finally, a string theory model is presented which exhibits the mentioned Z{sup R}{sub 4} symmetry and other desirable features. (orig.)

Discrete symmetries in the MSSM

International Nuclear Information System (INIS)

Schieren, Roland

2010-01-01

The use of discrete symmetries, especially abelian ones, in physics beyond the standard model of particle physics is discussed. A method is developed how a general, abelian, discrete symmetry can be obtained via spontaneous symmetry breaking. In addition, anomalies are treated in the path integral approach with special attention to anomaly cancellation via the Green-Schwarz mechanism. All this is applied to the minimal supersymmetric standard model. A unique Z R 4 symmetry is discovered which solves the μ-problem as well as problems with proton decay and allows to embed the standard model gauge group into a simple group, i.e. the Z R 4 is compatible with grand unification. Also the flavor problem in the context of minimal flavor violation is addressed. Finally, a string theory model is presented which exhibits the mentioned Z R 4 symmetry and other desirable features. (orig.)

Discrete mathematics using a computer

CERN Document Server

Hall, Cordelia

2000-01-01

Several areas of mathematics find application throughout computer science, and all students of computer science need a practical working understanding of them. These core subjects are centred on logic, sets, recursion, induction, relations and functions. The material is often called discrete mathematics, to distinguish it from the traditional topics of continuous mathematics such as integration and differential equations. The central theme of this book is the connection between computing and discrete mathematics. This connection is useful in both directions: • Mathematics is used in many branches of computer science, in applica­ tions including program specification, datastructures,design and analysis of algorithms, database systems, hardware design, reasoning about the correctness of implementations, and much more; • Computers can help to make the mathematics easier to learn and use, by making mathematical terms executable, making abstract concepts more concrete, and through the use of software tools su...

Effect of surface topography upon micro-impact dynamics

International Nuclear Information System (INIS)

Mohammadpour, M; Morris, N J; Leighton, M; Rahnejat, H

2016-01-01

Often the effect of interactions at nano-scale determines the tribological performance of load bearing contacts. This is particularly the case for lightly loaded conjunctions where a plethora of short range kinetic interactions occur. It is also true of larger load bearing conjunctions where boundary interactions become dominant. At the diminutive scale of fairly smooth surface topography the cumulative discrete interactions give rise to the dominance of boundary effects rather than the bulk micro-scale phenomena, based on continuum mechanics. The integration of the manifold localized discrete interactions into a continuum is the pre-requisite to the understanding of characteristic boundary effects, which transcend the physical length scales and affect the key observed system attributes. These are energy efficiency and vibration refinement. This paper strives to present such an approach. It is shown that boundary and near boundary interactions can be adequately described by surface topographical measures, as well the thermodynamic conditions. (paper)

SURF: a subroutine code to draw the axonometric projection of a surface generated by a scalar function over a discretized plane domain using finite element computations

International Nuclear Information System (INIS)

Giuliani, Giovanni; Giuliani, Silvano.

1980-01-01

The FORTRAN IV subroutine SURF has been designed to help visualising the results of Finite Element computations. It drawns the axonometric projection of a surface generated in 3-dimensional space by a scalar function over a discretized plane domain. The most important characteristic of the routine is to remove the hidden lines and in this way it enables a clear vision of the details of the generated surface

The discrete cones method for two-dimensional neutron transport calculations

International Nuclear Information System (INIS)

Watanabe, Y.; Maynard, C.W.

1986-01-01

A novel method, the discrete cones method (DC/sub N/), is proposed as an alternative to the discrete ordinates method (S/sub N/) for solutions of the two-dimensional neutron transport equation. The new method utilizes a new concept, discrete cones, which are made by partitioning a unit spherical surface that the direction vector of particles covers. In this method particles in a cone are simultaneously traced instead of those in discrete directions so that an anomaly of the S/sub N/ method, the ray effects, can be eliminated. The DC/sub N/ method has been formulated for X-Y geometry and a program has been creaed by modifying the standard S/sub N/ program TWOTRAN-II. Our sample calculations demonstrate a strong mitigation of the ray effects without a computing cost penalty

Uniform surface-to-line integral reduction of physical optics for curved surfaces by modified edge representation with higher-order correction

Science.gov (United States)

Lyu, Pengfei; Ando, Makoto

2017-09-01

The modified edge representation is one of the equivalent edge currents approximation methods for calculating the physical optics surface radiation integrals in diffraction analysis. The Stokes' theorem is used in the derivation of the modified edge representation from the physical optics for the planar scatterer case, which implies that the surface integral is rigorously reduced into the line integral of the modified edge representation equivalent edge currents, defined in terms of the local shape of the edge. On the contrary, for curved surfaces, the results of radiation integrals depend upon the global shape of the scatterer. The physical optics surface integral consists of two components, from the inner stationary phase point and the edge. The modified edge representation is defined independently from the orientation of the actual edge, and therefore, it could be available not only at the edge but also at the arbitrary points on the scatterer except the stationary phase point where the modified edge representation equivalent edge currents becomes infinite. If stationary phase point exists inside the illuminated region, the physical optics surface integration is reduced into two kinds of the modified edge representation line integrations, along the edge and infinitesimally small integration around the inner stationary phase point, the former and the latter give the diffraction and reflection components, respectively. The accuracy of the latter has been discussed for the curved surfaces and published. This paper focuses on the errors of the former and discusses its correction. It has been numerically observed that the modified edge representation works well for the physical optics diffraction in flat and concave surfaces; errors appear especially for the observer near the reflection shadow boundary if the frequency is low for the convex scatterer. This paper gives the explicit expression of the higher-order correction for the modified edge representation.

An extended discrete gradient formula for oscillatory Hamiltonian systems

International Nuclear Information System (INIS)

Liu Kai; Shi Wei; Wu Xinyuan

2013-01-01

In this paper, incorporating the idea of the discrete gradient method into the extended Runge–Kutta–Nyström integrator, we derive and analyze an extended discrete gradient formula for the oscillatory Hamiltonian system with the Hamiltonian H(p,q)= 1/2 p T p+ 1/2 q T Mq+U(q), where q:R→R d represents generalized positions, p:R→R d represents generalized momenta and M is an element of R dxd is a symmetric and positive semi-definite matrix. The solution of this system is a nonlinear oscillator. Basically, many nonlinear oscillatory mechanical systems with a partitioned Hamiltonian function lend themselves to this approach. The extended discrete gradient formula presented in this paper exactly preserves the energy H(p, q). We derive some properties of the new formula. The convergence is analyzed for the implicit schemes based on the discrete gradient formula, and it turns out that the convergence of the implicit schemes based on the extended discrete gradient formula is independent of ‖M‖, which is a significant property for the oscillatory Hamiltonian system. Thus, it transpires that a larger step size can be chosen for the new energy-preserving schemes than that for the traditional discrete gradient methods when applied to the oscillatory Hamiltonian system. Illustrative examples show the competence and efficiency of the new schemes in comparison with the traditional discrete gradient methods in the scientific literature. (paper)

Galerkin v. discrete-optimal projection in nonlinear model reduction

Energy Technology Data Exchange (ETDEWEB)

Carlberg, Kevin Thomas [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Barone, Matthew Franklin [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Antil, Harbir [George Mason Univ., Fairfax, VA (United States)

2015-04-01

Discrete-optimal model-reduction techniques such as the Gauss{Newton with Approximated Tensors (GNAT) method have shown promise, as they have generated stable, accurate solutions for large-scale turbulent, compressible ow problems where standard Galerkin techniques have failed. However, there has been limited comparative analysis of the two approaches. This is due in part to difficulties arising from the fact that Galerkin techniques perform projection at the time-continuous level, while discrete-optimal techniques do so at the time-discrete level. This work provides a detailed theoretical and experimental comparison of the two techniques for two common classes of time integrators: linear multistep schemes and Runge{Kutta schemes. We present a number of new ndings, including conditions under which the discrete-optimal ROM has a time-continuous representation, conditions under which the two techniques are equivalent, and time-discrete error bounds for the two approaches. Perhaps most surprisingly, we demonstrate both theoretically and experimentally that decreasing the time step does not necessarily decrease the error for the discrete-optimal ROM; instead, the time step should be `matched' to the spectral content of the reduced basis. In numerical experiments carried out on a turbulent compressible- ow problem with over one million unknowns, we show that increasing the time step to an intermediate value decreases both the error and the simulation time of the discrete-optimal reduced-order model by an order of magnitude.

Surfaces immersed in Lie algebras associated with elliptic integrals

International Nuclear Information System (INIS)

Grundland, A M; Post, S

2012-01-01

The objective of this work is to adapt the Fokas–Gel’fand immersion formula to ordinary differential equations written in the Lax representation. The formalism of generalized vector fields and their prolongation structure is employed to establish necessary and sufficient conditions for the existence and integration of immersion functions for surfaces in Lie algebras. As an example, a class of second-order, integrable, ordinary differential equations is considered and the most general solutions for the wavefunctions of the linear spectral problem are found. Several explicit examples of surfaces associated with Jacobian and P-Weierstrass elliptic functions are presented. (paper)

Mechanical model for steel frames with discretely connected precast concrete infill panels with window openings

NARCIS (Netherlands)

Teeuwen, P.A.; Kleinman, C.S.; Snijder, H.H.

2012-01-01

This paper presents a mechanical model for a structure comprising of steel frames with discretely connected precast concrete infill panels having window openings, termed semi-integral infilled frames. The discrete panel-to-frame connections are realized by structural bolts acting under compression.

Discrete tuning concept for fiber-integrated lasers based on tailored FBG arrays and a theta cavity layout.

Science.gov (United States)

Tiess, Tobias; Becker, Martin; Rothhardt, Manfred; Bartelt, Hartmut; Jäger, Matthias

2017-03-15

We demonstrate a novel tuning concept for pulsed fiber-integrated lasers with a fiber Bragg grating (FBG) array as a discrete and tailored spectral filter, as well as a modified laser design. Based on a theta cavity layout, the structural delay lines originating from the FBG array are balanced, enabling a constant repetition rate and stable pulse properties over the full tuning range. The emission wavelength is electrically tuned with respect to the filter properties based on an adapted temporal gating scheme using an acousto-optic modulator. This concept has been investigated with an Yb-doped fiber laser, demonstrating excellent emission properties with high signal contrast (>35  dB) and narrow linewidth (<150  pm) over a tuning range of 25 nm.

Discretization model for nonlinear dynamic analysis of three dimensional structures

International Nuclear Information System (INIS)

Hayashi, Y.

1982-12-01

A discretization model for nonlinear dynamic analysis of three dimensional structures is presented. The discretization is achieved through a three dimensional spring-mass system and the dynamic response obtained by direct integration of the equations of motion using central diferences. First the viability of the model is verified through the analysis of homogeneous linear structures and then its performance in the analysis of structures subjected to impulsive or impact loads, taking into account both geometrical and physical nonlinearities is evaluated. (Author) [pt

Near-Surface Engineered Environmental Barrier Integrity

International Nuclear Information System (INIS)

Piet, S.J.; Breckenridge, R.P.

2002-01-01

The INEEL Environmental Systems Research and Analysis (ESRA) program has launched a new R and D project on Near-Surface Engineered Environmental Barrier Integrity to increase knowledge and capabilities for using engineering and ecological components to improve the integrity of near-surface barriers used to confine contaminants from the public and the environment. The knowledge gained and the capabilities built will help verify the adequacy of past remedial decisions and enable improved solutions for future cleanup decisions. The research is planned to (a) improve the knowledge of degradation mechanisms (weathering, biological, geological, chemical, radiological, and catastrophic) in times shorter than service life, (b) improve modeling of barrier degradation dynamics, (c) develop sensor systems to identify degradation prior to failure, and (d) provide a better basis for developing and testing of new barrier systems to increase reliability and reduce the risk of failure. Our project combine s selected exploratory studies (benchtop and field scale), coupled effects accelerated aging testing and the meso-scale, testing of new monitoring concepts, and modeling of dynamic systems. The performance of evapo-transpiration, capillary, and grout-based barriers will be examined

Applications of the discrete element method in mechanical engineering

International Nuclear Information System (INIS)

Fleissner, Florian; Gaugele, Timo; Eberhard, Peter

2007-01-01

Compared to other fields of engineering, in mechanical engineering, the Discrete Element Method (DEM) is not yet a well known method. Nevertheless, there is a variety of simulation problems where the method has obvious advantages due to its meshless nature. For problems where several free bodies can collide and break after having been largely deformed, the DEM is the method of choice. Neighborhood search and collision detection between bodies as well as the separation of large solids into smaller particles are naturally incorporated in the method. The main DEM algorithm consists of a relatively simple loop that basically contains the three substeps contact detection, force computation and integration. However, there exists a large variety of different algorithms to choose the substeps to compose the optimal method for a given problem. In this contribution, we describe the dynamics of particle systems together with appropriate numerical integration schemes and give an overview over different types of particle interactions that can be composed to adapt the method to fit to a given simulation problem. Surface triangulations are used to model complicated, non-convex bodies in contact with particle systems. The capabilities of the method are finally demonstrated by means of application examples

A discrete variational identity on semi-direct sums of Lie algebras

Energy Technology Data Exchange (ETDEWEB)

M, Wenxiu [Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700 (United States)

2007-12-14

The discrete variational identity under general bilinear forms on semi-direct sums of Lie algebras is established. The constant {gamma} involved in the variational identity is determined through the corresponding solution to the stationary discrete zero-curvature equation. An application of the resulting variational identity to a class of semi-direct sums of Lie algebras in the Volterra lattice case furnishes Hamiltonian structures for the associated integrable couplings of the Volterra lattice hierarchy.

A discrete variational identity on semi-direct sums of Lie algebras

International Nuclear Information System (INIS)

M, Wenxiu

2007-01-01

The discrete variational identity under general bilinear forms on semi-direct sums of Lie algebras is established. The constant γ involved in the variational identity is determined through the corresponding solution to the stationary discrete zero-curvature equation. An application of the resulting variational identity to a class of semi-direct sums of Lie algebras in the Volterra lattice case furnishes Hamiltonian structures for the associated integrable couplings of the Volterra lattice hierarchy

Path integration in conical space

International Nuclear Information System (INIS)

Inomata, Akira; Junker, Georg

2012-01-01

Quantum mechanics in conical space is studied by the path integral method. It is shown that the curvature effect gives rise to an effective potential in the radial path integral. It is further shown that the radial path integral in conical space can be reduced to a form identical with that in flat space when the discrete angular momentum of each partial wave is replaced by a specific non-integral angular momentum. The effective potential is found proportional to the squared mean curvature of the conical surface embedded in Euclidean space. The path integral calculation is compatible with the Schrödinger equation modified with the Gaussian and the mean curvature. -- Highlights: ► We study quantum mechanics on a cone by the path integral approach. ► The path integral depends only on the metric and the curvature effect is built in. ► The approach is consistent with the Schrödinger equation modified by an effective potential. ► The effective potential is found to be of the “Jensen–Koppe” and “da Costa” type.

Ion association at discretely-charged dielectric interfaces: Giant charge inversion [Dielectric response controlled ion association at physically heterogeneous surfaces: Giant charge reversal

Energy Technology Data Exchange (ETDEWEB)

Wang, Zhi -Yong [Chongqing Univ. of Technology, Chongqing (China); Univ. of California, Riverside, CA (United States); Wu, Jianzhong [Univ. of California, Riverside, CA (United States)

2017-07-11

Giant charge reversal has been identified for the first time by Monte Carlo simulation for a discretely charged surface in contact with a trivalent electrolyte solution. It takes place regardless of the surface charge density under study and the monovalent salt. In stark contrast to earlier predictions based on the 2-dimensional Wigner crystal model to describe strong correlation of counterions at the macroion surface, we find that giant charge reversal reflects an intricate interplay of ionic volume effects, electrostatic correlations, surface charge heterogeneity, and the dielectric response of the confined fluids. While the novel phenomenon is yet to be confirmed with experiment, the simulation results appear in excellent agreement with a wide range of existing observations in the subregime of charge inversion. Lastly, our findings may have far-reaching implications to understanding complex electrochemical phenomena entailing ionic fluids under dielectric confinements.

Effective use of surface-water management to control saltwater intrusion

Science.gov (United States)

Hughes, J. D.; White, J.

2012-12-01

The Biscayne aquifer in southeast Florida is susceptible to saltwater intrusion and inundation from rising sea-level as a result of high groundwater withdrawal rates and low topographic relief. Groundwater levels in the Biscayne aquifer are managed by an extensive canal system that is designed to control flooding, supply recharge to municipal well fields, and control saltwater intrusion. We present results from an integrated surface-water/groundwater model of a portion of the Biscayne aquifer to evaluate the ability of the existing managed surface-water control network to control saltwater intrusion. Surface-water stage and flow are simulated using a hydrodynamic model that solves the diffusive-wave approximation of the depth-integrated shallow surface-water equations. Variable-density groundwater flow and fluid density are solved using the Oberbeck--Boussinesq approximation of the three-dimensional variable-density groundwater flow equation and a sharp interface approximation, respectively. The surface-water and variable-density groundwater domains are implicitly coupled during each Picard iteration. The Biscayne aquifer is discretized into a multi-layer model having a 500-m square horizontal grid spacing. All primary and secondary surface-water features in the active model domain are discretized into segments using the 500-m square horizontal grid. A 15-year period of time is simulated and the model includes 66 operable surface-water control structures, 127 municipal production wells, and spatially-distributed daily internal and external hydrologic stresses. Numerical results indicate that the existing surface-water system can be effectively used in many locations to control saltwater intrusion in the Biscayne aquifer resulting from increases in groundwater withdrawals or sea-level rise expected to occur over the next 25 years. In other locations, numerical results indicate surface-water control structures and/or operations may need to be modified to control

Laser microtexturing of implant surfaces for enhanced tissue integration

Energy Technology Data Exchange (ETDEWEB)

Ricci, J.L. [Univ. of Medicine and Dentistry of New Jersey, Newark, NJ (United States). Dept. of Orthodontics; Alexander, H. [Orthogen Corp., Springfield, NJ (United States)

2001-07-01

The success or failure of bone and soft tissue-fixed medical devices, such as dental and orthopaedic implants, depends on a complex combination of biological and mechanical factors. These factors are intimately associated with the interface between the implant surface and the surrounding tissue, and are largely determined by the composition, surface chemistry, and surface microgeometry of the implant. The relative contributions of these factors are difficult to assess. This study addresses the contribution of surface microtexture, on a controlled level, to tissue integration. (orig.)

Non-integrability of geodesic flow on certain algebraic surfaces

International Nuclear Information System (INIS)

Waters, T.J.

2012-01-01

This Letter addresses an open problem recently posed by V. Kozlov: a rigorous proof of the non-integrability of the geodesic flow on the cubic surface xyz=1. We prove this is the case using the Morales–Ramis theorem and Kovacic algorithm. We also consider some consequences and extensions of this result. -- Highlights: ► The behaviour of geodesics on surfaces defined by algebraic expressions is studied. ► The non-integrability of the geodesic equations is rigorously proved using differential Galois theory. ► Morales–Ramis theory and Kovacic's algorithm is used and the normal variational equation is of Fuchsian type. ► Some extensions and limitations are discussed.

Discrete dynamic modeling of cellular signaling networks.

Science.gov (United States)

Albert, Réka; Wang, Rui-Sheng

2009-01-01

Understanding signal transduction in cellular systems is a central issue in systems biology. Numerous experiments from different laboratories generate an abundance of individual components and causal interactions mediating environmental and developmental signals. However, for many signal transduction systems there is insufficient information on the overall structure and the molecular mechanisms involved in the signaling network. Moreover, lack of kinetic and temporal information makes it difficult to construct quantitative models of signal transduction pathways. Discrete dynamic modeling, combined with network analysis, provides an effective way to integrate fragmentary knowledge of regulatory interactions into a predictive mathematical model which is able to describe the time evolution of the system without the requirement for kinetic parameters. This chapter introduces the fundamental concepts of discrete dynamic modeling, particularly focusing on Boolean dynamic models. We describe this method step-by-step in the context of cellular signaling networks. Several variants of Boolean dynamic models including threshold Boolean networks and piecewise linear systems are also covered, followed by two examples of successful application of discrete dynamic modeling in cell biology.

Surface characteristics of bioactive Ti fabricated by chemical treatment for cartilaginous-integration.

Science.gov (United States)

Miyajima, Hiroyuki; Ozer, Fusun; Imazato, Satoshi; Mante, Francis K

2017-09-01

Artificial hip joints are generally expected to fail due to wear after approximately 15years and then have to be replaced by revision surgery. If articular cartilage can be integrated onto the articular surfaces of artificial joints in the same way as osseo-integration of titanium dental implants, the wear of joint implants may be reduced or prevented. However, very few studies have focused on the relationship between Ti surface and cartilage. To explore the possibility of cartilaginous-integration, we fabricated chemically treated Ti surfaces with H 2 O 2 /HCl, collagen type II and SBF, respectively. Then, we evaluated surface characteristics of the prepared Ti samples and assessed the cartilage formation by culturing chondrocytes on the Ti samples. When oxidized Ti was immersed in SBF for 7days, apatite was formed on the Ti surface. The surface characteristics of Ti indicated that the wettability was increased by all chemical treatments compared to untreated Ti, and that H 2 O 2 /HCl treated surface had significantly higher roughness compared to the other three groups. Chondrocytes produced significantly more cartilage matrix on all chemically treated Ti surfaces compared to untreated Ti. Thus, to realize cartilaginous-integration and to prevent wear of the implants in joints, application of bioactive Ti formed by chemical treatment would be a promising and effective strategy to improve durability of joint replacement. Copyright © 2017 Elsevier B.V. All rights reserved.

Explanation of the surface peak in charge integrated LEIS spectra

CERN Document Server

Draxler, M; Taglauer, E; Schmid, K; Gruber, R; Ermolov, S N; Bauer, P

2003-01-01

Low energy ion scattering is very surface sensitive if scattered ions are analyzed. By time-of-flight (TOF) techniques, also neutral and charge integrated spectra (ions plus neutrals) can be obtained, which yield information about deeper layers. In the literature, the observation of a more or less pronounced surface peak was reported for charge integrated spectra, the intensity of the surface peak being higher at low energies and for heavy projectiles. Aiming at a more profound physical understanding of this surface peak, we performed TOF-experiments and computer simulations for He projectiles and a copper target. Experiments were done in the range 1-9 keV for a scattering angle of 129 deg. . The simulation was performed using the MARLOWE code for the given experimental parameters and a polycrystalline target. At low energies, a pronounced surface peak was observed, which fades away at higher energies. This peak is quantitatively reproduced by the simulation, and corresponds to scattering from approx 2 atomic...

Fractured reservoir discrete feature network technologies. Final report, March 7, 1996 to September 30, 1998

Energy Technology Data Exchange (ETDEWEB)

Dershowitz, William S.; Einstein, Herbert H.; LaPoint, Paul R.; Eiben, Thorsten; Wadleigh, Eugene; Ivanova, Violeta

1998-12-01

This report summarizes research conducted for the Fractured Reservoir Discrete Feature Network Technologies Project. The five areas studied are development of hierarchical fracture models; fractured reservoir compartmentalization, block size, and tributary volume analysis; development and demonstration of fractured reservoir discrete feature data analysis tools; development of tools for data integration and reservoir simulation through application of discrete feature network technologies for tertiary oil production; quantitative evaluation of the economic value of this analysis approach.

Discrete variational methods and their application to electronic structures

International Nuclear Information System (INIS)

Ellis, D.E.

1987-01-01

Some general concepts concerning Discrete Variational methods are developed and applied to problems of determination of eletronic spectra, charge densities and bonding of free molecules, surface-chemisorbed species and bulk solids. (M.W.O.) [pt

Development of a discrete gas-kinetic scheme for simulation of two-dimensional viscous incompressible and compressible flows.

Science.gov (United States)

Yang, L M; Shu, C; Wang, Y

2016-03-01

In this work, a discrete gas-kinetic scheme (DGKS) is presented for simulation of two-dimensional viscous incompressible and compressible flows. This scheme is developed from the circular function-based GKS, which was recently proposed by Shu and his co-workers [L. M. Yang, C. Shu, and J. Wu, J. Comput. Phys. 274, 611 (2014)]. For the circular function-based GKS, the integrals for conservation forms of moments in the infinity domain for the Maxwellian function-based GKS are simplified to those integrals along the circle. As a result, the explicit formulations of conservative variables and fluxes are derived. However, these explicit formulations of circular function-based GKS for viscous flows are still complicated, which may not be easy for the application by new users. By using certain discrete points to represent the circle in the phase velocity space, the complicated formulations can be replaced by a simple solution process. The basic requirement is that the conservation forms of moments for the circular function-based GKS can be accurately satisfied by weighted summation of distribution functions at discrete points. In this work, it is shown that integral quadrature by four discrete points on the circle, which forms the D2Q4 discrete velocity model, can exactly match the integrals. Numerical results showed that the present scheme can provide accurate numerical results for incompressible and compressible viscous flows with roughly the same computational cost as that needed by the Roe scheme.

Second-degree discrete Painleve equations conceal first-degree ones

International Nuclear Information System (INIS)

Ramani, A; Grammaticos, B; Joshi, N

2010-01-01

We examine various second-degree difference equations which have been proposed over the years and according to their authors' claims should be integrable. This study is motivated by the fact that we consider that second-degree discrete systems cannot be integrable due to the proliferation of the images (and pre-images) of the initial point. We show that in the present cases no contradiction exists. In all cases examined, we show that there exists an underlying integrable first-degree mapping which allows us to obtain an appropriate solution of the second-degree one.

Entropy-stable summation-by-parts discretization of the Euler equations on general curved elements

Science.gov (United States)

Crean, Jared; Hicken, Jason E.; Del Rey Fernández, David C.; Zingg, David W.; Carpenter, Mark H.

2018-03-01

We present and analyze an entropy-stable semi-discretization of the Euler equations based on high-order summation-by-parts (SBP) operators. In particular, we consider general multidimensional SBP elements, building on and generalizing previous work with tensor-product discretizations. In the absence of dissipation, we prove that the semi-discrete scheme conserves entropy; significantly, this proof of nonlinear L2 stability does not rely on integral exactness. Furthermore, interior penalties can be incorporated into the discretization to ensure that the total (mathematical) entropy decreases monotonically, producing an entropy-stable scheme. SBP discretizations with curved elements remain accurate, conservative, and entropy stable provided the mapping Jacobian satisfies the discrete metric invariants; polynomial mappings at most one degree higher than the SBP operators automatically satisfy the metric invariants in two dimensions. In three-dimensions, we describe an elementwise optimization that leads to suitable Jacobians in the case of polynomial mappings. The properties of the semi-discrete scheme are verified and investigated using numerical experiments.

The invisible hand illusion: multisensory integration leads to the embodiment of a discrete volume of empty space.

Science.gov (United States)

Guterstam, Arvid; Gentile, Giovanni; Ehrsson, H Henrik

2013-07-01

The dynamic integration of signals from different sensory modalities plays a key role in bodily self-perception. When visual information is used in the multisensory process of localizing and identifying one's own limbs, the sight of a body part often plays a dominant role. For example, it has repeatedly been shown that a viewed object must resemble a humanoid body part to permit illusory self-attribution of that object. Here, we report a perceptual illusion that challenges these assumptions by demonstrating that healthy (nonamputated) individuals can refer somatic sensations to a discrete volume of empty space and experience having an invisible hand. In 10 behavioral and one fMRI experiment, we characterized the perceptual rules and multisensory brain mechanisms that produced this "invisible hand illusion." Our behavioral results showed that the illusion depends on visuotactile-proprioceptive integration that obeys key spatial and temporal multisensory rules confined to near-personal space. The fMRI results associate the illusion experience with increased activity in regions related to the integration of multisensory body-related signals, most notably the bilateral ventral premotor, intraparietal, and cerebellar cortices. We further showed that a stronger feeling of having an invisible hand is associated with a higher degree of effective connectivity between the intraparietal and ventral premotor cortices. These findings demonstrate that the integration of temporally and spatially congruent multisensory signals in a premotor-intraparietal circuit is sufficient to redefine the spatial boundaries of the bodily self, even when visual information directly contradicts the presence of a physical limb at the location of the perceived illusory hand.

Asymptotic analysis of discrete schemes for non-equilibrium radiation diffusion

International Nuclear Information System (INIS)

Cui, Xia; Yuan, Guang-wei; Shen, Zhi-jun

2016-01-01

Motivated by providing well-behaved fully discrete schemes in practice, this paper extends the asymptotic analysis on time integration methods for non-equilibrium radiation diffusion in [2] to space discretizations. Therein studies were carried out on a two-temperature model with Larsen's flux-limited diffusion operator, both the implicitly balanced (IB) and linearly implicit (LI) methods were shown asymptotic-preserving. In this paper, we focus on asymptotic analysis for space discrete schemes in dimensions one and two. First, in construction of the schemes, in contrast to traditional first-order approximations, asymmetric second-order accurate spatial approximations are devised for flux-limiters on boundary, and discrete schemes with second-order accuracy on global spatial domain are acquired consequently. Then by employing formal asymptotic analysis, the first-order asymptotic-preserving property for these schemes and furthermore for the fully discrete schemes is shown. Finally, with the help of manufactured solutions, numerical tests are performed, which demonstrate quantitatively the fully discrete schemes with IB time evolution indeed have the accuracy and asymptotic convergence as theory predicts, hence are well qualified for both non-equilibrium and equilibrium radiation diffusion. - Highlights: • Provide AP fully discrete schemes for non-equilibrium radiation diffusion. • Propose second order accurate schemes by asymmetric approach for boundary flux-limiter. • Show first order AP property of spatially and fully discrete schemes with IB evolution. • Devise subtle artificial solutions; verify accuracy and AP property quantitatively. • Ideas can be generalized to 3-dimensional problems and higher order implicit schemes.

Linear diffusion-wave channel routing using a discrete Hayami convolution method

Science.gov (United States)

Li Wang; Joan Q. Wu; William J. Elliot; Fritz R. Feidler; Sergey. Lapin

2014-01-01

The convolution of an input with a response function has been widely used in hydrology as a means to solve various problems analytically. Due to the high computation demand in solving the functions using numerical integration, it is often advantageous to use the discrete convolution instead of the integration of the continuous functions. This approach greatly reduces...

Stationary solutions and self-trapping in discrete quadratic nonlinear systems

DEFF Research Database (Denmark)

Bang, Ole; Christiansen, Peter Leth; Clausen, Carl A. Balslev

1998-01-01

We consider the simplest equations describing coupled quadratic nonlinear (chi((2))) systems, which each consists of a fundamental mode resonantly interacting with its second harmonic. Such discrete equations apply, e.g., to optics, where they can describe arrays of chi((2)) waveguides...... the nonintegrable dimer reduce to the discrete nonlinear Schrodinger (DNLS) equation with two degrees of freedom, which is integrable. We show how the stationary solutions to the two systems correspond to each other and how the self-trapped DNLS solutions gradually develop chaotic dynamics in the chi((2)) system...

Dissolved inorganic carbon, pH, oxygen, and other variables collected from surface discrete and surface underway observations using flow-through pump from NOAA Ship Gordon Gunter off the U.S. East Coast during the East Coast Ocean Acidification (ECOA) Cruise from 2015-06-19 to 2015-07-24 (NCEI Accession 0157485)

Data.gov (United States)

National Oceanic and Atmospheric Administration, Department of Commerce — This archival package contains dissolved inorganic carbon, pH, oxygen, and other variables collected from surface discrete and surface underway observations during...

Surface-complexation models for sorption onto heterogeneous surfaces

International Nuclear Information System (INIS)

Harvey, K.B.

1997-10-01

This report provides a description of the discrete-logK spectrum model, together with a description of its derivation, and of its place in the larger context of surface-complexation modelling. The tools necessary to apply the discrete-logK spectrum model are discussed, and background information appropriate to this discussion is supplied as appendices. (author)

Local bounds preserving stabilization for continuous Galerkin discretization of hyperbolic systems

Science.gov (United States)

Mabuza, Sibusiso; Shadid, John N.; Kuzmin, Dmitri

2018-05-01

The objective of this paper is to present a local bounds preserving stabilized finite element scheme for hyperbolic systems on unstructured meshes based on continuous Galerkin (CG) discretization in space. A CG semi-discrete scheme with low order artificial dissipation that satisfies the local extremum diminishing (LED) condition for systems is used to discretize a system of conservation equations in space. The low order artificial diffusion is based on approximate Riemann solvers for hyperbolic conservation laws. In this case we consider both Rusanov and Roe artificial diffusion operators. In the Rusanov case, two designs are considered, a nodal based diffusion operator and a local projection stabilization operator. The result is a discretization that is LED and has first order convergence behavior. To achieve high resolution, limited antidiffusion is added back to the semi-discrete form where the limiter is constructed from a linearity preserving local projection stabilization operator. The procedure follows the algebraic flux correction procedure usually used in flux corrected transport algorithms. To further deal with phase errors (or terracing) common in FCT type methods, high order background dissipation is added to the antidiffusive correction. The resulting stabilized semi-discrete scheme can be discretized in time using a wide variety of time integrators. Numerical examples involving nonlinear scalar Burgers equation, and several shock hydrodynamics simulations for the Euler system are considered to demonstrate the performance of the method. For time discretization, Crank-Nicolson scheme and backward Euler scheme are utilized.

Finite Volumes Discretization of Topology Optimization Problems

DEFF Research Database (Denmark)

Evgrafov, Anton; Gregersen, Misha Marie; Sørensen, Mads Peter

, FVMs represent a standard method of discretization within engineering communities dealing with computational uid dy- namics, transport, and convection-reaction problems. Among various avours of FVMs, cell based approaches, where all variables are associated only with cell centers, are particularly...... computations is done using nite element methods (FEMs). Despite some limited recent eorts [1, 2], we have only started to develop our understanding of the interplay between the control in the coecients and FVMs. Recent advances in discrete functional analysis allow us to analyze convergence of FVM...... of the induced parametrization of the design space that allows optimization algorithms to eciently explore it, and the ease of integration with existing computational codes in a variety of application areas, the simplicity and eciency of sensitivity analyses|all stemming from the use of the same grid throughout...

Discretely tunable micromachined injection-locked lasers

International Nuclear Information System (INIS)

Cai, H; Yu, M B; Lo, G Q; Kwong, D L; Zhang, X M; Liu, A Q; Liu, B

2010-01-01

This paper reports a micromachined injection-locked laser (ILL) to provide tunable discrete wavelengths. It utilizes a non-continuously tunable laser as the master to lock a Fabry–Pérot semiconductor laser chip. Both lasers are integrated into a deep-etched silicon chip with dimensions of 3 mm × 3 mm × 0.8 mm. Based on the experimental results, significant improvements in the optical power and spectral purity have been achieved in the fully locked state, and optical hysteresis and bistability have also been observed in response to the changes of the output wavelength and optical power of the master laser. As a whole system, the micromachined ILL is able to provide single mode, discrete wavelength tuning, high power and direct modulation with small size and single-chip solution, making it promising for advanced optical communications such as wavelength division multiplexing optical access networks.

DISCRETE MATHEMATICS/NUMBER THEORY

OpenAIRE

Mrs. Manju Devi*

2017-01-01

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics such as integers, graphs, and statements do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus and analysis. Discrete objects can often be enumerated by ...

On the initial condition problem of the time domain PMCHWT surface integral equation

KAUST Repository

Uysal, Ismail Enes

2017-05-13

Non-physical, linearly increasing and constant current components are induced in marching on-in-time solution of time domain surface integral equations when initial conditions on time derivatives of (unknown) equivalent currents are not enforced properly. This problem can be remedied by solving the time integral of the surface integral for auxiliary currents that are defined to be the time derivatives of the equivalent currents. Then the equivalent currents are obtained by numerically differentiating the auxiliary ones. In this work, this approach is applied to the marching on-in-time solution of the time domain Poggio-Miller-Chan-Harrington-Wu-Tsai surface integral equation enforced on dispersive/plasmonic scatterers. Accuracy of the proposed method is demonstrated by a numerical example.

Surfaces and slabs of fractional topological insulator heterostructures

Science.gov (United States)

Sahoo, Sharmistha; Sirota, Alexander; Cho, Gil Young; Teo, Jeffrey C. Y.

2017-10-01

Fractional topological insulators (FTIs) are electronic topological phases in (3 +1 ) dimensions enriched by time reversal (TR) and charge U (1 ) conservation symmetries. We focus on the simplest series of fermionic FTIs, whose bulk quasiparticles consist of deconfined partons that carry fractional electric charges in integral units of e*=e /(2 n +1 ) and couple to a discrete Z2 n +1 gauge theory. We propose massive symmetry preserving or breaking FTI surface states. Combining the long-ranged entangled bulk with these topological surface states, we deduce the novel topological order of quasi-(2 +1 ) -dimensional FTI slabs as well as their corresponding edge conformal field theories.

The discrete adjoint method for parameter identification in multibody system dynamics.

Science.gov (United States)

Lauß, Thomas; Oberpeilsteiner, Stefan; Steiner, Wolfgang; Nachbagauer, Karin

2018-01-01

The adjoint method is an elegant approach for the computation of the gradient of a cost function to identify a set of parameters. An additional set of differential equations has to be solved to compute the adjoint variables, which are further used for the gradient computation. However, the accuracy of the numerical solution of the adjoint differential equation has a great impact on the gradient. Hence, an alternative approach is the discrete adjoint method , where the adjoint differential equations are replaced by algebraic equations. Therefore, a finite difference scheme is constructed for the adjoint system directly from the numerical time integration method. The method provides the exact gradient of the discretized cost function subjected to the discretized equations of motion.

Infant differential behavioral responding to discrete emotions.

Science.gov (United States)

Walle, Eric A; Reschke, Peter J; Camras, Linda A; Campos, Joseph J

2017-10-01

Emotional communication regulates the behaviors of social partners. Research on individuals' responding to others' emotions typically compares responses to a single negative emotion compared with responses to a neutral or positive emotion. Furthermore, coding of such responses routinely measure surface level features of the behavior (e.g., approach vs. avoidance) rather than its underlying function (e.g., the goal of the approach or avoidant behavior). This investigation examined infants' responding to others' emotional displays across 5 discrete emotions: joy, sadness, fear, anger, and disgust. Specifically, 16-, 19-, and 24-month-old infants observed an adult communicate a discrete emotion toward a stimulus during a naturalistic interaction. Infants' responses were coded to capture the function of their behaviors (e.g., exploration, prosocial behavior, and security seeking). The results revealed a number of instances indicating that infants use different functional behaviors in response to discrete emotions. Differences in behaviors across emotions were clearest in the 24-month-old infants, though younger infants also demonstrated some differential use of behaviors in response to discrete emotions. This is the first comprehensive study to identify differences in how infants respond with goal-directed behaviors to discrete emotions. Additionally, the inclusion of a function-based coding scheme and interpersonal paradigms may be informative for future emotion research with children and adults. Possible developmental accounts for the observed behaviors and the benefits of coding techniques emphasizing the function of social behavior over their form are discussed. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

The Evaluation of Surface Integrity During Machining of Inconel 718 with Various Laser Assistance Strategies

Directory of Open Access Journals (Sweden)

Wojciechowski Szymon

2017-01-01

Full Text Available The paper is focused on the evaluation of surface integrity formed during turning of Inconel 718 with the application of various laser assistance strategies. The primary objective of the work was to determine the relations between the applied machining strategy and the obtained surface integrity, in order to select the effective cutting conditions allowing the obtainment of high surface quality. The carried out experiment included the machining of Inconel 718 in the conventional turning conditions, as well as during the continuous laser assisted machining and sequential laser assistance. The surface integrity was evaluated by the measurements of machined surface topographies, microstructures and the microhardness. Results revealed that surface integrity of Inconel 718 is strongly affected by the selected machining strategy. The significant improvement of the surface roughness formed during machining of Inconel 718, can be reached by the application of simultaneous laser heating and cutting (LAM.

Eco-hydrological process simulations within an integrated surface water-groundwater model

DEFF Research Database (Denmark)

Butts, Michael; Loinaz, Maria Christina; Bauer-Gottwein, Peter

2014-01-01

Integrated water resources management requires tools that can quantify changes in groundwater, surface water, water quality and ecosystem health, as a result of changes in catchment management. To address these requirements we have developed an integrated eco-hydrological modelling framework...... that allows hydrologists and ecologists to represent the complex and dynamic interactions occurring between surface water, ground water, water quality and freshwater ecosystems within a catchment. We demonstrate here the practical application of this tool to two case studies where the interaction of surface...... water and ground water are important for the ecosystem. In the first, simulations are performed to understand the importance of surface water-groundwater interactions for a restored riparian wetland on the Odense River in Denmark as part of a larger investigation of water quality and nitrate retention...

Relativity and the question of discretization in astronomy

CERN Document Server

Edelen, Dominic G B

1970-01-01

Theoretical researches in general relativity and observational data from galactic astronomy combine in this volume in contributions to one of the oldest questions of natural philosophy: Is the structure of the physical world more adequately described by a continuous or a discrete mode of representation? Since the days of the Pythagoreans, this question has surfaced from time to time in various guises in science as well as in philosophy. One of the most bitterly contested and illuminating controversies between the continuous and the discrete viewpoints is to be found in the wave versus corpuscular description of optical phenom­ enae. This controversy was not resolved to the satisfaction of most of its protaganists until the development of the quantum theory. However, several obscurities that still becloud the question suggest that some deeper formulation may be necessary before more satisfactory answers can be given 1. The firm establishment of the validity of quantized structure and discrete energy distribut...

Conforming discretizations of boundary element solutions to the electroencephalography forward problem

Science.gov (United States)

Rahmouni, Lyes; Adrian, Simon B.; Cools, Kristof; Andriulli, Francesco P.

2018-01-01

In this paper, we present a new discretization strategy for the boundary element formulation of the Electroencephalography (EEG) forward problem. Boundary integral formulations, classically solved with the Boundary Element Method (BEM), are widely used in high resolution EEG imaging because of their recognized advantages, in several real case scenarios, in terms of numerical stability and effectiveness when compared with other differential equation based techniques. Unfortunately, however, it is widely reported in literature that the accuracy of standard BEM schemes for the forward EEG problem is often limited, especially when the current source density is dipolar and its location approaches one of the brain boundary surfaces. This is a particularly limiting problem given that during an high-resolution EEG imaging procedure, several EEG forward problem solutions are required, for which the source currents are near or on top of a boundary surface. This work will first present an analysis of standardly and classically discretized EEG forward problem operators, reporting on a theoretical issue of some of the formulations that have been used so far in the community. We report on the fact that several standardly used discretizations of these formulations are consistent only with an L2-framework, requiring the expansion term to be a square integrable function (i.e., in a Petrov-Galerkin scheme with expansion and testing functions). Instead, those techniques are not consistent when a more appropriate mapping in terms of fractional-order Sobolev spaces is considered. Such a mapping allows the expansion function term to be a less regular function, thus sensibly reducing the need for mesh refinements and low-precisions handling strategies that are currently required. These more favorable mappings, however, require a different and conforming discretization, which must be suitably adapted to them. In order to appropriately fulfill this requirement, we adopt a mixed

Effect of surface integrity of hard turned AISI 52100 steel on fatigue performance

International Nuclear Information System (INIS)

Smith, Stephen; Melkote, Shreyes N.; Lara-Curzio, Edgar; Watkins, Thomas R.; Allard, Larry; Riester, Laura

2007-01-01

This paper addresses the relationship between surface integrity and fatigue life of hard turned AISI 52100 steel (60-62 HRC), with grinding as a benchmark. The impact of superfinishing on the fatigue performance of hard turned and ground surfaces is also discussed. Specifically, the surface integrity and fatigue life of the following five distinct surface conditions are examined: hard turned with continuous white layer, hard turned with no white layer, ground, and superfinished hard turned and ground specimens. Surface integrity of the specimens is characterized via surface topography measurement, metallography, residual stress measurements, transmission electron microscopy (TEM), and nano-indentation tests. High cycle tension-tension fatigue tests show that the presence of white layer does not adversely affect fatigue life and that, on average, the hard turned surface performs as well or better than the ground surface. The effect of superfinishing is to exaggerate these differences in performance. The results obtained from this study suggest that the effect of residual stress on fatigue life is more significant than the effect of white layer. For the hard turned surfaces, the fatigue life is found to be directly proportional to both the surface compressive residual stress and the maximum compressive residual stress. Possible explanations for the observed effects are discussed

Discrete-time Calogero-Moser system and Lagrangian 1-form structure

International Nuclear Information System (INIS)

Yoo-Kong, Sikarin; Lobb, Sarah; Nijhoff, Frank

2011-01-01

We study the Lagrange formalism of the (rational) Calogero-Moser (CM) system, both in discrete time and continuous time, as a first example of a Lagrangian 1-form structure in the sense of the recent paper (Lobb and Nijhoff 2009 J. Phys. A: Math. Theor.42 454013). The discrete-time model of the CM system was established some time ago arising as a pole reduction of a semi-discrete version of the Kadomtsev-Petviashvili (KP) equation, and was shown to lead to an exactly integrable correspondence (multivalued map). In this paper, we present the full KP solution based on the commutativity of the discrete-time flows in the two discrete KP variables. The compatibility of the corresponding Lax matrices is shown to lead directly to the relevant closure relation on the level of the Lagrangians. Performing successive continuum limits on both the level of the KP equation and the level of the CM system, we establish the proper Lagrangian 1-form structure for the continuum case of the CM model. We use the example of the three-particle case to elucidate the implementation of the novel least-action principle, which was presented in Lobb and Nijhoff (2009), for the simpler case of Lagrangian 1-forms. (paper)

Ambiguities of functional integrals for fermionic systems

International Nuclear Information System (INIS)

Cordero, P.

1981-01-01

We study the path integral quantization of a purely fermionic system in the semiclassical approximation. It is crucial that the analogue of the usual method of stationary phase works for integrals over Grassmann variables. Our analysis is based on a quite trivial example (the exact solution is known), and therefore we can check when the results make sense. It is shown that just as in the boson case the path integral method depends on the discretization (we use the Faddeev discretization) and some attempts to do the same derivations directly in the continuous time limit are shown to yield either ill-defined objects or simply wrong results. It seems correct to conclude that the key point is the discretization

PREFACE: Symmetries and integrability of difference equations Symmetries and integrability of difference equations

Science.gov (United States)

Levi, Decio; Olver, Peter; Thomova, Zora; Winternitz, Pavel

2009-11-01

The concept of integrability was introduced in classical mechanics in the 19th century for finite dimensional continuous Hamiltonian systems. It was extended to certain classes of nonlinear differential equations in the second half of the 20th century with the discovery of the inverse scattering transform and the birth of soliton theory. Also at the end of the 19th century Lie group theory was invented as a powerful tool for obtaining exact analytical solutions of large classes of differential equations. Together, Lie group theory and integrability theory in its most general sense provide the main tools for solving nonlinear differential equations. Like differential equations, difference equations play an important role in physics and other sciences. They occur very naturally in the description of phenomena that are genuinely discrete. Indeed, they may actually be more fundamental than differential equations if space-time is actually discrete at very short distances. On the other hand, even when treating continuous phenomena described by differential equations it is very often necessary to resort to numerical methods. This involves a discretization of the differential equation, i.e. a replacement of the differential equation by a difference one. Given the well developed and understood techniques of symmetry and integrability for differential equations a natural question to ask is whether it is possible to develop similar techniques for difference equations. The aim is, on one hand, to obtain powerful methods for solving `integrable' difference equations and to establish practical integrability criteria, telling us when the methods are applicable. On the other hand, Lie group methods can be adapted to solve difference equations analytically. Finally, integrability and symmetry methods can be combined with numerical methods to obtain improved numerical solutions of differential equations. The origin of the SIDE meetings goes back to the early 1990s and the first

ZN graded discrete Lax pairs and Yang–Baxter maps

Science.gov (United States)

Fordy, Allan P.

2017-01-01

We recently introduced a class of ZN graded discrete Lax pairs and studied the associated discrete integrable systems (lattice equations). In this paper, we introduce the corresponding Yang–Baxter maps. Many well-known examples belong to this scheme for N=2, so, for N≥3, our systems may be regarded as generalizations of these. In particular, for each N we introduce a class of multi-component Yang–Baxter maps, which include HBIII (of Papageorgiou et al. 2010 SIGMA 6, 003 (9 p). (doi:10.3842/SIGMA.2010.033)), when N=2, and that associated with the discrete modified Boussinesq equation, for N=3. For N≥5 we introduce a new family of Yang–Baxter maps, which have no lower dimensional analogue. We also present new multi-component versions of the Yang–Baxter maps FIV and FV (given in the classification of Adler et al. 2004 Commun. Anal. Geom. 12, 967–1007. (doi:10.4310/CAG.2004.v12.n5.a1)). PMID:28588406

Discrete gradient methods for solving variational image regularisation models

International Nuclear Information System (INIS)

Grimm, V; McLachlan, Robert I; McLaren, David I; Quispel, G R W; Schönlieb, C-B

2017-01-01

Discrete gradient methods are well-known methods of geometric numerical integration, which preserve the dissipation of gradient systems. In this paper we show that this property of discrete gradient methods can be interesting in the context of variational models for image processing, that is where the processed image is computed as a minimiser of an energy functional. Numerical schemes for computing minimisers of such energies are desired to inherit the dissipative property of the gradient system associated to the energy and consequently guarantee a monotonic decrease of the energy along iterations, avoiding situations in which more computational work might lead to less optimal solutions. Under appropriate smoothness assumptions on the energy functional we prove that discrete gradient methods guarantee a monotonic decrease of the energy towards stationary states, and we promote their use in image processing by exhibiting experiments with convex and non-convex variational models for image deblurring, denoising, and inpainting. (paper)

Sparse signal reconstruction from polychromatic X-ray CT measurements via mass attenuation discretization

International Nuclear Information System (INIS)

Gu, Renliang; Dogandžić, Aleksandar

2014-01-01

We propose a method for reconstructing sparse images from polychromatic x-ray computed tomography (ct) measurements via mass attenuation coefficient discretization. The material of the inspected object and the incident spectrum are assumed to be unknown. We rewrite the Lambert-Beer’s law in terms of integral expressions of mass attenuation and discretize the resulting integrals. We then present a penalized constrained least-squares optimization approach for reconstructing the underlying object from log-domain measurements, where an active set approach is employed to estimate incident energy density parameters and the nonnegativity and sparsity of the image density map are imposed using negative-energy and smooth ℓ 1 -norm penalty terms. We propose a two-step scheme for refining the mass attenuation discretization grid by using higher sampling rate over the range with higher photon energy, and eliminating the discretization points that have little effect on accuracy of the forward projection model. This refinement allows us to successfully handle the characteristic lines (Dirac impulses) in the incident energy density spectrum. We compare the proposed method with the standard filtered backprojection, which ignores the polychromatic nature of the measurements and sparsity of the image density map. Numerical simulations using both realistic simulated and real x-ray ct data are presented

Discrete control systems

CERN Document Server

Okuyama, Yoshifumi

2014-01-01

Discrete Control Systems establishes a basis for the analysis and design of discretized/quantized control systemsfor continuous physical systems. Beginning with the necessary mathematical foundations and system-model descriptions, the text moves on to derive a robust stability condition. To keep a practical perspective on the uncertain physical systems considered, most of the methods treated are carried out in the frequency domain. As part of the design procedure, modified Nyquist–Hall and Nichols diagrams are presented and discretized proportional–integral–derivative control schemes are reconsidered. Schemes for model-reference feedback and discrete-type observers are proposed. Although single-loop feedback systems form the core of the text, some consideration is given to multiple loops and nonlinearities. The robust control performance and stability of interval systems (with multiple uncertainties) are outlined. Finally, the monograph describes the relationship between feedback-control and discrete ev...

SR 97 - Alternative models project. Discrete fracture network modelling for performance assessment of Aberg

International Nuclear Information System (INIS)

Dershowitz, B.; Eiben, T.; Follin, S.; Andersson, Johan

1999-08-01

As part of studies into the siting of a deep repository for nuclear waste, Swedish Nuclear Fuel and Waste Management Company (SKB) has commissioned the Alternative Models Project (AMP). The AMP is a comparison of three alternative modeling approaches for geosphere performance assessment for a single hypothetical site. The hypothetical site, arbitrarily named Aberg is based on parameters from the Aespoe Hard Rock Laboratory in southern Sweden. The Aberg model domain, boundary conditions and canister locations are defined as a common reference case to facilitate comparisons between approaches. This report presents the results of a discrete fracture pathways analysis of the Aberg site, within the context of the SR 97 performance assessment exercise. The Aberg discrete fracture network (DFN) site model is based on consensus Aberg parameters related to the Aespoe HRL site. Discrete fracture pathways are identified from canister locations in a prototype repository design to the surface of the island or to the sea bottom. The discrete fracture pathways analysis presented in this report is used to provide the following parameters for SKB's performance assessment transport codes FARF31 and COMP23: * F-factor: Flow wetted surface normalized with regards to flow rate (yields an appreciation of the contact area available for diffusion and sorption processes) [TL -1 ]. * Travel Time: Advective transport time from a canister location to the environmental discharge [T]. * Canister Flux: Darcy flux (flow rate per unit area) past a representative canister location [LT -1 ]. In addition to the above, the discrete fracture pathways analysis in this report also provides information about: additional pathway parameters such as pathway length, pathway width, transport aperture, reactive surface area and transmissivity, percentage of canister locations with pathways to the surface discharge, spatial pattern of pathways and pathway discharges, visualization of pathways, and statistical

SR 97 - Alternative models project. Discrete fracture network modelling for performance assessment of Aberg

Energy Technology Data Exchange (ETDEWEB)

Dershowitz, B.; Eiben, T. [Golder Associates Inc., Seattle (United States); Follin, S.; Andersson, Johan [Golder Grundteknik KB, Stockholm (Sweden)

1999-08-01

As part of studies into the siting of a deep repository for nuclear waste, Swedish Nuclear Fuel and Waste Management Company (SKB) has commissioned the Alternative Models Project (AMP). The AMP is a comparison of three alternative modeling approaches for geosphere performance assessment for a single hypothetical site. The hypothetical site, arbitrarily named Aberg is based on parameters from the Aespoe Hard Rock Laboratory in southern Sweden. The Aberg model domain, boundary conditions and canister locations are defined as a common reference case to facilitate comparisons between approaches. This report presents the results of a discrete fracture pathways analysis of the Aberg site, within the context of the SR 97 performance assessment exercise. The Aberg discrete fracture network (DFN) site model is based on consensus Aberg parameters related to the Aespoe HRL site. Discrete fracture pathways are identified from canister locations in a prototype repository design to the surface of the island or to the sea bottom. The discrete fracture pathways analysis presented in this report is used to provide the following parameters for SKB's performance assessment transport codes FARF31 and COMP23: * F-factor: Flow wetted surface normalized with regards to flow rate (yields an appreciation of the contact area available for diffusion and sorption processes) [TL{sup -1}]. * Travel Time: Advective transport time from a canister location to the environmental discharge [T]. * Canister Flux: Darcy flux (flow rate per unit area) past a representative canister location [LT{sup -1}]. In addition to the above, the discrete fracture pathways analysis in this report also provides information about: additional pathway parameters such as pathway length, pathway width, transport aperture, reactive surface area and transmissivity, percentage of canister locations with pathways to the surface discharge, spatial pattern of pathways and pathway discharges, visualization of pathways, and

Integrability of Liouville system on high genus Riemann surface: Pt. 1

International Nuclear Information System (INIS)

Chen Yixin; Gao Hongbo

1992-01-01

By using the theory of uniformization of Riemann-surfaces, we study properties of the Liouville equation and its general solution on a Riemann surface of genus g>1. After obtaining Hamiltonian formalism in terms of free fields and calculating classical exchange matrices, we prove the classical integrability of Liouville system on high genus Riemann surface

Dynamical barrier for the formation of solitary waves in discrete lattices

International Nuclear Information System (INIS)

Kevrekidis, P.G.; Espinola-Rocha, J.A.; Drossinos, Y.; Stefanov, A.

2008-01-01

We consider the problem of the existence of a dynamical barrier of 'mass' that needs to be excited on a lattice site to lead to the formation and subsequent persistence of localized modes for a nonlinear Schroedinger lattice. We contrast the existence of a dynamical barrier with its absence in the static theory of localized modes in one spatial dimension. We suggest an energetic criterion that provides a sufficient, but not necessary, condition on the amplitude of a single-site initial condition required to form a solitary wave. We show that this effect is not one-dimensional by considering its two-dimensional analog. The existence of a sufficient condition for the excitation of localized modes in the non-integrable, discrete, nonlinear Schroedinger equation is compared to the dynamics of excitations in the integrable, both discrete and continuum, version of the nonlinear Schroedinger equation

Discrete Biogeography Based Optimization for Feature Selection in Molecular Signatures.

Science.gov (United States)

Liu, Bo; Tian, Meihong; Zhang, Chunhua; Li, Xiangtao

2015-04-01

Biomarker discovery from high-dimensional data is a complex task in the development of efficient cancer diagnoses and classification. However, these data are usually redundant and noisy, and only a subset of them present distinct profiles for different classes of samples. Thus, selecting high discriminative genes from gene expression data has become increasingly interesting in the field of bioinformatics. In this paper, a discrete biogeography based optimization is proposed to select the good subset of informative gene relevant to the classification. In the proposed algorithm, firstly, the fisher-markov selector is used to choose fixed number of gene data. Secondly, to make biogeography based optimization suitable for the feature selection problem; discrete migration model and discrete mutation model are proposed to balance the exploration and exploitation ability. Then, discrete biogeography based optimization, as we called DBBO, is proposed by integrating discrete migration model and discrete mutation model. Finally, the DBBO method is used for feature selection, and three classifiers are used as the classifier with the 10 fold cross-validation method. In order to show the effective and efficiency of the algorithm, the proposed algorithm is tested on four breast cancer dataset benchmarks. Comparison with genetic algorithm, particle swarm optimization, differential evolution algorithm and hybrid biogeography based optimization, experimental results demonstrate that the proposed method is better or at least comparable with previous method from literature when considering the quality of the solutions obtained. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Discrete Element Modeling

Energy Technology Data Exchange (ETDEWEB)

Morris, J; Johnson, S

2007-12-03

The Distinct Element Method (also frequently referred to as the Discrete Element Method) (DEM) is a Lagrangian numerical technique where the computational domain consists of discrete solid elements which interact via compliant contacts. This can be contrasted with Finite Element Methods where the computational domain is assumed to represent a continuum (although many modern implementations of the FEM can accommodate some Distinct Element capabilities). Often the terms Discrete Element Method and Distinct Element Method are used interchangeably in the literature, although Cundall and Hart (1992) suggested that Discrete Element Methods should be a more inclusive term covering Distinct Element Methods, Displacement Discontinuity Analysis and Modal Methods. In this work, DEM specifically refers to the Distinct Element Method, where the discrete elements interact via compliant contacts, in contrast with Displacement Discontinuity Analysis where the contacts are rigid and all compliance is taken up by the adjacent intact material.

Dynamic nonlinear interaction of elastic plates on discrete supports

International Nuclear Information System (INIS)

Coutinho, A.L.G.A.; Landau, L.; Lima, E.C.P. de; Ebecken, N.F.F.

1984-01-01

A study on the dynamic nonlinear interaction of elastic plates using the finite element method is presented. The elastic plate is discretized by 4-node isoparametric Mindlin elements. The constitutive relation of the discrete supports can be any nonlinear curve given by pairs of force-displacement points. The nonlinear behaviour is represented by the overlay approach. This model also allows the simulation of a progressive decrease on the supports stiffnesses during load cycles. The dynamic nonlinear incremental movement equations are integrated by the Newmark implicit operator. Two alternatives for the incremental-iterative formulation are compared. The paper ends with a discussion of the advantages and limitations of the presented numerical models. (Author) [pt

The Effects of Discrete-Trial Training Commission Errors on Learner Outcomes: An Extension

Science.gov (United States)

Jenkins, Sarah R.; Hirst, Jason M.; DiGennaro Reed, Florence D.

2015-01-01

We conducted a parametric analysis of treatment integrity errors during discrete-trial training and investigated the effects of three integrity conditions (0, 50, or 100 % errors of commission) on performance in the presence and absence of programmed errors. The presence of commission errors impaired acquisition for three of four participants.…

Accelerated sampling by infinite swapping of path integral molecular dynamics with surface hopping

Science.gov (United States)

Lu, Jianfeng; Zhou, Zhennan

2018-02-01

To accelerate the thermal equilibrium sampling of multi-level quantum systems, the infinite swapping limit of a recently proposed multi-level ring polymer representation is investigated. In the infinite swapping limit, the ring polymer evolves according to an averaged Hamiltonian with respect to all possible surface index configurations of the ring polymer and thus connects the surface hopping approach to the mean-field path-integral molecular dynamics. A multiscale integrator for the infinite swapping limit is also proposed to enable efficient sampling based on the limiting dynamics. Numerical results demonstrate the huge improvement of sampling efficiency of the infinite swapping compared with the direct simulation of path-integral molecular dynamics with surface hopping.

Solving the incompressible surface Navier-Stokes equation by surface finite elements

Science.gov (United States)

Reuther, Sebastian; Voigt, Axel

2018-01-01

We consider a numerical approach for the incompressible surface Navier-Stokes equation on surfaces with arbitrary genus g (S ) . The approach is based on a reformulation of the equation in Cartesian coordinates of the embedding R3, penalization of the normal component, a Chorin projection method, and discretization in space by surface finite elements for each component. The approach thus requires only standard ingredients which most finite element implementations can offer. We compare computational results with discrete exterior calculus simulations on a torus and demonstrate the interplay of the flow field with the topology by showing realizations of the Poincaré-Hopf theorem on n-tori.

Design of self-supporting surfaces

KAUST Repository

Vouga, Etienne; Hö binger, Mathias; Wallner, Johannes; Pottmann, Helmut

2012-01-01

us to close connections between diverse topics in discrete differential geometry, such as a finite-element discretization of the Airy stress potential, perfect graph Laplacians, and computing admissible loads via curvatures of polyhedral surfaces

Application of network methods for understanding evolutionary dynamics in discrete habitats.

Science.gov (United States)

Greenbaum, Gili; Fefferman, Nina H

2017-06-01

In populations occupying discrete habitat patches, gene flow between habitat patches may form an intricate population structure. In such structures, the evolutionary dynamics resulting from interaction of gene-flow patterns with other evolutionary forces may be exceedingly complex. Several models describing gene flow between discrete habitat patches have been presented in the population-genetics literature; however, these models have usually addressed relatively simple settings of habitable patches and have stopped short of providing general methodologies for addressing nontrivial gene-flow patterns. In the last decades, network theory - a branch of discrete mathematics concerned with complex interactions between discrete elements - has been applied to address several problems in population genetics by modelling gene flow between habitat patches using networks. Here, we present the idea and concepts of modelling complex gene flows in discrete habitats using networks. Our goal is to raise awareness to existing network theory applications in molecular ecology studies, as well as to outline the current and potential contribution of network methods to the understanding of evolutionary dynamics in discrete habitats. We review the main branches of network theory that have been, or that we believe potentially could be, applied to population genetics and molecular ecology research. We address applications to theoretical modelling and to empirical population-genetic studies, and we highlight future directions for extending the integration of network science with molecular ecology. © 2017 John Wiley & Sons Ltd.

A Systematic Controller Design for a Grid-Connected Inverter with LCL Filter Using a Discrete-Time Integral State Feedback Control and State Observer

Directory of Open Access Journals (Sweden)

Seung-Jin Yoon

2018-02-01

Full Text Available Inductive-capacitive-inductive (LCL-type filters are currently preferred as a replacement for L-type filters in distributed generation (DG power systems, due to their superior harmonic attenuation capability. However, the third-order dynamics introduced by LCL filters pose a challenge to design a satisfactory controller for such a system. Conventionally, an LCL-filtered grid-connected inverter can be effectively controlled by using a full-state feedback control. However, this control approach requires the measurement of all system state variables, which brings about more complexity for the inverter system. To address this issue, this paper presents a systematic procedure to design an observer-based integral state feedback control for a LCL-filtered grid-connected inverter in the discrete-time domain. The proposed control scheme consists of an integral state feedback controller and a full-state observer which uses the control input, grid-side currents, and grid voltages to predict all the system state variables. Therefore, only the grid-side current sensors and grid voltage sensors are required to implement the proposed control scheme. Due to the discrete-time integrator incorporated in the state feedback controller, the proposed control scheme ensures both the reference tracking and disturbance rejection performance of the inverter system in a practical and simple way. As a result, superior control performance can be achieved by using the reduced number of sensors, which significantly reduces the cost and complexity of the LCL-filtered grid-connected inverter system in DG applications. To verify the practical usefulness of the proposed control scheme, a 2 kW three-phase prototype grid-connected inverter has been constructed, and the proposed control system has been implemented based on 32-bit floating-point digital signal processor (DSP TMS320F28335. The effectiveness of the proposed scheme is demonstrated through the comprehensive simulation

Association of lipids with integral membrane surface proteins of Mycoplasma hyorhinis

International Nuclear Information System (INIS)

Bricker, T.M.; Boyer, M.J.; Keith, J.; Watson-McKown, R.; Wise, K.S.

1988-01-01

Triton X-114 (TX-114)-phase fractionation was used to identify and characterize integral membrane surface proteins of the wall-less procaryote Mycoplasma hyorhinis GDL. Phase fractionation of mycoplasmas followed by analysis by sodium dodecyl sulfate-polyacrylamide gel electrophoresis revealed selective partitioning of approximately 30 [ 35 S]methionine-labeled intrinsic membrane proteins into the TX-114 phase. Similar analysis of [ 3 H]palmitate-labeled cells showed that approximately 20 proteins of this organism were associated with lipid, all of which also efficiently partitioned as integral membrane components into the detergent phase. Immunoblotting and immunoprecipitation of TX-114-phase proteins from 125 I-surface-labeled cells with four monoclonal antibodies to distinct surface epitopes of M. hyorhinis identified surface proteins p120, p70, p42, and p23 as intrinsic membrane components. Immunoprecipitation of [ 3 H]palmitate-labeled TX-114-phase proteins further established that surface proteins p120, p70, and p23 (a molecule that mediates complement-dependent mycoplasmacidal monoclonal antibody activity) were among the lipid-associated proteins of this organism. Two of these proteins, p120 and p123, were acidic (pI less than or equal to 4.5), as shown by two-dimensional isoelectric focusing. This study established that M. hyorhinis contains an abundance of integral membrane proteins tightly associated with lipids and that many of these proteins are exposed at the external surface of the single limiting plasma membrane. Monoclonal antibodies are reported that will allow detailed analysis of the structure and processing of lipid-associated mycoplasma proteins

Discrete-ordinates finite-element method for atmospheric radiative transfer and remote sensing

International Nuclear Information System (INIS)

Gerstl, S.A.W.; Zardecki, A.

1985-01-01

Advantages and disadvantages of modern discrete-ordinates finite-element methods for the solution of radiative transfer problems in meteorology, climatology, and remote sensing applications are evaluated. After the common basis of the formulation of radiative transfer problems in the fields of neutron transport and atmospheric optics is established, the essential features of the discrete-ordinates finite-element method are described including the limitations of the method and their remedies. Numerical results are presented for 1-D and 2-D atmospheric radiative transfer problems where integral as well as angular dependent quantities are compared with published results from other calculations and with measured data. These comparisons provide a verification of the discrete-ordinates results for a wide spectrum of cases with varying degrees of absorption, scattering, and anisotropic phase functions. Accuracy and computational speed are also discussed. Since practically all discrete-ordinates codes offer a builtin adjoint capability, the general concept of the adjoint method is described and illustrated by sample problems. Our general conclusion is that the strengths of the discrete-ordinates finite-element method outweight its weaknesses. We demonstrate that existing general-purpose discrete-ordinates codes can provide a powerful tool to analyze radiative transfer problems through the atmosphere, especially when 2-D geometries must be considered

A three–step discretization scheme for direct numerical solution of ...

African Journals Online (AJOL)

In this paper, a three-step discretization (numerical) formula is developed for direct integration of second-order initial value problems in ordinary differential equations. The development of the method and analysis of its basic properties adopt Taylor series expansion and Dahlquist stability test methods. The results show that ...

Discrete space charge affected field emission: Flat and hemisphere emitters

Energy Technology Data Exchange (ETDEWEB)

Jensen, Kevin L., E-mail: kevin.jensen@nrl.navy.mil [Code 6854, Naval Research Laboratory, Washington, DC 20375 (United States); Shiffler, Donald A.; Tang, Wilkin [Air Force Research Laboratory, Kirtland AFB, New Mexico 87117 (United States); Rittersdorf, Ian M. [Code 6770, Naval Research Laboratory, Washington, DC 20375 (United States); Lebowitz, Joel L. [Department of Mathematics and Department of Physics, Rutgers University, Piscataway, New Jersey 08854-8019 (United States); Harris, John R. [U.S. Navy Reserve, New Orleans, Louisiana 70143 (United States); Lau, Y. Y. [Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, Michigan 48109 (United States); Petillo, John J. [Leidos, Billerica, Massachusetts 01821 (United States); Luginsland, John W. [Physics and Electronics Directorate, AFOSR, Arlington, Virginia 22203 (United States)

2015-05-21

Models of space-charge affected thermal-field emission from protrusions, able to incorporate the effects of both surface roughness and elongated field emitter structures in beam optics codes, are desirable but difficult. The models proposed here treat the meso-scale diode region separate from the micro-scale regions characteristic of the emission sites. The consequences of discrete emission events are given for both one-dimensional (sheets of charge) and three dimensional (rings of charge) models: in the former, results converge to steady state conditions found by theory (e.g., Rokhlenko et al. [J. Appl. Phys. 107, 014904 (2010)]) but show oscillatory structure as they do. Surface roughness or geometric features are handled using a ring of charge model, from which the image charges are found and used to modify the apex field and emitted current. The roughness model is shown to have additional constraints related to the discrete nature of electron charge. The ability of a unit cell model to treat field emitter structures and incorporate surface roughness effects inside a beam optics code is assessed.

An essay on discrete foundations for physics

International Nuclear Information System (INIS)

Noyes, H.P.; McGoveran, D.O.

1988-07-01

We base our theory of physics and cosmology on the five principles of finiteness, discreteness, finite computability, absolute non-uniqueness, and strict construction. Our modeling methodology starts from the current practice of physics, constructs a self-consistent representation based on the ordering operator calculus and provides rules of correspondence that allow us to test the theory by experiment. We use program universe to construct a growing collection of bit strings whose initial portions (labels) provide the quantum numbers that are conserved in the events defined by the construction. The labels are followed by content strings which are used to construct event-based finite and discrete coordinates. On general grounds such a theory has a limiting velocity, and positions and velocities do not commute. We therefore reconcile quantum mechanics with relativity at an appropriately fundamental stage in the construction. We show that events in different coordinate systems are connected by the appropriate finite and discrete version of the Lorentz transformation, that 3-momentum is conserved in events, and that this conservation law is the same as the requirement that different paths can ''interfere'' only when they differ by an integral number of deBroglie wavelengths. 38 refs., 12 figs., 3 tabs

Time-Discrete Higher-Order ALE Formulations: Stability

KAUST Repository

Bonito, Andrea

2013-01-01

Arbitrary Lagrangian Eulerian (ALE) formulations deal with PDEs on deformable domains upon extending the domain velocity from the boundary into the bulk with the purpose of keeping mesh regularity. This arbitrary extension has no effect on the stability of the PDE but may influence that of a discrete scheme. We examine this critical issue for higher-order time stepping without space discretization. We propose time-discrete discontinuous Galerkin (dG) numerical schemes of any order for a time-dependent advection-diffusion-model problem in moving domains, and study their stability properties. The analysis hinges on the validity of the Reynold\\'s identity for dG. Exploiting the variational structure and assuming exact integration, we prove that our conservative and nonconservative dG schemes are equivalent and unconditionally stable. The same results remain true for piecewise polynomial ALE maps of any degree and suitable quadrature that guarantees the validity of the Reynold\\'s identity. This approach generalizes the so-called geometric conservation law to higher-order methods. We also prove that simpler Runge-Kutta-Radau methods of any order are conditionally stable, that is, subject to a mild ALE constraint on the time steps. Numerical experiments corroborate and complement our theoretical results. © 2013 Society for Industrial and Applied Mathematics.

An essay on discrete foundations for physics

International Nuclear Information System (INIS)

Noyes, H.P.; McGoveran, D.O.

1988-01-01

We base our theory of physics and cosmology on the five principles of finiteness, discreteness, finite computability, absolute non- uniqueness, and strict construction. Our modeling methodology starts from the current practice of physics, constructs a self-consistent representation based on the ordering operator calculus and provides rules of correspondence that allow us to test the theory by experiment. We use program universe to construct a growing collection of bit strings whose initial portions (labels) provide the quantum numbers that are conserved in the events defined by the construction. The labels are followed by content strings which are used to construct event-based finite and discrete coordinates. On general grounds such a theory has a limiting velocity, and positions and velocities do not commute. We therefore reconcile quantum mechanics with relativity at an appropriately fundamental stage in the construction. We show that events in different coordinate systems are connected by the appropriate finite and discrete version of the Lorentz transformation, that 3-momentum is conserved in events, and that this conservation law is the same as the requirement that different paths can ''interfere'' only when they differ by an integral number of deBroglie wavelengths. 38 refs., 12 figs., 3 tabs

An essay on discrete foundations for physics

Energy Technology Data Exchange (ETDEWEB)

Noyes, H.P.; McGoveran, D.O.

1988-07-01

We base our theory of physics and cosmology on the five principles of finiteness, discreteness, finite computability, absolute non-uniqueness, and strict construction. Our modeling methodology starts from the current practice of physics, constructs a self-consistent representation based on the ordering operator calculus and provides rules of correspondence that allow us to test the theory by experiment. We use program universe to construct a growing collection of bit strings whose initial portions (labels) provide the quantum numbers that are conserved in the events defined by the construction. The labels are followed by content strings which are used to construct event-based finite and discrete coordinates. On general grounds such a theory has a limiting velocity, and positions and velocities do not commute. We therefore reconcile quantum mechanics with relativity at an appropriately fundamental stage in the construction. We show that events in different coordinate systems are connected by the appropriate finite and discrete version of the Lorentz transformation, that 3-momentum is conserved in events, and that this conservation law is the same as the requirement that different paths can ''interfere'' only when they differ by an integral number of deBroglie wavelengths. 38 refs., 12 figs., 3 tabs.

An essay on discrete foundations for physics

Energy Technology Data Exchange (ETDEWEB)

Noyes, H.P.; McGoveran, D.O.

1988-10-05

We base our theory of physics and cosmology on the five principles of finiteness, discreteness, finite computability, absolute non- uniqueness, and strict construction. Our modeling methodology starts from the current practice of physics, constructs a self-consistent representation based on the ordering operator calculus and provides rules of correspondence that allow us to test the theory by experiment. We use program universe to construct a growing collection of bit strings whose initial portions (labels) provide the quantum numbers that are conserved in the events defined by the construction. The labels are followed by content strings which are used to construct event-based finite and discrete coordinates. On general grounds such a theory has a limiting velocity, and positions and velocities do not commute. We therefore reconcile quantum mechanics with relativity at an appropriately fundamental stage in the construction. We show that events in different coordinate systems are connected by the appropriate finite and discrete version of the Lorentz transformation, that 3-momentum is conserved in events, and that this conservation law is the same as the requirement that different paths can ''interfere'' only when they differ by an integral number of deBroglie wavelengths. 38 refs., 12 figs., 3 tabs.

Dynamical barrier for the formation of solitary waves in discrete lattices

Energy Technology Data Exchange (ETDEWEB)

Kevrekidis, P.G. [Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003 (United States)], E-mail: kevrekid@math.umass.edu; Espinola-Rocha, J.A. [Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003 (United States); Drossinos, Y. [European Commission, Joint Research Centre, I-21020 Ispra (Vatican City State, Holy See,) (Italy); School of Mechanical and Systems Engineering, University of Newcastle upon Tyne, Newcastle upon Tyne NE1 7RU (United Kingdom); Stefanov, A. [Department of Mathematics, University of Kansas, 1460 Jayhawk Blvd., Lawrence, KS 66045-7523 (United States)

2008-03-24

We consider the problem of the existence of a dynamical barrier of 'mass' that needs to be excited on a lattice site to lead to the formation and subsequent persistence of localized modes for a nonlinear Schroedinger lattice. We contrast the existence of a dynamical barrier with its absence in the static theory of localized modes in one spatial dimension. We suggest an energetic criterion that provides a sufficient, but not necessary, condition on the amplitude of a single-site initial condition required to form a solitary wave. We show that this effect is not one-dimensional by considering its two-dimensional analog. The existence of a sufficient condition for the excitation of localized modes in the non-integrable, discrete, nonlinear Schroedinger equation is compared to the dynamics of excitations in the integrable, both discrete and continuum, version of the nonlinear Schroedinger equation.

Representations of classical groups on the lattice and its application to the field theory on discrete space-time

OpenAIRE

Lorente, M.

2003-01-01

We explore the mathematical consequences of the assumption of a discrete space-time. The fundamental laws of physics have to be translated into the language of discrete mathematics. We find integral transformations that leave the lattice of any dimension invariant and apply these transformations to field equations.

Asymptotic behavior of discrete holomorphic maps z^c, log(z) and discrete Painleve transcedents

OpenAIRE

Agafonov, S. I.

2005-01-01

It is shown that discrete analogs of z^c and log(z) have the same asymptotic behavior as their smooth counterparts. These discrete maps are described in terms of special solutions of discrete Painleve-II equations, asymptotics of these solutions providing the behaviour of discrete z^c and log(z) at infinity.

A high-order boundary integral method for surface diffusions on elastically stressed axisymmetric rods

OpenAIRE

Li, Xiaofan; Nie, Qing

2009-01-01

Many applications in materials involve surface diffusion of elastically stressed solids. Study of singularity formation and long-time behavior of such solid surfaces requires accurate simulations in both space and time. Here we present a high-order boundary integral method for an elastically stressed solid with axi-symmetry due to surface diffusions. In this method, the boundary integrals for isotropic elasticity in axi-symmetric geometry are approximated through modified alternating quadratu...

Soliton surfaces associated with generalized symmetries of integrable equations

International Nuclear Information System (INIS)

Grundland, A M; Post, S

2011-01-01

In this paper, based on the Fokas et al approach (Fokas and Gel'fand 1996 Commun. Math. Phys. 177 203-20; Fokas et al 2000 Sel. Math. 6 347-75), we provide a symmetry characterization of continuous deformations of soliton surfaces immersed in a Lie algebra using the formalism of generalized vector fields, their prolongation structure and links with the Frechet derivatives. We express the necessary and sufficient condition for the existence of such surfaces in terms of the invariance criterion for generalized symmetries and identify additional sufficient conditions which admit an explicit integration of the immersion functions of 2D surfaces in Lie algebras. We discuss in detail the su(N)-valued immersion functions generated by conformal symmetries of the CP N-1 sigma model defined on either the Minkowski or Euclidean space. We further show that the sufficient conditions for explicit integration of such immersion functions impose additional restrictions on the admissible conformal symmetries of the model defined on Minkowski space. On the other hand, the sufficient conditions are identically satisfied for arbitrary conformal symmetries of finite action solutions of the CP N-1 sigma model defined on Euclidean space.

An Integrated Software Suite for Surface-based Analyses of Cerebral Cortex

Science.gov (United States)

Van Essen, David C.; Drury, Heather A.; Dickson, James; Harwell, John; Hanlon, Donna; Anderson, Charles H.

2001-01-01

The authors describe and illustrate an integrated trio of software programs for carrying out surface-based analyses of cerebral cortex. The first component of this trio, SureFit (Surface Reconstruction by Filtering and Intensity Transformations), is used primarily for cortical segmentation, volume visualization, surface generation, and the mapping of functional neuroimaging data onto surfaces. The second component, Caret (Computerized Anatomical Reconstruction and Editing Tool Kit), provides a wide range of surface visualization and analysis options as well as capabilities for surface flattening, surface-based deformation, and other surface manipulations. The third component, SuMS (Surface Management System), is a database and associated user interface for surface-related data. It provides for efficient insertion, searching, and extraction of surface and volume data from the database. PMID:11522765

An integrated software suite for surface-based analyses of cerebral cortex

Science.gov (United States)

Van Essen, D. C.; Drury, H. A.; Dickson, J.; Harwell, J.; Hanlon, D.; Anderson, C. H.

2001-01-01

The authors describe and illustrate an integrated trio of software programs for carrying out surface-based analyses of cerebral cortex. The first component of this trio, SureFit (Surface Reconstruction by Filtering and Intensity Transformations), is used primarily for cortical segmentation, volume visualization, surface generation, and the mapping of functional neuroimaging data onto surfaces. The second component, Caret (Computerized Anatomical Reconstruction and Editing Tool Kit), provides a wide range of surface visualization and analysis options as well as capabilities for surface flattening, surface-based deformation, and other surface manipulations. The third component, SuMS (Surface Management System), is a database and associated user interface for surface-related data. It provides for efficient insertion, searching, and extraction of surface and volume data from the database.

Computation of Surface Integrals of Curl Vector Fields

Science.gov (United States)

Hu, Chenglie

2007-01-01

This article presents a way of computing a surface integral when the vector field of the integrand is a curl field. Presented in some advanced calculus textbooks such as [1], the technique, as the author experienced, is simple and applicable. The computation is based on Stokes' theorem in 3-space calculus, and thus provides not only a means to…

Geometric Integration Of The Valsov-Maxwell System With A Variational Particle-in-cell Scheme

International Nuclear Information System (INIS)

Squire, J.; Qin, H.; Tang, W.M.

2012-01-01

A fully variational, unstructured, electromagnetic particle-in-cell integrator is developed for integration of the Vlasov-Maxwell equations. Using the formalism of Discrete Exterior Calculus [1], the field solver, interpolation scheme and particle advance algorithm are derived through minimization of a single discrete field theory action. As a consequence of ensuring that the action is invariant under discrete electromagnetic gauge transformations, the integrator exactly conserves Gauss's law.

SARDA: An Integrated Concept for Airport Surface Operations Management

Science.gov (United States)

Gupta, Gautam; Hoang, Ty; Jung, Yoon Chul

2013-01-01

The Spot and Runway Departure Advisor (SARDA) is an integrated decision support tool for airlines and air traffic control tower enabling surface collaborative decision making (CDM) and departure metering in order to enhance efficiency of surface operations at congested airports. The presentation describes the concept and architecture of the SARDA as a CDM tool, and the results from a human-in-the-loop simulation of the tool conducted in 2012 at the FutureFlight Central, the tower simulation facility. Also, presented is the current activities and future plan for SARDA development. The presentation was given at the meeting with the FAA senior advisor of the Surface Operations Office.

The inverse of winnowing: a FORTRAN subroutine and discussion of unwinnowing discrete data

Science.gov (United States)

Bracken, Robert E.

2004-01-01

This report describes an unwinnowing algorithm that utilizes a discrete Fourier transform, and a resulting Fortran subroutine that winnows or unwinnows a 1-dimensional stream of discrete data; the source code is included. The unwinnowing algorithm effectively increases (by integral factors) the number of available data points while maintaining the original frequency spectrum of a data stream. This has utility when an increased data density is required together with an availability of higher order derivatives that honor the original data.

Discrete port-Hamiltonian systems

NARCIS (Netherlands)

Talasila, V.; Clemente-Gallardo, J.; Schaft, A.J. van der

2006-01-01

Either from a control theoretic viewpoint or from an analysis viewpoint it is necessary to convert smooth systems to discrete systems, which can then be implemented on computers for numerical simulations. Discrete models can be obtained either by discretizing a smooth model, or by directly modeling

Discrete transforms

CERN Document Server

Firth, Jean M

1992-01-01

The analysis of signals and systems using transform methods is a very important aspect of the examination of processes and problems in an increasingly wide range of applications. Whereas the initial impetus in the development of methods appropriate for handling discrete sets of data occurred mainly in an electrical engineering context (for example in the design of digital filters), the same techniques are in use in such disciplines as cardiology, optics, speech analysis and management, as well as in other branches of science and engineering. This text is aimed at a readership whose mathematical background includes some acquaintance with complex numbers, linear differen­ tial equations, matrix algebra, and series. Specifically, a familiarity with Fourier series (in trigonometric and exponential forms) is assumed, and an exposure to the concept of a continuous integral transform is desirable. Such a background can be expected, for example, on completion of the first year of a science or engineering degree cour...

Applied discrete-time queues

CERN Document Server

Alfa, Attahiru S

2016-01-01

This book introduces the theoretical fundamentals for modeling queues in discrete-time, and the basic procedures for developing queuing models in discrete-time. There is a focus on applications in modern telecommunication systems. It presents how most queueing models in discrete-time can be set up as discrete-time Markov chains. Techniques such as matrix-analytic methods (MAM) that can used to analyze the resulting Markov chains are included. This book covers single node systems, tandem system and queueing networks. It shows how queues with time-varying parameters can be analyzed, and illustrates numerical issues associated with computations for the discrete-time queueing systems. Optimal control of queues is also covered. Applied Discrete-Time Queues targets researchers, advanced-level students and analysts in the field of telecommunication networks. It is suitable as a reference book and can also be used as a secondary text book in computer engineering and computer science. Examples and exercises are includ...

Time Discretization Techniques

KAUST Repository

Gottlieb, S.; Ketcheson, David I.

2016-01-01

The time discretization of hyperbolic partial differential equations is typically the evolution of a system of ordinary differential equations obtained by spatial discretization of the original problem. Methods for this time evolution include

Design integration of liquid surface divertors

International Nuclear Information System (INIS)

Nygren, R.E.; Cowgill, D.F.; Ulrickson, M.A.; Nelson, B.E.; Fogarty, P.J.; Rognlien, T.D.; Rensink, M.E.; Hassanein, A.; Smolentsev, S.S.; Kotschenreuther, M.

2004-01-01

The US Enabling Technology Program in fusion is investigating the use of free flowing liquid surfaces facing the plasma. We have been studying the issues in integrating a liquid surface divertor into a configuration based upon an advanced tokamak, specifically the ARIES-RS configuration. The simplest form of such a divertor is to extend the flow of the liquid first wall into the divertor and thereby avoid introducing additional fluid streams. In this case, one can modify the flow above the divertor to enhance thermal mixing. For divertors with flowing liquid metals (or other electrically conductive fluids) MHD (magneto-hydrodynamics) effects are a major concern and can produce forces that redirect flow and suppress turbulence. An evaluation of Flibe (a molten salt) as a working fluid was done to assess a case in which the MHD forces could be largely neglected. Initial studies indicate that, for a tokamak with high power density, an integrated Flibe first wall and divertor does not seem workable. We have continued work with molten salts and replaced Flibe with Flinabe, a mixture of lithium, sodium and beryllium fluorides, that has some potential because of its lower melting temperature. Sn and Sn-Li have also been considered, and the initial evaluations on heat removal with minimal plasma contamination show promise, although the complicated 3D MHD flows cannot yet be fully modeled. Particle pumping in these design concepts is accomplished by conventional means (ports and pumps). However, trapping of hydrogen in these flowing liquids seems plausible and novel concepts for entrapping helium are also being studied

Coarse-mesh discretized low-order quasi-diffusion equations for subregion averaged scalar fluxes

International Nuclear Information System (INIS)

Anistratov, D. Y.

2004-01-01

In this paper we develop homogenization procedure and discretization for the low-order quasi-diffusion equations on coarse grids for core-level reactor calculations. The system of discretized equations of the proposed method is formulated in terms of the subregion averaged group scalar fluxes. The coarse-mesh solution is consistent with a given fine-mesh discretization of the transport equation in the sense that it preserves a set of average values of the fine-mesh transport scalar flux over subregions of coarse-mesh cells as well as the surface currents, and eigenvalue. The developed method generates numerical solution that mimics the large-scale behavior of the transport solution within assemblies. (authors)

Stabilisation of discrete-time polynomial fuzzy systems via a polynomial lyapunov approach

Science.gov (United States)

Nasiri, Alireza; Nguang, Sing Kiong; Swain, Akshya; Almakhles, Dhafer

2018-02-01

This paper deals with the problem of designing a controller for a class of discrete-time nonlinear systems which is represented by discrete-time polynomial fuzzy model. Most of the existing control design methods for discrete-time fuzzy polynomial systems cannot guarantee their Lyapunov function to be a radially unbounded polynomial function, hence the global stability cannot be assured. The proposed control design in this paper guarantees a radially unbounded polynomial Lyapunov functions which ensures global stability. In the proposed design, state feedback structure is considered and non-convexity problem is solved by incorporating an integrator into the controller. Sufficient conditions of stability are derived in terms of polynomial matrix inequalities which are solved via SOSTOOLS in MATLAB. A numerical example is presented to illustrate the effectiveness of the proposed controller.

Discrete repulsive oscillator wavefunctions

International Nuclear Information System (INIS)

Munoz, Carlos A; Rueda-Paz, Juvenal; Wolf, Kurt Bernardo

2009-01-01

For the study of infinite discrete systems on phase space, the three-dimensional Lorentz algebra and group, so(2,1) and SO(2,1), provide a discrete model of the repulsive oscillator. Its eigenfunctions are found in the principal irreducible representation series, where the compact generator-that we identify with the position operator-has the infinite discrete spectrum of the integers Z, while the spectrum of energies is a double continuum. The right- and left-moving wavefunctions are given by hypergeometric functions that form a Dirac basis for l 2 (Z). Under contraction, the discrete system limits to the well-known quantum repulsive oscillator. Numerical computations of finite approximations raise further questions on the use of Dirac bases for infinite discrete systems.

Topological horseshoes in travelling waves of discretized nonlinear wave equations

International Nuclear Information System (INIS)

Chen, Yi-Chiuan; Chen, Shyan-Shiou; Yuan, Juan-Ming

2014-01-01

Applying the concept of anti-integrable limit to coupled map lattices originated from space-time discretized nonlinear wave equations, we show that there exist topological horseshoes in the phase space formed by the initial states of travelling wave solutions. In particular, the coupled map lattices display spatio-temporal chaos on the horseshoes

Topological horseshoes in travelling waves of discretized nonlinear wave equations

Energy Technology Data Exchange (ETDEWEB)

Chen, Yi-Chiuan, E-mail: YCChen@math.sinica.edu.tw [Institute of Mathematics, Academia Sinica, Taipei 10617, Taiwan (China); Chen, Shyan-Shiou, E-mail: sschen@ntnu.edu.tw [Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan (China); Yuan, Juan-Ming, E-mail: jmyuan@pu.edu.tw [Department of Financial and Computational Mathematics, Providence University, Shalu, Taichung 43301, Taiwan (China)

2014-04-15

Applying the concept of anti-integrable limit to coupled map lattices originated from space-time discretized nonlinear wave equations, we show that there exist topological horseshoes in the phase space formed by the initial states of travelling wave solutions. In particular, the coupled map lattices display spatio-temporal chaos on the horseshoes.

Discrete Hamiltonian evolution and quantum gravity

International Nuclear Information System (INIS)

Husain, Viqar; Winkler, Oliver

2004-01-01

We study constrained Hamiltonian systems by utilizing general forms of time discretization. We show that for explicit discretizations, the requirement of preserving the canonical Poisson bracket under discrete evolution imposes strong conditions on both allowable discretizations and Hamiltonians. These conditions permit time discretizations for a limited class of Hamiltonians, which does not include homogeneous cosmological models. We also present two general classes of implicit discretizations which preserve Poisson brackets for any Hamiltonian. Both types of discretizations generically do not preserve first class constraint algebras. Using this observation, we show that time discretization provides a complicated time gauge fixing for quantum gravity models, which may be compared with the alternative procedure of gauge fixing before discretization

Discrete Control Processes, Dynamic Games and Multicriterion Control Problems

Directory of Open Access Journals (Sweden)

Dumitru Lozovanu

2002-07-01

Full Text Available The discrete control processes with state evaluation in time of dynamical system is considered. A general model of control problems with integral-time cost criterion by a trajectory is studied and a general scheme for solving such classes of problems is proposed. In addition the game-theoretical and multicriterion models for control problems are formulated and studied.

Adaptive discrete-ordinates algorithms and strategies

International Nuclear Information System (INIS)

Stone, J.C.; Adams, M.L.

2005-01-01

We present our latest algorithms and strategies for adaptively refined discrete-ordinates quadrature sets. In our basic strategy, which we apply here in two-dimensional Cartesian geometry, the spatial domain is divided into regions. Each region has its own quadrature set, which is adapted to the region's angular flux. Our algorithms add a 'test' direction to the quadrature set if the angular flux calculated at that direction differs by more than a user-specified tolerance from the angular flux interpolated from other directions. Different algorithms have different prescriptions for the method of interpolation and/or choice of test directions and/or prescriptions for quadrature weights. We discuss three different algorithms of different interpolation orders. We demonstrate through numerical results that each algorithm is capable of generating solutions with negligible angular discretization error. This includes elimination of ray effects. We demonstrate that all of our algorithms achieve a given level of error with far fewer unknowns than does a standard quadrature set applied to an entire problem. To address a potential issue with other algorithms, we present one algorithm that retains exact integration of high-order spherical-harmonics functions, no matter how much local refinement takes place. To address another potential issue, we demonstrate that all of our methods conserve partial currents across interfaces where quadrature sets change. We conclude that our approach is extremely promising for solving the long-standing problem of angular discretization error in multidimensional transport problems. (authors)

Discrete Bose-Einstein systems in a box with low adiabatic invariant

International Nuclear Information System (INIS)

Vlad, V.I.; Ionescu-Pallas, N.

2002-03-01

The Bose-Einstein energy spectrum of a quantum gas, confined in a (cubic) box, is discrete and strongly dependent on the box geometry and temperature, for low product of the atomic mass number, A at and the adiabatic invariant, TV 2/3 , i.e. on γ=A at TV 2/3 . Even within the approximation of noninteracting particles in the gas, the calculation of the thermodynamic properties of Bose-Einstein systems turns out to be a difficult mathematical problem. It is solved in the textbooks and most papers by approximating the sums by integrals. The present study compares the total number of particles and the total energy obtained by summing up the exact contributions of the eigenvalues and their weights, for defined values of γ, to the results of the approximate integrals. Then, the passage from sums to integrals is done in a more rigorous manner and better analytical approximations are found. The corrected thermodynamic functions depend on γ. The critical temperature is corrected also in order to describe more accurately the discrete Bose-Einstein systems and their onset of the phase transition. (author)

Explicit solutions to the semi-discrete modified KdV equation and motion of discrete plane curves

International Nuclear Information System (INIS)

Inoguchi, Jun-ichi; Kajiwara, Kenji; Matsuura, Nozomu; Ohta, Yasuhiro

2012-01-01

We construct explicit solutions to continuous motion of discrete plane curves described by a semi-discrete potential modified KdV equation. Explicit formulas in terms of the τ function are presented. Bäcklund transformations of the discrete curves are also discussed. We finally consider the continuous limit of discrete motion of discrete plane curves described by the discrete potential modified KdV equation to motion of smooth plane curves characterized by the potential modified KdV equation. (paper)

Variational integrators for electric circuits

International Nuclear Information System (INIS)

Ober-Blöbaum, Sina; Tao, Molei; Cheng, Mulin; Owhadi, Houman; Marsden, Jerrold E.

2013-01-01

In this contribution, we develop a variational integrator for the simulation of (stochastic and multiscale) electric circuits. When considering the dynamics of an electric circuit, one is faced with three special situations: 1. The system involves external (control) forcing through external (controlled) voltage sources and resistors. 2. The system is constrained via the Kirchhoff current (KCL) and voltage laws (KVL). 3. The Lagrangian is degenerate. Based on a geometric setting, an appropriate variational formulation is presented to model the circuit from which the equations of motion are derived. A time-discrete variational formulation provides an iteration scheme for the simulation of the electric circuit. Dependent on the discretization, the intrinsic degeneracy of the system can be canceled for the discrete variational scheme. In this way, a variational integrator is constructed that gains several advantages compared to standard integration tools for circuits; in particular, a comparison to BDF methods (which are usually the method of choice for the simulation of electric circuits) shows that even for simple LCR circuits, a better energy behavior and frequency spectrum preservation can be observed using the developed variational integrator

Time-discrete higher order ALE formulations: a priori error analysis

KAUST Repository

Bonito, Andrea

2013-03-16

We derive optimal a priori error estimates for discontinuous Galerkin (dG) time discrete schemes of any order applied to an advection-diffusion model defined on moving domains and written in the Arbitrary Lagrangian Eulerian (ALE) framework. Our estimates hold without any restrictions on the time steps for dG with exact integration or Reynolds\\' quadrature. They involve a mild restriction on the time steps for the practical Runge-Kutta-Radau methods of any order. The key ingredients are the stability results shown earlier in Bonito et al. (Time-discrete higher order ALE formulations: stability, 2013) along with a novel ALE projection. Numerical experiments illustrate and complement our theoretical results. © 2013 Springer-Verlag Berlin Heidelberg.

Discretization of Lévy semistationary processes with application to estimation

DEFF Research Database (Denmark)

Bennedsen, Mikkel; Lunde, Asger; Pakkanen, Mikko

Motivated by the construction of the Ito stochastic integral, we consider a step function method to discretize and simulate volatility modulated Lévy semistationary processes. Moreover, we assess the accuracy of the method with a particular focus on integrating kernels with a singularity...... at the origin. Using the simulation method, we study the finite sample properties of some recently developed estimators of realized volatility and associated parametric estimators for Brownian semistationary processes. Although the theoretical properties of these estimators have been established under high...

A discrete exterior approach to structure-preserving discretization of distributed-parameter port-Hamiltonian systems

NARCIS (Netherlands)

Seslija, Marko; Scherpen, Jacquelien M.A.; van der Schaft, Arjan

2011-01-01

This paper addresses the issue of structure-preserving discretization of open distributed-parameter systems with Hamiltonian dynamics. Employing the formalism of discrete exterior calculus, we introduce simplicial Dirac structures as discrete analogues of the Stokes-Dirac structure and demonstrate

Flexible Visual Quality Inspection in Discrete Manufacturing

OpenAIRE

Petković, Tomislav; Jurić, Darko; Lončarić, Sven

2013-01-01

Most visual quality inspections in discrete manufacturing are composed of length, surface, angle or intensity measurements. Those are implemented as end-user configurable inspection tools that should not require an image processing expert to set up. Currently available software solutions providing such capability use a flowchart based programming environment, but do not fully address an inspection flowchart robustness and can require a redefinition of the flowchart if a small variation is int...

Discrete exterior geometry approach to structure-preserving discretization of distributed-parameter port-Hamiltonian systems

NARCIS (Netherlands)

Seslija, Marko; van der Schaft, Arjan; Scherpen, Jacquelien M.A.

This paper addresses the issue of structure-preserving discretization of open distributed-parameter systems with Hamiltonian dynamics. Employing the formalism of discrete exterior calculus, we introduce a simplicial Dirac structure as a discrete analogue of the Stokes-Dirac structure and demonstrate

Discrete computational mechanics for stiff phenomena

KAUST Repository

Michels, Dominik L.

2016-11-28

Many natural phenomena which occur in the realm of visual computing and computational physics, like the dynamics of cloth, fibers, fluids, and solids as well as collision scenarios are described by stiff Hamiltonian equations of motion, i.e. differential equations whose solution spectra simultaneously contain extremely high and low frequencies. This usually impedes the development of physically accurate and at the same time efficient integration algorithms. We present a straightforward computationally oriented introduction to advanced concepts from classical mechanics. We provide an easy to understand step-by-step introduction from variational principles over the Euler-Lagrange formalism and the Legendre transformation to Hamiltonian mechanics. Based on such solid theoretical foundations, we study the underlying geometric structure of Hamiltonian systems as well as their discrete counterparts in order to develop sophisticated structure preserving integration algorithms to efficiently perform high fidelity simulations.

Lax pair and exact solutions of a discrete coupled system related to coupled KdV and coupled mKdV equations

International Nuclear Information System (INIS)

Liu Ping; Jia Man; Lou Senyue

2007-01-01

A modified Korteweg-de Vries (mKdV) lattice is also found to be a discrete Korteweg-de Vries (KdV) equation in this paper. The Lax pair for the discrete equation is found with the help of the Lax pair for a similar discrete equation. A Lax-integrable coupled extension of the lattice is posed, which is a common discrete version of both the coupled KdV and coupled mKdV systems. Some rational expansions of the Jacobian elliptic, trigonometric and hyperbolic functions are used to construct cnoidal waves, negaton and positon solutions of the discrete coupled system

The discrete null space method for the energy-consistent integration of constrained mechanical systems. Part III: Flexible multibody dynamics

International Nuclear Information System (INIS)

Leyendecker, Sigrid; Betsch, Peter; Steinmann, Paul

2008-01-01

In the present work, the unified framework for the computational treatment of rigid bodies and nonlinear beams developed by Betsch and Steinmann (Multibody Syst. Dyn. 8, 367-391, 2002) is extended to the realm of nonlinear shells. In particular, a specific constrained formulation of shells is proposed which leads to the semi-discrete equations of motion characterized by a set of differential-algebraic equations (DAEs). The DAEs provide a uniform description for rigid bodies, semi-discrete beams and shells and, consequently, flexible multibody systems. The constraints may be divided into two classes: (i) internal constraints which are intimately connected with the assumption of rigidity of the bodies, and (ii) external constraints related to the presence of joints in a multibody framework. The present approach thus circumvents the use of rotational variables throughout the whole time discretization, facilitating the design of energy-momentum methods for flexible multibody dynamics. After the discretization has been completed a size-reduction of the discrete system is performed by eliminating the constraint forces. Numerical examples dealing with a spatial slider-crank mechanism and with intersecting shells illustrate the performance of the proposed method

The Role of Discrete Global Grid Systems in the Global Statistical Geospatial Framework

Science.gov (United States)

Purss, M. B. J.; Peterson, P.; Minchin, S. A.; Bermudez, L. E.

2016-12-01

The United Nations Committee of Experts on Global Geospatial Information Management (UN-GGIM) has proposed the development of a Global Statistical Geospatial Framework (GSGF) as a mechanism for the establishment of common analytical systems that enable the integration of statistical and geospatial information. Conventional coordinate reference systems address the globe with a continuous field of points suitable for repeatable navigation and analytical geometry. While this continuous field is represented on a computer in a digitized and discrete fashion by tuples of fixed-precision floating point values, it is a non-trivial exercise to relate point observations spatially referenced in this way to areal coverages on the surface of the Earth. The GSGF states the need to move to gridded data delivery and the importance of using common geographies and geocoding. The challenges associated with meeting these goals are not new and there has been a significant effort within the geospatial community to develop nested gridding standards to tackle these issues over many years. These efforts have recently culminated in the development of a Discrete Global Grid Systems (DGGS) standard which has been developed under the auspices of Open Geospatial Consortium (OGC). DGGS provide a fixed areal based geospatial reference frame for the persistent location of measured Earth observations, feature interpretations, and modelled predictions. DGGS address the entire planet by partitioning it into a discrete hierarchical tessellation of progressively finer resolution cells, which are referenced by a unique index that facilitates rapid computation, query and analysis. The geometry and location of the cell is the principle aspect of a DGGS. Data integration, decomposition, and aggregation is optimised in the DGGS hierarchical structure and can be exploited for efficient multi-source data processing, storage, discovery, transmission, visualization, computation, analysis, and modelling. During

Numerical Method for Darcy Flow Derived Using Discrete Exterior Calculus

Science.gov (United States)

Hirani, A. N.; Nakshatrala, K. B.; Chaudhry, J. H.

2015-05-01

We derive a numerical method for Darcy flow, and also for Poisson's equation in mixed (first order) form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is one of its discretizations on simplicial complexes such as triangle and tetrahedral meshes. DEC is a coordinate invariant discretization, in that it does not depend on the embedding of the simplices or the whole mesh. We start by rewriting the governing equations of Darcy flow using the language of exterior calculus. This yields a formulation in terms of flux differential form and pressure. The numerical method is then derived by using the framework provided by DEC for discretizing differential forms and operators that act on forms. We also develop a discretization for a spatially dependent Hodge star that varies with the permeability of the medium. This also allows us to address discontinuous permeability. The matrix representation for our discrete non-homogeneous Hodge star is diagonal, with positive diagonal entries. The resulting linear system of equations for flux and pressure are saddle type, with a diagonal matrix as the top left block. The performance of the proposed numerical method is illustrated on many standard test problems. These include patch tests in two and three dimensions, comparison with analytically known solutions in two dimensions, layered medium with alternating permeability values, and a test with a change in permeability along the flow direction. We also show numerical evidence of convergence of the flux and the pressure. A convergence experiment is included for Darcy flow on a surface. A short introduction to the relevant parts of smooth and discrete exterior calculus is included in this article. We also include a discussion of the boundary condition in terms of exterior calculus.

A New Approach to Rational Discrete-Time Approximations to Continuous-Time Fractional-Order Systems

OpenAIRE

Matos , Carlos; Ortigueira , Manuel ,

2012-01-01

Part 10: Signal Processing; International audience; In this paper a new approach to rational discrete-time approximations to continuous fractional-order systems of the form 1/(sα+p) is proposed. We will show that such fractional-order LTI system can be decomposed into sub-systems. One has the classic behavior and the other is similar to a Finite Impulse Response (FIR) system. The conversion from continuous-time to discrete-time systems will be done using the Laplace transform inversion integr...

Discrete Mathematics

DEFF Research Database (Denmark)

Sørensen, John Aasted

2010-01-01

The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18...

Discrete Mathematics

DEFF Research Database (Denmark)

Sørensen, John Aasted

2010-01-01

The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15...

Space-Time Discrete KPZ Equation

Science.gov (United States)

Cannizzaro, G.; Matetski, K.

2018-03-01

We study a general family of space-time discretizations of the KPZ equation and show that they converge to its solution. The approach we follow makes use of basic elements of the theory of regularity structures (Hairer in Invent Math 198(2):269-504, 2014) as well as its discrete counterpart (Hairer and Matetski in Discretizations of rough stochastic PDEs, 2015. arXiv:1511.06937). Since the discretization is in both space and time and we allow non-standard discretization for the product, the methods mentioned above have to be suitably modified in order to accommodate the structure of the models under study.

Geometric integration of the Vlasov-Maxwell system with a variational particle-in-cell scheme

Energy Technology Data Exchange (ETDEWEB)

Squire, J.; Tang, W. M. [Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States); Qin, H. [Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States); Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026 (China)

2012-08-15

A fully variational, unstructured, electromagnetic particle-in-cell integrator is developed for integration of the Vlasov-Maxwell equations. Using the formalism of discrete exterior calculus [Desbrun et al., e-print arXiv:math/0508341 (2005)], the field solver, interpolation scheme, and particle advance algorithm are derived through minimization of a single discrete field theory action. As a consequence of ensuring that the action is invariant under discrete electromagnetic gauge transformations, the integrator exactly conserves Gauss's law.

Integrated nanohole array surface plasmon resonance sensing device using a dual-wavelength source

International Nuclear Information System (INIS)

Escobedo, C; Vincent, S; Choudhury, A I K; Campbell, J; Gordon, R; Brolo, A G; Sinton, D

2011-01-01

In this paper, we demonstrate a compact integrated nanohole array-based surface plasmon resonance sensing device. The unit includes a LED light source, driving circuitry, CCD detector, microfluidic network and computer interface, all assembled from readily available commercial components. A dual-wavelength LED scheme was implemented to increase spectral diversity and isolate intensity variations to be expected in the field. The prototype shows bulk sensitivity of 266 pixel intensity units/RIU and a limit of detection of 6 × 10 −4 RIU. Surface binding tests were performed, demonstrating functionality as a surface-based sensing system. This work is particularly relevant for low-cost point-of-care applications, especially those involving multiple tests and field studies. While nanohole arrays have been applied to many sensing applications, and their suitability to device integration is well established, this is the first demonstration of a fully integrated nanohole array-based sensing device.

Poisson hierarchy of discrete strings

International Nuclear Information System (INIS)

Ioannidou, Theodora; Niemi, Antti J.

2016-01-01

The Poisson geometry of a discrete string in three dimensional Euclidean space is investigated. For this the Frenet frames are converted into a spinorial representation, the discrete spinor Frenet equation is interpreted in terms of a transfer matrix formalism, and Poisson brackets are introduced in terms of the spinor components. The construction is then generalised, in a self-similar manner, into an infinite hierarchy of Poisson algebras. As an example, the classical Virasoro (Witt) algebra that determines reparametrisation diffeomorphism along a continuous string, is identified as a particular sub-algebra, in the hierarchy of the discrete string Poisson algebra. - Highlights: • Witt (classical Virasoro) algebra is derived in the case of discrete string. • Infinite dimensional hierarchy of Poisson bracket algebras is constructed for discrete strings. • Spinor representation of discrete Frenet equations is developed.

Poisson hierarchy of discrete strings

Energy Technology Data Exchange (ETDEWEB)

Ioannidou, Theodora, E-mail: ti3@auth.gr [Faculty of Civil Engineering, School of Engineering, Aristotle University of Thessaloniki, 54249, Thessaloniki (Greece); Niemi, Antti J., E-mail: Antti.Niemi@physics.uu.se [Department of Physics and Astronomy, Uppsala University, P.O. Box 803, S-75108, Uppsala (Sweden); Laboratoire de Mathematiques et Physique Theorique CNRS UMR 6083, Fédération Denis Poisson, Université de Tours, Parc de Grandmont, F37200, Tours (France); Department of Physics, Beijing Institute of Technology, Haidian District, Beijing 100081 (China)

2016-01-28

The Poisson geometry of a discrete string in three dimensional Euclidean space is investigated. For this the Frenet frames are converted into a spinorial representation, the discrete spinor Frenet equation is interpreted in terms of a transfer matrix formalism, and Poisson brackets are introduced in terms of the spinor components. The construction is then generalised, in a self-similar manner, into an infinite hierarchy of Poisson algebras. As an example, the classical Virasoro (Witt) algebra that determines reparametrisation diffeomorphism along a continuous string, is identified as a particular sub-algebra, in the hierarchy of the discrete string Poisson algebra. - Highlights: • Witt (classical Virasoro) algebra is derived in the case of discrete string. • Infinite dimensional hierarchy of Poisson bracket algebras is constructed for discrete strings. • Spinor representation of discrete Frenet equations is developed.

Discrete nature of thermodynamics in confined ideal Fermi gases

International Nuclear Information System (INIS)

Aydin, Alhun; Sisman, Altug

2014-01-01

Intrinsic discrete nature in thermodynamic properties of Fermi gases appears under strongly confined and degenerate conditions. For a rectangular confinement domain, thermodynamic properties of an ideal Fermi gas are expressed in their exact summation forms. For 1D, 2D and 3D nano domains, variations of both number of particles and internal energy per particle with chemical potential are examined. It is shown that their relation with chemical potential exhibits a discrete nature which allows them to take only some definite values. Furthermore, quasi-irregular oscillatory-like sharp peaks are observed in heat capacity. New nano devices can be developed based on these behaviors. - Highlights: • “Discrete behaviors” appear in thermodynamic properties of ideal Fermi gases at nano scale. • Variations of particle number and internal energy with chemical potential have stepwise behavior. • There are oscillations and peaks in the variation of heat capacity with domain size and particle number. • Fermi line and Fermi surface at nano scale are not continuous but “discrete”. • Heat capacity oscillations can be used for excess thermal energy storage at nano scale

Ultradiscrete sine-Gordon Equation over Symmetrized Max-Plus Algebra, and Noncommutative Discrete and Ultradiscrete sine-Gordon Equations

Directory of Open Access Journals (Sweden)

Kenichi Kondo

2013-11-01

Full Text Available Ultradiscretization with negative values is a long-standing problem and several attempts have been made to solve it. Among others, we focus on the symmetrized max-plus algebra, with which we ultradiscretize the discrete sine-Gordon equation. Another ultradiscretization of the discrete sine-Gordon equation has already been proposed by previous studies, but the equation and the solutions obtained here are considered to directly correspond to the discrete counterpart. We also propose a noncommutative discrete analogue of the sine-Gordon equation, reveal its relations to other integrable systems including the noncommutative discrete KP equation, and construct multisoliton solutions by a repeated application of Darboux transformations. Moreover, we derive a noncommutative ultradiscrete analogue of the sine-Gordon equation and its 1-soliton and 2-soliton solutions, using the symmetrized max-plus algebra. As a result, we have a complete set of commutative and noncommutative versions of continuous, discrete, and ultradiscrete sine-Gordon equations.

Discrete energy formulation of neutron transport theory applied to solving the discrete ordinates equations

International Nuclear Information System (INIS)

Ching, J.; Oblow, E.M.; Goldstein, H.

1976-01-01

An algebraic equivalence between the point-energy and multigroup forms of the Boltzmann transport equation is demonstrated that allows the development of a discrete energy, discrete ordinates method for the solution of radiation transport problems. In the discrete energy method, the group averaging required in the cross-section processing for multigroup calculations is replaced by a faster numerical quadrature scheme capable of generating transfer cross sections describing all the physical processes of interest on a fine point-energy grid. Test calculations in which the discrete energy method is compared with the multigroup method show that, for the same energy grid, the discrete energy method is much faster, although somewhat less accurate, than the multigroup method. However, the accuracy of the discrete energy method increases rapidly as the spacing between energy grid points is decreased, approaching that of multigroup calculations. For problems requiring great detail in the energy spectrum, the discrete energy method is therefore expected to be far more economical than the multigroup technique for equivalent accuracy solutions. This advantage of the point method is demonstrated by application to the study of neutron transport in a thick iron slab

3-D Discrete Analytical Ridgelet Transform

OpenAIRE

Helbert , David; Carré , Philippe; Andrès , Éric

2006-01-01

International audience; In this paper, we propose an implementation of the 3-D Ridgelet transform: the 3-D discrete analytical Ridgelet transform (3-D DART). This transform uses the Fourier strategy for the computation of the associated 3-D discrete Radon transform. The innovative step is the definition of a discrete 3-D transform with the discrete analytical geometry theory by the construction of 3-D discrete analytical lines in the Fourier domain. We propose two types of 3-D discrete lines:...

Discrete fractional calculus

CERN Document Server

Goodrich, Christopher

2015-01-01

This text provides the first comprehensive treatment of the discrete fractional calculus. Experienced researchers will find the text useful as a reference for discrete fractional calculus and topics of current interest. Students who are interested in learning about discrete fractional calculus will find this text to provide a useful starting point. Several exercises are offered at the end of each chapter and select answers have been provided at the end of the book. The presentation of the content is designed to give ample flexibility for potential use in a myriad of courses and for independent study. The novel approach taken by the authors includes a simultaneous treatment of the fractional- and integer-order difference calculus (on a variety of time scales, including both the usual forward and backwards difference operators). The reader will acquire a solid foundation in the classical topics of the discrete calculus while being introduced to exciting recent developments, bringing them to the frontiers of the...

Intelligent shell feedback control in EXTRAP T2R reversed field pinch with partial coverage of the toroidal surface by a discrete active coil array

Science.gov (United States)

Yadikin, D.; Brunsell, P. R.; Drake, J. R.

2006-01-01

An active feedback system is required for long pulse operation of the reversed field pinch (RFP) device to suppress resistive wall modes (RWMs). A general feature of a feedback system using a discrete active coil array is a coupling effect which arises when a set of side band modes determined by the number of active coils is produced. Recent results obtained on the EXTRAP T2R RFP demonstrated the suppression of independent m = 1 RWMs using an active feedback system with a two-dimensional array of discrete active coils in the poloidal and toroidal directions. One of the feedback algorithms used is the intelligent shell feedback scheme. Active feedback systems having different number of active coils in the poloidal (Mc) and toroidal (Nc) directions (Mc × Nc = 2 × 32 and Mc × Nc = 4 × 16) are studied. Different side band effects are seen for these configurations. A significant prolongation of the plasma discharge is achieved for the intelligent shell feedback scheme using the 2 × 32 active coil configuration. This is attributed to the side band sets including only one of the dominant unstable RWMs and avoiding coupling to resonant modes. Analog proportional-integral-derivative controllers are used in the feedback system. Regimes with different values of the proportional gain are studied. The requirement of the proportional-integral control for low proportional gain and proportional-derivative control for high proportional gain is seen in the experiments.

Flat norm decomposition of integral currents

Directory of Open Access Journals (Sweden)

Sharif Ibrahim

2016-05-01

Full Text Available Currents represent generalized surfaces studied in geometric measure theory. They range from relatively tame integral currents representing oriented compact manifolds with boundary and integer multiplicities, to arbitrary elements of the dual space of differential forms. The flat norm provides a natural distance in the space of currents, and works by decomposing a $d$-dimensional current into $d$- and (the boundary of $(d+1$-dimensional pieces in an optimal way.Given an integral current, can we expect its at norm decomposition to be integral as well? This is not known in general, except in the case of $d$-currents that are boundaries of $(d+1$-currents in $\\mathbb{R}^{d+1}$ (following results from a corresponding problem on the $L^1$ total variation ($L^1$TV of functionals. On the other hand, for a discretized at norm on a finite simplicial complex, the analogous statement holds even when the inputs are not boundaries. This simplicial version relies on the total unimodularity of the boundary matrix of the simplicial complex; a result distinct from the $L^1$TV approach.We develop an analysis framework that extends the result in the simplicial setting to one for $d$-currents in $\\mathbb{R}^{d+1}$, provided a suitable triangulation result holds. In $\\mathbb{R}^2$, we use a triangulation result of Shewchuk (bounding both the size and location of small angles, and apply the framework to show that the discrete result implies the continuous result for $1$-currents in $\\mathbb{R}^2$ .

[Correlative analysis of the diversity patterns of regional surface water, NDVI and thermal environment].

Science.gov (United States)

Duan, Jin-Long; Zhang, Xue-Lei

2012-10-01

Taking Zhengzhou City, the capital of Henan Province in Central China, as the study area, and by using the theories and methodologies of diversity, a discreteness evaluation on the regional surface water, normalized difference vegetation index (NDVI), and land surface temperature (LST) distribution was conducted in a 2 km x 2 km grid scale. Both the NDVI and the LST were divided into 4 levels, their spatial distribution diversity indices were calculated, and their connections were explored. The results showed that it was of operability and practical significance to use the theories and methodologies of diversity in the discreteness evaluation of the spatial distribution of regional thermal environment. There was a higher overlap of location between the distributions of surface water and the lowest temperature region, and the high vegetation coverage was often accompanied by low land surface temperature. In 1988-2009, the discreteness of the surface water distribution in the City had an obvious decreasing trend. The discreteness of the surface water distribution had a close correlation with the discreteness of the temperature region distribution, while the discreteness of the NDVI classification distribution had a more complicated correlation with the discreteness of the temperature region distribution. Therefore, more environmental factors were needed to be included for a better evaluation.

Unfolding and effective bandstructure calculations as discrete real- and reciprocal-space operations

Energy Technology Data Exchange (ETDEWEB)

Boykin, Timothy B., E-mail: boykin@ece.uah.edu [Department of Electrical and Computer Engineering, The University of Alabama in Huntsville, Huntsville, AL 35899 (United States); Ajoy, Arvind [School of Electrical and Computer Engineering, Cornell University, Ithaca, NY 14853 (United States); Ilatikhameneh, Hesameddin; Povolotskyi, Michael; Klimeck, Gerhard [Network for Computational Nanotechnology, School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907 (United States)

2016-06-15

In recent years, alloy electronic structure calculations based on supercell Brillouin zone unfolding have become popular. There are a number of formulations of the method which on the surface might appear different. Here we show that a discrete real-space description, based on discrete Fourier transforms, is fully general. Furthermore, such an approach can more easily show the effects of alloy scattering. We present such a method for treating the random alloy problem. This treatment features straightforward mathematics and a transparent physical interpretation of the calculated effective (i.e., approximate) energy bands.

Roughness Versus Charge Contributions to Representative Discrete Heterogeneity Underlying Mechanistic Prediction of Colloid Attachment, Detachment and Breakthrough-Elution Behavior Under Environmental Conditions.

Science.gov (United States)

Johnson, William; Farnsworth, Anna; Vanness, Kurt; Hilpert, Markus

2017-04-01

The key element of a mechanistic theory to predict colloid attachment in porous media under environmental conditions where colloid-collector repulsion exists (unfavorable conditions for attachment) is representation of the nano-scale surface heterogeneity (herein called discrete heterogeneity) that drives colloid attachment under unfavorable conditions. The observed modes of colloid attachment under unfavorable conditions emerge from simulations that incorporate discrete heterogeneity. Quantitative prediction of attachment (and detachment) requires capturing the sizes, spatial frequencies, and other properties of roughness asperities and charge heterodomains in discrete heterogeneity representations of different surfaces. The fact that a given discrete heterogeneity representation will interact differently with different-sized colloids as well as different ionic strengths for a given sized colloid allows backing out representative discrete heterogeneity via comparison of simulations to experiments performed across a range of colloid size, solution IS, and fluid velocity. This has been achieved on unfavorable smooth surfaces yielding quantitative prediction of attachment, and qualitative prediction of detachment in response to ionic strength or flow perturbations. Extending this treatment to rough surfaces, and representing the contributions of nanoscale roughness as well as charge heterogeneity is a focus of this talk. Another focus of this talk is the upscaling the pore scale simulations to produce contrasting breakthrough-elution behaviors at the continuum (column) scale that are observed, for example, for different-sized colloids, or same-sized colloids under different ionic strength conditions. The outcome of mechanistic pore scale simulations incorporating discrete heterogeneity and subsequent upscaling is that temporal processes such as blocking and ripening will emerge organically from these simulations, since these processes fundamentally stem from the

Modeling nanostructural surface modifications in metal cutting by an approach of thermodynamic irreversibility: Derivation and experimental validation

Science.gov (United States)

Buchkremer, S.; Klocke, F.

2017-01-01

Performance and operational safety of many metal parts in engineering depend on their surface integrity. During metal cutting, large thermomechanical loads and high gradients of the loads concerning time and location act on the surfaces and may yield significant structural material modifications, which alter the surface integrity. In this work, the derivation and validation of a model of nanostructural surface modifications in metal cutting are presented. For the first time in process modeling, initiation and kinetics of these modifications are predicted using a thermodynamic potential, which considers the interdependent developments of plastic work, dissipation, heat conduction and interface energy as well as the associated productions and flows of entropy. The potential is expressed based on the free Helmholtz energy. The irreversible thermodynamic state changes in the workpiece surface are homogenized over the volume in order to bridge the gap between discrete phenomena involved with the initiation and kinetics of dynamic recrystallization and its macroscopic implications for surface integrity. The formulation of the thermodynamic potential is implemented into a finite element model of orthogonal cutting of steel AISI 4140. Close agreement is achieved between predicted nanostructures and those obtained in transmission electron microscopical investigations of specimen produced in cutting experiments.

Homogenization of discrete media

International Nuclear Information System (INIS)

Pradel, F.; Sab, K.

1998-01-01

Material such as granular media, beam assembly are easily seen as discrete media. They look like geometrical points linked together thanks to energetic expressions. Our purpose is to extend discrete kinematics to the one of an equivalent continuous material. First we explain how we build the localisation tool for periodic materials according to estimated continuum medium type (classical Cauchy, and Cosserat media). Once the bridge built between discrete and continuum media, we exhibit its application over two bidimensional beam assembly structures : the honey comb and a structural reinforced variation. The new behavior is then applied for the simple plan shear problem in a Cosserat continuum and compared with the real discrete solution. By the mean of this example, we establish the agreement of our new model with real structures. The exposed method has a longer range than mechanics and can be applied to every discrete problems like electromagnetism in which relationship between geometrical points can be summed up by an energetic function. (orig.)

Homogenization of discrete media

Energy Technology Data Exchange (ETDEWEB)

Pradel, F.; Sab, K. [CERAM-ENPC, Marne-la-Vallee (France)

1998-11-01

Material such as granular media, beam assembly are easily seen as discrete media. They look like geometrical points linked together thanks to energetic expressions. Our purpose is to extend discrete kinematics to the one of an equivalent continuous material. First we explain how we build the localisation tool for periodic materials according to estimated continuum medium type (classical Cauchy, and Cosserat media). Once the bridge built between discrete and continuum media, we exhibit its application over two bidimensional beam assembly structures : the honey comb and a structural reinforced variation. The new behavior is then applied for the simple plan shear problem in a Cosserat continuum and compared with the real discrete solution. By the mean of this example, we establish the agreement of our new model with real structures. The exposed method has a longer range than mechanics and can be applied to every discrete problems like electromagnetism in which relationship between geometrical points can be summed up by an energetic function. (orig.) 7 refs.

Continuous limits for an integrable coupling system of Toda equation hierarchy

International Nuclear Information System (INIS)

Li Li; Yu Fajun

2009-01-01

In this Letter, we present an integrable coupling system of lattice hierarchy and its continuous limits by using of Lie algebra sl(4). By introducing a complex discrete spectral problem, the integrable coupling system of Toda lattice hierarchy is derived. It is shown that a new complex lattice spectral problem converges to the integrable couplings of discrete soliton equation hierarchy, which has the integrable coupling system of C-KdV hierarchy as a new kind of continuous limit.

Continuous limits for an integrable coupling system of Toda equation hierarchy

Energy Technology Data Exchange (ETDEWEB)

Li Li [College of Maths and Systematic Science, Shenyang Normal University, Shenyang 110034 (China); Yu Fajun, E-mail: yfajun@163.co [College of Maths and Systematic Science, Shenyang Normal University, Shenyang 110034 (China)

2009-09-21

In this Letter, we present an integrable coupling system of lattice hierarchy and its continuous limits by using of Lie algebra sl(4). By introducing a complex discrete spectral problem, the integrable coupling system of Toda lattice hierarchy is derived. It is shown that a new complex lattice spectral problem converges to the integrable couplings of discrete soliton equation hierarchy, which has the integrable coupling system of C-KdV hierarchy as a new kind of continuous limit.

Discrete-Time Sliding-Mode Control of Uncertain Systems with Time-Varying Delays via Descriptor Approach

Directory of Open Access Journals (Sweden)

Maode Yan

2008-01-01

Full Text Available This paper considers the problem of robust discrete-time sliding-mode control (DT-SMC design for a class of uncertain linear systems with time-varying delays. By applying a descriptor model transformation and Moon's inequality for bounding cross terms, a delay-dependent sufficient condition for the existence of stable sliding surface is given in terms of linear matrix inequalities (LMIs. Based on this existence condition, the synthesized sliding mode controller can guarantee the sliding-mode reaching condition of the specified discrete-time sliding surface for all admissible uncertainties and time-varying delays. An illustrative example verifies the effectiveness of the proposed method.

A discrete fibre dispersion method for excluding fibres under compression in the modelling of fibrous tissues.

Science.gov (United States)

Li, Kewei; Ogden, Ray W; Holzapfel, Gerhard A

2018-01-01

Recently, micro-sphere-based methods derived from the angular integration approach have been used for excluding fibres under compression in the modelling of soft biological tissues. However, recent studies have revealed that many of the widely used numerical integration schemes over the unit sphere are inaccurate for large deformation problems even without excluding fibres under compression. Thus, in this study, we propose a discrete fibre dispersion model based on a systematic method for discretizing a unit hemisphere into a finite number of elementary areas, such as spherical triangles. Over each elementary area, we define a representative fibre direction and a discrete fibre density. Then, the strain energy of all the fibres distributed over each elementary area is approximated based on the deformation of the representative fibre direction weighted by the corresponding discrete fibre density. A summation of fibre contributions over all elementary areas then yields the resultant fibre strain energy. This treatment allows us to exclude fibres under compression in a discrete manner by evaluating the tension-compression status of the representative fibre directions only. We have implemented this model in a finite-element programme and illustrate it with three representative examples, including simple tension and simple shear of a unit cube, and non-homogeneous uniaxial extension of a rectangular strip. The results of all three examples are consistent and accurate compared with the previously developed continuous fibre dispersion model, and that is achieved with a substantial reduction of computational cost. © 2018 The Author(s).

A Fully Integrated Discrete-Time Superheterodyne Receiver

NARCIS (Netherlands)

Tohidian, M.; Madadi, I.; Staszewski, R.B.

2017-01-01

The zero/low intermediate frequency (IF) receiver (RX) architecture has enabled full CMOS integration. As the technology scales and wireless standards become ever more challenging, the issues related to time-varying dc offsets, the second-order nonlinearity, and flicker noise become more critical.

Distributed mean curvature on a discrete manifold for Regge calculus

International Nuclear Information System (INIS)

Conboye, Rory; Miller, Warner A; Ray, Shannon

2015-01-01

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

Distributed mean curvature on a discrete manifold for Regge calculus

Science.gov (United States)

Conboye, Rory; Miller, Warner A.; Ray, Shannon

2015-09-01

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

Signal Integrity Applications of an EBG Surface

Directory of Open Access Journals (Sweden)

MATEKOVITS, L.

2015-05-01

Full Text Available Electromagnetic band-gap (EBG surfaces have found applications in mitigation of parallel-plate noise that occurs in high speed circuits. A 2D periodic structure previously introduced by the same authors is dimensioned here for adjusting EBG parameters in view of meeting applications requirements by decreasing the phase velocity of the propagating waves. This adjustment corresponds to decreasing the lower bound of the EBG spectra. The positions of the EBGs' in frequency are determined through full-wave simulation, by solving the corresponding eigenmode equation and by imposing the appropriate boundary conditions on all faces of the unit cell. The operation of a device relying on a finite surface is also demonstrated. Obtained results show that the proposed structure fits for the signal integrity related applications as verified also by comparing the transmission along a finite structure of an ideal signal line and one with an induced discontinuity.

Discrete fracture in quasi-brittle materials under compressive and tensile stress states

CSIR Research Space (South Africa)

Klerck, PA

2004-01-01

Full Text Available A method for modelling discrete fracture in geomaterials under tensile and compressive stress fields has been developed based on a Mohr-Coulomb failure surface in compression and three independent anisotropic rotating crack models in tension...

A discrete element based simulation framework to investigate particulate spray deposition processes

KAUST Repository

Mukherjee, Debanjan; Zohdi, Tarek I.

2015-01-01

© 2015 Elsevier Inc. This work presents a computer simulation framework based on discrete element method to analyze manufacturing processes that comprise a loosely flowing stream of particles in a carrier fluid being deposited on a target surface

The discrete ordinates method for solving the azimuthally dependent transport equation in plane geometry

International Nuclear Information System (INIS)

Chalhoub, Ezzat Selim

1997-01-01

The method of discrete ordinates is applied to the solution of the slab albedo problem with azimuthal dependence in transport theory. A new set of quadratures appropriate to the problem is introduced. In addition to the ANISN code, modified to include the proposed formalism, two new programs, PEESNC and PEESNA, which were created on the basis of the discrete ordinates formalism, using the direct integration method and the analytic solution method respectively, are used in the generation of results for a few sample problems. Program PEESNC was created to validate the results obtained with the discrete ordinates method and the finite difference approximation (ANISN), while program PEESNA was developed in order to implement an analytical discrete ordinates formalism, which provides more accurate results. The obtained results for selected sample problems are compared with highly accurate numerical results published in the literature. Compared to ANISN and PEESNC, program PEESNA presents a greater efficiency in execution time and much more precise numerical results. (author)

The approximate inverse in action: IV. Semi-discrete equations in a Banach space setting

International Nuclear Information System (INIS)

Schuster, T; Schöpfer, F; Rieder, A

2012-01-01

This article concerns the method of approximate inverse to solve semi-discrete, linear operator equations in Banach spaces. Semi-discrete means that we search for a solution in an infinite-dimensional Banach space having only a finite number of data available. In this sense the situation is applicable to a large variety of applications where a measurement process delivers a discretization of an infinite-dimensional data space. The method of approximate inverse computes scalar products of the data with pre-computed reconstruction kernels which are associated with mollifiers and the dual of the model operator. The convergence, approximation power and regularization property of this method when applied to semi-discrete operator equations in Hilbert spaces has been investigated in three prequels to this paper. Here we extend these results to a Banach space setting. We prove convergence and stability for general Banach spaces and reproduce the results specifically for the integration operator acting on the space of continuous functions. (paper)

Integrating Satellite, Radar and Surface Observation with Time and Space Matching

Science.gov (United States)

Ho, Y.; Weber, J.

2015-12-01

The Integrated Data Viewer (IDV) from Unidata is a Java™-based software framework for analyzing and visualizing geoscience data. It brings together the ability to display and work with satellite imagery, gridded data, surface observations, balloon soundings, NWS WSR-88D Level II and Level III RADAR data, and NOAA National Profiler Network data, all within a unified interface. Applying time and space matching on the satellite, radar and surface observation datasets will automatically synchronize the display from different data sources and spatially subset to match the display area in the view window. These features allow the IDV users to effectively integrate these observations and provide 3 dimensional views of the weather system to better understand the underlying dynamics and physics of weather phenomena.

Discrete complex images in modeling antennas over, below or penetrating the ground

International Nuclear Information System (INIS)

Arnautovski-Toseva, Vesna; Smokvarski, Aleksandar; Popovski, Borislav; Grcev, Leonid

2002-01-01

In this paper discrete complex images (DCI) are used to obtain approximate, efficient and fast solution of Sommerfeld integrals that appear in the analysis of vertical electric dipole (VED) in presence of air-ground half-space. The results are used to model vertical antenna above, below or penetrating the ground using the moment method technique with triangular expansion functions. Thus, the time consuming direct numerical evaluation of the Sommerfeld integrals is completely or partially avoided. (Author)

Discrete anti-gravity

International Nuclear Information System (INIS)

Noyes, H.P.; Starson, S.

1991-03-01

Discrete physics, because it replaces time evolution generated by the energy operator with a global bit-string generator (program universe) and replaces ''fields'' with the relativistic Wheeler-Feynman ''action at a distance,'' allows the consistent formulation of the concept of signed gravitational charge for massive particles. The resulting prediction made by this version of the theory is that free anti-particles near the surface of the earth will ''fall'' up with the same acceleration that the corresponding particles fall down. So far as we can see, no current experimental information is in conflict with this prediction of our theory. The experiment crusis will be one of the anti-proton or anti-hydrogen experiments at CERN. Our prediction should be much easier to test than the small effects which those experiments are currently designed to detect or bound. 23 refs

High order backward discretization of the neutron diffusion equation

Energy Technology Data Exchange (ETDEWEB)

Ginestar, D.; Bru, R.; Marin, J. [Universidad Politecnica de Valencia (Spain). Departamento de Matematica Aplicada; Verdu, G.; Munoz-Cobo, J.L. [Universidad Politecnica de Valencia (Spain). Departamento de Ingenieria Quimica y Nuclear; Vidal, V. [Universidad Politecnica de Valencia (Spain). Departamento de Sistemas Informaticos y Computacion

1997-11-21

Fast codes capable of dealing with three-dimensional geometries, are needed to be able to simulate spatially complicated transients in a nuclear reactor. We propose a new discretization technique for the time integration of the neutron diffusion equation, based on the backward difference formulas for systems of stiff ordinary differential equations. This method needs to solve a system of linear equations for each integration step, and for this purpose, we have developed an iterative block algorithm combined with a variational acceleration technique. We tested the algorithm with two benchmark problems, and compared the results with those provided by other codes, concluding that the performance and overall agreement are very good. (author).

A new doubly discrete analogue of smoke ring flow and the real time simulation of fluid flow

International Nuclear Information System (INIS)

Pinkall, Ulrich; Springborn, Boris; Weissmann, Steffen

2007-01-01

Modelling incompressible ideal fluids as a finite collection of vortex filaments is important in physics (super-fluidity, models for the onset of turbulence) as well as for numerical algorithms used in computer graphics for the real time simulation of smoke. Here we introduce a time-discrete evolution equation for arbitrary closed polygons in 3-space that is a discretization of the localized induction approximation of filament motion. This discretization shares with its continuum limit the property that it is a completely integrable system. We apply this polygon evolution to a significant improvement of the numerical algorithms used in computer graphics

Discrete elements method of neutron transport

International Nuclear Information System (INIS)

Mathews, K.A.

1988-01-01

In this paper a new neutron transport method, called discrete elements (L N ) is derived and compared to discrete ordinates methods, theoretically and by numerical experimentation. The discrete elements method is based on discretizing the Boltzmann equation over a set of elements of angle. The discrete elements method is shown to be more cost-effective than discrete ordinates, in terms of accuracy versus execution time and storage, for the cases tested. In a two-dimensional test case, a vacuum duct in a shield, the L N method is more consistently convergent toward a Monte Carlo benchmark solution

Discrete Sparse Coding.

Science.gov (United States)

Exarchakis, Georgios; Lücke, Jörg

2017-11-01

Sparse coding algorithms with continuous latent variables have been the subject of a large number of studies. However, discrete latent spaces for sparse coding have been largely ignored. In this work, we study sparse coding with latents described by discrete instead of continuous prior distributions. We consider the general case in which the latents (while being sparse) can take on any value of a finite set of possible values and in which we learn the prior probability of any value from data. This approach can be applied to any data generated by discrete causes, and it can be applied as an approximation of continuous causes. As the prior probabilities are learned, the approach then allows for estimating the prior shape without assuming specific functional forms. To efficiently train the parameters of our probabilistic generative model, we apply a truncated expectation-maximization approach (expectation truncation) that we modify to work with a general discrete prior. We evaluate the performance of the algorithm by applying it to a variety of tasks: (1) we use artificial data to verify that the algorithm can recover the generating parameters from a random initialization, (2) use image patches of natural images and discuss the role of the prior for the extraction of image components, (3) use extracellular recordings of neurons to present a novel method of analysis for spiking neurons that includes an intuitive discretization strategy, and (4) apply the algorithm on the task of encoding audio waveforms of human speech. The diverse set of numerical experiments presented in this letter suggests that discrete sparse coding algorithms can scale efficiently to work with realistic data sets and provide novel statistical quantities to describe the structure of the data.

A paradigm for discrete physics

International Nuclear Information System (INIS)

Noyes, H.P.; McGoveran, D.; Etter, T.; Manthey, M.J.; Gefwert, C.

1987-01-01

An example is outlined for constructing a discrete physics using as a starting point the insight from quantum physics that events are discrete, indivisible and non-local. Initial postulates are finiteness, discreteness, finite computability, absolute nonuniqueness (i.e., homogeneity in the absence of specific cause) and additivity

Development of an Integrated Nonlinear Aeroservoelastic Flight Dynamic Model of the NASA Generic Transport Model

Science.gov (United States)

Nguyen, Nhan; Ting, Eric

2018-01-01

This paper describes a recent development of an integrated fully coupled aeroservoelastic flight dynamic model of the NASA Generic Transport Model (GTM). The integrated model couples nonlinear flight dynamics to a nonlinear aeroelastic model of the GTM. The nonlinearity includes the coupling of the rigid-body aircraft states in the partial derivatives of the aeroelastic angle of attack. Aeroservoelastic modeling of the control surfaces which are modeled by the Variable Camber Continuous Trailing Edge Flap is also conducted. The R.T. Jones' method is implemented to approximate unsteady aerodynamics. Simulations of the GTM are conducted with simulated continuous and discrete gust loads..

Bi-integrable and tri-integrable couplings of a soliton hierarchy associated with SO(4

Directory of Open Access Journals (Sweden)

Zhang Jian

2017-03-01

Full Text Available In our paper, the theory of bi-integrable and tri-integrable couplings is generalized to the discrete case. First, based on the six-dimensional real special orthogonal Lie algebra SO(4, we construct bi-integrable and tri-integrable couplings associated with SO(4 for a hierarchy from the enlarged matrix spectral problems and the enlarged zero curvature equations. Moreover, Hamiltonian structures of the obtained bi-integrable and tri-integrable couplings are constructed by the variational identities.

Discrete-Event Simulation

Directory of Open Access Journals (Sweden)

Prateek Sharma

2015-04-01

Full Text Available Abstract Simulation can be regarded as the emulation of the behavior of a real-world system over an interval of time. The process of simulation relies upon the generation of the history of a system and then analyzing that history to predict the outcome and improve the working of real systems. Simulations can be of various kinds but the topic of interest here is one of the most important kind of simulation which is Discrete-Event Simulation which models the system as a discrete sequence of events in time. So this paper aims at introducing about Discrete-Event Simulation and analyzing how it is beneficial to the real world systems.

The discrete ordinate method in association with the finite-volume method in non-structured mesh; Methode des ordonnees discretes associee a la methode des volumes finis en maillage non structure

Energy Technology Data Exchange (ETDEWEB)

Le Dez, V; Lallemand, M [Ecole Nationale Superieure de Mecanique et d` Aerotechnique (ENSMA), 86 - Poitiers (France); Sakami, M; Charette, A [Quebec Univ., Chicoutimi, PQ (Canada). Dept. des Sciences Appliquees

1997-12-31

The description of an efficient method of radiant heat transfer field determination in a grey semi-transparent environment included in a 2-D polygonal cavity with surface boundaries that reflect the radiation in a purely diffusive manner is proposed, at the equilibrium and in radiation-conduction coupling situation. The technique uses simultaneously the finite-volume method in non-structured triangular mesh, the discrete ordinate method and the ray shooting method. The main mathematical developments and comparative results with the discrete ordinate method in orthogonal curvilinear coordinates are included. (J.S.) 10 refs.

The discrete ordinate method in association with the finite-volume method in non-structured mesh; Methode des ordonnees discretes associee a la methode des volumes finis en maillage non structure

Energy Technology Data Exchange (ETDEWEB)

Le Dez, V.; Lallemand, M. [Ecole Nationale Superieure de Mecanique et d`Aerotechnique (ENSMA), 86 - Poitiers (France); Sakami, M.; Charette, A. [Quebec Univ., Chicoutimi, PQ (Canada). Dept. des Sciences Appliquees

1996-12-31

The description of an efficient method of radiant heat transfer field determination in a grey semi-transparent environment included in a 2-D polygonal cavity with surface boundaries that reflect the radiation in a purely diffusive manner is proposed, at the equilibrium and in radiation-conduction coupling situation. The technique uses simultaneously the finite-volume method in non-structured triangular mesh, the discrete ordinate method and the ray shooting method. The main mathematical developments and comparative results with the discrete ordinate method in orthogonal curvilinear coordinates are included. (J.S.) 10 refs.

Modeling of Graphene Planar Grating in the THz Range by the Method of Singular Integral Equations

Science.gov (United States)

Kaliberda, Mstislav E.; Lytvynenko, Leonid M.; Pogarsky, Sergey A.

2018-04-01

Diffraction of the H-polarized electromagnetic wave by the planar graphene grating in the THz range is considered. The scattering and absorption characteristics are studied. The scattered field is represented in the spectral domain via unknown spectral function. The mathematical model is based on the graphene surface impedance and the method of singular integral equations. The numerical solution is obtained by the Nystrom-type method of discrete singularities.

Discrete breathers for a discrete nonlinear Schrödinger ring coupled to a central site.

Science.gov (United States)

Jason, Peter; Johansson, Magnus

2016-01-01

We examine the existence and properties of certain discrete breathers for a discrete nonlinear Schrödinger model where all but one site are placed in a ring and coupled to the additional central site. The discrete breathers we focus on are stationary solutions mainly localized on one or a few of the ring sites and possibly also the central site. By numerical methods, we trace out and study the continuous families the discrete breathers belong to. Our main result is the discovery of a split bifurcation at a critical value of the coupling between neighboring ring sites. Below this critical value, families form closed loops in a certain parameter space, implying that discrete breathers with and without central-site occupation belong to the same family. Above the split bifurcation the families split up into several separate ones, which bifurcate with solutions with constant ring amplitudes. For symmetry reasons, the families have different properties below the split bifurcation for even and odd numbers of sites. It is also determined under which conditions the discrete breathers are linearly stable. The dynamics of some simpler initial conditions that approximate the discrete breathers are also studied and the parameter regimes where the dynamics remain localized close to the initially excited ring site are related to the linear stability of the exact discrete breathers.

Discrete dynamics versus analytic dynamics

DEFF Research Database (Denmark)

Toxværd, Søren

2014-01-01

For discrete classical Molecular dynamics obtained by the “Verlet” algorithm (VA) with the time increment h there exists a shadow Hamiltonian H˜ with energy E˜(h) , for which the discrete particle positions lie on the analytic trajectories for H˜ . Here, we proof that there, independent...... of such an analytic analogy, exists an exact hidden energy invariance E * for VA dynamics. The fact that the discrete VA dynamics has the same invariances as Newtonian dynamics raises the question, which of the formulations that are correct, or alternatively, the most appropriate formulation of classical dynamics....... In this context the relation between the discrete VA dynamics and the (general) discrete dynamics investigated by Lee [Phys. Lett. B122, 217 (1983)] is presented and discussed....

A high-order boundary integral method for surface diffusions on elastically stressed axisymmetric rods.

Science.gov (United States)

Li, Xiaofan; Nie, Qing

2009-07-01

Many applications in materials involve surface diffusion of elastically stressed solids. Study of singularity formation and long-time behavior of such solid surfaces requires accurate simulations in both space and time. Here we present a high-order boundary integral method for an elastically stressed solid with axi-symmetry due to surface diffusions. In this method, the boundary integrals for isotropic elasticity in axi-symmetric geometry are approximated through modified alternating quadratures along with an extrapolation technique, leading to an arbitrarily high-order quadrature; in addition, a high-order (temporal) integration factor method, based on explicit representation of the mean curvature, is used to reduce the stability constraint on time-step. To apply this method to a periodic (in axial direction) and axi-symmetric elastically stressed cylinder, we also present a fast and accurate summation method for the periodic Green's functions of isotropic elasticity. Using the high-order boundary integral method, we demonstrate that in absence of elasticity the cylinder surface pinches in finite time at the axis of the symmetry and the universal cone angle of the pinching is found to be consistent with the previous studies based on a self-similar assumption. In the presence of elastic stress, we show that a finite time, geometrical singularity occurs well before the cylindrical solid collapses onto the axis of symmetry, and the angle of the corner singularity on the cylinder surface is also estimated.

3-D discrete analytical ridgelet transform.

Science.gov (United States)

Helbert, David; Carré, Philippe; Andres, Eric

2006-12-01

In this paper, we propose an implementation of the 3-D Ridgelet transform: the 3-D discrete analytical Ridgelet transform (3-D DART). This transform uses the Fourier strategy for the computation of the associated 3-D discrete Radon transform. The innovative step is the definition of a discrete 3-D transform with the discrete analytical geometry theory by the construction of 3-D discrete analytical lines in the Fourier domain. We propose two types of 3-D discrete lines: 3-D discrete radial lines going through the origin defined from their orthogonal projections and 3-D planes covered with 2-D discrete line segments. These discrete analytical lines have a parameter called arithmetical thickness, allowing us to define a 3-D DART adapted to a specific application. Indeed, the 3-D DART representation is not orthogonal, It is associated with a flexible redundancy factor. The 3-D DART has a very simple forward/inverse algorithm that provides an exact reconstruction without any iterative method. In order to illustrate the potentiality of this new discrete transform, we apply the 3-D DART and its extension to the Local-DART (with smooth windowing) to the denoising of 3-D image and color video. These experimental results show that the simple thresholding of the 3-D DART coefficients is efficient.

Discrete dislocation simulations of the flattening of nanoimprinted surfaces

International Nuclear Information System (INIS)

Zhang, Yunhe; Nicola, Lucia; Van der Giessen, Erik

2010-01-01

Simulations of rough surface flattening are performed on thin metal films whose roughness is created by nanoimprinting flat single crystals. The imprinting is carried out by means of a rigid template with equal flat contacts at varying spacing. The imprinted surfaces are subsequently flattened by a rigid platen, while the change of roughness and surface profile is computed. Attention is focused mainly on comparing the response of the film surfaces with those of identical films cleared of the dislocations and residual stresses left by the imprinting process. The aim of these studies is to understand to what extent the loading history affects deformation and roughness during flattening. The limiting cases of sticking and frictionless contact between rough surface and platen are analyzed. Results show that when the asperities are flattened such that the contact area is up to about one third of the surface area, the loading history strongly affects the flattening. Specifically, the presence of initial dislocations facilitates the squeezing of asperities independently of the friction conditions of the contact. For larger contact areas, the initial conditions affect only sticking contacts, while frictionless contacts lead to a homogeneous flattening of the asperities due to yield of the metal film. In all cases studied the final surface profile obtained after flattening has little to no resemblance to the original imprinted surface

Analysis of Discrete Mittag - Leffler Functions

Directory of Open Access Journals (Sweden)

N. Shobanadevi

2015-03-01

Full Text Available Discrete Mittag - Leffler functions play a major role in the development of the theory of discrete fractional calculus. In the present article, we analyze qualitative properties of discrete Mittag - Leffler functions and establish sufficient conditions for convergence, oscillation and summability of the infinite series associated with discrete Mittag - Leffler functions.

Difference Discrete Variational Principles, Euler-Lagrange Cohomology and Symplectic, Multisymplectic Structures I: Difference Discrete Variational Principle

Institute of Scientific and Technical Information of China (English)

GUO Han-Ying,; LI Yu-Qi; WU Ke1; WANG Shi-Kun

2002-01-01

In this first paper of a series, we study the difference discrete variational principle in the framework of multi-parameter differential approach by regarding the forward difference as an entire geometric object in view of noncommutative differential geometry. Regarding the difference as an entire geometric object, the difference discrete version of Legendre transformation can be introduced. By virtue of this variational principle, we can discretely deal with the variation problems in both the Lagrangian and Hamiltonian formalisms to get difference discrete Euler-Lagrange equations and canonical ones for the difference discrete versions of the classical mechanics and classical field theory.

Discrete focusing effect of positive ions by a plasma-sheath lens

International Nuclear Information System (INIS)

Stamate, E.; Sugai, H.

2005-01-01

We demonstrate that the sheath created adjacent to the surface of a negatively biased electrode that interfaces an insulator acts as a lens that focuses the positive ions to distinct regions on the surface. Thus, the positive ion flux is discrete, leading to the formation of a passive surface, of no ion impact, near the edge and an active surface at the center. Trajectories of positive ions within the sheath are obtained by solving in three dimensions the Poisson equation for electrodes of different geometry. Simulations are confirmed by developing the ion flux profile on the electrode surface as the sputtering pattern produced by ion impact. Measurements are performed in a dc plasma produced in Ar gas

Investigation of Selected Surface Integrity Features of Duplex Stainless Steel (DSS) after Turning

Czech Academy of Sciences Publication Activity Database

Krolczyk, G.; Nieslony, P.; Legutko, S.; Hloch, Sergej; Samardžić, I.

2015-01-01

Roč. 54, č. 1 (2015), s. 91-94 ISSN 0543-5846 Institutional support: RVO:68145535 Keywords : duplex stainless steel * machining * turning * surface integrity * surface roughness Subject RIV: JQ - Machines ; Tools Impact factor: 0.959, year: 2014 http://hrcak.srce.hr/126702

Discrete and modal focusing effects: principles and applications

DEFF Research Database (Denmark)

Stamate, Eugen

2012-01-01

Charge flux distribution on the surface of biased electrodes of different geometries immersed in a plasma is investigated by three-dimensional simulations and experiments. It is demonstrated that the sheath surrounding the electrodes that interface insulators acts as an electrostatic lens, focusing...... the charges to distinct locations on the electrode surface depending on the entrance coordinates at the sheath edge. Two focusing effects are identified. Discrete focusing leads to the formation of a passive surface of no ion impact, near the edge of the electrodes interfacing insulators. Modal focusing...... results in the formation of certain ‘modal spots’ and/or ‘modal lines’. Several phenomenological aspects and potential applications are reviewed and further discussed, including charge focusing by a three-dimensional plasma–sheath–lens, ion dose uniformity during plasma immersion ion implantation, mass...

Discrete mechanics

CERN Document Server

Caltagirone, Jean-Paul

2014-01-01

This book presents the fundamental principles of mechanics to re-establish the equations of Discrete Mechanics. It introduces physics and thermodynamics associated to the physical modeling.  The development and the complementarity of sciences lead to review today the old concepts that were the basis for the development of continuum mechanics. The differential geometry is used to review the conservation laws of mechanics. For instance, this formalism requires a different location of vector and scalar quantities in space. The equations of Discrete Mechanics form a system of equations where the H

Discrete mechanics

International Nuclear Information System (INIS)

Lee, T.D.

1985-01-01

This paper reviews the role of time throughout all phases of mechanics: classical mechanics, non-relativistic quantum mechanics, and relativistic quantum theory. As an example of the relativistic quantum field theory, the case of a massless scalar field interacting with an arbitrary external current is discussed. The comparison between the new discrete theory and the usual continuum formalism is presented. An example is given of a two-dimensional random lattice and its duel. The author notes that there is no evidence that the discrete mechanics is more appropriate than the usual continuum mechanics

New Positive and Negative Hierarchies of Integrable Differential-Difference Equations and Conservation Laws

International Nuclear Information System (INIS)

Li Xinyue; Zhao Qiulan

2009-01-01

Two hierarchies of nonlinear integrable positive and negative lattice equations are derived from a discrete spectral problem. The two lattice hierarchies are proved to have discrete zero curvature representations associated with a discrete spectral problem, which also shows that the positive and negative hierarchies correspond to positive and negative power expansions of Lax operators with respect to the spectral parameter, respectively. Moreover, the integrable lattice models in the positive hierarchy are of polynomial type, and the integrable lattice models in the negative hierarchy are of rational type. Further, we construct infinite conservation laws about the positive hierarchy.

Impacts of model initialization on an integrated surface water - groundwater model

KAUST Repository

Ajami, Hoori; McCabe, Matthew; Evans, Jason P.

2015-01-01

Integrated hydrologic models characterize catchment responses by coupling the subsurface flow with land surface processes. One of the major areas of uncertainty in such models is the specification of the initial condition and its influence

Synchronization Techniques in Parallel Discrete Event Simulation

OpenAIRE

Lindén, Jonatan

2018-01-01

Discrete event simulation is an important tool for evaluating system models in many fields of science and engineering. To improve the performance of large-scale discrete event simulations, several techniques to parallelize discrete event simulation have been developed. In parallel discrete event simulation, the work of a single discrete event simulation is distributed over multiple processing elements. A key challenge in parallel discrete event simulation is to ensure that causally dependent ...

Analysis of discrete reaction-diffusion equations for autocatalysis and continuum diffusion equations for transport

Energy Technology Data Exchange (ETDEWEB)

Wang, Chi-Jen [Iowa State Univ., Ames, IA (United States)

2013-01-01

In this thesis, we analyze both the spatiotemporal behavior of: (A) non-linear “reaction” models utilizing (discrete) reaction-diffusion equations; and (B) spatial transport problems on surfaces and in nanopores utilizing the relevant (continuum) diffusion or Fokker-Planck equations. Thus, there are some common themes in these studies, as they all involve partial differential equations or their discrete analogues which incorporate a description of diffusion-type processes. However, there are also some qualitative differences, as shall be discussed below.

A variational integrators approach to second order modeling and identification of linear mechanical systems

NARCIS (Netherlands)

Bruschetta, M.; Saccon, A.; Picci, G.

2014-01-01

The theory of variational integration provides a systematic procedure to discretize the equations of motion of a mechanical system, preserving key properties of the continuous time flow. The discrete-time model obtained by variational integration theory inherits structural conditions which in

New integrable lattice hierarchies

International Nuclear Information System (INIS)

Pickering, Andrew; Zhu Zuonong

2006-01-01

In this Letter we give a new integrable four-field lattice hierarchy, associated to a new discrete spectral problem. We obtain our hierarchy as the compatibility condition of this spectral problem and an associated equation, constructed herein, for the time-evolution of eigenfunctions. We consider reductions of our hierarchy, which also of course admit discrete zero curvature representations, in detail. We find that our hierarchy includes many well-known integrable hierarchies as special cases, including the Toda lattice hierarchy, the modified Toda lattice hierarchy, the relativistic Toda lattice hierarchy, and the Volterra lattice hierarchy. We also obtain here a new integrable two-field lattice hierarchy, to which we give the name of Suris lattice hierarchy, since the first equation of this hierarchy has previously been given by Suris. The Hamiltonian structure of the Suris lattice hierarchy is obtained by means of a trace identity formula