Hyperbolic manifolds as vacuum solutions in Kaluza-Klein theories

International Nuclear Information System (INIS)

Aref'eva, I.Ya.; Volovich, I.V.

1985-08-01

The relevance of compact hyperbolic manifolds in the context of Kaluza-Klein theories is discussed. Examples of spontaneous compactification on hyperbolic manifolds including d dimensional (d>=8) Einstein-Yang-Mills gravity and 11-dimensional supergravity are considered. Some mathematical facts about hyperbolic manifolds essential for the physical content of the theory are briefly summarized. Non-linear σ-models based on hyperbolic manifolds are discussed. (author)

[Hyperbolic growth of marine and continental biodiversity through the phanerozoic and community evolution].

Science.gov (United States)

Markov, A V; Korotaev, A V

2008-01-01

models, the hyperbolic pattern of the world population growth arises from a non-linear second-order positive feedback between the demographic growth and technological development (more people - more potential inventors - faster technological growth - the carrying capacity of the Earth grows faster - faster population growth - more people - more potential inventors, and so on). Based on the analogy with macrosociological models and diverse paleontological data, we suggest that the hyperbolic character of biodiversity growth can be similarly accounted for by a non-linear second-order positive feedback between the diversity growth and community structure complexity. The feedback can work via two parallel mechanisms: 1) decreasing extinction rate (more taxa- higher alpha diversity, or mean number of taxa in a community - communities become more complex and stable - extinction rate decreases - more taxa, and so on) and 2) increasing origination rate (new taxa facilitate niche construction; newly formed niches can be occupied by the next "generation" of taxa). The latter possibility makes the mechanisms underlying the hyperbolic growth of biodiversity and human population even more similar, because the total ecospace of the biota is analogous to the "carrying capacity of the Earth" in demography. As far as new species can increase ecospace and facilitate opportunities for additional species entering the community, they are analogous to the "inventors" of the demographic models whose inventions increase the carrying capacity of the Earth. The hyperbolic growth of the Phanerozoic biodiverstiy suggests that "cooperative" interactions between taxa can play an important role in evolution, along with generally accepted competitive interactions. Due to this "cooperation", the evolution of biodiversity acquires some features of a self-accelerating process. Macroevolutionary "cooperation" reveals itself in: 1) increasing stability of communities that arises from alpha diversity growth

Dynamic hyperbolic geometry: building intuition and understanding mediated by a Euclidean model

Science.gov (United States)

Moreno-Armella, Luis; Brady, Corey; Elizondo-Ramirez, Rubén

2018-05-01

This paper explores a deep transformation in mathematical epistemology and its consequences for teaching and learning. With the advent of non-Euclidean geometries, direct, iconic correspondences between physical space and the deductive structures of mathematical inquiry were broken. For non-Euclidean ideas even to become thinkable the mathematical community needed to accumulate over twenty centuries of reflection and effort: a precious instance of distributed intelligence at the cultural level. In geometry education after this crisis, relations between intuitions and geometrical reasoning must be established philosophically, rather than taken for granted. One approach seeks intuitive supports only for Euclidean explorations, viewing non-Euclidean inquiry as fundamentally non-intuitive in nature. We argue for moving beyond such an impoverished approach, using dynamic geometry environments to develop new intuitions even in the extremely challenging setting of hyperbolic geometry. Our efforts reverse the typical direction, using formal structures as a source for a new family of intuitions that emerge from exploring a digital model of hyperbolic geometry. This digital model is elaborated within a Euclidean dynamic geometry environment, enabling a conceptual dance that re-configures Euclidean knowledge as a support for building intuitions in hyperbolic space-intuitions based not directly on physical experience but on analogies extending Euclidean concepts.

Conformal hyperbolicity of Lorentzian warped products

International Nuclear Information System (INIS)

Markowitz, M.J.

1982-01-01

A space-time M is said to be conformally hyperbolic if the intrinsic conformal Lorentz pseudodistance dsub(M) is a true distance. In this paper criteria are derived which insure the conformal hyperbolicity of certain space-times which are generalizations of the Robertson-Walker spaces. Then dsub(M) is determined explicitly for Einstein-de Sitter space, and important cosmological model. (author)

Conformal hyperbolicity of Lorentzian warped products

Energy Technology Data Exchange (ETDEWEB)

Markowitz, M.J. (Chicago Univ., IL (USA). Dept. of Mathematics)

1982-12-01

A space-time M is said to be conformally hyperbolic if the intrinsic conformal Lorentz pseudodistance dsub(M) is a true distance. In this paper criteria are derived which insure the conformal hyperbolicity of certain space-times which are generalizations of the Robertson-Walker spaces. Then dsub(M) is determined explicitly for Einstein-de Sitter space, and important cosmological model.

p-Capacity and p-Hyperbolicity of Submanifolds

DEFF Research Database (Denmark)

Holopainen, Ilkka; Markvorsen, Steen; Palmer, Vicente

2009-01-01

We use explicit solutions to a drifted Laplace equation in warped product model spaces as comparison constructions to show p-hyperbolicity of a large class of submanifolds for p >= 2. The condition for p-hyperbolicity is expressed in terms of upper support functions for the radial sectional curva...

Hyperbolicity in median graphs

Indian Academy of Sciences (India)

mic problems in hyperbolic spaces and hyperbolic graphs have been .... that in general the main obstacle is that we do not know the location of ...... [25] Jonckheere E and Lohsoonthorn P, A hyperbolic geometry approach to multipath routing,.

Piecewise linear regression splines with hyperbolic covariates

International Nuclear Information System (INIS)

Cologne, John B.; Sposto, Richard

1992-09-01

Consider the problem of fitting a curve to data that exhibit a multiphase linear response with smooth transitions between phases. We propose substituting hyperbolas as covariates in piecewise linear regression splines to obtain curves that are smoothly joined. The method provides an intuitive and easy way to extend the two-phase linear hyperbolic response model of Griffiths and Miller and Watts and Bacon to accommodate more than two linear segments. The resulting regression spline with hyperbolic covariates may be fit by nonlinear regression methods to estimate the degree of curvature between adjoining linear segments. The added complexity of fitting nonlinear, as opposed to linear, regression models is not great. The extra effort is particularly worthwhile when investigators are unwilling to assume that the slope of the response changes abruptly at the join points. We can also estimate the join points (the values of the abscissas where the linear segments would intersect if extrapolated) if their number and approximate locations may be presumed known. An example using data on changing age at menarche in a cohort of Japanese women illustrates the use of the method for exploratory data analysis. (author)

Modeling and analysis of linear hyperbolic systems of balance laws

CERN Document Server

Bartecki, Krzysztof

2016-01-01

This monograph focuses on the mathematical modeling of distributed parameter systems in which mass/energy transport or wave propagation phenomena occur and which are described by partial differential equations of hyperbolic type. The case of linear (or linearized) 2 x 2 hyperbolic systems of balance laws is considered, i.e., systems described by two coupled linear partial differential equations with two variables representing physical quantities, depending on both time and one-dimensional spatial variable. Based on practical examples of a double-pipe heat exchanger and a transportation pipeline, two typical configurations of boundary input signals are analyzed: collocated, wherein both signals affect the system at the same spatial point, and anti-collocated, in which the input signals are applied to the two different end points of the system. The results of this book emerge from the practical experience of the author gained during his studies conducted in the experimental installation of a heat exchange cente...

Hyperbolic Rendezvous at Mars: Risk Assessments and Mitigation Strategies

Science.gov (United States)

Jedrey, Ricky; Landau, Damon; Whitley, Ryan

2015-01-01

Given the current interest in the use of flyby trajectories for human Mars exploration, a key requirement is the capability to execute hyperbolic rendezvous. Hyperbolic rendezvous is used to transport crew from a Mars centered orbit, to a transiting Earth bound habitat that does a flyby. Representative cases are taken from future potential missions of this type, and a thorough sensitivity analysis of the hyperbolic rendezvous phase is performed. This includes early engine cutoff, missed burn times, and burn misalignment. A finite burn engine model is applied that assumes the hyperbolic rendezvous phase is done with at least two burns.

Chaotic Dynamics in Smart Grid and Suppression Scheme via Generalized Fuzzy Hyperbolic Model

NARCIS (Netherlands)

Sun, Q.; Wang, Y.; Yang, J.; Qiu, Y.; Zhang, H.

2014-01-01

This paper presents a method to control chaotic behavior of a typical Smart Grid based on generalized fuzzy hyperbolic model (GFHM). As more and more distributed generations (DG) are incorporated into the Smart Grid, the chaotic behavior occurs increasingly. To verify the behavior, a dynamic model

Hyperbolic prisms and foams in Hele-Shaw cells

Energy Technology Data Exchange (ETDEWEB)

Tufaile, A., E-mail: tufaile@usp.br [Soft Matter Laboratory, Escola de Artes, Ciencias e Humanidades, Universidade de Sao Paulo, 03828-000, Sao Paulo (Brazil); Tufaile, A.P.B. [Soft Matter Laboratory, Escola de Artes, Ciencias e Humanidades, Universidade de Sao Paulo, 03828-000, Sao Paulo (Brazil)

2011-10-03

The propagation of light in foams creates patterns which are generated due to the reflection and refraction of light. One of these patterns is observed by the formation of multiple mirror images inside liquid bridges in a layer of bubbles in a Hele-Shaw cell. We are presenting the existence of these patterns in foams and their relation with hyperbolic geometry and Sierpinski gaskets using the Poincare disk model. The images obtained from the experiment in foams are compared to the case of hyperbolic optical elements. -- Highlights: → The chaotic scattering of light in foams generating deltoid patterns is based on hyperbolic geometry. → The deltoid patterns are obtained through the Plateau borders in a Hele-Shaw cell. → The Plateau borders act like hyperbolic prism. → Some effects of the refraction and reflection of the light rays were studied using a hyperbolic prism.

Hyperbolic-symmetry vector fields.

Science.gov (United States)

Gao, Xu-Zhen; Pan, Yue; Cai, Meng-Qiang; Li, Yongnan; Tu, Chenghou; Wang, Hui-Tian

2015-12-14

We present and construct a new kind of orthogonal coordinate system, hyperbolic coordinate system. We present and design a new kind of local linearly polarized vector fields, which is defined as the hyperbolic-symmetry vector fields because the points with the same polarization form a series of hyperbolae. We experimentally demonstrate the generation of such a kind of hyperbolic-symmetry vector optical fields. In particular, we also study the modified hyperbolic-symmetry vector optical fields with the twofold and fourfold symmetric states of polarization when introducing the mirror symmetry. The tight focusing behaviors of these vector fields are also investigated. In addition, we also fabricate micro-structures on the K9 glass surfaces by several tightly focused (modified) hyperbolic-symmetry vector fields patterns, which demonstrate that the simulated tightly focused fields are in good agreement with the fabricated micro-structures.

Admissibility and hyperbolicity

CERN Document Server

Barreira, Luís; Valls, Claudia

2018-01-01

This book gives a comprehensive overview of the relationship between admissibility and hyperbolicity. Essential theories and selected developments are discussed with highlights to applications. The dedicated readership includes researchers and graduate students specializing in differential equations and dynamical systems (with emphasis on hyperbolicity) who wish to have a broad view of the topic and working knowledge of its techniques. The book may also be used as a basis for appropriate graduate courses on hyperbolicity; the pointers and references given to further research will be particularly useful. The material is divided into three parts: the core of the theory, recent developments, and applications. The first part pragmatically covers the relation between admissibility and hyperbolicity, starting with the simpler case of exponential contractions. It also considers exponential dichotomies, both for discrete and continuous time, and establishes corresponding results building on the arguments for exponent...

Right-angled polyhedra and hyperbolic 3-manifolds

Science.gov (United States)

Vesnin, A. Yu.

2017-04-01

Hyperbolic 3-manifolds whose fundamental groups are subgroups of finite index in right-angled Coxeter groups are under consideration. The construction of such manifolds is associated with regular colourings of the faces of polyhedra and, in particular, with 4-colourings. The following questions are discussed: the structure of the set of right-angled polytopes in Lobachevskii space; examples of orientable and non-orientable manifolds, including the classical Löbell manifold constructed in 1931; connections between the Hamiltonian property of a polyhedron and the existence of hyperelliptic involutions of manifolds; the volumes and complexity of manifolds; isometry between hyperbolic manifolds constructed from 4-colourings. Bibliography: 89 titles.

Hyperbolic space for tourists

NARCIS (Netherlands)

Blasjo, Viktor|info:eu-repo/dai/nl/338038108

2013-01-01

We discuss how a creature accustomed to Euclidean space would fare in a world of hyperbolic or spherical geometry, and conversely. Various optical illusions and counterintuitive experiences arise, which can be explicated mathematically using plane models of these geometries.

Curvature and temperature of complex networks.

Science.gov (United States)

Krioukov, Dmitri; Papadopoulos, Fragkiskos; Vahdat, Amin; Boguñá, Marián

2009-09-01

We show that heterogeneous degree distributions in observed scale-free topologies of complex networks can emerge as a consequence of the exponential expansion of hidden hyperbolic space. Fermi-Dirac statistics provides a physical interpretation of hyperbolic distances as energies of links. The hidden space curvature affects the heterogeneity of the degree distribution, while clustering is a function of temperature. We embed the internet into the hyperbolic plane and find a remarkable congruency between the embedding and our hyperbolic model. Besides proving our model realistic, this embedding may be used for routing with only local information, which holds significant promise for improving the performance of internet routing.

Vortices on hyperbolic surfaces

International Nuclear Information System (INIS)

Manton, Nicholas S; Rink, Norman A

2010-01-01

It is shown that Abelian Higgs vortices on a hyperbolic surface M can be constructed geometrically from holomorphic maps f: M → N, where N is also a hyperbolic surface. The fields depend on f and on the metrics of M and N. The vortex centres are the ramification points, where the derivative of f vanishes. The magnitude of the Higgs field measures the extent to which f is locally an isometry. Witten's construction of vortices on the hyperbolic plane is rederived, and new examples of vortices on compact surfaces and on hyperbolic surfaces of revolution are obtained. The interpretation of these solutions as SO(3)-invariant, self-dual SU(2) Yang-Mills fields on R 4 is also given.

Random walks on the braid group B3 and magnetic translations in hyperbolic geometry

International Nuclear Information System (INIS)

Voituriez, Raphaeel

2002-01-01

We study random walks on the three-strand braid group B 3 , and in particular compute the drift, or average topological complexity of a random braid, as well as the probability of trivial entanglement. These results involve the study of magnetic random walks on hyperbolic graphs (hyperbolic Harper-Hofstadter problem), what enables to build a faithful representation of B 3 as generalized magnetic translation operators for the problem of a quantum particle on the hyperbolic plane

Hyperbolic partial differential equations

CERN Document Server

Witten, Matthew

1986-01-01

Hyperbolic Partial Differential Equations III is a refereed journal issue that explores the applications, theory, and/or applied methods related to hyperbolic partial differential equations, or problems arising out of hyperbolic partial differential equations, in any area of research. This journal issue is interested in all types of articles in terms of review, mini-monograph, standard study, or short communication. Some studies presented in this journal include discretization of ideal fluid dynamics in the Eulerian representation; a Riemann problem in gas dynamics with bifurcation; periodic M

Nonlinear hyperbolic waves in multidimensions

CERN Document Server

Prasad, Phoolan

2001-01-01

The propagation of curved, nonlinear wavefronts and shock fronts are very complex phenomena. Since the 1993 publication of his work Propagation of a Curved Shock and Nonlinear Ray Theory, author Phoolan Prasad and his research group have made significant advances in the underlying theory of these phenomena. This volume presents their results and provides a self-contained account and gradual development of mathematical methods for studying successive positions of these fronts.Nonlinear Hyperbolic Waves in Multidimensions includes all introductory material on nonlinear hyperbolic waves and the theory of shock waves. The author derives the ray theory for a nonlinear wavefront, discusses kink phenomena, and develops a new theory for plane and curved shock propagation. He also derives a full set of conservation laws for a front propagating in two space dimensions, and uses these laws to obtain successive positions of a front with kinks. The treatment includes examples of the theory applied to converging wavefronts...

Output Tracking for Systems with Non-Hyperbolic and Near Non-Hyperbolic Internal Dynamics: Helicopter Hover Control

Science.gov (United States)

Devasia, Santosh

1996-01-01

A technique to achieve output tracking for nonminimum phase linear systems with non-hyperbolic and near non-hyperbolic internal dynamics is presented. This approach integrates stable inversion techniques, that achieve exact-tracking, with approximation techniques, that modify the internal dynamics to achieve desirable performance. Such modification of the internal dynamics is used (1) to remove non-hyperbolicity which an obstruction to applying stable inversion techniques and (2) to reduce large pre-actuation time needed to apply stable inversion for near non-hyperbolic cases. The method is applied to an example helicopter hover control problem with near non-hyperbolic internal dynamic for illustrating the trade-off between exact tracking and reduction of pre-actuation time.

From Anosov dynamics to hyperbolic attractors

Indian Academy of Sciences (India)

the dynamics on the attractive sets of the self-oscillatory systems and for the original Anosov geodesic flow. The hyperbolic nature ... Hyperbolic theory is a branch of the theory of dynami- ..... Figure 5. Verification of the hyperbolicity criterion for.

Hyperbolic strings

International Nuclear Information System (INIS)

Popov, A.D.

1991-01-01

We introduce hyperbolic strings as closed bosonic strings with the target space R d-1,1 xT q+1,1 which has an additional time-like dimension in the internal space. The Fock spaces of the q-parametric family of standard bosonic, fermionic and heterotic strings with the target spaces of dimension n≤d+q are shown to be embedded into the Fock space of hyperbolic strings. The condition of the absence of anomaly fixes d and q for all three types of strings written in a bosonized form. (orig.)

A discussion of hyperbolicity in CATHENA 4. Virtual mass and phase-to-interface pressure differences

International Nuclear Information System (INIS)

Aydemir, Nusret U.

2012-01-01

It is well known that the one-dimensional equations of motion for two-phase flow are non-hyperbolic. Non-hyperbolicity can lead to numerical instabilities, destroying the solution. However, researchers in the last few decades were able to show that inclusion of virtual mass and/or phase-to-interface pressure differences in the momentum equations successfully render the equations of motion hyperbolic. In the present paper, the effect of including virtual mass and phase-to-interface pressure terms in the momentum equations on the hyperbolicity of the two-phase model in the CATHENA 4 code is discussed. The study is motivated by the fact that the inclusion of either model has been shown in the open literature to lead to a hyperbolic system separately. However, no known study exists that examine hyperbolicity in the presence of both these terms in the momentum equations. In this work, both terms are considered in the model equations simultaneously and their implications on the hyperbolicity of the two-phase model are discussed. Specifically, it is shown that in the case of mixed flow, there is a distinct region of non-hyperbolicity that developers need to be aware of when their equations include both the virtual mass and the phase-to-interface terms. Selecting the coefficients of phase-to-interface pressure difference terms properly ensures that the equations are hyperbolic for a wide range of conditions. (orig.)

Angles in hyperbolic lattices

DEFF Research Database (Denmark)

Risager, Morten S.; Södergren, Carl Anders

2017-01-01

It is well known that the angles in a lattice acting on hyperbolic n -space become equidistributed. In this paper we determine a formula for the pair correlation density for angles in such hyperbolic lattices. Using this formula we determine, among other things, the asymptotic behavior of the den......It is well known that the angles in a lattice acting on hyperbolic n -space become equidistributed. In this paper we determine a formula for the pair correlation density for angles in such hyperbolic lattices. Using this formula we determine, among other things, the asymptotic behavior...... of the density function in both the small and large variable limits. This extends earlier results by Boca, Pasol, Popa and Zaharescu and Kelmer and Kontorovich in dimension 2 to general dimension n . Our proofs use the decay of matrix coefficients together with a number of careful estimates, and lead...

Proof of Concept: Model Based Bionic Muscle with Hyperbolic Force-Velocity Relation

Directory of Open Access Journals (Sweden)

D. F. B. Haeufle

2012-01-01

Full Text Available Recently, the hyperbolic Hill-type force-velocity relation was derived from basic physical components. It was shown that a contractile element CE consisting of a mechanical energy source (active element AE, a parallel damper element (PDE, and a serial element (SE exhibits operating points with hyperbolic force-velocity dependency. In this paper, a technical proof of this concept was presented. AE and PDE were implemented as electric motors, SE as a mechanical spring. The force-velocity relation of this artificial CE was determined in quick release experiments. The CE exhibited hyperbolic force-velocity dependency. This proof of concept can be seen as a well-founded starting point for the development of Hill-type artificial muscles.

On a new class of hyperbolic functions

International Nuclear Information System (INIS)

Stakhov, Alexey; Rozin, Boris

2005-01-01

This article presents the results of some new research on a new class of hyperbolic functions that unite the characteristics of the classical hyperbolic functions and the recurring Fibonacci and Lucas series. The hyperbolic Fibonacci and Lucas functions, which are the being extension of Binet's formulas for the Fibonacci and Lucas numbers in continuous domain, transform the Fibonacci numbers theory into 'continuous' theory because every identity for the hyperbolic Fibonacci and Lucas functions has its discrete analogy in the framework of the Fibonacci and Lucas numbers. Taking into consideration a great role played by the hyperbolic functions in geometry and physics, ('Lobatchevski's hyperbolic geometry', 'Four-dimensional Minkowski's world', etc.), it is possible to expect that the new theory of the hyperbolic functions will bring to new results and interpretations on mathematics, biology, physics, and cosmology. In particular, the result is vital for understanding the relation between transfinitness i.e. fractal geometry and the hyperbolic symmetrical character of the disintegration of the neural vacuum, as pointed out by El Naschie [Chaos Solitons and Fractals 17 (2003) 631

Origin of hyperbolicity in brain-to-brain coordination networks

Science.gov (United States)

Tadić, Bosiljka; Andjelković, Miroslav; Šuvakov, Milovan

2018-02-01

Hyperbolicity or negative curvature of complex networks is the intrinsic geometric proximity of nodes in the graph metric space, which implies an improved network function. Here, we investigate hidden combinatorial geometries in brain-to-brain coordination networks arising through social communications. The networks originate from correlations among EEG signals previously recorded during spoken communications comprising of 14 individuals with 24 speaker-listener pairs. We find that the corresponding networks are delta-hyperbolic with delta_max=1 and the graph diameter D=3 in each brain. While the emergent hyperbolicity in the two-brain networks satisfies delta_max/D/2 neuronal correlation patterns ranging from weak coordination to super-brain structure. These topology features are in qualitative agreement with the listener’s self-reported ratings of own experience and quality of the speaker, suggesting that studies of the cross-brain connector networks can reveal new insight into the neural mechanisms underlying human social behavior.

Hyperbolic Chaos A Physicist’s View

CERN Document Server

Kuznetsov, Sergey P

2012-01-01

"Hyperbolic Chaos: A Physicist’s View” presents recent progress on uniformly hyperbolic attractors in dynamical systems from a physical rather than mathematical perspective (e.g. the Plykin attractor, the Smale – Williams solenoid). The structurally stable attractors manifest strong stochastic properties, but are insensitive to variation of functions and parameters in the dynamical systems. Based on these characteristics of hyperbolic chaos, this monograph shows how to find hyperbolic chaotic attractors in physical systems and how to design a physical systems that possess hyperbolic chaos.   This book is designed as a reference work for university professors and researchers in the fields of physics, mechanics, and engineering.   Dr. Sergey P. Kuznetsov is a professor at the Department of Nonlinear Processes, Saratov State University, Russia.  

A parabolic-hyperbolic system modelling a moving cell

Directory of Open Access Journals (Sweden)

Fabiana Cardetti

2009-08-01

Full Text Available In this article, we study the existence and uniqueness of local solutions for a moving boundary problem governed by a coupled parabolic-hyperbolic system. The results can be applied to cell movement, extending a result obtained by Choi, Groulx, and Lui in 2005.

Dynamical chaos and uniformly hyperbolic attractors: from mathematics to physics

Energy Technology Data Exchange (ETDEWEB)

Kuznetsov, Sergei P [Saratov Branch, Kotel' nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences, Saratov (Russian Federation)

2011-02-28

Research is reviewed on the identification and construction of physical systems with chaotic dynamics due to uniformly hyperbolic attractors (such as the Plykin attraction or the Smale-Williams solenoid). Basic concepts of the mathematics involved and approaches proposed in the literature for constructing systems with hyperbolic attractors are discussed. Topics covered include periodic pulse-driven models; dynamics models consisting of periodically repeated stages, each described by its own differential equations; the construction of systems of alternately excited coupled oscillators; the use of parametrically excited oscillations; and the introduction of delayed feedback. Some maps, differential equations, and simple mechanical and electronic systems exhibiting chaotic dynamics due to the presence of uniformly hyperbolic attractors are presented as examples. (reviews of topical problems)

Path integration on hyperbolic spaces

Energy Technology Data Exchange (ETDEWEB)

Grosche, C [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik

1991-11-01

Quantum mechanics on the hyperbolic spaces of rank one is discussed by path integration technique. Hyperbolic spaces are multi-dimensional generalisation of the hyperbolic plane, i.e. the Poincare upper half-plane endowed with a hyperbolic geometry. We evalute the path integral on S{sub 1} {approx equal} SO (n,1)/SO(n) and S{sub 2} {approx equal} SU(n,1)/S(U(1) x U(n)) in a particular coordinate system, yielding explicitly the wave-functions and the energy spectrum. Futhermore we can exploit a general property of all these spaces, namely that they can be parametrized by a pseudopolar coordinate system. This allows a separation in path integration over spheres and an additional path integration over the remaining hyperbolic coordinate, yielding effectively a path integral for a modified Poeschl-Teller potential. Only continuous spectra can exist in all the cases. For all the hyperbolic spaces of rank one we find a general formula for the largest lower bound (zero-point energy) of the spectrum which is given by E{sub O} = h{sup 2} /8m(m{sub {alpha}} +2m{sub 2} {alpha}){sup 2} (m {alpha} and m{sub 2}{alpha} denote the dimension of the root subspace corresponding to the roots {alpha} and 2{alpha}, respectively). I also discuss the case, where a constant magnetic field on H{sup n} is incorporated. (orig.).

Path integration on hyperbolic spaces

International Nuclear Information System (INIS)

Grosche, C.

1991-11-01

Quantum mechanics on the hyperbolic spaces of rank one is discussed by path integration technique. Hyperbolic spaces are multi-dimensional generalisation of the hyperbolic plane, i.e. the Poincare upper half-plane endowed with a hyperbolic geometry. We evalute the path integral on S 1 ≅ SO (n,1)/SO(n) and S 2 ≅ SU(n,1)/S[U(1) x U(n)] in a particular coordinate system, yielding explicitly the wave-functions and the energy spectrum. Futhermore we can exploit a general property of all these spaces, namely that they can be parametrized by a pseudopolar coordinate system. This allows a separation in path integration over spheres and an additional path integration over the remaining hyperbolic coordinate, yielding effectively a path integral for a modified Poeschl-Teller potential. Only continuous spectra can exist in all the cases. For all the hyperbolic spaces of rank one we find a general formula for the largest lower bound (zero-point energy) of the spectrum which is given by E O = h 2 /8m(m α +2m 2 α) 2 (m α and m 2 α denote the dimension of the root subspace corresponding to the roots α and 2α, respectively). I also discuss the case, where a constant magnetic field on H n is incorporated. (orig.)

Hyperbolic metamaterial lens with hydrodynamic nonlocal response.

Science.gov (United States)

Yan, Wei; Mortensen, N Asger; Wubs, Martijn

2013-06-17

We investigate the effects of hydrodynamic nonlocal response in hyperbolic metamaterials (HMMs), focusing on the experimentally realizable parameter regime where unit cells are much smaller than an optical wavelength but much larger than the wavelengths of the longitudinal pressure waves of the free-electron plasma in the metal constituents. We derive the nonlocal corrections to the effective material parameters analytically, and illustrate the noticeable nonlocal effects on the dispersion curves numerically. As an application, we find that the focusing characteristics of a HMM lens in the local-response approximation and in the hydrodynamic Drude model can differ considerably. In particular, the optimal frequency for imaging in the nonlocal theory is blueshifted with respect to that in the local theory. Thus, to detect whether nonlocal response is at work in a hyperbolic metamaterial, we propose to measure the near-field distribution of a hyperbolic metamaterial lens.

Inozemtsev's hyperbolic spin model and its related spin chain

International Nuclear Information System (INIS)

Barba, J.C.; Finkel, F.; Gonzalez-Lopez, A.; Rodriguez, M.A.

2010-01-01

In this paper we study Inozemtsev's su(m) quantum spin model with hyperbolic interactions and the associated spin chain of Haldane-Shastry type introduced by Frahm and Inozemtsev. We compute the spectrum of Inozemtsev's model, and use this result and the freezing trick to derive a simple analytic expression for the partition function of the Frahm-Inozemtsev chain. We show that the energy levels of the latter chain can be written in terms of the usual motifs for the Haldane-Shastry chain, although with a different dispersion relation. The formula for the partition function is used to analyze the behavior of the level density and the distribution of spacings between consecutive unfolded levels. We discuss the relevance of our results in connection with two well-known conjectures in quantum chaos.

Shock and rarefaction waves in a hyperbolic model of incompressible materials

Directory of Open Access Journals (Sweden)

Tommaso Ruggeri

2013-01-01

Full Text Available The aim of the present paper is to investigate shock and rarefaction waves in a hyperbolic model of incompressible materials. To this aim, we use the so-called extended quasi-thermal-incompressible (EQTI model, recently proposed by Gouin & Ruggeri (H. Gouin, T. Ruggeri, Internat. J. Non-Linear Mech. 47 688–693 (2012. In particular, we use as constitutive equation a variant of the well-known Bousinnesq approximation in which the specific volume depends not only on the temperature but also on the pressure. The limit case of ideal incompressibility, namely when the thermal expansion coefficient and the compressibility factor vanish, is also considered.

Hyperbolic partial differential equations populations, reactors, tides and waves theory and applications

CERN Document Server

Witten, Matthew

1983-01-01

Hyperbolic Partial Differential Equations, Volume 1: Population, Reactors, Tides and Waves: Theory and Applications covers three general areas of hyperbolic partial differential equation applications. These areas include problems related to the McKendrick/Von Foerster population equations, other hyperbolic form equations, and the numerical solution.This text is composed of 15 chapters and begins with surveys of age specific population interactions, populations models of diffusion, nonlinear age dependent population growth with harvesting, local and global stability for the nonlinear renewal eq

Layered van der Waals crystals with hyperbolic light dispersion

DEFF Research Database (Denmark)

Gjerding, Morten Niklas; Petersen, R.; Pedersen, T.G.

2017-01-01

Compared to artificially structured hyperbolic metamaterials, whose performance is limited by the finite size of the metallic components, the sparse number of naturally hyperbolic materials recently discovered are promising candidates for the next generation of hyperbolic materials. Using first......-principles calculations, we extend the number of known naturally hyperbolic materials to the broad class of layered transition metal dichalcogenides (TMDs). The diverse electronic properties of the transition metal dichalcogenides result in a large variation of the hyperbolic frequency regimes ranging from the near...... materials with hyperbolic dispersion among the family of layered transition metal dichalcogenides....

Solving hyperbolic heat conduction using electrical simulation

International Nuclear Information System (INIS)

Gheitaghy, A. M.; Talaee, M. R.

2013-01-01

In the present study, the electrical network simulation method is proposed to solve the hyperbolic and parabolic heat conduction problem considering Cattaneo-Vernoute (C.V) constitutive relation. Using this new proposed numerical model and the electrical circuit simulation program HSPICE, transient temperature and heat flux profiles at slab can be obtained easily and quickly. To verify the proposed method, the obtained numerical results for cases of one dimensional two-layer slab under periodic boundary temperature with perfect and imperfect thermal contact are compared with the published results. Comparisons show the proposed technique might be considered as a useful tool in the analysis of parabolic and hyperbolic thermal problems.

The art and science of hyperbolic tessellations.

Science.gov (United States)

Van Dusen, B; Taylor, R P

2013-04-01

The visual impact of hyperbolic tessellations has captured artists' imaginations ever since M.C. Escher generated his Circle Limit series in the 1950s. The scaling properties generated by hyperbolic geometry are different to the fractal scaling properties found in nature's scenery. Consequently, prevalent interpretations of Escher's art emphasize the lack of connection with nature's patterns. However, a recent collaboration between the two authors proposed that Escher's motivation for using hyperbolic geometry was as a method to deliberately distort nature's rules. Inspired by this hypothesis, this year's cover artist, Ben Van Dusen, embeds natural fractals such as trees, clouds and lightning into a hyperbolic scaling grid. The resulting interplay of visual structure at multiple size scales suggests that hybridizations of fractal and hyperbolic geometries provide a rich compositional tool for artists.

Hyperbolic geometry

CERN Document Server

Iversen, Birger

1992-01-01

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

The relation among the hyperbolic-function-type exact solutions of nonlinear evolution equations

International Nuclear Information System (INIS)

Liu Chunping; Liu Xiaoping

2004-01-01

First, we investigate the solitary wave solutions of the Burgers equation and the KdV equation, which are obtained by using the hyperbolic function method. Then we present a theorem which will not only give us a clear relation among the hyperbolic-function-type exact solutions of nonlinear evolution equations, but also provide us an approach to construct new exact solutions in complex scalar field. Finally, we apply the theorem to the KdV-Burgers equation and obtain its new exact solutions

Exact Solutions for Einstein's Hyperbolic Geometric Flow

International Nuclear Information System (INIS)

He Chunlei

2008-01-01

In this paper we investigate the Einstein's hyperbolic geometric flow and obtain some interesting exact solutions for this kind of flow. Many interesting properties of these exact solutions have also been analyzed and we believe that these properties of Einstein's hyperbolic geometric flow are very helpful to understanding the Einstein equations and the hyperbolic geometric flow

A strictly hyperbolic equilibrium phase transition model

International Nuclear Information System (INIS)

Allaire, G; Faccanoni, G; Kokh, S.

2007-01-01

This Note is concerned with the strict hyperbolicity of the compressible Euler equations equipped with an equation of state that describes the thermodynamical equilibrium between the liquid phase and the vapor phase of a fluid. The proof is valid for a very wide class of fluids. The argument only relies on smoothness assumptions and on the classical thermodynamical stability assumptions, that requires a definite negative Hessian matrix for each phase entropy as a function of the specific volume and internal energy. (authors)

Outcrossings of safe regions by generalized hyperbolic processes

DEFF Research Database (Denmark)

Klüppelberg, Claudia; Rasmussen, Morten Grud

2013-01-01

We present a simple Gaussian mixture model in space and time with generalized hyperbolic marginals. Starting with Rice’s celebrated formula for level upcrossings and outcrossings of safe regions we investigate the consequences of the mean-variance mixture model on such quantities. We obtain...

Fourier and Gegenbauer expansions for a fundamental solution of the Laplacian in the hyperboloid model of hyperbolic geometry

International Nuclear Information System (INIS)

Cohl, H S; Kalnins, E G

2012-01-01

Due to the isotropy of d-dimensional hyperbolic space, there exists a spherically symmetric fundamental solution for its corresponding Laplace–Beltrami operator. The R-radius hyperboloid model of hyperbolic geometry with R > 0 represents a Riemannian manifold with negative-constant sectional curvature. We obtain a spherically symmetric fundamental solution of Laplace’s equation on this manifold in terms of its geodesic radius. We give several matching expressions for this fundamental solution including a definite integral over reciprocal powers of the hyperbolic sine, finite summation expressions over hyperbolic functions, Gauss hypergeometric functions and in terms of the associated Legendre function of the second kind with order and degree given by d/2 − 1 with real argument greater than unity. We also demonstrate uniqueness for a fundamental solution of Laplace’s equation on this manifold in terms of a vanishing decay at infinity. In rotationally invariant coordinate systems, we compute the azimuthal Fourier coefficients for a fundamental solution of Laplace’s equation on the R-radius hyperboloid. For d ⩾ 2, we compute the Gegenbauer polynomial expansion in geodesic polar coordinates for a fundamental solution of Laplace’s equation on this negative-constant curvature Riemannian manifold. In three dimensions, an addition theorem for the azimuthal Fourier coefficients of a fundamental solution for Laplace’s equation is obtained through comparison with its corresponding Gegenbauer expansion. (paper)

Computation of Hyperbolic Structures in Knot Theory

OpenAIRE

Weeks, Jeffrey R.

2003-01-01

This chapter from the upcoming Handbook of Knot Theory (eds. Menasco and Thistlethwaite) shows how to construct hyperbolic structures on link complements and perform hyperbolic Dehn filling. Along with a new elementary exposition of the standard ideas from Thurston's work, the article includes never-before-published explanations of SnapPea's algorithms for triangulating a link complement efficiently and for converging quickly to the hyperbolic structure while avoiding singularities in the par...

Casimir effect in hyperbolic polygons

International Nuclear Information System (INIS)

Ahmedov, H

2007-01-01

Using the point splitting regularization method and the trace formula for the spectra of quantum-mechanical systems in hyperbolic polygons which are the fundamental domains of discrete isometry groups acting in the two-dimensional hyperboloid we calculate the Casimir energy for massless scalar fields in hyperbolic polygons. The dependence of the vacuum energy on the number of vertices is established

Stability problems for linear hyperbolic systems

International Nuclear Information System (INIS)

Eckhoff, K.S.

1975-05-01

The stability properties for the trivial solution of a general linear hyperbolic system of partial differential equations of the first order are studied. It is shown that results may be obtained by studying the stability properties of certain systems of ordinary differential equations which can be constructed from the hyperbolic system (the so-called transport equations). In some cases the associated stability problem for the transport equations can in fact be shown to be equivalent to the stability problem for the hyperbolic system, but in general the transport equations will only give the necessary conditions for stability. (Auth.)

Critical opalescence in hyperbolic metamaterials

International Nuclear Information System (INIS)

Smolyaninov, Igor I

2011-01-01

Hyperbolic metamaterials in which the dielectric component exhibits critical opalescence have been considered. It appears that fluctuations of the effective refractive index in these materials are strongly enhanced and so 'virtual electromagnetic black holes' may appear as a result of these fluctuations. Therefore, the behaviour of 'optical space' inside hyperbolic metamaterials looks somewhat similar to the behaviour of real physical space-time on the Planck scale

Critical opalescence in hyperbolic metamaterials

Science.gov (United States)

Smolyaninov, Igor I.

2011-12-01

Hyperbolic metamaterials in which the dielectric component exhibits critical opalescence have been considered. It appears that fluctuations of the effective refractive index in these materials are strongly enhanced and so 'virtual electromagnetic black holes' may appear as a result of these fluctuations. Therefore, the behaviour of 'optical space' inside hyperbolic metamaterials looks somewhat similar to the behaviour of real physical space-time on the Planck scale.

Contact Geometry of Hyperbolic Equations of Generic Type

Directory of Open Access Journals (Sweden)

Dennis The

2008-08-01

Full Text Available We study the contact geometry of scalar second order hyperbolic equations in the plane of generic type. Following a derivation of parametrized contact-invariants to distinguish Monge-Ampère (class 6-6, Goursat (class 6-7 and generic (class 7-7 hyperbolic equations, we use Cartan's equivalence method to study the generic case. An intriguing feature of this class of equations is that every generic hyperbolic equation admits at most a nine-dimensional contact symmetry algebra. The nine-dimensional bound is sharp: normal forms for the contact-equivalence classes of these maximally symmetric generic hyperbolic equations are derived and explicit symmetry algebras are presented. Moreover, these maximally symmetric equations are Darboux integrable. An enumeration of several submaximally symmetric (eight and seven-dimensional generic hyperbolic structures is also given.

A Hyperbolic Ontology Visualization Tool for Model Application Programming Interface Documentation

Science.gov (United States)

Hyman, Cody

2011-01-01

Spacecraft modeling, a critically important portion in validating planned spacecraft activities, is currently carried out using a time consuming method of mission to mission model implementations and integration. A current project in early development, Integrated Spacecraft Analysis (ISCA), aims to remedy this hindrance by providing reusable architectures and reducing time spent integrating models with planning and sequencing tools. The principle objective of this internship was to develop a user interface for an experimental ontology-based structure visualization of navigation and attitude control system modeling software. To satisfy this, a number of tree and graph visualization tools were researched and a Java based hyperbolic graph viewer was selected for experimental adaptation. Early results show promise in the ability to organize and display large amounts of spacecraft model documentation efficiently and effectively through a web browser. This viewer serves as a conceptual implementation for future development but trials with both ISCA developers and end users should be performed to truly evaluate the effectiveness of continued development of such visualizations.

Estimates of the Hyperbolic Radius Gradient and Schwarz–Pick Inequalities for the Eccentric Annulus

Directory of Open Access Journals (Sweden)

D.Kh. Giniyatova

2016-06-01

Full Text Available Let Ω and Π be hyperbolic domains in the complex plane C. By A(Ω, Π we shall designate the class of functions f which are holomorphic or meromorphic in Ω and such that f(Ω ϲ Π. Estimates of the higher derivatives |f(n(z| of the analytic functions from the class A(Ω, Π with the punishing factor Cn(Ω, Π is one of the main problems of geometric theory of functions. These estimates are commonly referred to as Schwarz–Pick inequalities. Many results concerning this problem have been obtained for simply connected domains. Therefore, the research interest in such problems for finitely connected domains is natural. As known, the constant C2(Ω, Π for any pairs of hyperbolic domains depends only on the hyperbolic radius gradient of the corresponding domains. The main result of this paper is estimates of the hyperbolic radius gradient and the punishing factor in the Schwarz–Pick inequality for the eccentric annulus. We also consider the extreme case – the randomly punctured circle.

Homoclinic Ω-explosion and domains of hyperbolicity

International Nuclear Information System (INIS)

Sten'kin, O V; Shil'nikov, L P

1998-01-01

The existence of domains of hyperbolicity is proved for general one-parameter families of multidimensional systems that undergo a homoclinic Ω-explosion and the structure of the hyperbolic sets is studied for such families

Higher order Godunov methods for general systems of hyperbolic conservation laws

International Nuclear Information System (INIS)

Bell, J.B.; Colella, P.; Trangenstein, J.A.

1989-01-01

We describe an extension of higher order Godunov methods to general systems of hyperbolic conservation laws. This extension allow the method to be applied to problems that are not strictly hyperbolic and exhibit local linear degeneracies in the wave fields. The method constructs an approximation of the Riemann problem from local wave information. A generalization of the Engquist--Osher flux for systems is then used to compute a numerical flux based on this approximation. This numerical flux replaces the Godunov numerical flux in the algorithm, thereby eliminating the need for a global Riemann problem solution. The additional modifications to the Godunov methodology that are needed to treat loss of strict hyperbolicity are described in detail. The method is applied to some simple model problems for which the glocal analytic structure is known. The method is also applied to the black-oil model for multiphase flow in petroleum reservoirs. copyright 1989 Academic Press, Inc

Entropic Constitutive Relation and Modeling for Fourier and Hyperbolic Heat Conductions

Directory of Open Access Journals (Sweden)

Shu-Nan Li

2017-12-01

Full Text Available Most existing phenomenological heat conduction models are expressed by temperature and heat flux distributions, whose definitions might be debatable in heat conductions with strong non-equilibrium. The constitutive relations of Fourier and hyperbolic heat conductions are here rewritten by the entropy and entropy flux distributions in the frameworks of classical irreversible thermodynamics (CIT and extended irreversible thermodynamics (EIT. The entropic constitutive relations are then generalized by Boltzmann–Gibbs–Shannon (BGS statistical mechanics, which can avoid the debatable definitions of thermodynamic quantities relying on local equilibrium. It shows a possibility of modeling heat conduction through entropic constitutive relations. The applicability of the generalizations by BGS statistical mechanics is also discussed based on the relaxation time approximation, and it is found that the generalizations require a sufficiently small entropy production rate.

Hyperbolic metamaterial lens with hydrodynamic nonlocal response

DEFF Research Database (Denmark)

Yan, Wei; Mortensen, N. Asger; Wubs, Martijn

2013-01-01

We investigate the effects of hydrodynamic nonlocal response in hyperbolic metamaterials (HMMs), focusing on the experimentally realizable parameter regime where unit cells are much smaller than an optical wavelength but much larger than the wavelengths of the longitudinal pressure waves...... of the free-electron plasma in the metal constituents. We derive the nonlocal corrections to the effective material parameters analytically, and illustrate the noticeable nonlocal effects on the dispersion curves numerically. As an application, we find that the focusing characteristics of a HMM lens...... in the local-response approximation and in the hydrodynamic Drude model can differ considerably. In particular, the optimal frequency for imaging in the nonlocal theory is blueshifted with respect to that in the local theory. Thus, to detect whether nonlocal response is at work in a hyperbolic metamaterial, we...

Hyperbolicity measures democracy in real-world networks

Science.gov (United States)

Borassi, Michele; Chessa, Alessandro; Caldarelli, Guido

2015-09-01

In this work, we analyze the hyperbolicity of real-world networks, a geometric quantity that measures if a space is negatively curved. We provide two improvements in our understanding of this quantity: first of all, in our interpretation, a hyperbolic network is "aristocratic", since few elements "connect" the system, while a non-hyperbolic network has a more "democratic" structure with a larger number of crucial elements. The second contribution is the introduction of the average hyperbolicity of the neighbors of a given node. Through this definition, we outline an "influence area" for the vertices in the graph. We show that in real networks the influence area of the highest degree vertex is small in what we define "local" networks (i.e., social or peer-to-peer networks), and large in "global" networks (i.e., power grid, metabolic networks, or autonomous system networks).

Hyperbolicity and constrained evolution in linearized gravity

International Nuclear Information System (INIS)

Matzner, Richard A.

2005-01-01

Solving the 4-d Einstein equations as evolution in time requires solving equations of two types: the four elliptic initial data (constraint) equations, followed by the six second order evolution equations. Analytically the constraint equations remain solved under the action of the evolution, and one approach is to simply monitor them (unconstrained evolution). Since computational solution of differential equations introduces almost inevitable errors, it is clearly 'more correct' to introduce a scheme which actively maintains the constraints by solution (constrained evolution). This has shown promise in computational settings, but the analysis of the resulting mixed elliptic hyperbolic method has not been completely carried out. We present such an analysis for one method of constrained evolution, applied to a simple vacuum system, linearized gravitational waves. We begin with a study of the hyperbolicity of the unconstrained Einstein equations. (Because the study of hyperbolicity deals only with the highest derivative order in the equations, linearization loses no essential details.) We then give explicit analytical construction of the effect of initial data setting and constrained evolution for linearized gravitational waves. While this is clearly a toy model with regard to constrained evolution, certain interesting features are found which have relevance to the full nonlinear Einstein equations

Reversed phase propagation for hyperbolic surface waves

DEFF Research Database (Denmark)

Repän, Taavi; Novitsky, Andrey; Willatzen, Morten

2018-01-01

Magnetic properties can be used to control phase propagation in hyperbolic metamaterials. However, in the visible spectrum magnetic properties are difficult to obtain. We discuss hyperbolic surface waves allowing for a similar control over phase, achieved without magnetic properties....

Clawpack: Building an open source ecosystem for solving hyperbolic PDEs

Science.gov (United States)

Iverson, Richard M.; Mandli, K.T.; Ahmadia, Aron J.; Berger, M.J.; Calhoun, Donna; George, David L.; Hadjimichael, Y.; Ketcheson, David I.; Lemoine, Grady L.; LeVeque, Randall J.

2016-01-01

Clawpack is a software package designed to solve nonlinear hyperbolic partial differential equations using high-resolution finite volume methods based on Riemann solvers and limiters. The package includes a number of variants aimed at different applications and user communities. Clawpack has been actively developed as an open source project for over 20 years. The latest major release, Clawpack 5, introduces a number of new features and changes to the code base and a new development model based on GitHub and Git submodules. This article provides a summary of the most significant changes, the rationale behind some of these changes, and a description of our current development model. Clawpack: building an open source ecosystem for solving hyperbolic PDEs.

Super-Coulombic atom-atom interactions in hyperbolic media

Science.gov (United States)

Cortes, Cristian L.; Jacob, Zubin

2017-01-01

Dipole-dipole interactions, which govern phenomena such as cooperative Lamb shifts, superradiant decay rates, Van der Waals forces and resonance energy transfer rates, are conventionally limited to the Coulombic near-field. Here we reveal a class of real-photon and virtual-photon long-range quantum electrodynamic interactions that have a singularity in media with hyperbolic dispersion. The singularity in the dipole-dipole coupling, referred to as a super-Coulombic interaction, is a result of an effective interaction distance that goes to zero in the ideal limit irrespective of the physical distance. We investigate the entire landscape of atom-atom interactions in hyperbolic media confirming the giant long-range enhancement. We also propose multiple experimental platforms to verify our predicted effect with phonon-polaritonic hexagonal boron nitride, plasmonic super-lattices and hyperbolic meta-surfaces as well. Our work paves the way for the control of cold atoms above hyperbolic meta-surfaces and the study of many-body physics with hyperbolic media.

Layered van der Waals crystals with hyperbolic light dispersion

DEFF Research Database (Denmark)

Gjerding, Morten Niklas; Petersen, R.; Pedersen, T.G.

2017-01-01

candidates for Purcell factor control of emission from diamond nitrogen-vacancy centers.Natural hyperbolic materials retain the peculiar optical properties of traditional metamaterials whilst not requiring artificial structuring. Here, the authors perform a theoretical screening of a large class of natural......Compared to artificially structured hyperbolic metamaterials, whose performance is limited by the finite size of the metallic components, the sparse number of naturally hyperbolic materials recently discovered are promising candidates for the next generation of hyperbolic materials. Using first......-infrared to the ultraviolet. Combined with the emerging field of van der Waals heterostructuring, we demonstrate how the hyperbolic properties can be further controlled by stacking different two-dimensional crystals opening new perspectives for atomic-scale design of photonic metamaterials. As an application, we identify...

Action-angle duality between the Cn-type hyperbolic Sutherland and the rational Ruijsenaars-Schneider-van Diejen models

International Nuclear Information System (INIS)

Pusztai, B.G.

2011-01-01

In a symplectic reduction framework we construct action-angle systems of canonical coordinates for both the hyperbolic Sutherland and the rational Ruijsenaars-Schneider-van Diejen integrable models associated with the C n root system. The presented dual reduction picture permits us to establish the action-angle duality between these many-particle systems.

On Hubbard-Stratonovich transformations over hyperbolic domains

International Nuclear Information System (INIS)

Fyodorov, Yan V

2005-01-01

We discuss and prove the validity of the Hubbard-Stratonovich (HS) identities over hyperbolic domains which are used frequently in studies on disordered systems and random matrices. We also introduce a counterpart of the HS identity arising in disordered systems with 'chiral' symmetry. Apart from this we outline a way of deriving the nonlinear σ-model from the gauge-invariant Wegner k-orbital model avoiding the use of the HS transformations

A Gyrovector Space Approach to Hyperbolic Geometry

CERN Document Server

Ungar, Abraham

2009-01-01

The mere mention of hyperbolic geometry is enough to strike fear in the heart of the undergraduate mathematics and physics student. Some regard themselves as excluded from the profound insights of hyperbolic geometry so that this enormous portion of human achievement is a closed door to them. The mission of this book is to open that door by making the hyperbolic geometry of Bolyai and Lobachevsky, as well as the special relativity theory of Einstein that it regulates, accessible to a wider audience in terms of novel analogies that the modern and unknown share with the classical and familiar. T

Analysis of magnetic electron lens with secant hyperbolic field distribution

International Nuclear Information System (INIS)

Pany, S.S.; Ahmed, Z.; Dubey, B.P.

2014-01-01

Electron-optical imaging instruments like Scanning Electron Microscope (SEM) and Transmission Electron Microscope (TEM) use specially designed solenoid electromagnets for focusing of the electron beam. Indicators of imaging performance of these instruments, like spatial resolution, have a strong correlation with the focal characteristics of the magnetic lenses, which in turn have been shown to be sensitive to the details of the spatial distribution of the axial magnetic field. Owing to the complexity of designing practical lenses, empirical mathematical expressions are important to obtain the desired focal properties. Thus the degree of accuracy of such models in representing the actual field distribution determines accuracy of the calculations and ultimately the performance of the lens. Historically, the mathematical models proposed by Glaser [1] and Ramberg [2] have been extensively used. In this paper the authors discuss another model with a secant-hyperbolic type magnetic field distribution function, and present a comparison between models, utilizing results from finite element-based field simulations as the reference for evaluating performance

The spectrum of hyperbolic surfaces

CERN Document Server

Bergeron, Nicolas

2016-01-01

This text is an introduction to the spectral theory of the Laplacian on compact or finite area hyperbolic surfaces. For some of these surfaces, called “arithmetic hyperbolic surfaces”, the eigenfunctions are of arithmetic nature, and one may use analytic tools as well as powerful methods in number theory to study them. After an introduction to the hyperbolic geometry of surfaces, with a special emphasis on those of arithmetic type, and then an introduction to spectral analytic methods on the Laplace operator on these surfaces, the author develops the analogy between geometry (closed geodesics) and arithmetic (prime numbers) in proving the Selberg trace formula. Along with important number theoretic applications, the author exhibits applications of these tools to the spectral statistics of the Laplacian and the quantum unique ergodicity property. The latter refers to the arithmetic quantum unique ergodicity theorem, recently proved by Elon Lindenstrauss. The fruit of several graduate level courses at Orsay...

Theory of hyperbolic stratified nanostructures for surface-enhanced Raman scattering

Science.gov (United States)

Wong, Herman M. K.; Dezfouli, Mohsen Kamandar; Axelrod, Simon; Hughes, Stephen; Helmy, Amr S.

2017-11-01

We theoretically investigate the enhancement of surface enhanced Raman spectroscopy (SERS) using hyperbolic stratified nanostructures and compare to metal nanoresonators. The photon Green function of each nanostructure within its environment is first obtained from a semianalytical modal theory, which is used in a quantum optics formalism of the molecule-nanostructure interaction to model the SERS spectrum. An intuitive methodology is presented for calculating the single-molecule enhancement factor (SMEF), which is also able to predict known experimental SERS enhancement factors of a gold nanodimer. We elucidate the important figures-of-merit of the enhancement and explore these for different designs. We find that the use of hyperbolic stratified materials can enhance the photonic local density of states (LDOS) by close to two times in comparison to pure metal nanostructures, when both designed to work at the same operating wavelengths. However, the increased LDOS is accompanied by higher electric field concentration within the lossy hyperbolic material, which leads to increased quenching that serves to reduce the overall detected SERS enhancement in the far field. For nanoresonators with resonant localized surface plasmon wavelengths in the near-infrared, the SMEF for the hyperbolic stratified nanostructure is approximately one order of magnitude lower than the pure metal counterpart. Conversely, we show that by detecting the Raman signal using a near-field probe, hyperbolic materials can provide an improvement in SERS enhancement compared to using pure metal nanostructures when the probe is sufficiently close (<50 nm ) to the Raman active molecule at the plasmonic hotspot.

How to fold a spin chain: Integrable boundaries of the Heisenberg XXX and Inozemtsev hyperbolic models

Science.gov (United States)

De La Rosa Gomez, Alejandro; MacKay, Niall; Regelskis, Vidas

2017-04-01

We present a general method of folding an integrable spin chain, defined on a line, to obtain an integrable open spin chain, defined on a half-line. We illustrate our method through two fundamental models with sl2 Lie algebra symmetry: the Heisenberg XXX and the Inozemtsev hyperbolic spin chains. We obtain new long-range boundary Hamiltonians and demonstrate that they exhibit Yangian symmetries, thus ensuring integrability of the models we obtain. The method presented provides a ;bottom-up; approach for constructing integrable boundaries and can be applied to any spin chain model.

arXiv The Hyperbolic Higgs

CERN Document Server

Cohen, Timothy; Giudice, Gian F.; Mccullough, Matthew

2018-05-15

We introduce the Hyperbolic Higgs, a novel solution to the little hierarchy problem that features Standard Model neutral scalar top partners. At one-loop order, the protection from ultraviolet sensitivity is due to an accidental non-compact symmetry of the Higgs potential that emerges in the infrared. Once the general features of the effective description are detailed, a completion that relies on a five dimensional supersymmetric framework is provided. Novel phenomenology is compared and contrasted with the Twin Higgs scenario.

Computing the Gromov hyperbolicity of a discrete metric space

KAUST Repository

Fournier, Hervé

2015-02-12

We give exact and approximation algorithms for computing the Gromov hyperbolicity of an n-point discrete metric space. We observe that computing the Gromov hyperbolicity from a fixed base-point reduces to a (max,min) matrix product. Hence, using the (max,min) matrix product algorithm by Duan and Pettie, the fixed base-point hyperbolicity can be determined in O(n2.69) time. It follows that the Gromov hyperbolicity can be computed in O(n3.69) time, and a 2-approximation can be found in O(n2.69) time. We also give a (2log2⁡n)-approximation algorithm that runs in O(n2) time, based on a tree-metric embedding by Gromov. We also show that hyperbolicity at a fixed base-point cannot be computed in O(n2.05) time, unless there exists a faster algorithm for (max,min) matrix multiplication than currently known.

Hyperbolic functions with configuration theorems and equivalent and equidecomposable figures

CERN Document Server

Shervatov, V G; Skornyakov, L A; Boltyanskii, V G

2007-01-01

This single-volume compilation of three books centers on Hyperbolic Functions, an introduction to the relationship between the hyperbolic sine, cosine, and tangent, and the geometric properties of the hyperbola. The development of the hyperbolic functions, in addition to those of the trigonometric (circular) functions, appears in parallel columns for comparison. A concluding chapter introduces natural logarithms and presents analytic expressions for the hyperbolic functions.The second book, Configuration Theorems, requires only the most elementary background in plane and solid geometry. It dis

The hyperbolic BCn Sutherland and the rational BCn Ruijsenaars-Schneider-van Diejen models: Lax matrices and duality

International Nuclear Information System (INIS)

Pusztai, B.G.

2012-01-01

In this paper, we construct canonical action-angle variables for both the hyperbolic BC n Sutherland and the rational BC n Ruijsenaars-Schneider-van Diejen models with three independent coupling constants. As a byproduct of our symplectic reduction approach, we establish the action-angle duality between these many-particle systems. The presented dual reduction picture builds upon the construction of a Lax matrix for the BC n -type rational Ruijsenaars-Schneider-van Diejen model.

Infinite periodic minimal surfaces and their crystallography in the hyperbolic plane

International Nuclear Information System (INIS)

Sadoc, J.F.; Charvolin, J.

1989-01-01

Infinite periodic minimal surfaces are now being introduced to describe some complex structures with large cells, formed by inorganic and organic materials, which can be considered as crystals of surfaces or films. Among them are the spectacular cubic crystalline structures built by amphiphilic molecules in the presence of water. The crystallographic properties of these surfaces are studied from an intrinsic point of view, using operations of groups of symmetry defined by displacements on their surface. This approach takes advantage of the relation existing between these groups and those characterizing the tilings of the hyperbolic plane. First, the general bases of the particular crystallography of the hyperbolic plane are presented. Then the translation subgroups of the hyperbolic plane are determined in one particular case, that of the tiling involved in the problem of cubic structures of liquid crystals. Finally, it is shown that the infinite periodic minimal surfaces used to describe these structures can be obtained from the hyperbolic plane when some translations are forced to identity. This is indeed formally analogous to the simple process of transformation of a Euclidean plane into a cylinder, when a translation of the plane is forced to identity by rolling the plane onto itself. Thus, this approach transforms the 3D problem of infinite periodic minimal surfaces into a 2D problem and, although the latter is to be treated in a non-Euclidean space, provides a relatively simple formalism for the investigation of infinite periodic surfaces in general and the study of the geometrical transformations relating them. (orig.)

An inspection to the hyperbolic heat conduction problem in processed meat

Directory of Open Access Journals (Sweden)

Liu Kuo-Chi

2017-01-01

Full Text Available This paper analyzes a hyperbolic heat conduction problem in processed meat with the non-homogenous initial temperature. This problem is related to an experimental study for the exploration of thermal wave behavior in biological tissue. Because the fundamental solution of the hyperbolic heat conduction model is difficult to be obtained, a modified numerical scheme is extended to solve the problem. The present results deviate from that in the literature and depict that the reliability of the experimentally measured properties presented in the literature is doubtful.

Multilayer cladding with hyperbolic dispersion for plasmonic waveguides

DEFF Research Database (Denmark)

Babicheva, Viktoriia; Shalaginov, Mikhail Y.; Ishii, Satoshi

2015-01-01

We study the properties of plasmonic waveguides with a dielectric core and multilayer metal-dielectric claddings that possess hyperbolic dispersion. The waveguides hyperbolic multilayer claddings show better performance in comparison to conventional plasmonic waveguides. © OSA 2015....

Consequence of nanofluid on peristaltic transport of a hyperbolic tangent fluid model in the occurrence of apt (tending) magnetic field

International Nuclear Information System (INIS)

Akram, Safia; Nadeem, S.

2014-01-01

In the current study, sway of nanofluid on peristaltic transport of a hyperbolic tangent fluid model in the incidence of tending magnetic field has been argued. The governing equations of a nanofluid are first modeled and then simplified under lubrication approach. The coupled nonlinear equations of temperature and nano particle volume fraction are solved analytically using a homotopy perturbation technique. The analytical solution of the stream function and pressure gradient are carried out using perturbation technique. The graphical results of the problem under discussion are also being brought under consideration to see the behavior of various physical parameters. - Highlights: • The main motivation of this work is that we want to see the behavior of nanofluids in peristaltic flows. • In literature few articles are available on this, but no article is available in asymmetric channel on the new fluid model hyperbolic tangent fluid. • So we want to fill the gap in literature studying this

Consequence of nanofluid on peristaltic transport of a hyperbolic tangent fluid model in the occurrence of apt (tending) magnetic field

Energy Technology Data Exchange (ETDEWEB)

Akram, Safia, E-mail: safia_akram@yahoo.com [Department of Basic Sciences, MCS, National University of Sciences and Technology, Rawalpindi 46000 (Pakistan); Nadeem, S. [Department of Mathematics, Quaid-i-Azam University 45320, Islamabad 44000 (Pakistan)

2014-05-01

In the current study, sway of nanofluid on peristaltic transport of a hyperbolic tangent fluid model in the incidence of tending magnetic field has been argued. The governing equations of a nanofluid are first modeled and then simplified under lubrication approach. The coupled nonlinear equations of temperature and nano particle volume fraction are solved analytically using a homotopy perturbation technique. The analytical solution of the stream function and pressure gradient are carried out using perturbation technique. The graphical results of the problem under discussion are also being brought under consideration to see the behavior of various physical parameters. - Highlights: • The main motivation of this work is that we want to see the behavior of nanofluids in peristaltic flows. • In literature few articles are available on this, but no article is available in asymmetric channel on the new fluid model hyperbolic tangent fluid. • So we want to fill the gap in literature studying this.

Computing the Gromov hyperbolicity constant of a discrete metric space

KAUST Repository

Ismail, Anas

2012-07-01

Although it was invented by Mikhail Gromov, in 1987, to describe some family of groups[1], the notion of Gromov hyperbolicity has many applications and interpretations in different fields. It has applications in Biology, Networking, Graph Theory, and many other areas of research. The Gromov hyperbolicity constant of several families of graphs and geometric spaces has been determined. However, so far, the only known algorithm for calculating the Gromov hyperbolicity constant δ of a discrete metric space is the brute force algorithm with running time O (n4) using the four-point condition. In this thesis, we first introduce an approximation algorithm which calculates a O (log n)-approximation of the hyperbolicity constant δ, based on a layering approach, in time O(n2), where n is the number of points in the metric space. We also calculate the fixed base point hyperbolicity constant δr for a fixed point r using a (max, min)−matrix multiplication algorithm by Duan in time O(n2.688)[2]. We use this result to present a 2-approximation algorithm for calculating the hyper-bolicity constant in time O(n2.688). We also provide an exact algorithm to compute the hyperbolicity constant δ in time O(n3.688) for a discrete metric space. We then present some partial results we obtained for designing some approximation algorithms to compute the hyperbolicity constant δ.

Geometry in a dynamical system without space: Hyperbolic Geometry in Kuramoto Oscillator Systems

Science.gov (United States)

Engelbrecht, Jan; Chen, Bolun; Mirollo, Renato

Kuramoto oscillator networks have the special property that their time evolution is constrained to lie on 3D orbits of the Möbius group acting on the N-fold torus TN which explains the N - 3 constants of motion discovered by Watanabe and Strogatz. The dynamics for phase models can be further reduced to 2D invariant sets in T N - 1 which have a natural geometry equivalent to the unit disk Δ with hyperbolic metric. We show that the classic Kuramoto model with order parameter Z1 (the first moment of the oscillator configuration) is a gradient flow in this metric with a unique fixed point on each generic 2D invariant set, corresponding to the hyperbolic barycenter of an oscillator configuration. This gradient property makes the dynamics especially easy to analyze. We exhibit several new families of Kuramoto oscillator models which reduce to gradient flows in this metric; some of these have a richer fixed point structure including non-hyperbolic fixed points associated with fixed point bifurcations. Work Supported by NSF DMS 1413020.

Dispersive optical soliton solutions for the hyperbolic and cubic-quintic nonlinear Schrödinger equations via the extended sinh-Gordon equation expansion method

Science.gov (United States)

Seadawy, Aly R.; Kumar, Dipankar; Chakrabarty, Anuz Kumar

2018-05-01

The (2+1)-dimensional hyperbolic and cubic-quintic nonlinear Schrödinger equations describe the propagation of ultra-short pulses in optical fibers of nonlinear media. By using an extended sinh-Gordon equation expansion method, some new complex hyperbolic and trigonometric functions prototype solutions for two nonlinear Schrödinger equations were derived. The acquired new complex hyperbolic and trigonometric solutions are expressed by dark, bright, combined dark-bright, singular and combined singular solitons. The obtained results are more compatible than those of other applied methods. The extended sinh-Gordon equation expansion method is a more powerful and robust mathematical tool for generating new optical solitary wave solutions for many other nonlinear evolution equations arising in the propagation of optical pulses.

The hyperbolic step potential: Anti-bound states, SUSY partners and Wigner time delays

Energy Technology Data Exchange (ETDEWEB)

Gadella, M. [Departamento de Física Teórica, Atómica y Óptica and IMUVA, Universidad de Valladolid, E-47011 Valladolid (Spain); Kuru, Ş. [Department of Physics, Faculty of Science, Ankara University, 06100 Ankara (Turkey); Negro, J., E-mail: jnegro@fta.uva.es [Departamento de Física Teórica, Atómica y Óptica and IMUVA, Universidad de Valladolid, E-47011 Valladolid (Spain)

2017-04-15

We study the scattering produced by a one dimensional hyperbolic step potential, which is exactly solvable and shows an unusual interest because of its asymmetric character. The analytic continuation of the scattering matrix in the momentum representation has a branch cut and an infinite number of simple poles on the negative imaginary axis which are related with the so called anti-bound states. This model does not show resonances. Using the wave functions of the anti-bound states, we obtain supersymmetric (SUSY) partners which are the series of Rosen–Morse II potentials. We have computed the Wigner reflection and transmission time delays for the hyperbolic step and such SUSY partners. Our results show that the more bound states a partner Hamiltonian has the smaller is the time delay. We also have evaluated time delays for the hyperbolic step potential in the classical case and have obtained striking similitudes with the quantum case. - Highlights: • The scattering matrix of hyperbolic step potential is studied. • The scattering matrix has a branch cut and an infinite number of poles. • The poles are associated to anti-bound states. • Susy partners using antibound states are computed. • Wigner time delays for the hyperbolic step and partner potentials are compared.

Elliptical, parabolic, and hyperbolic exchanges of energy in drag reducing plane Couette flows

Science.gov (United States)

Pereira, Anselmo S.; Mompean, Gilmar; Thompson, Roney L.; Soares, Edson J.

2017-11-01

In the present paper, we investigate the polymer-turbulence interaction by discriminating between the mechanical responses of this system to three different subdomains: elliptical, parabolic, and hyperbolic, corresponding to regions where the magnitude of vorticity is greater than, equal to, or less than the magnitude of the rate of strain, respectively, in accordance with the Q-criterion. Recently, it was recognized that hyperbolic structures play a crucial role in the drag reduction phenomenon of viscoelastic turbulent flows, thanks to the observation that hyperbolic structures, as well as vortical ones, are weakened by the action of polymers in turbulent flows in a process that can be referred to as flow parabolization. We employ direct numerical simulations of a viscoelastic finite extensible nonlinear elastic model with the Peterlin approximation to examine the transient evolution and statistically steady regimes of a plane Couette flow that has been perturbed from a laminar flow at an initial time and developed a turbulent regime as a result of this perturbation. We have found that even more activity is located within the confines of the hyperbolic structures than in the elliptical ones, which highlights the importance of considering the role of hyperbolic structures in the drag reduction mechanism.

Hyperbolic phonon polaritons in hexagonal boron nitride (Conference Presentation)

Science.gov (United States)

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

2016-09-01

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

Universal asymptotics in hyperbolicity breakdown

International Nuclear Information System (INIS)

Bjerklöv, Kristian; Saprykina, Maria

2008-01-01

We study a scenario for the disappearance of hyperbolicity of invariant tori in a class of quasi-periodic systems. In this scenario, the system loses hyperbolicity because two invariant directions come close to each other, losing their regularity. In a recent paper, based on numerical results, Haro and de la Llave (2006 Chaos 16 013120) discovered a quantitative universality in this scenario, namely, that the minimal angle between the two invariant directions has a power law dependence on the parameters and the exponents of the power law are universal. We present an analytic proof of this result

Coexistence of critical orbit types in sub-hyperbolic polynomial maps

OpenAIRE

Poirier, Alfredo

1994-01-01

We establish necessary and sufficient conditions for the realization of mapping schemata as post-critically finite polynomials, or more generally, as post-critically finite polynomial maps from a finite union of copies of the complex numbers {\\bf C} to itself which have degree two or more in each copy. As a consequence of these results we prove a transitivity relation between hyperbolic components in parameter space which was conjectured by Milnor.

Subwavelength optics with hyperbolic metamaterials: Waveguides, scattering, and optical topological transitions

DEFF Research Database (Denmark)

Ishii, Satoshi; Babicheva, Viktoriia E.; Shalaginov, Mikhail Y.

2016-01-01

Hyperbolic metamaterials possess unique optical properties owing to their hyperbolic dispersion. As hyperbolic metamaterials can be constructed just from periodic multilayers of metals and dielectrics, they have attracted considerable attention in the nanophotonics community. Here, we review some...

Electromagnetic ``black holes'' in hyperbolic metamaterials

Science.gov (United States)

Smolyaninov, Igor

2013-03-01

We demonstrate that spatial variations of the dielectric tensor components in a hyperbolic metamaterial may lead to formation of electromagnetic ``black holes'' inside this metamaterial. Similar to real black holes, horizon area of the electromagnetic ``black holes'' is quantized in units of the effective ``Planck scale'' squared. Potential experimental realizations of such electromagnetic ``black holes'' will be considered. For example, this situation may be realized in a hyperbolic metamaterial in which the dielectric component exhibits critical opalescence.

Causality and hyperbolicity of Lovelock theories

International Nuclear Information System (INIS)

Reall, Harvey S; Tanahashi, Norihiro; Way, Benson

2014-01-01

In Lovelock theories, gravity can travel faster or slower than light. The causal structure is determined by the characteristic hypersurfaces. We generalize a recent result of Izumi to prove that any Killing horizon is a characteristic hypersurface for all gravitational degrees of freedom of a Lovelock theory. Hence gravitational signals cannot escape from the region inside such a horizon. We investigate the hyperbolicity of Lovelock theories by determining the characteristic hypersurfaces for various backgrounds. First we consider Ricci flat type N spacetimes. We show that characteristic hypersurfaces are generically all non-null and that Lovelock theories are hyperbolic in any such spacetime. Next we consider static, maximally symmetric black hole solutions of Lovelock theories. Again, characteristic surfaces are generically non-null. For some small black holes, hyperbolicity is violated near the horizon. This implies that the stability of such black holes is not a well-posed problem. (paper)

On hyperbolic-dissipative systems of composite type

Science.gov (United States)

Tan, Zhong; Wang, Yanjin

2016-01-01

The Shizuta-Kawashima condition plays the fundamental role in guaranteeing global stability for systems of hyperbolic-parabolic/hyperbolic with relaxation. However, there are many important physical systems not satisfying this coupling condition, which are of composite type with regard to dissipation. The compressible Navier-Stokes equations with zero heat conductivity and Euler equations of adiabatic flow through porous media are two typical examples. In this paper, we construct the global unique solution near constant equilibria to these two systems in three dimensions for the small Hℓ (ℓ > 3) initial data. Our proof is based on a reformation of the systems in terms of the pressure, velocity and entropy, a scaled energy estimates with minimal fractional derivative counts in conjunction with the linear L2-L2 decay estimates to extract a fast enough decay of velocity gradient, which is used to close the energy estimates for the non-dissipative entropy. We also include an application to certain two-phase models.

Advanced Semi-Implicit Method (ASIM) for hyperbolic two-fluid model

International Nuclear Information System (INIS)

Lee, Sung Jae; Chung, Moon Sun

2003-01-01

Introducing the interfacial pressure jump terms based on the surface tension into the momentum equations of two-phase two-fluid model, the system of governing equations is turned mathematically into the hyperbolic system. The eigenvalues of the equation system become always real representing the void wave and the pressure wave propagation speeds as shown in the previous manuscript. To solve the interfacial pressure jump terms with void fraction gradients implicitly, the conventional semi-implicit method should be modified as an intermediate iteration method for void fraction at fractional time step. This Advanced Semi-Implicit Method (ASIM) then becomes stable without conventional additive terms. As a consequence, including the interfacial pressure jump terms with the advanced semi-implicit method, the numerical solutions of typical two-phase problems can be more stable and sound than those calculated exclusively by using any other terms like virtual mass, or artificial viscosity

Shadowing and hyperbolicity

CERN Document Server

Pilyugin, Sergei Yu

2017-01-01

Focusing on the theory of shadowing of approximate trajectories (pseudotrajectories) of dynamical systems, this book surveys recent progress in establishing relations between shadowing and such basic notions from the classical theory of structural stability as hyperbolicity and transversality. Special attention is given to the study of "quantitative" shadowing properties, such as Lipschitz shadowing (it is shown that this property is equivalent to structural stability both for diffeomorphisms and smooth flows), and to the passage to robust shadowing (which is also equivalent to structural stability in the case of diffeomorphisms, while the situation becomes more complicated in the case of flows). Relations between the shadowing property of diffeomorphisms on their chain transitive sets and the hyperbolicity of such sets are also described. The book will allow young researchers in the field of dynamical systems to gain a better understanding of new ideas in the global qualitative theory. It will also be of int...

Onto the stability analysis of hyperbolic secant-shaped Bose-Einstein condensate

Science.gov (United States)

Sabari, S.; Murali, R.

2018-05-01

We analyze the stability of the hyperbolic secant-shaped attractive Bose-Einstein condensate in the absence of external trapping potential. The appropriate theoretical model for the system is described by the nonlinear mean-field Gross-Pitaevskii equation with time varying two-body interaction effects. Using the variational method, the stability of the system is analyzed under the influence of time varying two-body interactions. Further we confirm that the stability of the attractive condensate increases by considering the hyperbolic secant-shape profile instead of Gaussian shape. The analytical results are compared with the numerical simulation by employing the split-step Crank-Nicholson method.

Near-field thermal radiation between hyperbolic metamaterials: Graphite and carbon nanotubes

Energy Technology Data Exchange (ETDEWEB)

Liu, X. L.; Zhang, R. Z.; Zhang, Z. M., E-mail: zhuomin.zhang@me.gatech.edu [G. W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332 (United States)

2013-11-18

The near-field radiative heat transfer for two hyperbolic metamaterials, namely, graphite and vertically aligned carbon nanotubes (CNTs), is investigated. Graphite is a naturally existing uniaxial medium, while CNT arrays can be modeled as an effective anisotropic medium. Different hyperbolic modes can be separately supported by these materials in certain infrared regions, resulting in a strong enhancement in near-field heat transfer. It is predicted that the heat flux between two CNT arrays can exceed that between SiC plates at any vacuum gap distance and is about 10 times higher with a 10 nm gap.

A novel grid multiwing chaotic system with only non-hyperbolic equilibria

Science.gov (United States)

Zhang, Sen; Zeng, Yicheng; Li, Zhijun; Wang, Mengjiao; Xiong, Le

2018-05-01

The structure of the chaotic attractor of a system is mainly determined by the nonlinear functions in system equations. By using a new saw-tooth wave function and a new stair function, a novel complex grid multiwing chaotic system which belongs to non-Shil'nikov chaotic system with non-hyperbolic equilibrium points is proposed in this paper. It is particularly interesting that the complex grid multiwing attractors are generated by increasing the number of non-hyperbolic equilibrium points, which are different from the traditional methods of realising multiwing attractors by adding the index-2 saddle-focus equilibrium points in double-wing chaotic systems. The basic dynamical properties of the new system, such as dissipativity, phase portraits, the stability of the equilibria, the time-domain waveform, power spectrum, bifurcation diagram, Lyapunov exponents, and so on, are investigated by theoretical analysis and numerical simulations. Furthermore, the corresponding electronic circuit is designed and simulated on the Multisim platform. The Multisim simulation results and the hardware experimental results are in good agreement with the numerical simulations of the same system on Matlab platform, which verify the feasibility of this new grid multiwing chaotic system.

Hyperbolic conservation laws in continuum physics

CERN Document Server

Dafermos, Constantine M

2016-01-01

This is a masterly exposition and an encyclopedic presentation of the theory of hyperbolic conservation laws. It illustrates the essential role of continuum thermodynamics in providing motivation and direction for the development of the mathematical theory while also serving as the principal source of applications. The reader is expected to have a certain mathematical sophistication and to be familiar with (at least) the rudiments of analysis and the qualitative theory of partial differential equations, whereas prior exposure to continuum physics is not required. The target group of readers would consist of (a) experts in the mathematical theory of hyperbolic systems of conservation laws who wish to learn about the connection with classical physics; (b) specialists in continuum mechanics who may need analytical tools; (c) experts in numerical analysis who wish to learn the underlying mathematical theory; and (d) analysts and graduate students who seek introduction to the theory of hyperbolic systems of conser...

The homogeneous geometries of real hyperbolic space

DEFF Research Database (Denmark)

Castrillón López, Marco; Gadea, Pedro Martínez; Swann, Andrew Francis

We describe the holonomy algebras of all canonical connections of homogeneous structures on real hyperbolic spaces in all dimensions. The structural results obtained then lead to a determination of the types, in the sense of Tricerri and Vanhecke, of the corresponding homogeneous tensors. We use...... our analysis to show that the moduli space of homogeneous structures on real hyperbolic space has two connected components....

Hyperbolic systems with analytic coefficients well-posedness of the Cauchy problem

CERN Document Server

Nishitani, Tatsuo

2014-01-01

This monograph focuses on the well-posedness of the Cauchy problem for linear hyperbolic systems with matrix coefficients. Mainly two questions are discussed: (A) Under which conditions on lower order terms is the Cauchy problem well posed? (B) When is the Cauchy problem well posed for any lower order term? For first order two by two systems with two independent variables with real analytic coefficients, we present complete answers for both (A) and (B). For first order systems with real analytic coefficients we prove general necessary conditions for question (B) in terms of minors of the principal symbols. With regard to sufficient conditions for (B), we introduce hyperbolic systems with nondegenerate characteristics, which contains strictly hyperbolic systems, and prove that the Cauchy problem for hyperbolic systems with nondegenerate characteristics is well posed for any lower order term. We also prove that any hyperbolic system which is close to a hyperbolic system with a nondegenerate characteristic of mu...

Hyperbolic Conservation Laws and Related Analysis with Applications

CERN Document Server

Holden, Helge; Karlsen, Kenneth

2014-01-01

This book presents thirteen papers, representing the most significant advances and current trends in nonlinear hyperbolic conservation laws and related analysis with applications. Topics covered include a survey on multidimensional systems of conservation laws as well as novel results  on liquid crystals, conservation laws with discontinuous flux functions, and applications to sedimentation.  Also included are articles on recent advances in the Euler equations and the Navier-Stokes-Fourier-Poisson system, in addition to new results on collective phenomena described by the Cucker-Smale model.    The Workshop on Hyperbolic Conservation Laws and Related Analysis with Applications at the International Centre for Mathematical Sciences (Edinburgh, UK) held in Edinburgh, September 2011, produced this fine collection of original research and survey articles. Many leading mathematicians attended the event and submitted their contributions for this volume. It is addressed to researchers and graduate students inter...

Computing the Gromov hyperbolicity of a discrete metric space

KAUST Repository

Fournier, Hervé ; Ismail, Anas; Vigneron, Antoine E.

2015-01-01

We give exact and approximation algorithms for computing the Gromov hyperbolicity of an n-point discrete metric space. We observe that computing the Gromov hyperbolicity from a fixed base-point reduces to a (max,min) matrix product. Hence, using

Long-range propagation of plasmon and phonon polaritons in hyperbolic-metamaterial waveguides

Science.gov (United States)

Babicheva, Viktoriia E.

2017-12-01

We study photonic multilayer waveguides that include layers of materials and metamaterials with a hyperbolic dispersion (HMM). We consider the long-range propagation of plasmon and phonon polaritons at the dielectric-HMM interface in different waveguide geometries (single boundary or different layers of symmetric cladding). In contrast to the traditional analysis of geometrical parameters, we make an emphasis on the optical properties of constituent materials: solving dispersion equations, we analyze how dielectric and HMM permittivities affect propagation length and mode size of waveguide eigenmodes. We derive figures of merit that should be used for each waveguide in a broad range of permittivity values as well as compare them with plasmonic waveguides. We show that the conventional plasmonic quality factor, which is the ratio of real to imaginary parts of permittivity, is not applicable to the case of waveguides with complex structure. Both telecommunication wavelengths and mid-infrared spectral ranges are of interest considering recent advances in van der Waals materials, such as hexagonal boron nitride. We evaluate the performance of the waveguides with hexagonal boron nitride in the range where it possesses hyperbolic dispersion (wavelength 6.3-7.3 μm), and we show that these waveguides with natural hyperbolic properties have higher propagation lengths than metal-based HMM waveguides.

Hyperbole, abstract motion and spatial knowledge: sequential versus simultaneous scanning.

Science.gov (United States)

Catricalà, Maria; Guidi, Annarita

2012-08-01

Hyperbole is an interesting trope in the perspective of Space Grammar, since it is related to the displacing of a limit (Lausberg in Elemente der literarischen Rhetorik. M.H. Verlag, Munchen 1967; see the Ancient Greek meaning 'to throw over' > 'exaggerate'). Hyperbole semantic mechanisms are related to virtual scanning (Holmqvist and Płuciennik in Imagery in language. Peter Lang, Frankfurt am Main, pp 777-785, 2004). Basic concepts of SIZE and QUANTITY, related image-schemas (IS) and conceptual metaphors (UP IS MORE; IMPORTANT IS BIG: Lakoff 1987, Johnson 1987) are implied in hyperbole processing. The virtual scanning is the simulation of a perceptual domain (here, the vertically oriented space). The virtual limit is defined by expected values on the relevant scale. Since hyperbole is a form of intensification, its linguistic interest lies in cases involving the extremes of a scale, for which a limit can be determined (Schemann 1994). In this experimental study, we analyze the concept of 'limit' in terms of 'abstract motion' and 'oriented space' domains (Langacker 1990) with respect to hyperboles expressed by Italian Verbs of movement. The IS considered are PATH and SOURCE-PATH-GOAL. The latter corresponds to a virtual scale whose limit is arrived at, or overcome, in hyperboles.

Control of the hyperbolic dispersion of dielectrics by an ultrashort laser pulse

Science.gov (United States)

Zhang, Xiaoqin; Wang, Feng; Zhang, Fengshou; Yao, Yugui

2018-01-01

An idea of controlling hyperbolic dispersion of dielectric materials by an ultrashort laser pulse is proposed. Taking the diamond as a concrete example and using time-dependent density functional theory calculations, we show that the permittivity tensor of the material can be effectively tuned by an ultrashort laser pulse, serving as a transient hyperbolic medium with wide working frequency window. With easily tunable laser parameters, the material can even be switched by reversal of both elliptic and hyperbolic for a particular light frequency. Our result points out a route toward transient hyperbolic materials, and it offers methods to achieve tunable hyperbolic dispersion with great potential for ultrafast device applications.

Infrared hyperbolic metasurface based on nanostructured van der Waals materials

Science.gov (United States)

Li, Peining; Dolado, Irene; Alfaro-Mozaz, Francisco Javier; Casanova, Fèlix; Hueso, Luis E.; Liu, Song; Edgar, James H.; Nikitin, Alexey Y.; Vélez, Saül; Hillenbrand, Rainer

2018-02-01

Metasurfaces with strongly anisotropic optical properties can support deep subwavelength-scale confined electromagnetic waves (polaritons), which promise opportunities for controlling light in photonic and optoelectronic applications. We developed a mid-infrared hyperbolic metasurface by nanostructuring a thin layer of hexagonal boron nitride that supports deep subwavelength-scale phonon polaritons that propagate with in-plane hyperbolic dispersion. By applying an infrared nanoimaging technique, we visualize the concave (anomalous) wavefronts of a diverging polariton beam, which represent a landmark feature of hyperbolic polaritons. The results illustrate how near-field microscopy can be applied to reveal the exotic wavefronts of polaritons in anisotropic materials and demonstrate that nanostructured van der Waals materials can form a highly variable and compact platform for hyperbolic infrared metasurface devices and circuits.

Chaotic Dynamics in Smart Grid and Suppression Scheme via Generalized Fuzzy Hyperbolic Model

Directory of Open Access Journals (Sweden)

Qiuye Sun

2014-01-01

Full Text Available This paper presents a method to control chaotic behavior of a typical Smart Grid based on generalized fuzzy hyperbolic model (GFHM. As more and more distributed generations (DG are incorporated into the Smart Grid, the chaotic behavior occurs increasingly. To verify the behavior, a dynamic model which describes a power system with DG is presented firstly. Then, the simulation result shows that the power system can lead to chaos under certain initial conditions. Based on the universal approximation of GFHM, we confirm that the chaotic behavior could be suppressed by a new controller, which is designed by means of solving a linear matrix inequality (LMI. This approach could make a good application to suppress the chaos in Smart Grid. Finally, a numerical example is given to demonstrate the effectiveness of the proposed chaotic suppression strategy.

Testable Implications of Quasi-Hyperbolic and Exponential Time Discounting

OpenAIRE

Echenique, Federico; Imai, Taisuke; Saito, Kota

2014-01-01

We present the first revealed-preference characterizations of the models of exponential time discounting, quasi-hyperbolic time discounting, and other time-separable models of consumers’ intertemporal decisions. The characterizations provide non-parametric revealed-preference tests, which we take to data using the results of a recent experiment conducted by Andreoni and Sprenger (2012). For such data, we find that less than half the subjects are consistent with exponential discounting, and on...

Hyperbolic Discounting of the Far-Distant Future

OpenAIRE

Anchugina, Nina; Ryan, Matthew; Slinko, Arkadii

2017-01-01

We prove an analogue of Weitzman's (1998) famous result that an exponential discounter who is uncertain of the appropriate exponential discount rate should discount the far-distant future using the lowest (i.e., most patient) of the possible discount rates. Our analogous result applies to a hyperbolic discounter who is uncertain about the appropriate hyperbolic discount rate. In this case, the far-distant future should be discounted using the probability-weighted harmonic mean of the possible...

On the non-hyperbolicity of a class of exponential polynomials

Directory of Open Access Journals (Sweden)

Gaspar Mora

2017-10-01

Full Text Available In this paper we have constructed a class of non-hyperbolic exponential polynomials that contains all the partial sums of the Riemann zeta function. An exponential polynomial been also defined to illustrate the complexity of the structure of the set defined by the closure of the real projections of its zeros. The sensitivity of this set, when the vector of delays is perturbed, has been analysed. These results have immediate implications in the theory of the neutral differential equations.

Properties of solutions in semi-hyperbolic patches for unsteady transonic small disturbance equations

Directory of Open Access Journals (Sweden)

Ilija Jegdic

2015-09-01

Full Text Available We consider a two-dimensional Riemann problem for the unsteady transonic small disturbance equation resulting in diverging rarefaction waves. We write the problem in self-similar coordinates and we obtain a mixed type (hyperbolic-elliptic system. Resolving the one-dimensional discontinuities in the far field, where the system is hyperbolic, and using characteristics, we formulate the problem in a semi-hyperbolic patch that is between the hyperbolic and the elliptic regions. A semi-hyperbolic patch is known as a region where one family out of two nonlinear families of characteristics starts on a sonic curve and ends on a transonic shock. We obtain existence of a smooth local solution in this semi-hyperbolic patch and we prove various properties of global smooth solutions based on a characteristic decomposition using directional derivatives.

Discontinuous Galerkin Method for Hyperbolic Conservation Laws

KAUST Repository

Mousikou, Ioanna

2016-11-11

Hyperbolic conservation laws form a special class of partial differential equations. They describe phenomena that involve conserved quantities and their solutions show discontinuities which reflect the formation of shock waves. We consider one-dimensional systems of hyperbolic conservation laws and produce approximations using finite difference, finite volume and finite element methods. Due to stability issues of classical finite element methods for hyperbolic conservation laws, we study the discontinuous Galerkin method, which was recently introduced. The method involves completely discontinuous basis functions across each element and it can be considered as a combination of finite volume and finite element methods. We illustrate the implementation of discontinuous Galerkin method using Legendre polynomials, in case of scalar equations and in case of quasi-linear systems, and we review important theoretical results about stability and convergence of the method. The applications of finite volume and discontinuous Galerkin methods to linear and non-linear scalar equations, as well as to the system of elastodynamics, are exhibited.

Discontinuous Galerkin Method for Hyperbolic Conservation Laws

KAUST Repository

Mousikou, Ioanna

2016-01-01

Hyperbolic conservation laws form a special class of partial differential equations. They describe phenomena that involve conserved quantities and their solutions show discontinuities which reflect the formation of shock waves. We consider one-dimensional systems of hyperbolic conservation laws and produce approximations using finite difference, finite volume and finite element methods. Due to stability issues of classical finite element methods for hyperbolic conservation laws, we study the discontinuous Galerkin method, which was recently introduced. The method involves completely discontinuous basis functions across each element and it can be considered as a combination of finite volume and finite element methods. We illustrate the implementation of discontinuous Galerkin method using Legendre polynomials, in case of scalar equations and in case of quasi-linear systems, and we review important theoretical results about stability and convergence of the method. The applications of finite volume and discontinuous Galerkin methods to linear and non-linear scalar equations, as well as to the system of elastodynamics, are exhibited.

Hyperbolic metamaterials: Nonlocal response regularizes broadband supersingularity

DEFF Research Database (Denmark)

Yan, Wei; Wubs, Martijn; Mortensen, N. Asger

2012-01-01

We study metamaterials known as hyperbolic media that in the usual local-response approximation exhibit hyperbolic dispersion and an associated broadband singularity in the density of states. Instead, from the more microscopic hydrodynamic Drude theory we derive qualitatively different optical...... properties of these metamaterials, due to the free-electron nonlocal optical response of their metal constituents. We demonstrate that nonlocal response gives rise to a large-wavevector cutoff in the dispersion that is inversely proportional to the Fermi velocity of the electron gas, but also for small...

A Synthesizable VHDL Model of the Exact Solution for Three-dimensional Hyperbolic Positioning System

Directory of Open Access Journals (Sweden)

Ralph Bucher

2002-01-01

Full Text Available This paper presents a synthesizable VHDL model of a three-dimensional hyperbolic positioning system algorithm. The algorithm obtains an exact solution for the three-dimensional location of a mobile given the locations of four fixed stations (like a global positioning system [GPS] satellite or a base station in a cell and the signal time of arrival (TOA from the mobile to each station. The detailed derivation of the steps required in the algorithm is presented. A VHDL model of the algorithm was implemented and simulated using the IEEE numeric_std package. Signals were described by a 32-bit vector. Simulation results predict location of the mobile is off by 1 m for best case and off by 36 m for worst case. A C + + program using real numbers was used as a benchmark for the accuracy and precision of the VHDL model. The model can be easily synthesized for low power hardware implementation.

Computing the Gromov hyperbolicity constant of a discrete metric space

KAUST Repository

Ismail, Anas

2012-01-01

, and many other areas of research. The Gromov hyperbolicity constant of several families of graphs and geometric spaces has been determined. However, so far, the only known algorithm for calculating the Gromov hyperbolicity constant δ of a discrete metric

Finite-width plasmonic waveguides with hyperbolic multilayer cladding

DEFF Research Database (Denmark)

Babicheva, Viktoriia; Shalaginov, Mikhail Y.; Ishii, Satoshi

2015-01-01

Engineering plasmonic metamaterials with anisotropic optical dispersion enables us to tailor the properties of metamaterial-based waveguides. We investigate plasmonic waveguides with dielectric cores and multilayer metal-dielectric claddings with hyperbolic dispersion. Without using any homogeniz......Engineering plasmonic metamaterials with anisotropic optical dispersion enables us to tailor the properties of metamaterial-based waveguides. We investigate plasmonic waveguides with dielectric cores and multilayer metal-dielectric claddings with hyperbolic dispersion. Without using any...

Impact of hyperbolicity on chimera states in ensembles of nonlocally coupled chaotic oscillators

Energy Technology Data Exchange (ETDEWEB)

Semenova, N.; Anishchenko, V. [Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov (Russian Federation); Zakharova, A.; Schöll, E. [Institut für Theoretische Physik, TU Berlin, Hardenbergstraße 36, 10623 Berlin (Germany)

2016-06-08

In this work we analyse nonlocally coupled networks of identical chaotic oscillators. We study both time-discrete and time-continuous systems (Henon map, Lozi map, Lorenz system). We hypothesize that chimera states, in which spatial domains of coherent (synchronous) and incoherent (desynchronized) dynamics coexist, can be obtained only in networks of chaotic non-hyperbolic systems and cannot be found in networks of hyperbolic systems. This hypothesis is supported by numerical simulations for hyperbolic and non-hyperbolic cases.

Anomalously Weak Scattering in Metal-Semiconductor Multilayer Hyperbolic Metamaterials

Directory of Open Access Journals (Sweden)

Hao Shen

2015-05-01

Full Text Available In contrast to strong plasmonic scattering from metal particles or structures in metal films, we show that patterns of arbitrary shape fabricated out of multilayer hyperbolic metamaterials become invisible within a chosen band of optical frequencies. This is due to anomalously weak scattering when the in-plane permittivity of the multilayer hyperbolic metamaterials is tuned to match with the surrounding medium. This new phenomenon is described theoretically and demonstrated experimentally by optical characterization of various patterns in Au-Si multilayer hyperbolic metamaterials. This anomalously weak scattering is insensitive to pattern sizes, shapes, and incident angles, and has potential applications in scattering cross-section engineering, optical encryption, low-observable conductive probes, and optoelectric devices.

Cuspidal discrete series for projective hyperbolic spaces

DEFF Research Database (Denmark)

Andersen, Nils Byrial; Flensted-Jensen, Mogens

2013-01-01

Abstract. We have in [1] proposed a definition of cusp forms on semisimple symmetric spaces G/H, involving the notion of a Radon transform and a related Abel transform. For the real non-Riemannian hyperbolic spaces, we showed that there exists an infinite number of cuspidal discrete series......, and at most finitely many non-cuspidal discrete series, including in particular the spherical discrete series. For the projective spaces, the spherical discrete series are the only non-cuspidal discrete series. Below, we extend these results to the other hyperbolic spaces, and we also study the question...

Advanced Research Workshop on Nonlinear Hyperbolic Problems

CERN Document Server

Serre, Denis; Raviart, Pierre-Arnaud

1987-01-01

The field of nonlinear hyperbolic problems has been expanding very fast over the past few years, and has applications - actual and potential - in aerodynamics, multifluid flows, combustion, detonics amongst other. The difficulties that arise in application are of theoretical as well as numerical nature. In fact, the papers in this volume of proceedings deal to a greater extent with theoretical problems emerging in the resolution of nonlinear hyperbolic systems than with numerical methods. The volume provides an excellent up-to-date review of the current research trends in this area.

A note on sigular limits to hyperbolic systems

OpenAIRE

Bianchini, Stefano

2000-01-01

In this note we consider two different singular limits to hyperbolic system of conservation laws, namely the standard backward schemes for non linear semigroups and the semidiscrete scheme. Under the assumption that the rarefaction curve of the corresponding hyperbolic system are straight lines, we prove the stability of the solution and the convergence to the perturbed system to the unique solution of the limit system for initial data with small total variation.

Life Insurance and Annuity Demand under Hyperbolic Discounting

Directory of Open Access Journals (Sweden)

Siqi Tang

2018-04-01

Full Text Available In this paper, we analyse and construct a lifetime utility maximisation model with hyperbolic discounting. Within the model, a number of assumptions are made: complete markets, actuarially fair life insurance/annuity is available, and investors have time-dependent preferences. Time dependent preferences are in contrast to the usual case of constant preferences (exponential discounting. We find: (1 investors (realistically demand more life insurance after retirement (in contrast to the standard model, which showed strong demand for life annuities, and annuities are rarely purchased; (2 optimal consumption paths exhibit a humped shape (which is usually only found in incomplete markets under the assumptions of the standard model.

Stability and boundary stabilization of 1-D hyperbolic systems

CERN Document Server

Bastin, Georges

2016-01-01

This monograph explores the modeling of conservation and balance laws of one-dimensional hyperbolic systems using partial differential equations. It presents typical examples of hyperbolic systems for a wide range of physical engineering applications, allowing readers to understand the concepts in whichever setting is most familiar to them. With these examples, it also illustrates how control boundary conditions may be defined for the most commonly used control devices. The authors begin with the simple case of systems of two linear conservation laws and then consider the stability of systems under more general boundary conditions that may be differential, nonlinear, or switching. They then extend their discussion to the case of nonlinear conservation laws and demonstrate the use of Lyapunov functions in this type of analysis. Systems of balance laws are considered next, starting with the linear variety before they move on to more general cases of nonlinear ones. They go on to show how the problem of boundary...

Broadband enhancement of local density of states using silicon-compatible hyperbolic metamaterials

Energy Technology Data Exchange (ETDEWEB)

Wang, Yu; Inampudi, Sandeep; Capretti, Antonio [Department of Electrical and Computer Engineering and Photonics Center, Boston University, 8 Saint Mary' s Street Boston, Massachusetts 02215 (United States); Sugimoto, Hiroshi [Department of Electrical and Computer Engineering and Photonics Center, Boston University, 8 Saint Mary' s Street Boston, Massachusetts 02215 (United States); Department of Electrical and Electronic Engineering, Graduate School of Engineering, Kobe University, Rokkodai, Nada, Kobe 657-8501 (Japan); Fujii, Minoru [Department of Electrical and Electronic Engineering, Graduate School of Engineering, Kobe University, Rokkodai, Nada, Kobe 657-8501 (Japan); Dal Negro, Luca, E-mail: dalnegro@bu.edu [Department of Electrical and Computer Engineering and Photonics Center, Boston University, 8 Saint Mary' s Street Boston, Massachusetts 02215 (United States); Division of Materials Science and Engineering, Boston University, 15 Saint Mary' s Street, Brookline, Massachusetts 02446 (United States)

2015-06-15

Light emitting silicon quantum dots by colloidal synthesis were uniformly spin-coated into a 20 nm-thick film and deposited atop a hyperbolic metamaterial of alternating TiN and SiO{sub 2} sub-wavelength layers. Using steady-state and time-resolved photoluminescence spectroscopy as a function of the emission wavelength in partnership with rigorous electromagnetic modeling of dipolar emission, we demonstrate enhanced Local Density of States and coupling to high-k modes in a broad spectral range. These findings provide an alternative approach for the engineering of novel Si-compatible broadband sources that leverage the control of radiative transitions in hyperbolic metamaterials and the flexibility of the widespread Si platform.

Differentiable dynamical systems an introduction to structural stability and hyperbolicity

CERN Document Server

Wen, Lan

2016-01-01

This is a graduate text in differentiable dynamical systems. It focuses on structural stability and hyperbolicity, a topic that is central to the field. Starting with the basic concepts of dynamical systems, analyzing the historic systems of the Smale horseshoe, Anosov toral automorphisms, and the solenoid attractor, the book develops the hyperbolic theory first for hyperbolic fixed points and then for general hyperbolic sets. The problems of stable manifolds, structural stability, and shadowing property are investigated, which lead to a highlight of the book, the \\Omega-stability theorem of Smale. While the content is rather standard, a key objective of the book is to present a thorough treatment for some tough material that has remained an obstacle to teaching and learning the subject matter. The treatment is straightforward and hence could be particularly suitable for self-study. Selected solutions are available electronically for instructors only. Please send email to textbooks@ams.org for more informatio...

Congruence Approximations for Entrophy Endowed Hyperbolic Systems

Science.gov (United States)

Barth, Timothy J.; Saini, Subhash (Technical Monitor)

1998-01-01

Building upon the standard symmetrization theory for hyperbolic systems of conservation laws, congruence properties of the symmetrized system are explored. These congruence properties suggest variants of several stabilized numerical discretization procedures for hyperbolic equations (upwind finite-volume, Galerkin least-squares, discontinuous Galerkin) that benefit computationally from congruence approximation. Specifically, it becomes straightforward to construct the spatial discretization and Jacobian linearization for these schemes (given a small amount of derivative information) for possible use in Newton's method, discrete optimization, homotopy algorithms, etc. Some examples will be given for the compressible Euler equations and the nonrelativistic MHD equations using linear and quadratic spatial approximation.

Grammatical complexity for two-dimensional maps

International Nuclear Information System (INIS)

Hagiwara, Ryouichi; Shudo, Akira

2004-01-01

We calculate the grammatical complexity of the symbol sequences generated from the Henon map and the Lozi map using the recently developed methods to construct the pruning front. When the map is hyperbolic, the language of symbol sequences is regular in the sense of the Chomsky hierarchy and the corresponding grammatical complexity takes finite values. It is found that the complexity exhibits a self-similar structure as a function of the system parameter, and the similarity of the pruning fronts is discussed as an origin of such self-similarity. For non-hyperbolic cases, it is observed that the complexity monotonically increases as we increase the resolution of the pruning front

Grammatical complexity for two-dimensional maps

Energy Technology Data Exchange (ETDEWEB)

Hagiwara, Ryouichi; Shudo, Akira [Department of Physics, Tokyo Metropolitan University, Minami-Ohsawa, Hachioji, Tokyo 192-0397 (Japan)

2004-11-05

We calculate the grammatical complexity of the symbol sequences generated from the Henon map and the Lozi map using the recently developed methods to construct the pruning front. When the map is hyperbolic, the language of symbol sequences is regular in the sense of the Chomsky hierarchy and the corresponding grammatical complexity takes finite values. It is found that the complexity exhibits a self-similar structure as a function of the system parameter, and the similarity of the pruning fronts is discussed as an origin of such self-similarity. For non-hyperbolic cases, it is observed that the complexity monotonically increases as we increase the resolution of the pruning front.

Grammatical complexity for two-dimensional maps

Science.gov (United States)

Hagiwara, Ryouichi; Shudo, Akira

2004-11-01

We calculate the grammatical complexity of the symbol sequences generated from the Hénon map and the Lozi map using the recently developed methods to construct the pruning front. When the map is hyperbolic, the language of symbol sequences is regular in the sense of the Chomsky hierarchy and the corresponding grammatical complexity takes finite values. It is found that the complexity exhibits a self-similar structure as a function of the system parameter, and the similarity of the pruning fronts is discussed as an origin of such self-similarity. For non-hyperbolic cases, it is observed that the complexity monotonically increases as we increase the resolution of the pruning front.

Boundary causality versus hyperbolicity for spherical black holes in Gauss–Bonnet gravity

International Nuclear Information System (INIS)

Andrade, Tomás; Cáceres, Elena; Keeler, Cynthia

2017-01-01

We explore the constraints boundary causality places on the allowable Gauss–Bonnet gravitational couplings in asymptotically AdS spaces, specifically considering spherical black hole solutions. We additionally consider the hyperbolicity properties of these solutions, positing that hyperbolicity-violating solutions are sick solutions whose causality properties provide no information about the theory they reside in. For both signs of the Gauss–Bonnet coupling, spherical black holes violate boundary causality at smaller absolute values of the coupling than planar black holes do. For negative coupling, as we tune the Gauss–Bonnet coupling away from zero, both spherical and planar black holes violate hyperbolicity before they violate boundary causality. For positive coupling, the only hyperbolicity-respecting spherical black holes which violate boundary causality do not do so appreciably far from the planar bound. Consequently, eliminating hyperbolicity-violating solutions means the bound on Gauss–Bonnet couplings from the boundary causality of spherical black holes is no tighter than that from planar black holes. (paper)

Quantum mechanics of hyperbolic metamaterials: Modeling of quantum time and Everett's “universal wavefunction”

Energy Technology Data Exchange (ETDEWEB)

Smolyaninov, Igor I., E-mail: smoly@umd.edu

2014-11-15

Modern advances in transformation optics and electromagnetic metamaterials made possible experimental demonstrations of highly unusual curvilinear “optical spaces”, such as various geometries necessary for electromagnetic cloaking. Recently we demonstrated that mapping light intensity in a hyperbolic metamaterial may also model the flow of time in an effective (2+1) dimensional Minkowski spacetime. Curving such an effective spacetime creates experimental model of a toy “big bang”. Here we demonstrate that at low light levels this model may be used to emulate a fully covariant version of quantum mechanics in a (2+1) dimensional Minkowski spacetime. When quantum mechanical description is applied near the toy “big bang”, the Everett's “universal wave function” formalism arises naturally, in which the wave function of the model “universe” appears to be a quantum superposition of mutually orthogonal “parallel universe” states.

Euler and Navier-Stokes equations on the hyperbolic plane.

Science.gov (United States)

Khesin, Boris; Misiolek, Gerard

2012-11-06

We show that nonuniqueness of the Leray-Hopf solutions of the Navier-Stokes equation on the hyperbolic plane (2) observed by Chan and Czubak is a consequence of the Hodge decomposition. We show that this phenomenon does not occur on (n) whenever n ≥ 3. We also describe the corresponding general Hamiltonian framework of hydrodynamics on complete Riemannian manifolds, which includes the hyperbolic setting.

Cognitive Procedures and Hyperbolic Discounting

NARCIS (Netherlands)

Nir, A.

2004-01-01

"Hyperbolic discount functions are characterized by a relatively high discount rate over short horizons and a relatively low discount rate over long horizons" (Laibson 1997).We suggest two cognitive procedures where individuals perceive future utility as decreasing at a decreasing rate as a function

Euler and Navier–Stokes equations on the hyperbolic plane

Science.gov (United States)

Khesin, Boris; Misiołek, Gerard

2012-01-01

We show that nonuniqueness of the Leray–Hopf solutions of the Navier–Stokes equation on the hyperbolic plane ℍ2 observed by Chan and Czubak is a consequence of the Hodge decomposition. We show that this phenomenon does not occur on ℍn whenever n ≥ 3. We also describe the corresponding general Hamiltonian framework of hydrodynamics on complete Riemannian manifolds, which includes the hyperbolic setting. PMID:23091015

Mathematical and numerical study of nonlinear hyperbolic equations: model coupling and nonclassical shocks

International Nuclear Information System (INIS)

Boutin, B.

2009-11-01

This thesis concerns the mathematical and numerical study of nonlinear hyperbolic partial differential equations. A first part deals with an emergent problematic: the coupling of hyperbolic equations. The pursued applications are linked with the mathematical coupling of computing platforms, dedicated to an adaptative simulation of multi-scale phenomena. We propose and analyze a new coupling formalism based on extended PDE systems avoiding the geometric treatment of the interfaces. In addition, it allows to formulate the problem in a multidimensional setting, with possible covering of the coupled models. This formalism allows in particular to equip the coupling procedure with viscous regularization mechanisms, useful in the selection of natural discontinuous solutions. We analyze existence and uniqueness in the framework of a parabolic regularization a la Dafermos. Existence of a solution holds true under very general conditions but failure of uniqueness may naturally arise as soon as resonance occurs at the interfaces. Next, we highlight that our extended PDE framework gives rise to another regularization strategy based on thick interfaces. In this setting, we prove existence and uniqueness of the solutions of the Cauchy problem for initial data in L ∞ . The main tool consists in the derivation of a flexible and robust finite volume method for general triangulation which is analyzed in the setting of entropy measure-valued solutions by DiPerna. The second part is devoted to the definition of a finite volume scheme for the computing of nonclassical solutions of a scalar conservation law based on a kinetic relation. This scheme offers the feature to be stricto sensu conservative, in opposition to a Glimm approach that is only statistically conservative. The validity of our approach is illustrated through numerical examples. (author)

Some problems on nonlinear hyperbolic equations and applications

CERN Document Server

Peng, YueJun

2010-01-01

This volume is composed of two parts: Mathematical and Numerical Analysis for Strongly Nonlinear Plasma Models and Exact Controllability and Observability for Quasilinear Hyperbolic Systems and Applications. It presents recent progress and results obtained in the domains related to both subjects without attaching much importance to the details of proofs but rather to difficulties encountered, to open problems and possible ways to be exploited. It will be very useful for promoting further study on some important problems in the future.

Generalized hyperbolic functions to find soliton-like solutions for a system of coupled nonlinear Schroedinger equations

International Nuclear Information System (INIS)

Yomba, Emmanuel

2008-01-01

With the aid of symbolic computation, we demonstrate that the known method which is based on the new generalized hyperbolic functions and the new kinds of generalized hyperbolic function transformations, generates classes of exact solutions to a system of coupled nonlinear Schroedinger equations. This system includes the modified Hubbard model and the system of coupled nonlinear Schroedinger derived by Lazarides and Tsironis. Four types of solutions for this system are given explicitly, namely: new bright-bright, new dark-dark, new bright-dark and new dark-bright solitons

Novel Hyperbolic Homoclinic Solutions of the Helmholtz-Duffing Oscillators

Directory of Open Access Journals (Sweden)

Yang-Yang Chen

2016-01-01

Full Text Available The exact and explicit homoclinic solution of the undamped Helmholtz-Duffing oscillator is derived by a presented hyperbolic function balance procedure. The homoclinic solution of the self-excited Helmholtz-Duffing oscillator can also be obtained by an extended hyperbolic perturbation method. The application of the present homoclinic solutions to the chaos prediction of the nonautonomous Helmholtz-Duffing oscillator is performed. Effectiveness and advantage of the present solutions are shown by comparisons.

Scattering theory of the hyperbolic BC{sub n} Sutherland and the rational BC{sub n} Ruijsenaars–Schneider–van Diejen models

Energy Technology Data Exchange (ETDEWEB)

Pusztai, B.G., E-mail: gpusztai@math.u-szeged.hu

2013-09-11

In this paper, we investigate the scattering properties of the hyperbolic BC{sub n} Sutherland and the rational BC{sub n} Ruijsenaars–Schneider–van Diejen many-particle systems with three independent coupling constants. Utilizing the recently established action-angle duality between these classical integrable models, we construct their wave and scattering maps. In particular, we prove that for both particle systems the scattering map has a factorized form.

Decay Rates of Interactive Hyperbolic-Parabolic PDE Models with Thermal Effects on the Interface

International Nuclear Information System (INIS)

Lasiecka, I.; Lebiedzik, C.

2000-01-01

We consider coupled PDE systems comprising of a hyperbolic and a parabolic-like equation with an interface on a portion of the boundary. These models are motivated by structural acoustic problems. A specific prototype consists of a wave equation defined on a three-dimensional bounded domain Ω coupled with a thermoelastic plate equation defined on Γ 0 -a flat surface of the boundary Ω. Thus, the coupling between the wave and the plate takes place on the interface Γ 0 . The main issue studied here is that of uniform stability of the overall interactive model. Since the original (uncontrolled) model is only strongly stable, but not uniformly stable, the question becomes: what is the 'minimal amount' of dissipation necessary to obtain uniform decay rates for the energy of the overall system? Our main result states that boundary nonlinear dissipation placed only on a suitable portion of the part of the boundary which is complementary to Γ 0 , suffices for the stabilization of the entire structure. This result is new with respect to the literature on several accounts: (i) thermoelasticity is accounted for in the plate model; (ii) the plate model does not account for any type of mechanical damping, including the structural damping most often considered in the literature; (iii) there is no mechanical damping placed on the interface Γ 0 ; (iv) the boundary damping is nonlinear without a prescribed growth rate at the origin; (v) the undamped portions of the boundary partial Ω are subject to Neumann (rather than Dirichlet) boundary conditions, which is a recognized difficulty in the context of stabilization of wave equations, due to the fact that the strong Lopatinski condition does not hold. The main mathematical challenge is to show how the thermal energy is propagated onto the hyperbolic component of the structure. This is achieved by using a recently developed sharp theory of boundary traces corresponding to wave and plate equations, along with the analytic

Small universal cellular automata in hyperbolic spaces a collection of jewels

CERN Document Server

Margenstern, Maurice

2013-01-01

Hyperbolic geometry is an essential part of theoretical astrophysics and cosmology. Besides specialists of these domains, many specialists of new domains start to show a growing interest both to hyperbolic geometry and to cellular automata. This is especially the case in biology and computer science.    This book gives the reader a deep and efficient introduction to an algorithmic approach to hyperbolic geometry. It focuses the attention on the possibilities to obtain in this frame the power of computing everything a computer can compute, that is to say: universality.    The minimal ways to get universality are invistigated in a large family of tilings of the hyperbolic plane. In several cases the best results are obtained.In all cases, the results are close to the theoretical best values. This gives rise to fantastic illustrations: the results are jewels in all meanings of the word. ------------------------    Maurice MARGENSTERN is professor emeritus at the University of Lorraine, he is a member of LI...

Hyperbolic white noise functional solutions of Wick-type stochastic compound KdV-Burgers equations

International Nuclear Information System (INIS)

Han Xiu; Xie Yingchao

2009-01-01

Variable coefficient and Wick-type stochastic compound KdV-Burgers equations are investigated. By using white noise analysis, Hermite transform and the hyperbolic function method, we obtain a number of Wick versions of hyperbolic white noise functional solutions and hyperbolic function solutions for Wick-type stochastic and variable coefficient compound KdV-Burgers equations, respectively.

Computation of Quasi-Periodic Normally Hyperbolic Invariant Tori: Algorithms, Numerical Explorations and Mechanisms of Breakdown

Science.gov (United States)

Canadell, Marta; Haro, Àlex

2017-12-01

We present several algorithms for computing normally hyperbolic invariant tori carrying quasi-periodic motion of a fixed frequency in families of dynamical systems. The algorithms are based on a KAM scheme presented in Canadell and Haro (J Nonlinear Sci, 2016. doi: 10.1007/s00332-017-9389-y), to find the parameterization of the torus with prescribed dynamics by detuning parameters of the model. The algorithms use different hyperbolicity and reducibility properties and, in particular, compute also the invariant bundles and Floquet transformations. We implement these methods in several 2-parameter families of dynamical systems, to compute quasi-periodic arcs, that is, the parameters for which 1D normally hyperbolic invariant tori with a given fixed frequency do exist. The implementation lets us to perform the continuations up to the tip of the quasi-periodic arcs, for which the invariant curves break down. Three different mechanisms of breakdown are analyzed, using several observables, leading to several conjectures.

Doubly stratified MHD tangent hyperbolic nanofluid flow due to permeable stretched cylinder

Science.gov (United States)

Nagendramma, V.; Leelarathnam, A.; Raju, C. S. K.; Shehzad, S. A.; Hussain, T.

2018-06-01

An investigation is exhibited to analyze the presence of heat source and sink in doubly stratified MHD incompressible tangent hyperbolic fluid due to stretching of cylinder embedded in porous space under nanoparticles. To develop the mathematical model of tangent hyperbolic nanofluid, movement of Brownian and thermophoretic are accounted. The established equations of continuity, momentum, thermal and solutal boundary layers are reassembled into sets of non-linear expressions. These assembled expressions are executed with the help of Runge-Kutta scheme with MATLAB. The impacts of sundry parameters are illustrated graphically and the engineering interest physical quantities like skin friction, Nusselt and Sherwood number are examined by computing numerical values. It is clear that the power-law index parameter and curvature parameter shows favorable effect on momentum boundary layer thickness whereas Weissennberg number reveals inimical influence.

Relative entropy for hyperbolic-parabolic systems and application to the constitutive theory of thermoviscoelasticity

KAUST Repository

Christoforou, Cleopatra; Tzavaras, Athanasios

2017-01-01

We extend the relative entropy identity to the class of hyperbolic-parabolic systems whose hyperbolic part is symmetrizable. The resulting identity is useful to provide measure valued weak versus strong uniqueness theorems for the hyperbolic problem. Also, it yields a convergence result in the zero-viscosity limit to smooth solutions in an Lp framework. The relative entropy identity is also developed for the system of gas dynamics for viscous and heat conducting gases, and for the system of thermoviscoelasticity with viscosity and heat-conduction. Existing differences between the example and the general hyperbolic theory are underlined.

Relative entropy for hyperbolic-parabolic systems and application to the constitutive theory of thermoviscoelasticity

KAUST Repository

Christoforou, Cleopatra

2017-12-10

We extend the relative entropy identity to the class of hyperbolic-parabolic systems whose hyperbolic part is symmetrizable. The resulting identity is useful to provide measure valued weak versus strong uniqueness theorems for the hyperbolic problem. Also, it yields a convergence result in the zero-viscosity limit to smooth solutions in an Lp framework. The relative entropy identity is also developed for the system of gas dynamics for viscous and heat conducting gases, and for the system of thermoviscoelasticity with viscosity and heat-conduction. Existing differences between the example and the general hyperbolic theory are underlined.

Hyperbolic metamaterials based on quantum-dot plasmon-resonator nanocomposites

DEFF Research Database (Denmark)

Zhukovsky, Sergei; Ozel, T.; Mutlugun, E.

2014-01-01

We theoretically demonstrate that nanocomposites made of colloidal semiconductor quantum dot monolayers placed between metal nanoparticle monolayers can function as multilayer hyperbolic metamaterials. Depending on the thickness of the spacer between the quantum dot and nanoparticle layers......, the effective permittivity tensor of the nanocomposite is shown to become indefinite, resulting in increased photonic density of states and strong enhancement of quantum dot luminescence. This explains the results of recent experiments [T. Ozel et al., ACS Nano 5, 1328 (2011)] and confirms that hyperbolic...

Hawking into Unruh mapping for embeddings of hyperbolic type

International Nuclear Information System (INIS)

Paston, S A

2015-01-01

We study the conditions of the existence of Hawking into Unruh mapping for hyperbolic (Fronsdal-type) metric embeddings into the Minkowski space, for which timelines are hyperbolas. Many examples are known for global embeddings into the Minkowskian spacetime (GEMS), with such mapping for physically interesting metrics with some symmetry. However, examples of embeddings, both smooth and hyperbolic, for which there is no mapping, were also given. In the present work we prove that Hawking into Unruh mapping takes place for a hyperbolic embedding of an arbitrary metric with a time-like Killing vector and a Killing horizon if the embedding of such type exists and smoothly covers the horizon. At the same time, we do not assume any symmetry (spherical, for example), except the time translational invariance, which corresponds to the existence of a time-like Killing vector. We show that the known examples of the absence of mapping do not satisfy the formulated conditions of its existence. (paper)

Bioaccumulation of trace metals in the Antarctic amphipod Paramoera walkeri (Stebbing, 1906): comparison of two-compartment and hyperbolic toxicokinetic models

International Nuclear Information System (INIS)

Clason, B.; Duquesne, S.; Liess, M.; Schulz, R.; Zauke, G.-P.

2003-01-01

Bioaccumulation of Cd, Pb, Cu and Zn in the Antarctic gammaridean amphipod Paramoera walkeri (Stebbing, 1906) was investigated at Casey station (Australian Antarctic Territory). The main goals were to provide information on accumulation strategies of the organisms tested and to verify toxicokinetic models as a predictive tool. The organisms accumulated metals upon exposure and it was possible to estimate significant model parameters of two-compartment and hyperbolic models. These models were successfully verified in a second toxicokinetic study. However, the application of hyperbolic models appears to be more promising as a predictive tool for metals in amphipods compared to compartment models, which have failed to adequately predict metal accumulation in experiments with increasing external exposures in previous studies. The following kinetic bioconcentration factors (BCFs) for the theoretical equilibrium were determined: 150-630 (Cd), 1600-7000 (Pb), 1700-3800 (Cu) and 670-2400 (Zn). We find decreasing BCFs with increasing external metal dosing but similar results for treatments with and without natural UV radiation and for the combined effect of different exposure regimes (single versus multiple metal exposure) and/or the amphipod collective involved (Beall versus Denison Island). A tentative estimation showed the following sequence of sensitivity of P. walkeri to an increase of soluble metal exposure: 0.2-3.0 μg Cd l -1 , 0.12-0.25 μg Pb l -1 , 0.9-3.0 μg Cu l -1 and 9-26 μg Zn l -1 . Thus, the amphipod investigated proved to be more sensitive as biomonitor compared to gammarids from German coastal waters (with the exception of Cd) and to copepods from the Weddell Sea inferred from literature data

RG cascades in hyperbolic quiver gauge theories

International Nuclear Information System (INIS)

Ahl Laamara, R.; Ait Ben Haddou, M.; Belhaj, A.; Drissi, L.B.; Saidi, E.H.

2004-01-01

In this paper, we provide a general classification of supersymmatric QFT4s into three basic sets: ordinary, affine and indefinite classes. The last class, which has not been enough explored in literature, is shown to share most of properties of ordinary and affine super-QFT4s. This includes, amongst others, its embedding in type II string on local Calabi-Yau threefolds. We give realizations of these supersymmetric QFT4s as D-brane world volume gauge theories. A special interest is devoted to hyperbolic subset for its peculiar features and for the role it plays in type IIB background with non-zero axion. We also study RG flows and duality cascades in case of hyperbolic quiver theories. Comments regarding the full indefinite sector are made

Hyperbolic Cosines and Sines Theorems for the Triangle Formed by Arcs of Intersecting Semicircles on Euclidean Plane

Directory of Open Access Journals (Sweden)

Robert M. Yamaleev

2013-01-01

Full Text Available The hyperbolic cosines and sines theorems for the curvilinear triangle bounded by circular arcs of three intersecting circles are formulated and proved by using the general complex calculus. The method is based on a key formula establishing a relationship between exponential function and the cross-ratio. The proofs are carried out on Euclidean plane.

Atomic disintegrations for partially hyperbolic diffeomorphisms

NARCIS (Netherlands)

Homburg, Ale Jan

2017-01-01

Shub and Wilkinson and Ruelle and Wilkinson studied a class of volume preserving diffeomorphisms on the three dimensional torus that are stably ergodic. The diffeomorphisms are partially hyperbolic and admit an invariant central foliation of circles. The foliation is not absolutely continuous; in

First-order symmetrizable hyperbolic formulations of Einstein's equations including lapse and shift as dynamical fields

International Nuclear Information System (INIS)

Alvi, Kashif

2002-01-01

First-order hyperbolic systems are promising as a basis for numerical integration of Einstein's equations. In previous work, the lapse and shift have typically not been considered part of the hyperbolic system and have been prescribed independently. This can be expensive computationally, especially if the prescription involves solving elliptic equations. Therefore, including the lapse and shift in the hyperbolic system could be advantageous for numerical work. In this paper, two first-order symmetrizable hyperbolic systems are presented that include the lapse and shift as dynamical fields and have only physical characteristic speeds

Thermodynamics and stability of hyperbolic charged black holes

International Nuclear Information System (INIS)

Cai Ronggen; Wang Anzhong

2004-01-01

In AdS space the black hole horizon can be a hypersurface with a positive, zero, or negative constant curvature, resulting in different horizon topology. Thermodynamics and stability of black holes in AdS spaces are quite different for different horizon curvatures. In this paper we study thermodynamics and stability of hyperbolic charged black holes with negative constant curvature horizon in the grand canonical ensemble and canonical ensemble, respectively. They include hyperbolic Reissner-Nordstroem black holes in arbitrary dimensions and hyperbolic black holes in the D=5,4,7 gauged supergravities. It is found that associated Gibbs free energies are always negative, which implies that these black hole solutions are globally stable and the black hole phase is dominant in the grand canonical ensemble, but there is a region in the phase space where the black hole is not locally thermodynamically stable with a negative heat capacity for a given gauge potential. In the canonical ensemble, the Helmholtz free energies are not always negative and heat capacities with fixed electric charge are not always positive, which indicates that the Hawking-Page phase transition may happen and black holes are not always locally thermodynamically stable

Optic axis-driven new horizons for hyperbolic metamaterials

Directory of Open Access Journals (Sweden)

Boardman Allan D.

2015-01-01

Full Text Available The broad assertion here is that the current hyperbolic metamaterial world is only partially served by investigations that incorporate only some limited version of anisotropy. Even modest deviations of the optic axis from the main propagation axis lead to new phase shifts, which not only compete with those created by absorption but end up dominating them. Some progress has been attempted in the literature by introducing the terms “asymmetric hyperbolic media”, but it appears that this kind of asymmetry only involves an optic axis at an angle to the interface of a uniaxial crystal. From a device point of view, many new prospects should appear and the outcomes of the investigations presented here yield a new general theory. It is emphasised that the orientation of the optic axis is a significant determinant in the resulting optical properties. Whereas for conventional anisotropic waveguides homogeneous propagating waves occur over a limited range of angular dispositions of the optic axis it is shown that for a hyperbolic guide a critical angular setting exists, above which the guided waves are always homogeneous. This has significant implications for metawaveguide designs. The resulting structures are more tolerant to optic axis misalignment.

Cauchy problem for differential operators with double characteristics non-effectively hyperbolic characteristics

CERN Document Server

Nishitani, Tatsuo

2017-01-01

Combining geometrical and microlocal tools, this monograph gives detailed proofs of many well/ill-posed results related to the Cauchy problem for differential operators with non-effectively hyperbolic double characteristics. Previously scattered over numerous different publications, the results are presented from the viewpoint that the Hamilton map and the geometry of bicharacteristics completely characterizes the well/ill-posedness of the Cauchy problem. A doubly characteristic point of a differential operator P of order m (i.e. one where Pm = dPm = 0) is effectively hyperbolic if the Hamilton map FPm has real non-zero eigenvalues. When the characteristics are at most double and every double characteristic is effectively hyperbolic, the Cauchy problem for P can be solved for arbitrary lower order terms. If there is a non-effectively hyperbolic characteristic, solvability requires the subprincipal symbol of P to lie between − Pµj and P µj , where iµj are the positive imaginary eigenvalues of FPm ....

New Generalized Hyperbolic Functions to Find New Exact Solutions of the Nonlinear Partial Differential Equations

Directory of Open Access Journals (Sweden)

Yusuf Pandir

2013-01-01

Full Text Available We firstly give some new functions called generalized hyperbolic functions. By the using of the generalized hyperbolic functions, new kinds of transformations are defined to discover the exact approximate solutions of nonlinear partial differential equations. Based on the generalized hyperbolic function transformation of the generalized KdV equation and the coupled equal width wave equations (CEWE, we find new exact solutions of two equations and analyze the properties of them by taking different parameter values of the generalized hyperbolic functions. We think that these solutions are very important to explain some physical phenomena.

A Combination Theorem for Convex Hyperbolic Manifolds, with Applications to Surfaces in 3-Manifolds

OpenAIRE

Baker, Mark; Cooper, Daryl

2005-01-01

We prove the convex combination theorem for hyperbolic n-manifolds. Applications are given both in high dimensions and in 3 dimensions. One consequence is that given two geometrically finite subgroups of a discrete group of isometries of hyperbolic n-space, satisfying a natural condition on their parabolic subgroups, there are finite index subgroups which generate a subgroup that is an amalgamated free product. Constructions of infinite volume hyperbolic n-manifolds are described by gluing lo...

Perturbed Strong Stability Preserving Time-Stepping Methods For Hyperbolic PDEs

KAUST Repository

Hadjimichael, Yiannis

2017-09-30

A plethora of physical phenomena are modelled by hyperbolic partial differential equations, for which the exact solution is usually not known. Numerical methods are employed to approximate the solution to hyperbolic problems; however, in many cases it is difficult to satisfy certain physical properties while maintaining high order of accuracy. In this thesis, we develop high-order time-stepping methods that are capable of maintaining stability constraints of the solution, when coupled with suitable spatial discretizations. Such methods are called strong stability preserving (SSP) time integrators, and we mainly focus on perturbed methods that use both upwind- and downwind-biased spatial discretizations. Firstly, we introduce a new family of third-order implicit Runge–Kuttas methods with arbitrarily large SSP coefficient. We investigate the stability and accuracy of these methods and we show that they perform well on hyperbolic problems with large CFL numbers. Moreover, we extend the analysis of SSP linear multistep methods to semi-discretized problems for which different terms on the right-hand side of the initial value problem satisfy different forward Euler (or circle) conditions. Optimal perturbed and additive monotonicity-preserving linear multistep methods are studied in the context of such problems. Optimal perturbed methods attain augmented monotonicity-preserving step sizes when the different forward Euler conditions are taken into account. On the other hand, we show that optimal SSP additive methods achieve a monotonicity-preserving step-size restriction no better than that of the corresponding non-additive SSP linear multistep methods. Furthermore, we develop the first SSP linear multistep methods of order two and three with variable step size, and study their optimality. We describe an optimal step-size strategy and demonstrate the effectiveness of these methods on various one- and multi-dimensional problems. Finally, we establish necessary conditions

Operator-Based Preconditioning of Stiff Hyperbolic Systems

International Nuclear Information System (INIS)

Reynolds, Daniel R.; Samtaney, Ravi; Woodward, Carol S.

2009-01-01

We introduce an operator-based scheme for preconditioning stiff components encountered in implicit methods for hyperbolic systems of partial differential equations posed on regular grids. The method is based on a directional splitting of the implicit operator, followed by a characteristic decomposition of the resulting directional parts. This approach allows for solution to any number of characteristic components, from the entire system to only the fastest, stiffness-inducing waves. We apply the preconditioning method to stiff hyperbolic systems arising in magnetohydro- dynamics and gas dynamics. We then present numerical results showing that this preconditioning scheme works well on problems where the underlying stiffness results from the interaction of fast transient waves with slowly-evolving dynamics, scales well to large problem sizes and numbers of processors, and allows for additional customization based on the specific problems under study

Dynamics beyond uniform hyperbolicity a global geometric and probabilistic perspective

CERN Document Server

Bonatti, Christian; Viana, Marcelo

2005-01-01

The notion of uniform hyperbolicity, introduced by Steve Smale in the early sixties, unified important developments and led to a remarkably successful theory for a large class of systems: uniformly hyperbolic systems often exhibit complicated evolution which, nevertheless, is now rather well understood, both geometrically and statistically.Another revolution has been taking place in the last couple of decades, as one tries to build a global theory for "most" dynamical systems, recovering as much as possible of the conclusions of the uniformly hyperbolic case, in great generality. This book aims to put such recent developments in a unified perspective, and to point out open problems and likely directions for further progress. It is aimed at researchers, both young and senior, willing to get a quick, yet broad, view of this part of dynamics. Main ideas, methods, and results are discussed, at variable degrees of depth, with references to the original works for details and complementary information.

Waves in hyperbolic and double negative metamaterials including rogues and solitons

Science.gov (United States)

Boardman, A. D.; Alberucci, A.; Assanto, G.; Grimalsky, V. V.; Kibler, B.; McNiff, J.; Nefedov, I. S.; Rapoport, Yu G.; Valagiannopoulos, C. A.

2017-11-01

considered with a model of the response of hyperbolic metamaterials in terms of the homogenisation (‘effective medium’) approach. The model has a macroscopic dielectric tensor encompassing at least one negative eigenvalue. It is shown that light propagating in the presence of hyperbolic dispersion undergoes negative (anomalous) diffraction. The theory is ten broadened out to include the influence of the orientation of the optical axis with respect to the propagation wave vector. Optical rogue waves are discussed in terms of how they are influenced, but not suppressed, by a metamaterial background. It is strongly discussed that metamaterials and optical rogue waves have both been making headlines in recent years and that they are, separately, large areas of research to study. A brief background of the inevitable linkage of them is considered and important new possibilities are discussed. After this background is revealed some new rogue wave configurations combining the two areas are presented alongside a discussion of the way forward for the future.

Studies in the Hyperbolic Circle Problem

DEFF Research Database (Denmark)

Cherubini, Giacomo

In this thesis we study the remainder term e(s) in the hyperbolic lattice point counting problem. Our main approach to this problem is that of the spectral theory of automorphic forms. We show that the function e(s) exhibits properties similar to those of almost periodic functions, and we study d...

On some issues of the modeling and analysis of two phase flow systems

International Nuclear Information System (INIS)

Ndjinga, M.

2007-04-01

Two-fluid and multi-field models are commonly used in the modeling and numerical simulation of two phase flows. They however present several mathematical and numerical difficulties, such as their lack of hyperbolicity or their non trivial Eigen-structure. It is important to understand the well-posedness of such possibly non hyperbolic systems before solving them numerically. For this reason, we study the solutions of systems of first order partial differential equations having a possibly complex Eigen-structure. We then characterise the hyperbolicity of the six equations two-fluid model with interfacial forces having differential expressions such as the interfacial pressure term, virtual mass and lift forces. The study of the characteristic polynomial leads to a diagram representing the location and topology of the non hyperbolic regions. We eventually propose numerous closure laws that make the two-fluid and multi-field models unconditionally hyperbolic. In order to numerically solve the two-fluid and multi-field models equations in a finite volume approach using a Roe type scheme, we propose two new algorithms designed for an efficient computation of the matrix absolute value function. These algorithms are robust as they avoid the computation of the eigenvectors of the argument matrix. The first is based on an iterative approach and converges in a finite number of steps if the eigenvalues are real. The second is faster, and besides can handle the case of complex eigenvalues. Thanks to these new algorithms, it is now possible to solve efficiently the six equations two-fluid model with differential interfacial terms, or the multi-field model with an arbitrary number of fields. We finally show the results of some recent numerical simulations of the six equations two-fluid model and the multi-field model with interfacial forces having a differential expression. (author)

First-Order Hyperbolic System Method for Time-Dependent Advection-Diffusion Problems

Science.gov (United States)

2014-03-01

accuracy, with rapid convergence over each physical time step, typically less than five Newton iter - ations. 1 Contents 1 Introduction 3 2 Hyperbolic...however, we employ the Gauss - Seidel (GS) relaxation, which is also an O(N) method for the discretization arising from hyperbolic advection-diffusion system...advection-diffusion scheme. The linear dependency of the iterations on Table 1: Boundary layer problem ( Convergence criteria: Residuals < 10−8.) log10Re

Existence for a class of discrete hyperbolic problems

Directory of Open Access Journals (Sweden)

Luca Rodica

2006-01-01

Full Text Available We investigate the existence and uniqueness of solutions to a class of discrete hyperbolic systems with some nonlinear extreme conditions and initial data, in a real Hilbert space.

Front tracking for hyperbolic conservation laws

CERN Document Server

Holden, Helge

2015-01-01

This is the second edition of a well-received book providing the fundamentals of the theory hyperbolic conservation laws. Several chapters have been rewritten, new material has been added, in particular, a chapter on space dependent flux functions, and the detailed solution of the Riemann problem for the Euler equations. Hyperbolic conservation laws are central in the theory of nonlinear partial differential equations and in science and technology. The reader is given a self-contained presentation using front tracking, which is also a numerical method. The multidimensional scalar case and the case of systems on the line are treated in detail. A chapter on finite differences is included. From the reviews of the first edition: "It is already one of the few best digests on this topic. The present book is an excellent compromise between theory and practice. Students will appreciate the lively and accurate style." D. Serre, MathSciNet  "I have read the book with great pleasure, and I can recommend it to experts ...

Singularly perturbed hyperbolic problems on metric graphs: asymptotics of solutions

Directory of Open Access Journals (Sweden)

Golovaty Yuriy

2017-04-01

Full Text Available We are interested in the evolution phenomena on star-like networks composed of several branches which vary considerably in physical properties. The initial boundary value problem for singularly perturbed hyperbolic differential equation on a metric graph is studied. The hyperbolic equation becomes degenerate on a part of the graph as a small parameter goes to zero. In addition, the rates of degeneration may differ in different edges of the graph. Using the boundary layer method the complete asymptotic expansions of solutions are constructed and justified.

Spectral theory of infinite-area hyperbolic surfaces

CERN Document Server

Borthwick, David

2016-01-01

This text introduces geometric spectral theory in the context of infinite-area Riemann surfaces, providing a comprehensive account of the most recent developments in the field. For the second edition the context has been extended to general surfaces with hyperbolic ends, which provides a natural setting for development of the spectral theory while still keeping technical difficulties to a minimum. All of the material from the first edition is included and updated, and new sections have been added. Topics covered include an introduction to the geometry of hyperbolic surfaces, analysis of the resolvent of the Laplacian, scattering theory, resonances and scattering poles, the Selberg zeta function, the Poisson formula, distribution of resonances, the inverse scattering problem, Patterson-Sullivan theory, and the dynamical approach to the zeta function. The new sections cover the latest developments in the field, including the spectral gap, resonance asymptotics near the critical line, and sharp geometric constan...

On the Growth of the Number of Hyperbolic Gravitational Instantons with respect to Volume

OpenAIRE

Ratcliffe, John G.; Tschantz, Steven T.

2000-01-01

In this paper, we show that the number of hyperbolic gravitational instantons grows superexponentially with respect to volume. As an application, we show that the Hartle-Hawking wave function for the universe is infinitely peaked at a certain closed hyperbolic 3-manifold.

Exact moduli space metrics for hyperbolic vortex polygons

International Nuclear Information System (INIS)

Krusch, S.; Speight, J. M.

2010-01-01

Exact metrics on some totally geodesic submanifolds of the moduli space of static hyperbolic N-vortices are derived. These submanifolds, denoted as Σ n,m , are spaces of C n -invariant vortex configurations with n single vortices at the vertices of a regular polygon and m=N-n coincident vortices at the polygon's center. The geometric properties of Σ n,m are investigated, and it is found that Σ n,n-1 is isometric to the hyperbolic plane of curvature -(3πn) -1 . The geodesic flow on Σ n,m and a geometrically natural variant of geodesic flow recently proposed by Collie and Tong ['The dynamics of Chern-Simons vortices', Phys. Rev. D Part. Fields Gravit. Cosmol. 78, 065013 (2008);e-print arXiv:hep-th/0805.0602] are analyzed in detail.

Forced oscillation of hyperbolic equations with mixed nonlinearities

Directory of Open Access Journals (Sweden)

Yutaka Shoukaku

2012-04-01

Full Text Available In this paper, we consider the mixed nonlinear hyperbolic equations with forcing term via Riccati inequality. Some sufficient conditions for the oscillation are derived by using Young inequality and integral averaging method.

On the hyperbolicity condition in linear elasticity

Directory of Open Access Journals (Sweden)

Remigio Russo

1991-05-01

Full Text Available This talk, which is mainly expository and based on [2-5], discusses the hyperbolicity conditions in linear elastodynamics. Particular emphasis is devoted to the key role it plays in the uniqueness questions associated with the mixed boundary-initial value problem in unbounded domains.

Clawpack: building an open source ecosystem for solving hyperbolic PDEs

KAUST Repository

Mandli, Kyle T.; Ahmadia, Aron J.; Berger, Marsha; Calhoun, Donna; George, David L.; Hadjimichael, Yiannis; Ketcheson, David I.; Lemoine, Grady I.; LeVeque, Randall J.

2016-01-01

Clawpack is a software package designed to solve nonlinear hyperbolic partial differential equations using high-resolution finite volume methods based on Riemann solvers and limiters. The package includes a number of variants aimed at different applications and user communities. Clawpack has been actively developed as an open source project for over 20 years. The latest major release, Clawpack 5, introduces a number of new features and changes to the code base and a new development model based on GitHub and Git submodules. This article provides a summary of the most significant changes, the rationale behind some of these changes, and a description of our current development model.

Clawpack: building an open source ecosystem for solving hyperbolic PDEs

KAUST Repository

Mandli, Kyle T.

2016-08-08

Clawpack is a software package designed to solve nonlinear hyperbolic partial differential equations using high-resolution finite volume methods based on Riemann solvers and limiters. The package includes a number of variants aimed at different applications and user communities. Clawpack has been actively developed as an open source project for over 20 years. The latest major release, Clawpack 5, introduces a number of new features and changes to the code base and a new development model based on GitHub and Git submodules. This article provides a summary of the most significant changes, the rationale behind some of these changes, and a description of our current development model.

Some remarks on the topology of hyperbolic actions of Rn on n-manifolds

Science.gov (United States)

Bouloc, Damien

2017-11-01

This paper contains some results on the topology of a nondegenerate action of Rn on a compact connected n-manifold M when the action is totally hyperbolic (i.e. its toric degree is zero). We study the R-action generated by a fixed vector of Rn, that provides some results on the number of hyperbolic domains and the number of fixed points of the action. We study with more details the case of the 2-sphere, in particular we investigate some combinatorial properties of the associated 4-valent graph embedded in S2. We also construct hyperbolic actions in dimension 3, on the sphere S3 and on the projective space RP3.

Tangent-Impulse Interception for a Hyperbolic Target

Directory of Open Access Journals (Sweden)

Dongzhe Wang

2014-01-01

Full Text Available The two-body interception problem with an upper-bounded tangent impulse for the interceptor on an elliptic parking orbit to collide with a nonmaneuvering target on a hyperbolic orbit is studied. Firstly, four special initial true anomalies whose velocity vectors are parallel to either of the lines of asymptotes for the target hyperbolic orbit are obtained by using Newton-Raphson method. For different impulse points, the solution-existence ranges of the target true anomaly for any conic transfer are discussed in detail. Then, the time-of-flight equation is solved by the secant method for a single-variable piecewise function about the target true anomaly. Considering the sphere of influence of the Earth and the upper bound on the fuel, all feasible solutions are obtained for different impulse points. Finally, a numerical example is provided to apply the proposed technique for all feasible solutions and the global minimum-time solution with initial coasting time.

Cross-synergism in enzymatic hydrolysis of lignocellulosics: mathematical correlations according to a hyperbolic model

Energy Technology Data Exchange (ETDEWEB)

Tarantili, P.A.; Koullas, D.P.; Christakopoulos, P.; Kekos, D.; Koukios, E.G.; Macris, B.J. [National Technical Univ. of Athens (Greece). Dept. of Chemical Engineering

1996-10-01

The effect of cross-synergism in enzymatic hydrolysis of ball-milled Avicell, alkali-treated straw cellulose (ATSC), cotton and filter paper was investigated using mixtures of Fusarium oxysporum and Neurospora crassa enzymes. The experimental data were fitted according to an empirical hyperbolic model which utilized two parameters, the maximum conversion ({chi}{sub max}) and the enzymatic hydrolysis time corresponding to 50% of {chi}{sub max} (t{sub 1/2}). The model can predict conversion of polysaccharides as a function of hydrolysis time. Both model parameters were found to be strongly dependent on the crystallinity index as well as on the degree of delignification of the substrate. Up to 60% cellulose hydrolysis can be achieved when the crystallinity index of Avicell is reduced from 94.8% to 63.3%. The percentage increase of {chi}{sub max} due to delignification was higher than the corresponding increase of t{sub 1/2}. The extent of cross-synergism depends strongly on crystallinity index and degree of delignification. This type of synergism has been found to be significant in the case of substrates which are resistant to hydrolysis, such as Avicell (with high crystallinity index) or cotton. Cross-synergism phenomena caused by enzymatic mixtures can double cellulose hydrolysis yield with delignified straw as compared to the hydrolysis yields achieved by single-microorganism cellulases. (author)

Simultaneous exact controllability for Maxwell equations and for a second-order hyperbolic system

Directory of Open Access Journals (Sweden)

Boris V. Kapitonov

2010-02-01

Full Text Available We present a result on "simultaneous" exact controllability for two models that describe two hyperbolic dynamics. One is the system of Maxwell equations and the other a vector-wave equation with a pressure term. We obtain the main result using modified multipliers in order to generate a necessary observability estimate which allow us to use the Hilbert Uniqueness Method (HUM introduced by Lions.

Gromov hyperbolicity in lexicographic product graphs

Indian Academy of Sciences (India)

41

on the group [17]. The concept of hyperbolicity appears also in discrete mathematics, algorithms and networking. For .... graph (of a presentation with solvable word problem) there is an algorithm which allows to decide if it is ...... of Theorem 3.14, i.e., dG1◦{w}(Vp, [π(x)π(z)] ∪ [π(z)π(y)]) = δ(G1) with π the canonical projection.

Approximate Treatment of the Dirac Equation with Hyperbolic Potential Function

Science.gov (United States)

Durmus, Aysen

2018-03-01

The time independent Dirac equation is solved analytically for equal scalar and vector hyperbolic potential function in the presence of Greene and Aldrich approximation scheme. The bound state energy equation and spinor wave functions expressed by the hypergeometric function have been obtained in detail with asymptotic iteration approach. In order to indicate the accuracy of this different approach proposed to solve second order linear differential equations, we present that in the non-relativistic limit, analytical solutions of the Dirac equation converge to those of the Schrödinger one. We introduce numerical results of the theoretical analysis for hyperbolic potential function. Bound states corresponding to arbitrary values of n and l are reported for potential parameters covering a wide range of interaction. Also, we investigate relativistic vibrational energy spectra of alkali metal diatomic molecules in the different electronic states. It is observed that theoretical vibrational energy values are consistent with experimental Rydberg-Klein-Rees (RKR) results and vibrational energies of NaK, K_2 and KRb diatomic molecules interacting with hyperbolic potential smoothly converge to the experimental dissociation limit D_e=2508cm^{-1}, 254cm^{-1} and 4221cm^{-1}, respectively.

Hyperbolic statics in space-time

OpenAIRE

Pavlov, Dmitry; Kokarev, Sergey

2014-01-01

Based on the concept of material event as an elementary material source that is concentrated on metric sphere of zero radius --- light-cone of Minkowski space-time, we deduce the analog of Coulomb's law for hyperbolic space-time field universally acting between the events of space-time. Collective field that enables interaction of world lines of a pair of particles at rest contains a standard 3-dimensional Coulomb's part and logarithmic addendum. We've found that the Coulomb's part depends on...

The Hyperbolic Sine Cardinal and the Catenary

Science.gov (United States)

Sanchez-Reyes, Javier

2012-01-01

The hyperbolic function sinh(x)/x receives scant attention in the literature. We show that it admits a clear geometric interpretation as the ratio between length and chord of a symmetric catenary segment. The inverse, together with the use of dimensionless parameters, furnishes a compact, explicit construction of a general catenary segment of…

Rarefaction and shock waves for multi-dimensional hyperbolic conservation laws

International Nuclear Information System (INIS)

Dening, Li

1991-01-01

In this paper, the author wants to show the local existence of a solution of combination of shock and rarefaction waves for the multi-dimensional hyperbolic system of conservation laws. The typical example he has in mind is the Euler equations for compressible fluid. More generally, he studies the hyperbolic system of conservation laws ∂ t F 0 (u) + Σ j=1 n ∂ x j F j (u)=0 where u=(u 1 ....,u m ) and F j (u), j=0,...,n are m-dimensional vector-valued functions. He'll impose some conditions in the following on the systems (1.2). All these conditions are satisfied by the Euler equations

OSCILLATION OF IMPULSIVE HYPERBOLIC PARTIAL DIFFERENTIAL EQUATION WITH DELAY

Institute of Scientific and Technical Information of China (English)

无

2006-01-01

In this paper, oscillation properties of the solutions of impulsive hyperbolic equation with delay are investigated via the method of differential inequalities. Sufficient conditions for oscillations of the solutions are established.

High order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms

International Nuclear Information System (INIS)

Xing Yulong; Shu Chiwang

2006-01-01

Hyperbolic balance laws have steady state solutions in which the flux gradients are nonzero but are exactly balanced by the source term. In our earlier work [J. Comput. Phys. 208 (2005) 206-227; J. Sci. Comput., accepted], we designed a well-balanced finite difference weighted essentially non-oscillatory (WENO) scheme, which at the same time maintains genuine high order accuracy for general solutions, to a class of hyperbolic systems with separable source terms including the shallow water equations, the elastic wave equation, the hyperbolic model for a chemosensitive movement, the nozzle flow and a two phase flow model. In this paper, we generalize high order finite volume WENO schemes and Runge-Kutta discontinuous Galerkin (RKDG) finite element methods to the same class of hyperbolic systems to maintain a well-balanced property. Finite volume and discontinuous Galerkin finite element schemes are more flexible than finite difference schemes to treat complicated geometry and adaptivity. However, because of a different computational framework, the maintenance of the well-balanced property requires different technical approaches. After the description of our well-balanced high order finite volume WENO and RKDG schemes, we perform extensive one and two dimensional simulations to verify the properties of these schemes such as the exact preservation of the balance laws for certain steady state solutions, the non-oscillatory property for general solutions with discontinuities, and the genuine high order accuracy in smooth regions

The Arabic Hyperbolic Pattern 'Fa??al' in Two Recent Translations of the Qur'an

Directory of Open Access Journals (Sweden)

Amr M. El-Zawawy

2014-06-01

Full Text Available The present study addresses the problem of rendering the فعال'fa??al' hyperbolic pattern into English in two recent translations of the Qur'an. Due to the variety of Qur'an translations and the large amount of hyperbolic forms of Arabic verbs recorded in the Qur'an, only two translations of the Qur'an are consulted and analyzed: these two translations, namely Saheeh International Translation (1997 and Prof. Abdel-Haleem's (2004, are distinguished by the fact that they are recent and well-received. Moreover, the investigation of hyperbolic forms is confined to the Arabic formفعال    'fa??al'. The study reveals that the Saheeh translator has applied morphological shifting in many examples while Abdel-Haleem's translation exhibits a considerable amount of syntactic transposition, coupled with paraphrasing. The test of accuracy as administered here is to give a clear picture of the need to pay particular attention to hyperboles of the form examined and other ones not analyzed here for limitations of space.

Analytic vortex solutions on compact hyperbolic surfaces

International Nuclear Information System (INIS)

Maldonado, Rafael; Manton, Nicholas S

2015-01-01

We construct, for the first time, abelian Higgs vortices on certain compact surfaces of constant negative curvature. Such surfaces are represented by a tessellation of the hyperbolic plane by regular polygons. The Higgs field is given implicitly in terms of Schwarz triangle functions and analytic solutions are available for certain highly symmetric configurations. (paper)

Advanced fabrication of hyperbolic metamaterials

DEFF Research Database (Denmark)

Shkondin, Evgeniy; Sukham, Johneph; Panah, Mohammad Esmail Aryaee

2017-01-01

Hyperbolic metamaterials can provide unprecedented properties in accommodation of high-k (high wave vector) waves and enhancement of the optical density of states. To reach such performance the metamaterials have to be fabricated with as small imperfections as possible. Here we report on our...... advances in two approaches in fabrication of optical metamaterials. We deposit ultrathin ultrasmooth gold layers with the assistance of organic material (APTMS) adhesion layer. The technology supports the stacking of such layers in a multiperiod construction with alumina spacers between gold films, which...

The Arabic Hyperbolic Pattern "Fa??al" in Two Recent Translations of the Qur'an

Science.gov (United States)

El-Zawawy, Amr M.

2014-01-01

The present study addresses the problem of rendering the ?? ?? 'fa??al' hyperbolic pattern into English in two recent translations of the Qur'an. Due to the variety of Qur'an translations and the large amount of hyperbolic forms of Arabic verbs recorded in the Qur'an, only two translations of the Qur'an are consulted and analyzed: these two…

Near-field radiative heat transfer between graphene-covered hyperbolic metamaterials

Science.gov (United States)

Hong, Xiao-Juan; Li, Jian-Wen; Wang, Tong-Biao; Zhang, De-Jian; Liu, Wen-Xing; Liao, Qing-Hua; Yu, Tian-Bao; Liu, Nian-Hua

2018-04-01

We propose the use of graphene-covered silicon carbide (SiC) nanowire arrays (NWAs) for theoretical studies of near-field radiative heat transfer. The SiC NWAs exhibit a hyperbolic characteristic at an appropriately selected filling-volume fraction. The surface plasmon supported by graphene and the hyperbolic modes supported by SiC NWAs significantly affect radiative heat transfer. The heat-transfer coefficient (HTC) between the proposed structures is larger than that between SiC NWAs. We also find that the chemical potential of graphene plays an important role in modulating the HTC. The tunability of chemical potential through gate voltage enables flexible control of heat transfer using the graphene-covered SiC NWAs.

Blind Source Separation Algorithms Using Hyperbolic and Givens Rotations for High-Order QAM Constellations

KAUST Repository

Shah, Syed Awais Wahab

2017-11-24

This paper addresses the problem of blind demixing of instantaneous mixtures in a multiple-input multiple-output communication system. The main objective is to present efficient blind source separation (BSS) algorithms dedicated to moderate or high-order QAM constellations. Four new iterative batch BSS algorithms are presented dealing with the multimodulus (MM) and alphabet matched (AM) criteria. For the optimization of these cost functions, iterative methods of Givens and hyperbolic rotations are used. A pre-whitening operation is also utilized to reduce the complexity of design problem. It is noticed that the designed algorithms using Givens rotations gives satisfactory performance only for large number of samples. However, for small number of samples, the algorithms designed by combining both Givens and hyperbolic rotations compensate for the ill-whitening that occurs in this case and thus improves the performance. Two algorithms dealing with the MM criterion are presented for moderate order QAM signals such as 16-QAM. The other two dealing with the AM criterion are presented for high-order QAM signals. These methods are finally compared with the state of art batch BSS algorithms in terms of signal-to-interference and noise ratio, symbol error rate and convergence rate. Simulation results show that the proposed methods outperform the contemporary batch BSS algorithms.

Blind Source Separation Algorithms Using Hyperbolic and Givens Rotations for High-Order QAM Constellations

KAUST Repository

Shah, Syed Awais Wahab; Abed-Meraim, Karim; Al-Naffouri, Tareq Y.

2017-01-01

This paper addresses the problem of blind demixing of instantaneous mixtures in a multiple-input multiple-output communication system. The main objective is to present efficient blind source separation (BSS) algorithms dedicated to moderate or high-order QAM constellations. Four new iterative batch BSS algorithms are presented dealing with the multimodulus (MM) and alphabet matched (AM) criteria. For the optimization of these cost functions, iterative methods of Givens and hyperbolic rotations are used. A pre-whitening operation is also utilized to reduce the complexity of design problem. It is noticed that the designed algorithms using Givens rotations gives satisfactory performance only for large number of samples. However, for small number of samples, the algorithms designed by combining both Givens and hyperbolic rotations compensate for the ill-whitening that occurs in this case and thus improves the performance. Two algorithms dealing with the MM criterion are presented for moderate order QAM signals such as 16-QAM. The other two dealing with the AM criterion are presented for high-order QAM signals. These methods are finally compared with the state of art batch BSS algorithms in terms of signal-to-interference and noise ratio, symbol error rate and convergence rate. Simulation results show that the proposed methods outperform the contemporary batch BSS algorithms.

Tuning subwavelength-structured focus in the hyperbolic metamaterials

Science.gov (United States)

Pan, Rong; Tang, Zhixiang; Pan, Jin; Peng, Runwu

2016-10-01

In this paper, we have systematically investigated light propagating in the hyperbolic metamaterials (HMMs) covered by a subwavelength grating. Based on the equal-frequency contour analyses, light in the HMM is predicted to propagate along a defined direction because of its hyperbolic dispersion, which is similar to the self-collimating effects in photonic crystals. By using the finite-difference time-domain, numerical simulations demonstrate a subwavelength bright spot at the intersection of the adjacent directional beams. Different from the images in homogeneous media, the magnetic fields and electric fields at the spot are layered, especially for the electric fields Ez that is polarized to the propagating direction, i.e., the layer normal direction. Moreover, the Ez is hollow in the layer plane and is stronger than the other electric field component Ex. Therefore, the whole electric field is structured and its pattern can be tuned by the HMM's effective anisotropic electromagnetic parameters. Our results may be useful for generating subwavelength structured light.

Hyperbolic variables on surfaces with non-definite quadratic forms (extension of Beltrami equation); Le variabili iperboliche sulle superfici a metrica non definita (estensione dell'equazione di Beltrami)

Energy Technology Data Exchange (ETDEWEB)

Catoni, F.; Cannata, R.; Nichelatti, E.; Zampetti, P. [ENEA, Divisione Sistemi Energetici per la Mobilita' e l' Habitat, Centro Ricerche Casaccia, S. Maria di Galeria, Rome (Italy)

2001-07-01

Gauss showed the link between the definite quadratic differential forms and the complex functions. Beltrami, following Gauss' idea, linked the complex functions to elliptic partial differential equations. In this report it was shown how the use of hyperbolic numbers and hyperbolic functions allows to extend the same results to non definite quadratic differential forms. Using this kind of approach, one can tackle the hyperbolic partial differential equations by a different point of view. [Italian] In un famoso lavoro per la rappresentazione conforme di due superfici, Gauss scompose le forme differenziali quadratiche in due fattori complessi coniugati. In questo modo ridusse la soluzione del problema a quella di una forma differnziale lineare. Beltrami, partendo dalla stessa decomposizione, collego' le f.d.q. alle equazioni differenziali a derivate parziali di tipo ellittico aprendo cosi' nuove strade per la loro soluzione. Dalla relativita' ristretta hanno pero' assunto importanza fisica anche le forme differenziali quadratiche non definite. Viene qui mostrato come con i numeri ipercomplessi iperbolici si possono seguire i procedimenti di Gauss e Beltrami e collegare queste forme alle equazioni differenziali a derivate parziali di tipo iperbolico. Questo pero' permettere di vedere sotto nuovi aspetti questo tipo di equazioni.

On the limits of the effective description of hyperbolic materials in the presence of surface waves

International Nuclear Information System (INIS)

Tschikin, Maria; Biehs, Svend-Age; Messina, Riccardo; Ben-Abdallah, Philippe

2013-01-01

Here, we address the question of the validity of an effective description for hyperbolic metamaterials in the near-field region. We show that the presence of localized modes such as surface waves drastically limits the validity of the effective description, and requires revisiting the concept of homogenization in the near-field. We demonstrate, from exact scattering matrix calculations for multilayer hyperbolic structures, that one can find surface modes in spectral regions where the effective approach predicts hyperbolic modes only. Hence, the presence of surface modes which are not accounted for in the effective description can lead to physical misinterpretations in the description of hyperbolic materials and their related properties. In particular, we discuss in detail how the choice of the topmost layer affects the validity of the effective medium approach for calculating the local density of states and the super-Planckian thermal radiation. (paper)

Visualising very large phylogenetic trees in three dimensional hyperbolic space

Directory of Open Access Journals (Sweden)

Liberles David A

2004-04-01

Full Text Available Abstract Background Common existing phylogenetic tree visualisation tools are not able to display readable trees with more than a few thousand nodes. These existing methodologies are based in two dimensional space. Results We introduce the idea of visualising phylogenetic trees in three dimensional hyperbolic space with the Walrus graph visualisation tool and have developed a conversion tool that enables the conversion of standard phylogenetic tree formats to Walrus' format. With Walrus, it becomes possible to visualise and navigate phylogenetic trees with more than 100,000 nodes. Conclusion Walrus enables desktop visualisation of very large phylogenetic trees in 3 dimensional hyperbolic space. This application is potentially useful for visualisation of the tree of life and for functional genomics derivatives, like The Adaptive Evolution Database (TAED.

High-Order Hyperbolic Residual-Distribution Schemes on Arbitrary Triangular Grids

Science.gov (United States)

Mazaheri, Alireza; Nishikawa, Hiroaki

2015-01-01

In this paper, we construct high-order hyperbolic residual-distribution schemes for general advection-diffusion problems on arbitrary triangular grids. We demonstrate that the second-order accuracy of the hyperbolic schemes can be greatly improved by requiring the scheme to preserve exact quadratic solutions. We also show that the improved second-order scheme can be easily extended to third-order by further requiring the exactness for cubic solutions. We construct these schemes based on the LDA and the SUPG methodology formulated in the framework of the residual-distribution method. For both second- and third-order-schemes, we construct a fully implicit solver by the exact residual Jacobian of the second-order scheme, and demonstrate rapid convergence of 10-15 iterations to reduce the residuals by 10 orders of magnitude. We demonstrate also that these schemes can be constructed based on a separate treatment of the advective and diffusive terms, which paves the way for the construction of hyperbolic residual-distribution schemes for the compressible Navier-Stokes equations. Numerical results show that these schemes produce exceptionally accurate and smooth solution gradients on highly skewed and anisotropic triangular grids, including curved boundary problems, using linear elements. We also present Fourier analysis performed on the constructed linear system and show that an under-relaxation parameter is needed for stabilization of Gauss-Seidel relaxation.

Hybrid plasmonic/semiconductor nanoparticle monolayer assemblies as hyperbolic metamaterials

DEFF Research Database (Denmark)

Zhukovsky, Sergei; Ozel, Tuncay; Mutlugun, Evren

2014-01-01

effective permittivity tensor of the structure. This results in increased photonic density of states and strong enhancement of quantum dot luminescence, in line with recent experimental results. Our findings demonstrate that hyperbolic metamaterials can increase the radiative decay rate of emission centers...

Semilinear hyperbolic systems and equations with singular initial data

International Nuclear Information System (INIS)

Gramchev, T.

1991-07-01

We study the weak limits of solutions u ε (t, ·) for ε→0 to semilinear strictly hyperbolic systems and wave equations with initial data u ε (0, ·) approximating a distribution κ, 0 ε (t, ·) for ε→0 exists. 13 refs

arXiv Gravitational wave energy emission and detection rates of Primordial Black Hole hyperbolic encounters

CERN Document Server

García-Bellido, Juan

2018-01-01

We describe in detail gravitational wave bursts from Primordial Black Hole (PBH) hyperbolic encounters. The bursts are one-time events, with the bulk of the released energy happening during the closest approach, which can be emitted in frequencies that could be within the range of both LIGO (10-1000Hz) and LISA ($10^{-6}-1$ Hz). Furthermore, we correct the results for the power spectrum of hyperbolic encounters found in the literature and present new exact and approximate expressions for the peak frequency of the emission. Note that these GW bursts from hyperbolic encounters between PBH are complementary to the GW emission from the bounded orbits of BHB mergers detected by LIGO, and help breaking degeneracies in the determination of the PBH mass, spin and spatial distributions.

Iterated Crank-Nicolson method for hyperbolic and parabolic equations in numerical relativity

International Nuclear Information System (INIS)

Leiler, Gregor; Rezzolla, Luciano

2006-01-01

The iterated Crank-Nicolson is a predictor-corrector algorithm commonly used in numerical relativity for the solution of both hyperbolic and parabolic partial differential equations. We here extend the recent work on the stability of this scheme for hyperbolic equations by investigating the properties when the average between the predicted and corrected values is made with unequal weights and when the scheme is applied to a parabolic equation. We also propose a variant of the scheme in which the coefficients in the averages are swapped between two corrections leading to systematically larger amplification factors and to a smaller numerical dispersion

On the hyperbolicity of Einstein's and other gauge field equations

International Nuclear Information System (INIS)

Friedrich, H.

1985-01-01

It is shown that Einstein's vacuum field equations (respectively the conformal vacuum field equations) in a frame formalism imply a symmetric hyperbolic system of ''reduce'' propagation equations for any choice of coordinate system and frame field (and conformal factor). Certain freely specifiable ''gauge source'' functions occurring in the reduced equations reflect the choice of gauge. Together with the initial data they determine the gauge uniquely. Their choice does not affect the isometry class (conformal class) of a solution of an initial value problem. By the same method symmetric hyperbolic propagation equations are obtained from other gauge field equations, irrespective of the gauge. Using the concept of source functions one finds that Einstein's field equation, considered as second order equations for the metric coefficients, are of wave equation type in any coordinate system. (orig.)

High order ADER schemes for a unified first order hyperbolic formulation of continuum mechanics: Viscous heat-conducting fluids and elastic solids

Energy Technology Data Exchange (ETDEWEB)

Dumbser, Michael, E-mail: michael.dumbser@unitn.it [Department of Civil, Environmental and Mechanical Engineering, University of Trento, Via Mesiano 77, 38123 Trento (Italy); Peshkov, Ilya, E-mail: peshkov@math.nsc.ru [Open and Experimental Center for Heavy Oil, Université de Pau et des Pays de l' Adour, Avenue de l' Université, 64012 Pau (France); Romenski, Evgeniy, E-mail: evrom@math.nsc.ru [Sobolev Institute of Mathematics, 4 Acad. Koptyug Avenue, 630090 Novosibirsk (Russian Federation); Novosibirsk State University, 2 Pirogova Str., 630090 Novosibirsk (Russian Federation); Zanotti, Olindo, E-mail: olindo.zanotti@unitn.it [Department of Civil, Environmental and Mechanical Engineering, University of Trento, Via Mesiano 77, 38123 Trento (Italy)

2016-06-01

Highlights: • High order schemes for a unified first order hyperbolic formulation of continuum mechanics. • The mathematical model applies simultaneously to fluid mechanics and solid mechanics. • Viscous fluids are treated in the frame of hyper-elasticity as generalized visco-plastic solids. • Formal asymptotic analysis reveals the connection with the Navier–Stokes equations. • The distortion tensor A in the model appears to be well-suited for flow visualization. - Abstract: This paper is concerned with the numerical solution of the unified first order hyperbolic formulation of continuum mechanics recently proposed by Peshkov and Romenski [110], further denoted as HPR model. In that framework, the viscous stresses are computed from the so-called distortion tensor A, which is one of the primary state variables in the proposed first order system. A very important key feature of the HPR model is its ability to describe at the same time the behavior of inviscid and viscous compressible Newtonian and non-Newtonian fluids with heat conduction, as well as the behavior of elastic and visco-plastic solids. Actually, the model treats viscous and inviscid fluids as generalized visco-plastic solids. This is achieved via a stiff source term that accounts for strain relaxation in the evolution equations of A. Also heat conduction is included via a first order hyperbolic system for the thermal impulse, from which the heat flux is computed. The governing PDE system is hyperbolic and fully consistent with the first and the second principle of thermodynamics. It is also fundamentally different from first order Maxwell–Cattaneo-type relaxation models based on extended irreversible thermodynamics. The HPR model represents therefore a novel and unified description of continuum mechanics, which applies at the same time to fluid mechanics and solid mechanics. In this paper, the direct connection between the HPR model and the classical hyperbolic–parabolic Navier�

High order ADER schemes for a unified first order hyperbolic formulation of continuum mechanics: Viscous heat-conducting fluids and elastic solids

International Nuclear Information System (INIS)

Dumbser, Michael; Peshkov, Ilya; Romenski, Evgeniy; Zanotti, Olindo

2016-01-01

Highlights: • High order schemes for a unified first order hyperbolic formulation of continuum mechanics. • The mathematical model applies simultaneously to fluid mechanics and solid mechanics. • Viscous fluids are treated in the frame of hyper-elasticity as generalized visco-plastic solids. • Formal asymptotic analysis reveals the connection with the Navier–Stokes equations. • The distortion tensor A in the model appears to be well-suited for flow visualization. - Abstract: This paper is concerned with the numerical solution of the unified first order hyperbolic formulation of continuum mechanics recently proposed by Peshkov and Romenski [110], further denoted as HPR model. In that framework, the viscous stresses are computed from the so-called distortion tensor A, which is one of the primary state variables in the proposed first order system. A very important key feature of the HPR model is its ability to describe at the same time the behavior of inviscid and viscous compressible Newtonian and non-Newtonian fluids with heat conduction, as well as the behavior of elastic and visco-plastic solids. Actually, the model treats viscous and inviscid fluids as generalized visco-plastic solids. This is achieved via a stiff source term that accounts for strain relaxation in the evolution equations of A. Also heat conduction is included via a first order hyperbolic system for the thermal impulse, from which the heat flux is computed. The governing PDE system is hyperbolic and fully consistent with the first and the second principle of thermodynamics. It is also fundamentally different from first order Maxwell–Cattaneo-type relaxation models based on extended irreversible thermodynamics. The HPR model represents therefore a novel and unified description of continuum mechanics, which applies at the same time to fluid mechanics and solid mechanics. In this paper, the direct connection between the HPR model and the classical hyperbolic–parabolic Navier�

Hyperbolic metamaterial lens with hydrodynamic nonlocal response

OpenAIRE

Yan, Wei; Mortensen, N. Asger; Wubs, Martijn

2013-01-01

We investigate the effects of hydrodynamic nonlocal response in hyperbolic metamaterials (HMMs), focusing on the experimentally realizable parameter regime where unit cells are much smaller than an optical wavelength but much larger than the wavelengths of the longitudinal pressure waves of the free-electron plasma in the metal constituents. We derive the nonlocal corrections to the effective material parameters analytically, and illustrate the noticeable nonlocal effects on the dispersion cu...

One-loop effective potential on hyperbolic manifolds

International Nuclear Information System (INIS)

Cognola, G.; Kirsten, K.; Zerbini, S.

1993-01-01

The one-loop effective potential for a scalar field defined on an ultrastatic space-time whose spatial part is a compact hyperbolic manifold is studied using ζ-function regularization for the one-loop effective action. Other possible regularizations are discussed in detail. The renormalization group equations are derived, and their connection with the conformal anomaly is pointed out. The symmetry breaking and the topological mass generation are also discussed

Discontinuous Galerkin finite element methods for hyperbolic differential equations

NARCIS (Netherlands)

van der Vegt, Jacobus J.W.; van der Ven, H.; Boelens, O.J.; Boelens, O.J.; Toro, E.F.

2002-01-01

In this paper a suryey is given of the important steps in the development of discontinuous Galerkin finite element methods for hyperbolic partial differential equations. Special attention is paid to the application of the discontinuous Galerkin method to the solution of the Euler equations of gas

Analytical solution of Mori's equation with secant hyperbolic memory

International Nuclear Information System (INIS)

Tankeshwar, K.; Pathak, K.N.

1993-07-01

The equation of motion of the auto-correlation function has been solved analytically using a secant-hyperbolic form of the memory function. The analytical results obtained for the long time expansion together with the short time expansion provide a good description over the whole time domain as judged by their comparison with the numerical solution of Mori's equation of motion. We also find that the time evolution of the auto-correlation function is determined by a single parameter τ which is related to the frequency sum rules up to the fourth order. The auto-correlation function has been found to show simple decaying or oscillatory behaviour depending on whether the parameter τ is greater than or less than some critical values. Similarities as well as differences in time evolution of the auto-correlation have been discussed for exponential, secant-hyperbolic and Gaussian approaches of the memory function. (author). 16 refs, 5 figs

Low-dimensional geometry from euclidean surfaces to hyperbolic knots

CERN Document Server

Bonahon, Francis

2009-01-01

The study of 3-dimensional spaces brings together elements from several areas of mathematics. The most notable are topology and geometry, but elements of number theory and analysis also make appearances. In the past 30 years, there have been striking developments in the mathematics of 3-dimensional manifolds. This book aims to introduce undergraduate students to some of these important developments. Low-Dimensional Geometry starts at a relatively elementary level, and its early chapters can be used as a brief introduction to hyperbolic geometry. However, the ultimate goal is to describe the very recently completed geometrization program for 3-dimensional manifolds. The journey to reach this goal emphasizes examples and concrete constructions as an introduction to more general statements. This includes the tessellations associated to the process of gluing together the sides of a polygon. Bending some of these tessellations provides a natural introduction to 3-dimensional hyperbolic geometry and to the theory o...

Photonic-band-gap engineering for volume plasmon polaritons in multiscale multilayer hyperbolic metamaterials

DEFF Research Database (Denmark)

Zhukovsky, Sergei; Orlov, Alexey A.; Babicheva, Viktoriia E.

2014-01-01

) on a larger, wavelength scale, the propagation of volume plasmon polaritons in the resulting multiscale hyperbolic metamaterials is subject to photonic-band-gap phenomena. A great degree of control over such plasmons can be exerted by varying the superstructure geometry. When this geometry is periodic, stop......, fractal Cantor-like multiscale metamaterials are found to exhibit characteristic self-similar spectral signatures in the volume plasmonic band. Multiscale hyperbolic metamaterials are shown to be a promising platform for large-wave-vector bulk plasmonic waves, whether they are considered for use as a kind...

Qualitative behavior of global solutions to inhomogeneous quasilinear hyperbolic systems

International Nuclear Information System (INIS)

Hsiao, L.

1994-01-01

The emphasis is the influence to the qualitative behavior of solutions caused by the lower order term, which is certain dissipation, in quasilinear hyperbolic systems. Both classical solutions and discontinuous weak solutions are discussed. (author). 12 refs

An Efficient Numerical Approach for Solving Nonlinear Coupled Hyperbolic Partial Differential Equations with Nonlocal Conditions

Directory of Open Access Journals (Sweden)

A. H. Bhrawy

2014-01-01

Full Text Available One of the most important advantages of collocation method is the possibility of dealing with nonlinear partial differential equations (PDEs as well as PDEs with variable coefficients. A numerical solution based on a Jacobi collocation method is extended to solve nonlinear coupled hyperbolic PDEs with variable coefficients subject to initial-boundary nonlocal conservation conditions. This approach, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled hyperbolic PDEs with variable coefficients to a system of nonlinear ordinary differential equation which is far easier to solve. In fact, we deal with initial-boundary coupled hyperbolic PDEs with variable coefficients as well as initial-nonlocal conditions. Using triangular, soliton, and exponential-triangular solutions as exact solutions, the obtained results show that the proposed numerical algorithm is efficient and very accurate.

The hyperbolic problem

Science.gov (United States)

Gualdesi, Lavinio

2017-04-01

Mooring lines in the Ocean might be seen as a pretty simple seamanlike activity. Connecting valuable scientific instrumentation to it transforms this simple activity into a sophisticated engineering support which needs to be accurately designed, developed, deployed, monitored and hopefully recovered with its precious load of scientific data. This work is an historical travel along the efforts carried out by scientists all over the world to successfully predict mooring line behaviour through both mathematical simulation and experimental verifications. It is at first glance unexpected how many factors one must observe to get closer and closer to a real ocean situation. Most models have dual applications for mooring lines and towed bodies lines equations. Numerous references are provided starting from the oldest one due to Isaac Newton. In his "Philosophiae Naturalis Principia Matematica" (1687) the English scientist, while discussing about the law of motion for bodies in resistant medium, is envisaging a hyperbolic fitting to the phenomenon including asymptotic behaviour in non-resistant media. A non-exhaustive set of mathematical simulations of the mooring lines trajectory prediction is listed hereunder to document how the subject has been under scientific focus over almost a century. Pode (1951) Prior personal computers diffusion a tabular form of calculus of cable geometry was used by generations of engineers keeping in mind the following limitations and approximations: tangential drag coefficients were assumed to be negligible. A steady current flow was assumed as in the towed configuration. Cchabra (1982) Finite Element Method that assumes an arbitrary deflection angle for the top first section and calculates equilibrium equations down to the sea floor iterating up to a compliant solution. Gualdesi (1987) ANAMOOR. A Fortran Program based on iterative methods above including experimental data from intensive mooring campaign. Database of experimental drag

Strong coupling of collection of emitters on hyperbolic meta-material

Science.gov (United States)

Biehs, Svend-Age; Xu, Chenran; Agarwal, Girish S.

2018-04-01

Recently, considerable effort has been devoted to the realization of a strong coupling regime of the radiation matter interaction in the context of an emitter at a meta surface. The strong interaction is well realized in cavity quantum electrodynamics, which also show that strong coupling is much easier to realize using a collection of emitters. Keeping this in mind, we study if emitters on a hyperbolic meta materials can yield a strong coupling regime. We show that strong coupling can be realized for densities of emitters exceeding a critical value. A way to detect strong coupling between emitters and hyperbolic metamaterials is to use the Kretschman-Raether configuration. The strong coupling appears as the splitting of the reflectivity dip. In the weak coupling regime, the dip position shifts. The shift and splitting can be used to sense active molecules at surfaces.

Semi-local inversion of the geodesic ray transform in the hyperbolic plane

International Nuclear Information System (INIS)

Courdurier, Matias; Saez, Mariel

2013-01-01

The inversion of the ray transform on the hyperbolic plane has applications in geophysical exploration and in medical imaging techniques (such as electrical impedance tomography). The geodesic ray transform has been studied in more general geometries and including attenuation, but all of the available inversion formulas require knowledge of the ray transform for all the geodesics. In this paper we present a different inversion formula for the ray transform on the hyperbolic plane, which has the advantage of only requiring knowledge of the ray transform in a reduced family of geodesics. The required family of geodesics is directly related to the set where the original function is to be recovered. (paper)

Relatively hyperbolic extensions of groups and Cannon–Thurston ...

Indian Academy of Sciences (India)

In [6], the existence of a Cannon–Thurston map for the embedding i: K → G was proved, where K and G are respectively the Cayley graphs of K and G. In this paper, we will generalize these results to the case where the kernel is strongly hyperbolic relative to a cusp subgroup. One of our main theorems states: Theorem 2.10 ...

RDTM solution of Caputo time fractional-order hyperbolic telegraph equation

Directory of Open Access Journals (Sweden)

Vineet K. Srivastava

2013-03-01

Full Text Available In this study, a mathematical model has been developed for the second order hyperbolic one-dimensional time fractional Telegraph equation (TFTE. The fractional derivative has been described in the Caputo sense. The governing equations have been solved by a recent reliable semi-analytic method known as the reduced differential transformation method (RDTM. The method is a powerful mathematical technique for solving wide range of problems. Using RDTM method, it is possible to find exact solution as well as closed approximate solution of any ordinary or partial differential equation. Three numerical examples of TFTE have been provided in order to check the effectiveness, accuracy and convergence of the method. The computed results are also depicted graphically.

Source term boundary adaptive estimation in a first-order 1D hyperbolic PDE: Application to a one loop solar collector through

KAUST Repository

Mechhoud, Sarra; Laleg-Kirati, Taous-Meriem

2016-01-01

In this paper, boundary adaptive estimation of solar radiation in a solar collector plant is investigated. The solar collector is described by a 1D first-order hyperbolic partial differential equation where the solar radiation models the source term

The hidden hyperbolic geometry of international trade: World Trade Atlas 1870-2013.

Science.gov (United States)

García-Pérez, Guillermo; Boguñá, Marián; Allard, Antoine; Serrano, M Ángeles

2016-09-16

Here, we present the World Trade Atlas 1870-2013, a collection of annual world trade maps in which distance combines economic size and the different dimensions that affect international trade beyond mere geography. Trade distances, based on a gravity model predicting the existence of significant trade channels, are such that the closer countries are in trade space, the greater their chance of becoming connected. The atlas provides us with information regarding the long-term evolution of the international trade system and demonstrates that, in terms of trade, the world is not flat but hyperbolic, as a reflection of its complex architecture. The departure from flatness has been increasing since World War I, meaning that differences in trade distances are growing and trade networks are becoming more hierarchical. Smaller-scale economies are moving away from other countries except for the largest economies; meanwhile those large economies are increasing their chances of becoming connected worldwide. At the same time, Preferential Trade Agreements do not fit in perfectly with natural communities within the trade space and have not necessarily reduced internal trade barriers. We discuss an interpretation in terms of globalization, hierarchization, and localization; three simultaneous forces that shape the international trade system.

Adaptive aberration correction using a triode hyperbolic electron mirror

International Nuclear Information System (INIS)

Fitzgerald, J.P.S.; Word, R.C.; Koenenkamp, R.

2011-01-01

A converging electron mirror can be used to compensate spherical and chromatic aberrations in an electron microscope. This paper presents an analytical solution to a novel triode (three electrode) hyperbolic mirror as an improvement to the well-known diode (two electrode) hyperbolic mirror for aberration correction. A weakness of the diode mirror is a lack of flexibility in changing the chromatic and spherical aberration coefficients independently without changes in the mirror geometry. In order to remove this limitation, a third electrode can be added. We calculate the optical properties of the resulting triode mirror analytically on the basis of a simple model field distribution. We present the optical properties-the object/image distance, z 0 , and the coefficients of spherical and chromatic aberration, C s and C c , of both mirror types from an analysis of electron trajectories in the mirror field. From this analysis, we demonstrate that while the properties of both designs are similar, the additional parameters in the triode mirror improve the range of aberration that can be corrected. The triode mirror is also able to provide a dynamic adjustment range of chromatic aberration for fixed spherical aberration and focal length, or any permutation of these three parameters. While the dynamic range depends on the values of aberration correction needed, a nominal 10% tuning range is possible for most configurations accompanied by less than 1% change in the other two properties. -- Highlights: → Electrostatic aberration correction for chromatic and spherical aberration in electron optics. → Simultaneous correction of spherical and chromatic aberrations over a wide, adjustable range. → Analytic and quantitative description of correction parameters.

Minimality of invariant laminations for partially hyperbolic attractors

International Nuclear Information System (INIS)

Nobili, Felipe

2015-01-01

Let f : M → M be a C 1 -diffeomorphism over a compact boundaryless Riemannian manifold M, and Λ a compact f-invariant subset of M admitting a partially hyperbolic spliting T f Λ = E s  ⊕ E c  ⊕ E u over the tangent bundle T f Λ. It's known from the Hirsch–Pugh–Shub theory that Λ admits two invariant laminations associated to the extremal bundles E s and E u . These laminations are families of dynamically defined immersed submanifolds of the M tangent, respectively, to the bundles E s and E u at every point in Λ. In this work, we prove that at least one of the invariant laminations of a transitive partially hyperbolic attractor with a one-dimensional center bundle is minimal: the orbit of every leaf intersects Λ densely. This result extends those in Bonatti et al (2002 J. Inst. Math. Jussieu 1 513–41) and Hertz et al (2007 Fields Institute Communications vol 51 (Providence, RI: American Mathematical Society) pp 103–9) about minimal foliations for robustly transitive diffeomorphisms. (paper)

Uncertainty quantification for hyperbolic and kinetic equations

CERN Document Server

Pareschi, Lorenzo

2017-01-01

This book explores recent advances in uncertainty quantification for hyperbolic, kinetic, and related problems. The contributions address a range of different aspects, including: polynomial chaos expansions, perturbation methods, multi-level Monte Carlo methods, importance sampling, and moment methods. The interest in these topics is rapidly growing, as their applications have now expanded to many areas in engineering, physics, biology and the social sciences. Accordingly, the book provides the scientific community with a topical overview of the latest research efforts.

Hyperbolic spaces are of strictly negative type

DEFF Research Database (Denmark)

Hjorth, Poul G.; Kokkendorff, Simon L.; Markvorsen, Steen

2002-01-01

We study finite metric spaces with elements picked from, and distances consistent with, ambient Riemannian manifolds. The concepts of negative type and strictly negative type are reviewed, and the conjecture that hyperbolic spaces are of strictly negative type is settled, in the affirmative....... The technique of the proof is subsequently applied to show that every compact manifold of negative type must have trivial fundamental group, and to obtain a necessary criterion for product manifolds to be of negative type....

Spontaneously broken continuous symmetries in hyperbolic (or open) de Sitter spacetime

International Nuclear Information System (INIS)

Ratra, B.

1994-01-01

The functional Schroedinger approach is used to study scalar field theory in hyperbolic (or open) de Sitter spacetime. While on intermediate length scales (small compared to the spatial curvature length scale) the massless minimally coupled scalar field two-point correlation function does have a term that varies logarithmically with scale, as in flat and closed de Sitter spacetime, the spatial curvature tames the infrared behavior of this correlation function at larger scales in the open model. As a result, and contrary to what happens in flat and closed de Sitter spacetime, spontaneously broken continuous symmetries are not restored in open de Sitter spacetime (with more than one spatial dimension)

A graphene Zener-Klein transistor cooled by a hyperbolic substrate

Science.gov (United States)

Yang, Wei; Berthou, Simon; Lu, Xiaobo; Wilmart, Quentin; Denis, Anne; Rosticher, Michael; Taniguchi, Takashi; Watanabe, Kenji; Fève, Gwendal; Berroir, Jean-Marc; Zhang, Guangyu; Voisin, Christophe; Baudin, Emmanuel; Plaçais, Bernard

2018-01-01

The engineering of cooling mechanisms is a bottleneck in nanoelectronics. Thermal exchanges in diffusive graphene are mostly driven by defect-assisted acoustic phonon scattering, but the case of high-mobility graphene on hexagonal boron nitride (hBN) is radically different, with a prominent contribution of remote phonons from the substrate. Bilayer graphene on a hBN transistor with a local gate is driven in a regime where almost perfect current saturation is achieved by compensation of the decrease in the carrier density and Zener-Klein tunnelling (ZKT) at high bias. Using noise thermometry, we show that the ZKT triggers a new cooling pathway due to the emission of hyperbolic phonon polaritons in hBN by out-of-equilibrium electron-hole pairs beyond the super-Planckian regime. The combination of ZKT transport and hyperbolic phonon polariton cooling renders graphene on BN transistors a valuable nanotechnology for power devices and RF electronics.

The arbitrary l continuum states of the hyperbolic molecular potential

Energy Technology Data Exchange (ETDEWEB)

Wei, Gao-Feng, E-mail: fgwei_2000@163.com [School of Physics and Mechatronics Engineering, Xi' an University of Arts and Science, Xi' an 710065 (China); Chen, Wen-Li, E-mail: physwlchen@163.com [Department of Basic Science, Xi' an Peihua University, Xi' an 710065 (China); Dong, Shi-Hai, E-mail: dongsh2@yahoo.com [Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Edificio 9, Unidad Profesional Adolfo López Mateos, Mexico D.F. 07738 (Mexico); Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803-4001 (United States)

2014-06-27

Within the framework of partial-wave method, we study in this Letter the arbitrary l continuum states of the Schrödinger equation with the hyperbolic molecular potential in terms of an improved approximation to the centrifugal term. We present the normalized radial wave functions and obtain analytical formula of phase shifts. In addition, the corresponding bound states are also discussed by studying the analytical properties of the scattering amplitude. We calculate the energy spectra and scattering phase shifts by the improved, previous approximations and the accurate methods, respectively and find that the improved approximation is better than the previous one since the present results are in better agreement with the accurate ones. - Highlights: • The hyperbolic potential with arbitrary l state is solved. • Improved approximation to centrifugal term is used. • Phase shift formula is derived analytically. • Accurate results are compared with the present results.

7th International Conference on Hyperbolic Problems Theory, Numerics, Applications

CERN Document Server

Jeltsch, Rolf

1999-01-01

These proceedings contain, in two volumes, approximately one hundred papers presented at the conference on hyperbolic problems, which has focused to a large extent on the laws of nonlinear hyperbolic conservation. Two-fifths of the papers are devoted to mathematical aspects such as global existence, uniqueness, asymptotic behavior such as large time stability, stability and instabilities of waves and structures, various limits of the solution, the Riemann problem and so on. Roughly the same number of articles are devoted to numerical analysis, for example stability and convergence of numerical schemes, as well as schemes with special desired properties such as shock capturing, interface fitting and high-order approximations to multidimensional systems. The results in these contributions, both theoretical and numerical, encompass a wide range of applications such as nonlinear waves in solids, various computational fluid dynamics from small-scale combustion to relativistic astrophysical problems, multiphase phe...

A relationship between scalar Green functions on hyperbolic and Euclidean Rindler spaces

International Nuclear Information System (INIS)

Haba, Z

2007-01-01

We derive a formula connecting in any dimension the Green function on the (D + 1)-dimensional Euclidean Rindler space and the one for a minimally coupled scalar field with a mass m in the D-dimensional hyperbolic space. The relation takes a simple form in the momentum space where the Green functions are equal at the momenta (p 0 , p) for Rindler and (m,p-hat) for hyperbolic space with a simple additive relation between the squares of the mass and the momenta. The formula has applications to finite temperature Green functions, Green functions on the cone and on the (compactified) Milne spacetime. Analytic continuations and interacting quantum fields are briefly discussed

Matrix elements of a hyperbolic vector operator under SO(2,1)

International Nuclear Information System (INIS)

Zettili, N.; Boukahil, A.

2003-01-01

We deal here with the use of Wigner–Eckart type arguments to calculate the matrix elements of a hyperbolic vector operator V-vector by expressing them in terms of reduced matrix elements. In particular, we focus on calculating the matrix elements of this vector operator within the basis of the hyperbolic angular momentum T-vector whose components T-vector 1 , T-vector 2 , T-vector 3 satisfy an SO(2,1) Lie algebra. We show that the commutation rules between the components of V-vector and T-vector can be inferred from the algebra of ordinary angular momentum. We then show that, by analogy to the Wigner–Eckart theorem, we can calculate the matrix elements of V-vector within a representation where T-vector 2 and T-vector 3 are jointly diagonal. (author)

Analysis of generalized negative binomial distributions attached to hyperbolic Landau levels

International Nuclear Information System (INIS)

Chhaiba, Hassan; Demni, Nizar; Mouayn, Zouhair

2016-01-01

To each hyperbolic Landau level of the Poincaré disc is attached a generalized negative binomial distribution. In this paper, we compute the moment generating function of this distribution and supply its atomic decomposition as a perturbation of the negative binomial distribution by a finitely supported measure. Using the Mandel parameter, we also discuss the nonclassical nature of the associated coherent states. Next, we derive a Lévy-Khintchine-type representation of its characteristic function when the latter does not vanish and deduce that it is quasi-infinitely divisible except for the lowest hyperbolic Landau level corresponding to the negative binomial distribution. By considering the total variation of the obtained quasi-Lévy measure, we introduce a new infinitely divisible distribution for which we derive the characteristic function.

Analysis of generalized negative binomial distributions attached to hyperbolic Landau levels

Energy Technology Data Exchange (ETDEWEB)

Chhaiba, Hassan, E-mail: chhaiba.hassan@gmail.com [Department of Mathematics, Faculty of Sciences, Ibn Tofail University, P.O. Box 133, Kénitra (Morocco); Demni, Nizar, E-mail: nizar.demni@univ-rennes1.fr [IRMAR, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex (France); Mouayn, Zouhair, E-mail: mouayn@fstbm.ac.ma [Department of Mathematics, Faculty of Sciences and Technics (M’Ghila), Sultan Moulay Slimane, P.O. Box 523, Béni Mellal (Morocco)

2016-07-15

To each hyperbolic Landau level of the Poincaré disc is attached a generalized negative binomial distribution. In this paper, we compute the moment generating function of this distribution and supply its atomic decomposition as a perturbation of the negative binomial distribution by a finitely supported measure. Using the Mandel parameter, we also discuss the nonclassical nature of the associated coherent states. Next, we derive a Lévy-Khintchine-type representation of its characteristic function when the latter does not vanish and deduce that it is quasi-infinitely divisible except for the lowest hyperbolic Landau level corresponding to the negative binomial distribution. By considering the total variation of the obtained quasi-Lévy measure, we introduce a new infinitely divisible distribution for which we derive the characteristic function.

Hyperbolic orbits of Earth flybys and effects of ungravity-inspired conservative potentials

International Nuclear Information System (INIS)

Bertolami, O; Francisco, F; Gil, P J S

2016-01-01

In this work we take a critical look at the available data on the flyby anomaly and on the current limitations of attempts to develop an explanation. We aim to verify how conservative corrections to gravity could affect the hyperbolic trajectories of Earth flybys. We use ungravity-inspired potentials as illustrative examples and show how the resulting orbital simulations differ from the observed anomaly. We also get constraints on the model parameters from the observed flyby velocity shifts. The conclusion is that no kind of conservative potential can be the cause of the flyby anomaly. (paper)

Figurative framing: Shaping public discourse through metaphor, hyperbole and irony

NARCIS (Netherlands)

Burgers, C.F.; Konijn, E.A.; Steen, G.J.

2016-01-01

Framing is an important concept in communication, yet many framing studies set out to develop frames relevant to only one issue. We expand framing theory by introducing figurative framing. We posit that figurative language types like metaphor, hyperbole and irony are important in shaping public

Figurative framing : Shaping public discourse through metaphor, hyperbole and irony

NARCIS (Netherlands)

Burgers, C.; Konijn, E.A.; Steen, G.J.

2016-01-01

Framing is an important concept in communication, yet many framing studies set out to develop frames relevant to only one issue. We expand framing theory by introducing figurative framing. We posit that figurative language types like metaphor, hyperbole and irony are important in shaping public

Mixed hyperbolic-second-order-parabolic formulations of general relativity

International Nuclear Information System (INIS)

Paschalidis, Vasileios

2008-01-01

Two new formulations of general relativity are introduced. The first one is a parabolization of the Arnowitt-Deser-Misner formulation and is derived by the addition of combinations of the constraints and their derivatives to the right-hand side of the Arnowitt-Deser-Misner evolution equations. The desirable property of this modification is that it turns the surface of constraints into a local attractor because the constraint propagation equations become second-order parabolic independently of the gauge conditions employed. This system may be classified as mixed hyperbolic--second-order parabolic. The second formulation is a parabolization of the Kidder-Scheel-Teukolsky formulation and is a manifestly mixed strongly hyperbolic--second-order-parabolic set of equations, bearing thus resemblance to the compressible Navier-Stokes equations. As a first test, a stability analysis of flat space is carried out and it is shown that the first modification exponentially damps and smoothes all constraint-violating modes. These systems provide a new basis for constructing schemes for long-term and stable numerical integration of the Einstein field equations.

Quasilinear Hyperbolic Systems, Compressible Flows, and Waves

CERN Document Server

Sharma, Vishnu D

2010-01-01

Filled with practical examples, this book presents a self-contained discussion of quasilinear hyperbolic equations and systems with applications. It emphasizes nonlinear theory and introduces some of the most active research in the field. The author elucidates all necessary mathematical concepts in the first three chapters, including an introduction to general wave propagation problems. He highlights the application of various approaches, such as singular surface theory, asymptotic methods, and self-similarity, to solve practical physical problems from areas, including gasdynamics, radiation g

Photon gas with hyperbolic dispersion relations

International Nuclear Information System (INIS)

Mohseni, Morteza

2013-01-01

We investigate the density of states for a photon gas confined in a nonmagnetic metamaterial medium in which some components of the permittivity tensor are negative. We study the effect of the resulting hyperbolic dispersion relations on the black body spectral density. We show that for both of the possible wavevector space topologies, the spectral density vanishes at a certain frequency. We obtain the partition function and derive some thermodynamical quantities of the system. To leading order, the results resemble those of a one- or two-dimensional photon gas with an enhanced density of states. (paper)

Survey of time preference, delay discounting models

Directory of Open Access Journals (Sweden)

John R. Doyle

2013-03-01

Full Text Available The paper surveys over twenty models of delay discounting (also known as temporal discounting, time preference, time discounting, that psychologists and economists have put forward to explain the way people actually trade off time and money. Using little more than the basic algebra of powers and logarithms, I show how the models are derived, what assumptions they are based upon, and how different models relate to each other. Rather than concentrate only on discount functions themselves, I show how discount functions may be manipulated to isolate rate parameters for each model. This approach, consistently applied, helps focus attention on the three main components in any discounting model: subjectively perceived money; subjectively perceived time; and how these elements are combined. We group models by the number of parameters that have to be estimated, which means our exposition follows a trajectory of increasing complexity to the models. However, as the story unfolds it becomes clear that most models fall into a smaller number of families. We also show how new models may be constructed by combining elements of different models. The surveyed models are: Exponential; Hyperbolic; Arithmetic; Hyperboloid (Green and Myerson, Rachlin; Loewenstein and Prelec Generalized Hyperboloid; quasi-Hyperbolic (also known as beta-delta discounting; Benhabib et al's fixed cost; Benhabib et al's Exponential / Hyperbolic / quasi-Hyperbolic; Read's discounting fractions; Roelofsma's exponential time; Scholten and Read's discounting-by-intervals (DBI; Ebert and Prelec's constant sensitivity (CS; Bleichrodt et al.'s constant absolute decreasing impatience (CADI; Bleichrodt et al.'s constant relative decreasing impatience (CRDI; Green, Myerson, and Macaux's hyperboloid over intervals models; Killeen's additive utility; size-sensitive additive utility; Yi, Landes, and Bickel's memory trace models; McClure et al.'s two exponentials; and Scholten and Read's trade

Theoretical stability in coefficient inverse problems for general hyperbolic equations with numerical reconstruction

Science.gov (United States)

Yu, Jie; Liu, Yikan; Yamamoto, Masahiro

2018-04-01

In this article, we investigate the determination of the spatial component in the time-dependent second order coefficient of a hyperbolic equation from both theoretical and numerical aspects. By the Carleman estimates for general hyperbolic operators and an auxiliary Carleman estimate, we establish local Hölder stability with either partial boundary or interior measurements under certain geometrical conditions. For numerical reconstruction, we minimize a Tikhonov functional which penalizes the gradient of the unknown function. Based on the resulting variational equation, we design an iteration method which is updated by solving a Poisson equation at each step. One-dimensional prototype examples illustrate the numerical performance of the proposed iteration.

Exact boundary controllability of nodal profile for quasilinear hyperbolic systems

CERN Document Server

Li, Tatsien; Gu, Qilong

2016-01-01

This book provides a comprehensive overview of the exact boundary controllability of nodal profile, a new kind of exact boundary controllability stimulated by some practical applications. This kind of controllability is useful in practice as it does not require any precisely given final state to be attained at a suitable time t=T by means of boundary controls, instead it requires the state to exactly fit any given demand (profile) on one or more nodes after a suitable time t=T by means of boundary controls. In this book we present a general discussion of this kind of controllability for general 1-D first order quasilinear hyperbolic systems and for general 1-D quasilinear wave equations on an interval as well as on a tree-like network using a modular-structure construtive method, suggested in LI Tatsien's monograph "Controllability and Observability for Quasilinear Hyperbolic Systems"(2010), and we establish a complete theory on the local exact boundary controllability of nodal profile for 1-D quasilinear hyp...

8th International Conference on Hyperbolic Problems : Theory, Numerics, Applications

CERN Document Server

Warnecke, Gerald

2001-01-01

The Eighth International Conference on Hyperbolic Problems - Theory, Nu­ merics, Applications, was held in Magdeburg, Germany, from February 27 to March 3, 2000. It was attended by over 220 participants from many European countries as well as Brazil, Canada, China, Georgia, India, Israel, Japan, Taiwan, und the USA. There were 12 plenary lectures, 22 further invited talks, and around 150 con­ tributed talks in parallel sessions as well as posters. The speakers in the parallel sessions were invited to provide a poster in order to enhance the dissemination of information. Hyperbolic partial differential equations describe phenomena of material or wave transport in physics, biology and engineering, especially in the field of fluid mechanics. Despite considerable progress, the mathematical theory is still strug­ gling with fundamental open problems concerning systems of such equations in multiple space dimensions. For various applications the development of accurate and efficient numerical schemes for computat...

The Full—Discrete Mixed Finite Element Methods for Nonlinear Hyperbolic Equations

Institute of Scientific and Technical Information of China (English)

YanpingCHEN; YunqingHUANG

1998-01-01

This article treats mixed finite element methods for second order nonlinear hyperbolic equations.A fully discrete scheme is presented and improved L2-error estimates are established.The convergence of both the function value andthe flux is demonstrated.

Where the Solar system meets the solar neighbourhood: patterns in the distribution of radiants of observed hyperbolic minor bodies

Science.gov (United States)

de la Fuente Marcos, Carlos; de la Fuente Marcos, Raúl; Aarseth, Sverre J.

2018-05-01

Observed hyperbolic minor bodies might have an interstellar origin, but they can be natives of the Solar system as well. Fly-bys with the known planets or the Sun may result in the hyperbolic ejection of an originally bound minor body; in addition, members of the Oort cloud could be forced to follow inbound hyperbolic paths as a result of secular perturbations induced by the Galactic disc or, less frequently, due to impulsive interactions with passing stars. These four processes must leave distinctive signatures in the distribution of radiants of observed hyperbolic objects, both in terms of coordinates and velocity. Here, we perform a systematic numerical exploration of the past orbital evolution of known hyperbolic minor bodies using a full N-body approach and statistical analyses to study their radiants. Our results confirm the theoretical expectations that strong anisotropies are present in the data. We also identify a statistically significant overdensity of high-speed radiants towards the constellation of Gemini that could be due to the closest and most recent known fly-by of a star to the Solar system, that of the so-called Scholz's star. In addition to and besides 1I/2017 U1 (`Oumuamua), we single out eight candidate interstellar comets based on their radiants' velocities.

Out-of-plane heat transfer in van der Waals stacks through electron-hyperbolic phonon coupling

Science.gov (United States)

Tielrooij, Klaas-Jan; Hesp, Niels C. H.; Principi, Alessandro; Lundeberg, Mark B.; Pogna, Eva A. A.; Banszerus, Luca; Mics, Zoltán; Massicotte, Mathieu; Schmidt, Peter; Davydovskaya, Diana; Purdie, David G.; Goykhman, Ilya; Soavi, Giancarlo; Lombardo, Antonio; Watanabe, Kenji; Taniguchi, Takashi; Bonn, Mischa; Turchinovich, Dmitry; Stampfer, Christoph; Ferrari, Andrea C.; Cerullo, Giulio; Polini, Marco; Koppens, Frank H. L.

2018-01-01

Van der Waals heterostructures have emerged as promising building blocks that offer access to new physics, novel device functionalities and superior electrical and optoelectronic properties1-7. Applications such as thermal management, photodetection, light emission, data communication, high-speed electronics and light harvesting8-16 require a thorough understanding of (nanoscale) heat flow. Here, using time-resolved photocurrent measurements, we identify an efficient out-of-plane energy transfer channel, where charge carriers in graphene couple to hyperbolic phonon polaritons17-19 in the encapsulating layered material. This hyperbolic cooling is particularly efficient, giving picosecond cooling times for hexagonal BN, where the high-momentum hyperbolic phonon polaritons enable efficient near-field energy transfer. We study this heat transfer mechanism using distinct control knobs to vary carrier density and lattice temperature, and find excellent agreement with theory without any adjustable parameters. These insights may lead to the ability to control heat flow in van der Waals heterostructures.

Hyperboles not turning to metaphors : How to explain audience cooperativeness?

NARCIS (Netherlands)

van den Hoven, P.J.

2016-01-01

We observe that an audience attempts to interpret the relation between a source domain and a target domain as a hyperbole before interpreting it as a metaphor. It could also first try a metaphorical reading or attempt several possible readings and successively select the relevant outcome. But it

Correlation functions of σ fields with values in a hyperbolic space

International Nuclear Information System (INIS)

Haba, Z.

1989-01-01

It is shown that the functional integral for a σ field with values in the Poincare upper half-plane (and some other hyperbolic spaces) can be performed explicitly resulting in a conformal invariant noncanonical field theory in two dimensions

Correlation Functions of σ Fields with Values in a Hyperbolic Space

Science.gov (United States)

Haba, Z.

It is shown that the functional integral for a σ field with values in the Poincare upper half-plane (and some other hyperbolic spaces) can be performed explicitly resulting in a conformal invariant noncanonical field theory in two dimensions.

Development of neural network model of the multiparametric ...

African Journals Online (AJOL)

The best structure of the model was established for identifying a complex multiparameter object, using the example of statistics for the operation of a ball mill.It was a network with three hidden layers and 50, 35 and 25 neurons in them, with activation functions, respectively by layers - hyperbolic tangent, sigmoid function in 2 ...

Near-perfect broadband absorption from hyperbolic metamaterial nanoparticles

Science.gov (United States)

Riley, Conor T.; Smalley, Joseph S. T.; Brodie, Jeffrey R. J.; Fainman, Yeshaiahu; Sirbuly, Donald J.; Liu, Zhaowei

2017-02-01

Broadband absorbers are essential components of many light detection, energy harvesting, and camouflage schemes. Current designs are either bulky or use planar films that cause problems in cracking and delamination during flexing or heating. In addition, transferring planar materials to flexible, thin, or low-cost substrates poses a significant challenge. On the other hand, particle-based materials are highly flexible and can be transferred and assembled onto a more desirable substrate but have not shown high performance as an absorber in a standalone system. Here, we introduce a class of particle absorbers called transferable hyperbolic metamaterial particles (THMMP) that display selective, omnidirectional, tunable, broadband absorption when closely packed. This is demonstrated with vertically aligned hyperbolic nanotube (HNT) arrays composed of alternating layers of aluminum-doped zinc oxide and zinc oxide. The broadband absorption measures >87% from 1,200 nm to over 2,200 nm with a maximum absorption of 98.1% at 1,550 nm and remains large for high angles. Furthermore, we show the advantages of particle-based absorbers by transferring the HNTs to a polymer substrate that shows excellent mechanical flexibility and visible transparency while maintaining near-perfect absorption in the telecommunications region. In addition, other material systems and geometries are proposed for a wider range of applications.

Modulated electromagnetic fields in inhomogeneous media, hyperbolic pseudoanalytic functions, and transmutations

Energy Technology Data Exchange (ETDEWEB)

Khmelnytskaya, Kira V., E-mail: khmel@uaq.edu.mx [Faculty of Engineering, Autonomous University of Queretaro, Cerro de las Campanas s/n, col. Las Campanas Querétaro, Qro. CP 76010 (Mexico); Kravchenko, Vladislav V., E-mail: vkravchenko@math.cinvestav.edu.mx; Torba, Sergii M., E-mail: storba@math.cinvestav.edu.mx [Department of Mathematics, CINVESTAV del IPN, Unidad Querétaro, Libramiento Norponiente # 2000 Fracc. Real de Juriquilla Querétaro, Qro., CP 76230 (Mexico)

2016-05-15

The time-dependent Maxwell system describing electromagnetic wave propagation in inhomogeneous isotropic media in the one-dimensional case reduces to a Vekua-type equation for bicomplex-valued functions of a hyperbolic variable, see Kravchenko and Ramirez [Adv. Appl. Cliord Algebr. 21(3), 547–559 (2011)]. Using this relation, we solve the problem of the transmission through an inhomogeneous layer of a normally incident electromagnetic time-dependent plane wave. The solution is written in terms of a pair of Darboux-associated transmutation operators [Kravchenko, V. V. and Torba, S. M., J. Phys. A: Math. Theor. 45, 075201 (2012)], and combined with the recent results on their construction [Kravchenko, V. V. and Torba, S. M., Complex Anal. Oper. Theory 9, 379-429 (2015); Kravchenko, V. V. and Torba, S. M., J. Comput. Appl. Math. 275, 1–26 (2015)] can be used for efficient computation of the transmitted modulated signals. We develop the corresponding numerical method and illustrate its performance with examples.

The hidden hyperbolic geometry of international trade: World Trade Atlas 1870–2013

Science.gov (United States)

García-Pérez, Guillermo; Boguñá, Marián; Allard, Antoine; Serrano, M. Ángeles

2016-01-01

Here, we present the World Trade Atlas 1870–2013, a collection of annual world trade maps in which distance combines economic size and the different dimensions that affect international trade beyond mere geography. Trade distances, based on a gravity model predicting the existence of significant trade channels, are such that the closer countries are in trade space, the greater their chance of becoming connected. The atlas provides us with information regarding the long-term evolution of the international trade system and demonstrates that, in terms of trade, the world is not flat but hyperbolic, as a reflection of its complex architecture. The departure from flatness has been increasing since World War I, meaning that differences in trade distances are growing and trade networks are becoming more hierarchical. Smaller-scale economies are moving away from other countries except for the largest economies; meanwhile those large economies are increasing their chances of becoming connected worldwide. At the same time, Preferential Trade Agreements do not fit in perfectly with natural communities within the trade space and have not necessarily reduced internal trade barriers. We discuss an interpretation in terms of globalization, hierarchization, and localization; three simultaneous forces that shape the international trade system. PMID:27633649

Oscillation of solutions to neutral nonlinear impulsive hyperbolic equations with several delays

Directory of Open Access Journals (Sweden)

Jichen Yang

2013-01-01

Full Text Available In this article, we study oscillatory properties of solutions to neutral nonlinear impulsive hyperbolic partial differential equations with several delays. We establish sufficient conditions for oscillation of all solutions.

A simple finite element method for linear hyperbolic problems

International Nuclear Information System (INIS)

Mu, Lin; Ye, Xiu

2017-01-01

Here, we introduce a simple finite element method for solving first order hyperbolic equations with easy implementation and analysis. Our new method, with a symmetric, positive definite system, is designed to use discontinuous approximations on finite element partitions consisting of arbitrary shape of polygons/polyhedra. Error estimate is established. Extensive numerical examples are tested that demonstrate the robustness and flexibility of the method.

Hyperbolic Cross Truncations for Stochastic Fourier Cosine Series

Science.gov (United States)

Zhang, Zhihua

2014-01-01

Based on our decomposition of stochastic processes and our asymptotic representations of Fourier cosine coefficients, we deduce an asymptotic formula of approximation errors of hyperbolic cross truncations for bivariate stochastic Fourier cosine series. Moreover we propose a kind of Fourier cosine expansions with polynomials factors such that the corresponding Fourier cosine coefficients decay very fast. Although our research is in the setting of stochastic processes, our results are also new for deterministic functions. PMID:25147842

Hyperbolic planforms in relation to visual edges and textures perception.

Directory of Open Access Journals (Sweden)

Pascal Chossat

2009-12-01

Full Text Available We propose to use bifurcation theory and pattern formation as theoretical probes for various hypotheses about the neural organization of the brain. This allows us to make predictions about the kinds of patterns that should be observed in the activity of real brains through, e.g., optical imaging, and opens the door to the design of experiments to test these hypotheses. We study the specific problem of visual edges and textures perception and suggest that these features may be represented at the population level in the visual cortex as a specific second-order tensor, the structure tensor, perhaps within a hypercolumn. We then extend the classical ring model to this case and show that its natural framework is the non-Euclidean hyperbolic geometry. This brings in the beautiful structure of its group of isometries and certain of its subgroups which have a direct interpretation in terms of the organization of the neural populations that are assumed to encode the structure tensor. By studying the bifurcations of the solutions of the structure tensor equations, the analog of the classical Wilson and Cowan equations, under the assumption of invariance with respect to the action of these subgroups, we predict the appearance of characteristic patterns. These patterns can be described by what we call hyperbolic or H-planforms that are reminiscent of Euclidean planar waves and of the planforms that were used in previous work to account for some visual hallucinations. If these patterns could be observed through brain imaging techniques they would reveal the built-in or acquired invariance of the neural organization to the action of the corresponding subgroups.

Accuracy Assessment of a Complex Building 3d Model Reconstructed from Images Acquired with a Low-Cost Uas

Science.gov (United States)

Oniga, E.; Chirilă, C.; Stătescu, F.

2017-02-01

Nowadays, Unmanned Aerial Systems (UASs) are a wide used technique for acquisition in order to create buildings 3D models, providing the acquisition of a high number of images at very high resolution or video sequences, in a very short time. Since low-cost UASs are preferred, the accuracy of a building 3D model created using this platforms must be evaluated. To achieve results, the dean's office building from the Faculty of "Hydrotechnical Engineering, Geodesy and Environmental Engineering" of Iasi, Romania, has been chosen, which is a complex shape building with the roof formed of two hyperbolic paraboloids. Seven points were placed on the ground around the building, three of them being used as GCPs, while the remaining four as Check points (CPs) for accuracy assessment. Additionally, the coordinates of 10 natural CPs representing the building characteristic points were measured with a Leica TCR 405 total station. The building 3D model was created as a point cloud which was automatically generated based on digital images acquired with the low-cost UASs, using the image matching algorithm and different software like 3DF Zephyr, Visual SfM, PhotoModeler Scanner and Drone2Map for ArcGIS. Except for the PhotoModeler Scanner software, the interior and exterior orientation parameters were determined simultaneously by solving a self-calibrating bundle adjustment. Based on the UAS point clouds, automatically generated by using the above mentioned software and GNSS data respectively, the parameters of the east side hyperbolic paraboloid were calculated using the least squares method and a statistical blunder detection. Then, in order to assess the accuracy of the building 3D model, several comparisons were made for the facades and the roof with reference data, considered with minimum errors: TLS mesh for the facades and GNSS mesh for the roof. Finally, the front facade of the building was created in 3D based on its characteristic points using the PhotoModeler Scanner

Hyperbolic kaleidoscopes and Chaos in foams and Hele-Shaw cell

International Nuclear Information System (INIS)

Tufaile, A P B; Tufaile, A; Liger-Belair, G

2011-01-01

Liquid foams have fascinating optical properties, which are caused by the large number of light refractions and reflections by liquid films and Plateau borders. Due to refraction and reflection at the interfaces, the direction of the rays leaving a Plateau border can vary greatly for the same incident angle and a small positional offset. A close look in some configurations of the Plateau borders or liquid bridges reveals the existence of some triangular patterns surrounded by a complex structure, and these patterns bear a resemblance to those observed in some systems involving chaotic scattering and multiple light reflections between spheres. Provided the optical properties of the sphere surfaces are chosen appropriately, fractals are natural consequences of multiple scattering of light rays in these cavities. The cavity acts as a hyperbolic kaleidoscope multiplying the scattering of light rays generating patterns related to Poincare disks and Sierpinski gaskets in comparison to linear kaleidoscopes. We present some experimental results and simulations of these patterns explained by the light of the chaotic scattering.

Hyperbolic kaleidoscopes and Chaos in foams and Hele-Shaw cell

Energy Technology Data Exchange (ETDEWEB)

Tufaile, A P B; Tufaile, A [Escola de Artes, Ciencias e Humanidades da Universidade de Sao Paulo, R. Arlindo Bettio, 1000, 03828-000, Sao Paulo (Brazil); Liger-Belair, G, E-mail: atufaile@usp.br [Laboratoire d' OEnologie et Chimie Appliquee, UPRES EA 2069, URVVC, Faculte de Sciences de Reims, Moulin de la Housse, B. P. 1039, 51687 Reims, Cedex 2 (France)

2011-03-01

Liquid foams have fascinating optical properties, which are caused by the large number of light refractions and reflections by liquid films and Plateau borders. Due to refraction and reflection at the interfaces, the direction of the rays leaving a Plateau border can vary greatly for the same incident angle and a small positional offset. A close look in some configurations of the Plateau borders or liquid bridges reveals the existence of some triangular patterns surrounded by a complex structure, and these patterns bear a resemblance to those observed in some systems involving chaotic scattering and multiple light reflections between spheres. Provided the optical properties of the sphere surfaces are chosen appropriately, fractals are natural consequences of multiple scattering of light rays in these cavities. The cavity acts as a hyperbolic kaleidoscope multiplying the scattering of light rays generating patterns related to Poincare disks and Sierpinski gaskets in comparison to linear kaleidoscopes. We present some experimental results and simulations of these patterns explained by the light of the chaotic scattering.

Exponential spreading and singular behavior of quantum dynamics near hyperbolic points.

Science.gov (United States)

Iomin, A

2013-05-01

Quantum dynamics of a particle in the vicinity of a hyperbolic point is considered. Expectation values of dynamical variables are calculated, and the singular behavior is analyzed. Exponentially fast extension of quantum dynamics is obtained, and conditions for this realization are analyzed.

The limit space of a Cauchy sequence of globally hyperbolic spacetimes

Energy Technology Data Exchange (ETDEWEB)

Noldus, Johan [Universiteit Gent, Vakgroep Wiskundige analyse, Galglaan 2, 9000 Gent (Belgium)

2004-02-21

In this second paper, I construct a limit space of a Cauchy sequence of globally hyperbolic spacetimes. In section 2, I work gradually towards a construction of the limit space. I prove that the limit space is unique up to isometry. I also show that, in general, the limit space has quite complicated causal behaviour. This work prepares the final paper in which I shall study in more detail properties of the limit space and the moduli space of (compact) globally hyperbolic spacetimes (cobordisms). As a fait divers, I give in this paper a suitable definition of dimension of a Lorentz space in agreement with the one given by Gromov in the Riemannian case. The difference in philosophy between Lorentzian and Riemannian geometry is one of relativism versus absolutism. In the latter every point distinguishes itself while in the former in general two elements get distinguished by a third, different, one.

The limit space of a Cauchy sequence of globally hyperbolic spacetimes

International Nuclear Information System (INIS)

Noldus, Johan

2004-01-01

In this second paper, I construct a limit space of a Cauchy sequence of globally hyperbolic spacetimes. In section 2, I work gradually towards a construction of the limit space. I prove that the limit space is unique up to isometry. I also show that, in general, the limit space has quite complicated causal behaviour. This work prepares the final paper in which I shall study in more detail properties of the limit space and the moduli space of (compact) globally hyperbolic spacetimes (cobordisms). As a fait divers, I give in this paper a suitable definition of dimension of a Lorentz space in agreement with the one given by Gromov in the Riemannian case. The difference in philosophy between Lorentzian and Riemannian geometry is one of relativism versus absolutism. In the latter every point distinguishes itself while in the former in general two elements get distinguished by a third, different, one

Novel features of the nonlinear model arising in nano-ionic currents throughout microtubules

Science.gov (United States)

Celik, E.; Bulut, H.; Baskonus, H. M.

2018-05-01

In this manuscript, the modified exp (- Ω (ξ )) -expansion function method is implemented to find the new solutions to the nonlinear differential equation being the transmission line model. We obtain some new solutions to this model such as complex, exponential, trigonometric and hyperbolic functions. We plot the two- and three-dimensional surfaces of each solutions obtained in this manuscript.

Astroidal geometry of hypocycloids and the Hessian topology of hyperbolic polynomials

International Nuclear Information System (INIS)

Arnol'd, Vladimir I

2001-01-01

The Hessian topology has just begun to be developed (in connection with the study of parabolic curves on smooth surfaces in Euclidean or projective space), in contrast to the symplectic and contact topologies related to it. For instance, it is not known how many (compact) parabolic curves can belong to the graph of a polynomial of a given (even of the fourth) degree in two variables or to a smooth algebraic surface of a given degree. The astroid is a hypocycloid with four cusp points. A hyperbolic polynomial is a homogeneous polynomial whose second differential has the signature (+,-) at any non-zero point. Hyperbolic polynomials and functions are connected with Morse theory and Sturm theory and with hypocycloids via caustics (and wave fronts) of periodic functions. The astroid is the caustic of the cosine of a double angle. The caustic of any periodic function has at least four cusp points, and if there are four of them, as is the case for the astroid, then these points form a parallelogram. The theory developed in this paper, based on the study of envelopes and inequalities between derivatives of smooth functions, proves that hyperbolic polynomials of degree four form a connected set and those of degree six form a disconnected set. These topological generalizations of the Sturm and Hurwitz theorems about the zeros of Fourier series give algebraic-geometric results on caustics and wave fronts as well and also establish relationships between these results and the Morse theory of anti-Rolle functions (whose zeros alternate with those of their derivatives)

A zonally symmetric model for the monsoon-Hadley circulation with stochastic convective forcing

Science.gov (United States)

De La Chevrotière, Michèle; Khouider, Boualem

2017-02-01

Idealized models of reduced complexity are important tools to understand key processes underlying a complex system. In climate science in particular, they are important for helping the community improve our ability to predict the effect of climate change on the earth system. Climate models are large computer codes based on the discretization of the fluid dynamics equations on grids of horizontal resolution in the order of 100 km, whereas unresolved processes are handled by subgrid models. For instance, simple models are routinely used to help understand the interactions between small-scale processes due to atmospheric moist convection and large-scale circulation patterns. Here, a zonally symmetric model for the monsoon circulation is presented and solved numerically. The model is based on the Galerkin projection of the primitive equations of atmospheric synoptic dynamics onto the first modes of vertical structure to represent free tropospheric circulation and is coupled to a bulk atmospheric boundary layer (ABL) model. The model carries bulk equations for water vapor in both the free troposphere and the ABL, while the processes of convection and precipitation are represented through a stochastic model for clouds. The model equations are coupled through advective nonlinearities, and the resulting system is not conservative and not necessarily hyperbolic. This makes the design of a numerical method for the solution of this system particularly difficult. Here, we develop a numerical scheme based on the operator time-splitting strategy, which decomposes the system into three pieces: a conservative part and two purely advective parts, each of which is solved iteratively using an appropriate method. The conservative system is solved via a central scheme, which does not require hyperbolicity since it avoids the Riemann problem by design. One of the advective parts is a hyperbolic diagonal matrix, which is easily handled by classical methods for hyperbolic equations, while

Detecting topology in a nearly flat hyperbolic universe

OpenAIRE

Weeks, Jeffrey R.

2002-01-01

Cosmic microwave background data shows the observable universe to be nearly flat, but leaves open the question of whether it is simply or multiply connected. Several authors have investigated whether the topology of a multiply connect hyperbolic universe would be detectable when 0.9 < Omega < 1. However, the possibility of detecting a given topology varies depending on the location of the observer within the space. Recent studies have assumed the observer sits at a favorable location. The pre...

Construction of harmonic maps between pseudo-Riemannian spheres and hyperbolic spaces

International Nuclear Information System (INIS)

Konderak, J.

1988-09-01

Defined here is an orthogonal multiplication for vector spaces with indefinite nondegenerate scalar product. This is then used, via the Hopf construction, to obtain harmonic maps between pseudo-Riemannian spheres and hyperbolic spaces. Examples of harmonic maps are constructed using Clifford algebras. (author). 6 refs

Survey of a numerical procedure for the solution of hyperbolic systems of three dimensional fluid flow

International Nuclear Information System (INIS)

Graf, U.

1986-01-01

A combination of several numerical methods is used to construct a procedure for effective calculation of complex three-dimensional fluid flow problems. The split coefficient matrix (SCM) method is used so that the differenced equations of the hyperbolic system do not disturb correct signal propagation. The semi-discretisation of the equations of the SCM method is done with the asymmetric, separated region, weighted residual (ASWR) method to give accurate solutions on a relatively coarse mesh. For the resulting system of ordinary differential equations, a general-purpose ordinary differential equation solver is used in conjunction with a method of fractional steps for an economic solution of the large system of linear equations. (orig.) [de

The algebraic-hyperbolic approach to the linearized gravitational constraints on a Minkowski background

International Nuclear Information System (INIS)

Winicour, Jeffrey

2017-01-01

An algebraic-hyperbolic method for solving the Hamiltonian and momentum constraints has recently been shown to be well posed for general nonlinear perturbations of the initial data for a Schwarzschild black hole. This is a new approach to solving the constraints of Einstein’s equations which does not involve elliptic equations and has potential importance for the construction of binary black hole data. In order to shed light on the underpinnings of this approach, we consider its application to obtain solutions of the constraints for linearized perturbations of Minkowski space. In that case, we find the surprising result that there are no suitable Cauchy hypersurfaces in Minkowski space for which the linearized algebraic-hyperbolic constraint problem is well posed. (note)

Classical Liouville action on the sphere with three hyperbolic singularities

Energy Technology Data Exchange (ETDEWEB)

Hadasz, Leszek E-mail: hadasz@th.if.uj.edu.pl; Jaskolski, Zbigniew E-mail: jask@ift.uniwroc.pl

2004-08-30

The classical solution to the Liouville equation in the case of three hyperbolic singularities of its energy-momentum tensor is derived and analyzed. The recently proposed classical Liouville action is explicitly calculated in this case. The result agrees with the classical limit of the three-point function in the DOZZ solution of the quantum Liouville theory.

Classical Liouville action on the sphere with three hyperbolic singularities

Science.gov (United States)

Hadasz, Leszek; Jaskólski, Zbigniew

2004-08-01

The classical solution to the Liouville equation in the case of three hyperbolic singularities of its energy-momentum tensor is derived and analyzed. The recently proposed classical Liouville action is explicitly calculated in this case. The result agrees with the classical limit of the three-point function in the DOZZ solution of the quantum Liouville theory.

Classical Liouville action on the sphere with three hyperbolic singularities

International Nuclear Information System (INIS)

Hadasz, Leszek; Jaskolski, Zbigniew

2004-01-01

The classical solution to the Liouville equation in the case of three hyperbolic singularities of its energy-momentum tensor is derived and analyzed. The recently proposed classical Liouville action is explicitly calculated in this case. The result agrees with the classical limit of the three-point function in the DOZZ solution of the quantum Liouville theory

Free vibration of laminated composite stiffened hyperbolic paraboloid shell panel with cutout

Science.gov (United States)

Sahoo, Sarmila

2016-08-01

Composite shell structures are extensively used in aerospace, civil, marine and other engineering applications. In practical civil engineering applications, the necessity of covering large column free open areas is often an issue and hyperbolic paraboloid shells are used as roofing units. Quite often, to save weight and also to provide a facility for inspection, cutouts are provided in shell panels. The paper considers free vibration characteristics of stiffened composite hyperbolic paraboloid shell panel with cutout in terms of natural frequency and mode shapes. A finite element code is developed for the purpose by combining an eight noded curved shell element with a three noded curved beam element. The size of the cutouts and their positions with respect to the shell centre are varied for different edge conditions to arrive at a set of inferences of practical engineering significances.

Free vibration of laminated composite stiffened hyperbolic paraboloid shell panel with cutout

International Nuclear Information System (INIS)

Sahoo, Sarmila

2016-01-01

Composite shell structures are extensively used in aerospace, civil, marine and other engineering applications. In practical civil engineering applications, the necessity of covering large column free open areas is often an issue and hyperbolic paraboloid shells are used as roofing units. Quite often, to save weight and also to provide a facility for inspection, cutouts are provided in shell panels. The paper considers free vibration characteristics of stiffened composite hyperbolic paraboloid shell panel with cutout in terms of natural frequency and mode shapes. A finite element code is developed for the purpose by combining an eight noded curved shell element with a three noded curved beam element. The size of the cutouts and their positions with respect to the shell centre are varied for different edge conditions to arrive at a set of inferences of practical engineering significances. (paper)

Resonances for Obstacles in Hyperbolic Space

Science.gov (United States)

Hintz, Peter; Zworski, Maciej

2017-12-01

We consider scattering by star-shaped obstacles in hyperbolic space and show that resonances satisfy a universal bound { Im λ ≤ - 1/2 } , which is optimal in dimension 2. In odd dimensions we also show that { Im λ ≤ - μ/ρ } for a universal constant {μ} , where { ρ } is the radius of a ball containing the obstacle; this gives an improvement for small obstacles. In dimensions 3 and higher the proofs follow the classical vector field approach of Morawetz, while in dimension 2 we obtain our bound by working with spaces coming from general relativity. We also show that in odd dimensions resonances of small obstacles are close, in a suitable sense, to Euclidean resonances.

Symmetric positive differential equations and first order hyperbolic systems

International Nuclear Information System (INIS)

Tangmanee, S.

1981-12-01

We prove that under some conditions the first order hyperbolic system and its associated mixed initial boundary conditions considered, for example, in Kreiss (Math. Comp. 22, 703-704 (1968)) and Kreiss and Gustafsson (Math. Comp. 26, 649-686 (1972)), can be transformed into a symmetric positive system of P.D.E.'s with admissible boundary conditions of Friedrich's type (Comm. Pure Appl. Math 11, 333-418 (1958)). (author)

The Superconvergence of Mixed Finite Element Methods for Nonlinear Hyperbolic Equations

Institute of Scientific and Technical Information of China (English)

YanpingCHEN; YunqingHUANG

1998-01-01

Imprioved L2-error estimates are computed for mixed finte element methods for second order nonlinear hyperbolic equations.Superconvergence results,L∞ in time and discrete L2 in space,are derived for both the solution and gradients on the rectangular domain.Results are given for the continuous-time case.

Linear hyperbolic functional-differential equations with essentially bounded right-hand side

Czech Academy of Sciences Publication Activity Database

Domoshnitsky, A.; Lomtatidze, Alexander; Maghakyan, A.; Šremr, Jiří

2011-01-01

Roč. 2011, - (2011), s. 242965 ISSN 1085-3375 Institutional research plan: CEZ:AV0Z10190503 Keywords : linear functional-differential equation of hyperbolic type * Darboux problem * unique solvability Subject RIV: BA - General Mathematics Impact factor: 1.318, year: 2011 http://www.hindawi.com/journals/ aaa /2011/242965/

PT-symmetry breaking in complex nonlinear wave equations and their deformations

International Nuclear Information System (INIS)

Cavaglia, Andrea; Fring, Andreas; Bagchi, Bijan

2011-01-01

We investigate complex versions of the Korteweg-deVries equations and an Ito-type nonlinear system with two coupled nonlinear fields. We systematically construct rational, trigonometric/hyperbolic and elliptic solutions for these models including those which are physically feasible in an obvious sense, that is those with real energies, but also those with complex energy spectra. The reality of the energy is usually attributed to different realizations of an antilinear symmetry, as for instance PT-symmetry. It is shown that the symmetry can be spontaneously broken in two alternative ways either by specific choices of the domain or by manipulating the parameters in the solutions of the model, thus leading to complex energies. Surprisingly, the reality of the energies can be regained in some cases by a further breaking of the symmetry on the level of the Hamiltonian. In many examples, some of the fixed points in the complex solution for the field undergo a Hopf bifurcation in the PT-symmetry breaking process. By employing several different variants of the symmetries we propose many classes of new invariant extensions of these models and study their properties. The reduction of some of these models yields complex quantum mechanical models previously studied.

The features of sporadic hyperbolic meteors observed by television techniques in the period of 2007-2009

Science.gov (United States)

Guliyev, Ayyub; Nabiyev, Shaig

2015-12-01

The features of 238 hyperbolic meteors observed within the framework of the Japanese program SonotaCo in the period of 2007-2009 are investigated in this paper. Irregularity of the eccentricities, explicitly dominance of retrograde orbits over direct ones, absence of domination of perihelia closes the ecliptic, irregular distribution of angular elements for these bodies' orbits were noticed. The values of eccentricities are distributed in the interval from 1 up to 1.31. The significant concentration of these particles perihelia closes the anti-apex of the Sun's peculiarity movements in the Galaxy was noticed. Distribution of elements of orbits in the galactic system of coordinates was considered also, however it was not possible to find the appreciable regularities. The distributions of the distant nodes and MOID-Minimum Orbit Intersection Distance of the hyperbolic meteors relatively to the orbits of the planets-giants were investigated as well. However it was not possible to prove, that the majority of the particles could receive the hyperbolic excess of speed due to the gravitational influence of the planets-giants. The statistics of relation of the hyperbolic meteors with 14 known trans-Neptunian planetary bodies brighter 3m.5 is considered. Testing of the distant nodes and MOID values only for 2003 MW12, 2007 OR10 and Qaoaor have the positive results. In the next stage we have made analogical calculations for the 78 TNO having absolute brightness 5m.5 also and obtained the reasonable results for 9 of them.

Geometry in the large and hyperbolic chaos

Energy Technology Data Exchange (ETDEWEB)

Hasslacher, B.; Mainieri, R.

1998-11-01

This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). The authors calculated observables in strongly chaotic systems. This is difficult to do because of a lack of a workable orbit classification for such systems. This is due to global geometrical information from the original dynamical system being entangled in an unknown way throughout the orbit sequence. They used geometrical methods from modern mathematics and recent connections between global geometry and modern quantum field theory to study the natural geometrical objects belonging to hard chaos-hyperbolic manifolds.

One-way spatial integration of hyperbolic equations

Science.gov (United States)

Towne, Aaron; Colonius, Tim

2015-11-01

In this paper, we develop and demonstrate a method for constructing well-posed one-way approximations of linear hyperbolic systems. We use a semi-discrete approach that allows the method to be applied to a wider class of problems than existing methods based on analytical factorization of idealized dispersion relations. After establishing the existence of an exact one-way equation for systems whose coefficients do not vary along the axis of integration, efficient approximations of the one-way operator are constructed by generalizing techniques previously used to create nonreflecting boundary conditions. When physically justified, the method can be applied to systems with slowly varying coefficients in the direction of integration. To demonstrate the accuracy and computational efficiency of the approach, the method is applied to model problems in acoustics and fluid dynamics via the linearized Euler equations; in particular we consider the scattering of sound waves from a vortex and the evolution of hydrodynamic wavepackets in a spatially evolving jet. The latter problem shows the potential of the method to offer a systematic, convergent alternative to ad hoc regularizations such as the parabolized stability equations.

Extended Thermodynamics: a Theory of Symmetric Hyperbolic Field Equations

Science.gov (United States)

Müller, Ingo

2008-12-01

Extended thermodynamics is based on a set of equations of balance which are supplemented by local and instantaneous constitutive equations so that the field equations are quasi-linear first order differential equations. If the constitutive functions are subject to the requirements of the entropy principle, one may write them in symmetric hyperbolic form by a suitable choice of fields. The kinetic theory of gases, or the moment theories based on the Boltzmann equation provide an explicit example for extended thermodynamics. The theory proves its usefulness and practicality in the successful treatment of light scattering in rarefied gases. This presentation is based upon the book [1] of which the author of this paper is a co-author. For more details about the motivation and exploitation of the basic principles the interested reader is referred to that reference. It would seem that extended thermodynamics is worthy of the attention of mathematicians. It may offer them a non-trivial field of study concerning hyperbolic equations, if ever they get tired of the Burgers equation. Physicists may prefer to appreciate the success of extended thermodynamics in light scattering and to work on the open problems concerning the modification of the Navier-Stokes-Fourier theory in rarefied gases as predicted by extended thermodynamics of 13, 14, and more moments.

Demonstrator of atmospheric reentry system with hyperbolic velocity—DASH

Science.gov (United States)

Morita, Yasuhiro; Kawaguchi, Jun'ichiro; Inatani, Yoshifumi; Abe, Takashi

2003-01-01

Among a wide variety of challenging projects planned for the coming decade is the MUSES-C mission designed by the ISAS of Japan. Despite huge amount of data collected by the previous interplanetary spacecraft and probes, the origin and evolution of the solar system still remains unveiled due to their limited information. Thus, our concern has been directed toward a sample return to carry sample from an asteroid back to the earth, which will contribute to better understanding of the system. One of the keys to success is considered the reentry technology with hyperbolic velocity, which has not been demonstrated yet. With this as background, the demonstrator of atmospheric reentry system with hyperbolic velocity, DASH, has been given a commitment to demonstrate the high-speed reentry technology, which will be launched in summer of next year by Japan's H-IIA rocket in a piggyback configuration. The spaceship, composed of a reentry capsule and its carrier, will be injected into a geostationary transfer orbit (GTO) and after several revolutions it will deorbit by burn of a solid propellant deorbit motor. The capsule, identical to that of the sample return mission, can experience the targeted level of thermal environment even from the GTO by tracing a specially designed reentry trajectory.

Seismic data two-step recovery approach combining sparsity-promoting and hyperbolic Radon transform methods

International Nuclear Information System (INIS)

Wang, Hanchuang; Chen, Shengchang; Ren, Haoran; Liang, Donghui; Zhou, Huamin; She, Deping

2015-01-01

In current research of seismic data recovery problems, the sparsity-promoting method usually produces an insufficient recovery result at the locations of null traces. The HRT (hyperbolic Radon transform) method can be applied to problems of seismic data recovery with approximately hyperbolic events. Influenced by deviations of hyperbolic characteristics between real and ideal travel-time curves, some spurious events are usually introduced and the recovery effect of intermediate and far-offset traces is worse than that of near-offset traces. Sparsity-promoting recovery is primarily dependent on the sparsity of seismic data in the sparse transform domain (i.e. on the local waveform characteristics), whereas HRT recovery is severely affected by the global characteristics of the seismic events. Inspired by the above conclusion, a two-step recovery approach combining sparsity-promoting and time-invariant HRT methods is proposed, which is based on both local and global characteristics of the seismic data. Two implementation strategies are presented in detail, and the selection criteria of the relevant strategies is also discussed. Numerical examples of synthetic and real data verify that the new approach can achieve a better recovery effect by simultaneously overcoming the shortcomings of sparsity-promoting recovery and HRT recovery. (paper)

On a class of singular hyperbolic equation with a weighted integral condition

Directory of Open Access Journals (Sweden)

Said Mesloub

1999-01-01

for a class of second order singular hyperbolic equations. We prove the existence and uniqueness of a strong solution. The proof is based on a priori estimate and on the density of the range of the operator generated by the studied problem.

Big Data Clustering via Community Detection and Hyperbolic Network Embedding in IoT Applications.

Science.gov (United States)

Karyotis, Vasileios; Tsitseklis, Konstantinos; Sotiropoulos, Konstantinos; Papavassiliou, Symeon

2018-04-15

In this paper, we present a novel data clustering framework for big sensory data produced by IoT applications. Based on a network representation of the relations among multi-dimensional data, data clustering is mapped to node clustering over the produced data graphs. To address the potential very large scale of such datasets/graphs that test the limits of state-of-the-art approaches, we map the problem of data clustering to a community detection one over the corresponding data graphs. Specifically, we propose a novel computational approach for enhancing the traditional Girvan-Newman (GN) community detection algorithm via hyperbolic network embedding. The data dependency graph is embedded in the hyperbolic space via Rigel embedding, allowing more efficient computation of edge-betweenness centrality needed in the GN algorithm. This allows for more efficient clustering of the nodes of the data graph in terms of modularity, without sacrificing considerable accuracy. In order to study the operation of our approach with respect to enhancing GN community detection, we employ various representative types of artificial complex networks, such as scale-free, small-world and random geometric topologies, and frequently-employed benchmark datasets for demonstrating its efficacy in terms of data clustering via community detection. Furthermore, we provide a proof-of-concept evaluation by applying the proposed framework over multi-dimensional datasets obtained from an operational smart-city/building IoT infrastructure provided by the Federated Interoperable Semantic IoT/cloud Testbeds and Applications (FIESTA-IoT) testbed federation. It is shown that the proposed framework can be indeed used for community detection/data clustering and exploited in various other IoT applications, such as performing more energy-efficient smart-city/building sensing.

A high-order relaxation method with projective integration for solving nonlinear systems of hyperbolic conservation laws

Science.gov (United States)

Lafitte, Pauline; Melis, Ward; Samaey, Giovanni

2017-07-01

We present a general, high-order, fully explicit relaxation scheme which can be applied to any system of nonlinear hyperbolic conservation laws in multiple dimensions. The scheme consists of two steps. In a first (relaxation) step, the nonlinear hyperbolic conservation law is approximated by a kinetic equation with stiff BGK source term. Then, this kinetic equation is integrated in time using a projective integration method. After taking a few small (inner) steps with a simple, explicit method (such as direct forward Euler) to damp out the stiff components of the solution, the time derivative is estimated and used in an (outer) Runge-Kutta method of arbitrary order. We show that, with an appropriate choice of inner step size, the time step restriction on the outer time step is similar to the CFL condition for the hyperbolic conservation law. Moreover, the number of inner time steps is also independent of the stiffness of the BGK source term. We discuss stability and consistency, and illustrate with numerical results (linear advection, Burgers' equation and the shallow water and Euler equations) in one and two spatial dimensions.

Monitoring and modeling of long-term settlements of an experimental landfill in Brazil.

Science.gov (United States)

Simões, Gustavo Ferreira; Catapreta, Cícero Antônio Antunes

2013-02-01

Settlement evaluation in sanitary landfills is a complex process, due to the waste heterogeneity, time-varying properties and influencing factors and mechanisms, such as mechanical compression due to load application and creep, and physical-chemical and biological processes caused by the wastes decomposition. Many empirical models for the analysis of long-term settlement in landfills are reported in the literature. This paper presents the results of a settlement monitoring program carried out during 6 years in Belo Horizonte experimental landfill. Different sets of field data were used to calibrate three long-term settlement prediction models (rheological, hyperbolic and composite). The parameters obtained in the calibration were used to predict the settlements and to compare with actual field data. During the monitoring period of 6 years, significant vertical strains were observed (of up to 31%) in relation to the initial height of the experimental landfill. The results for the long-term settlement prediction obtained by the hyperbolic and rheological models significantly underestimate the settlements, regardless the period of data used in the calibration. The best fits were obtained with the composite model, except when 1 year field data were used in the calibration. The results of the composite model indicate settlements stabilization at larger times and with larger final settlements when compared to the hyperbolic and rheological models. Copyright © 2012 Elsevier Ltd. All rights reserved.

Landau levels on the hyperbolic plane

International Nuclear Information System (INIS)

Fakhri, H; Shariati, M

2004-01-01

The quantum states of a spinless charged particle on a hyperbolic plane in the presence of a uniform magnetic field with a generalized quantization condition are proved to be the bases of the irreducible Hilbert representation spaces of the Lie algebra u(1, 1). The dynamical symmetry group U(1, 1) with the explicit form of the Lie algebra generators is extracted. It is also shown that the energy has an infinite-fold degeneracy in each of the representation spaces which are allocated to the different values of the magnetic field strength. Based on the simultaneous shift of two parameters, it is also noted that the quantum states realize the representations of Lie algebra u(2) by shifting the magnetic field strength. (letter to the editor)

Landau levels on the hyperbolic plane

Energy Technology Data Exchange (ETDEWEB)

Fakhri, H [Institute for Studies in Theoretical Physics and Mathematics (IPM), Tehran 19395-5531 (Iran, Islamic Republic of); Shariati, M [Department of Physics, Khajeh Nassir-Al-Deen Toosi University of Technology, Tehran 15418 (Iran, Islamic Republic of)

2004-11-05

The quantum states of a spinless charged particle on a hyperbolic plane in the presence of a uniform magnetic field with a generalized quantization condition are proved to be the bases of the irreducible Hilbert representation spaces of the Lie algebra u(1, 1). The dynamical symmetry group U(1, 1) with the explicit form of the Lie algebra generators is extracted. It is also shown that the energy has an infinite-fold degeneracy in each of the representation spaces which are allocated to the different values of the magnetic field strength. Based on the simultaneous shift of two parameters, it is also noted that the quantum states realize the representations of Lie algebra u(2) by shifting the magnetic field strength. (letter to the editor)

Design of a hyperbolic microwave metallic lens

International Nuclear Information System (INIS)

Uckan, T.

1979-12-01

Due to problems caused by multiple reflections in the cavity walls of the EBT fusion research device, the use of a horn becomes important for the directivity of waves in the millimetric range. An ordinary dielectric lens cannot be used because of plasma-wall interactions. Microwave metallic lenses, designed to focus the energy into a plane wave, can improve the directivity considerably. By implementing a 70-GHz standard-gain horn with a delay-type hyperbolic lens, which consists of a solid metallic disk with a number of equal size small holes has indicated a gain of 15 dB over the no lens case

On the Smooth Dependence of SRB Measures for Partially Hyperbolic Systems

Science.gov (United States)

Zhang, Zhiyuan

2018-02-01

In this paper, we study the differentiability of SRB measures for partially hyperbolic systems. We show that for any {s ≥ 1}, for any integer {ℓ ≥ 2}, any sufficiently large r, any φ \\in Cr(T, R)} such that the map {f : T^2 \\to T^2, f(x,y) = (ℓ x, y + φ(x))} is {C^r}-stably ergodic, there exists an open neighbourhood of f in {C^r(T^2,T^2)} such that any map in this neighbourhood has a unique SRB measure with {C^{s-1}} density, which depends on the dynamics in a {C^s} fashion. We also construct a C^{∞} mostly contracting partially hyperbolic diffeomorphism {f: T^3 \\to T^3} such that all f' in a C 2 open neighbourhood of f possess a unique SRB measure {μ_{f'}} and the map {f' \\mapsto μ_{f'}} is strictly Hölder at f, in particular, non-differentiable. This gives a partial answer to Dolgopyat's Question 13.3 in Dolgopyat (Commun Math Phys 213:181-201, 2000).

A tolerance analysis on design parameters of parabolic and hyperbolic secant active GRIN materials for laser beam shaping purposes

International Nuclear Information System (INIS)

Gómez-Varela, A I; Bao-Varela, C; Flores-Arias, M T

2014-01-01

The present paper considers two gain GRIN media, characterized by a complex parabolic and hyperbolic secant refractive index profile, for the design of uniform beam shaper systems. A general condition for beam shaping is obtained from the equation describing the evolution of the half-width of a plane Gaussian beam in the GRIN media. The simulation of the irradiance evolution of an input plane Gaussian beam—operating at 575 nm and beam waist radius of 0.45 mm—in each material is shown, in order to examine the beam shaping quality in terms of thickness of the active GRIN media and input beam wavelength. (paper)

Dynamical zeta functions and dynamical determinants for hyperbolic maps a functional approach

CERN Document Server

Baladi, Viviane

2018-01-01

The spectra of transfer operators associated to dynamical systems, when acting on suitable Banach spaces, contain key information about the ergodic properties of the systems. Focusing on expanding and hyperbolic maps, this book gives a self-contained account on the relation between zeroes of dynamical determinants, poles of dynamical zeta functions, and the discrete spectra of the transfer operators. In the hyperbolic case, the first key step consists in constructing a suitable Banach space of anisotropic distributions. The first part of the book is devoted to the easier case of expanding endomorphisms, showing how the (isotropic) function spaces relevant there can be studied via Paley–Littlewood decompositions, and allowing easier access to the construction of the anisotropic spaces which is performed in the second part. This is the first book describing the use of anisotropic spaces in dynamics. Aimed at researchers and graduate students, it presents results and techniques developed since the beginning of...

Hyperbolic Location Fingerprinting: A Calibration-Free Solution for Handling Differences in Signal Strength

DEFF Research Database (Denmark)

Kjærgaard, Mikkel Baun; Munk, Carsten Valdemar

2008-01-01

records fingerprints as signal-strength ratios between pairs of base stations instead of absolute signal-strength values. The proposed solution has been evaluated by extending two well-known location fingerprinting techniques to hyperbolic location fingerprinting. The extended techniques have been tested...

Unfolding transitions in myosin give rise to the double-hyperbolic force-velocity relation in muscle

DEFF Research Database (Denmark)

Nielsen, Bjørn Gilbert

2003-01-01

This work presents an extension to a recent model of muscle contraction that was based on entropic elasticity (Nielsen 2002 J. Theor Biol. 219 99-119). By using entropic elasticity as the origin of muscle force, various possibilities emerge that can account for the presence of the double......-hyperbolic force-velocity relation in muscle that was observed by Edman (1988 J. Physiol. 404 301-21). In the present work, it will be argued that a slight change (elongation) of the contour length of the entropic springs involved in their high-force regions is sufficient to produce such a double...

Generation of new solutions of the stationary axisymmetric Einstein equations by a double complex function method

International Nuclear Information System (INIS)

Zhong, Z.

1985-01-01

A new approach to the solution of certain differential equations, the double complex function method, is developed, combining ordinary complex numbers and hyperbolic complex numbers. This method is applied to the theory of stationary axisymmetric Einstein equations in general relativity. A family of exact double solutions, double transformation groups, and n-soliton double solutions are obtained

Big Data Clustering via Community Detection and Hyperbolic Network Embedding in IoT Applications

Directory of Open Access Journals (Sweden)

Vasileios Karyotis

2018-04-01

Full Text Available In this paper, we present a novel data clustering framework for big sensory data produced by IoT applications. Based on a network representation of the relations among multi-dimensional data, data clustering is mapped to node clustering over the produced data graphs. To address the potential very large scale of such datasets/graphs that test the limits of state-of-the-art approaches, we map the problem of data clustering to a community detection one over the corresponding data graphs. Specifically, we propose a novel computational approach for enhancing the traditional Girvan–Newman (GN community detection algorithm via hyperbolic network embedding. The data dependency graph is embedded in the hyperbolic space via Rigel embedding, allowing more efficient computation of edge-betweenness centrality needed in the GN algorithm. This allows for more efficient clustering of the nodes of the data graph in terms of modularity, without sacrificing considerable accuracy. In order to study the operation of our approach with respect to enhancing GN community detection, we employ various representative types of artificial complex networks, such as scale-free, small-world and random geometric topologies, and frequently-employed benchmark datasets for demonstrating its efficacy in terms of data clustering via community detection. Furthermore, we provide a proof-of-concept evaluation by applying the proposed framework over multi-dimensional datasets obtained from an operational smart-city/building IoT infrastructure provided by the Federated Interoperable Semantic IoT/cloud Testbeds and Applications (FIESTA-IoT testbed federation. It is shown that the proposed framework can be indeed used for community detection/data clustering and exploited in various other IoT applications, such as performing more energy-efficient smart-city/building sensing.

Metaphor, hyperbole, and irony: Uses in isolation and in combination in written discourse

NARCIS (Netherlands)

Burgers, Christian; Renardel de Lavalette, Kiki Y.; Steen, Gerard J.

2018-01-01

While classical theories on rhetoric cluster figurative devices like metaphor, hyperbole, and irony under the encompassing category of tropes, current theories and research typically focus on one of the tropes in isolation. To determine how these different tropes are used in combinations, we

Global embedding of the Kerr black hole event horizon into hyperbolic 3-space

International Nuclear Information System (INIS)

Gibbons, G. W.; Herdeiro, C. A. R.; Rebelo, C.

2009-01-01

An explicit global and unique isometric embedding into hyperbolic 3-space, H 3 , of an axi-symmetric 2-surface with Gaussian curvature bounded below is given. In particular, this allows the embedding into H 3 of surfaces of revolution having negative, but finite, Gaussian curvature at smooth fixed points of the U(1) isometry. As an example, we exhibit the global embedding of the Kerr-Newman event horizon into H 3 , for arbitrary values of the angular momentum. For this example, considering a quotient of H 3 by the Picard group, we show that the hyperbolic embedding fits in a fundamental domain of the group up to a slightly larger value of the angular momentum than the limit for which a global embedding into Euclidean 3-space is possible. An embedding of the double-Kerr event horizon is also presented, as an example of an embedding that cannot be made global.

Plasma diagnostics by Abel inversion in hyperbolic geometry

International Nuclear Information System (INIS)

Alhasi, A.S.; Elliott, J.A.

1992-01-01

Plasma confined in the UMIST linear quadrupole adopts a configuration with approximately hyperbolic symmetry. The normal diagnostic is a Langmuir probe, but we have developed an alternative method using optical emission tomography based upon an analytic Abel inversion. Plasma radiance is obtained as a function of a parameter identifying magnetic flux surfaces. The inversion algorithm has been tested using artificial data. Experimentally, the results show that ionizing collisions cause the confined plasma distribution to broaden as the plasma travels through the confining field. This is shown to be a consequence of the approximate incompressibility of the E x B flow. (author)

On the landau levels on the hyperbolic plane

International Nuclear Information System (INIS)

Comtet, A.

1986-04-01

The classical and quantum mechanics of a charged particle moving on the hyperbolic plane in a constant magnetic field is discussed. The underlying SL(2,R) symmetry leads to a general description of various possible trajectories. In contrast with the flat case, it is shown that closed orbits only arise for sufficiently strong fields. At the quantum level a group theoretical approach including both bound and continuum states is presented. It is shown that the semiclassical approximation leads to the exact bound state spectrum. The resolvent and its flat space limit are constructed in closed form

Uniform approximations of Bernoulli and Euler polynomials in terms of hyperbolic functions

NARCIS (Netherlands)

J.L. López; N.M. Temme (Nico)

1998-01-01

textabstractBernoulli and Euler polynomials are considered for large values of the order. Convergent expansions are obtained for $B_n(nz+1/2)$ and $E_n(nz+1/2)$ in powers of $n^{-1$, with coefficients being rational functions of $z$ and hyperbolic functions of argument $1/2z$. These expansions are

Inextendibilty of the Maximal Global Hyperbolic Development in Electrogowdy spacetimes

Directory of Open Access Journals (Sweden)

Nungesser Ernesto

2013-09-01

Full Text Available The problem of determinism in General Relativity appears even if one assumes that the spacetime is globally hyperbolic, i.e. that it contains a hypersurface that is intersected by any causal curve exactly once. The strong cosmic censorship hypothesis is essentially the hypothesis that General Relativity is a predictable theory and thus a crucial issue in Classical General Relativity. We sketch here the proof for the case of Electrogowdy spacetimes.

Hyperbolic Method for Dispersive PDEs: Same High-Order of Accuracy for Solution, Gradient, and Hessian

Science.gov (United States)

Mazaheri, Alireza; Ricchiuto, Mario; Nishikawa, Hiroaki

2016-01-01

In this paper, we introduce a new hyperbolic first-order system for general dispersive partial differential equations (PDEs). We then extend the proposed system to general advection-diffusion-dispersion PDEs. We apply the fourth-order RD scheme of Ref. 1 to the proposed hyperbolic system, and solve time-dependent dispersive equations, including the classical two-soliton KdV and a dispersive shock case. We demonstrate that the predicted results, including the gradient and Hessian (second derivative), are in a very good agreement with the exact solutions. We then show that the RD scheme applied to the proposed system accurately captures dispersive shocks without numerical oscillations. We also verify that the solution, gradient and Hessian are predicted with equal order of accuracy.

Hyperbolic umbilic caustics from oblate water drops with tilted illumination: Observations

Science.gov (United States)

Jobe, Oli; Thiessen, David B.; Marston, Philip L.

2017-11-01

Various groups have reported observations of hyperbolic umbilic diffraction catastrophe patterns in the far-field scattering by oblate acoustically levitated drops with symmetric illumination. In observations of that type the drop's symmetry axis is vertical and the illuminating light beam (typically an expanded laser beam) travels horizontally. In the research summarized here, scattering patterns in the primary rainbow region and drop measurements were recorded with vertically tilted laser beam illumination having a grazing angle as large as 4 degrees. The findings from these observations may be summarized as follows: (a) It remains possible to adjust the drop aspect ratio (diameter/height) = D/H so as to produce a V-shaped hyperbolic umbilic focal section (HUFS) in the far-field scattering. (b) The shift in the required D/H was typically an increase of less than 1% and was quadratic in the tilt. (c) The apex of the V-shaped HUFS was shifted vertically by an amount proportional to the tilt with a coefficient close to unity. The levitated drops had negligible up-down asymmetry. Our method of investigation should be useful for other generalized rainbows with tilted illumination.

Global Classical Solutions for Partially Dissipative Hyperbolic System of Balance Laws

Science.gov (United States)

Xu, Jiang; Kawashima, Shuichi

2014-02-01

The basic existence theory of Kato and Majda enables us to obtain local-in-time classical solutions to generally quasilinear hyperbolic systems in the framework of Sobolev spaces (in x) with higher regularity. However, it remains a challenging open problem whether classical solutions still preserve well-posedness in the case of critical regularity. This paper is concerned with partially dissipative hyperbolic system of balance laws. Under the entropy dissipative assumption, we establish the local well-posedness and blow-up criterion of classical solutions in the framework of Besov spaces with critical regularity with the aid of the standard iteration argument and Friedrichs' regularization method. Then we explore the theory of function spaces and develop an elementary fact that indicates the relation between homogeneous and inhomogeneous Chemin-Lerner spaces (mixed space-time Besov spaces). This fact allows us to capture the dissipation rates generated from the partial dissipative source term and further obtain the global well-posedness and stability by assuming at all times the Shizuta-Kawashima algebraic condition. As a direct application, the corresponding well-posedness and stability of classical solutions to the compressible Euler equations with damping are also obtained.

New generalized hyperbolic functions to find new coupled ultraslow optical soliton pairs in a cold three-state double- and system

International Nuclear Information System (INIS)

Yomba, Emmanuel

2007-01-01

We demonstrate that the known method which is based on the new generalized hyperbolic functions and the new kinds of generalized hyperbolic function transformations, generates classes of exact solutions to a system of coupled nonlinear Schroedinger equations governing the nonlinear evolution of the envelopes probe fields in the four-mixing scheme. Four types of solutions are given explicitly, namely new bright-bright, new dark-dark, new bright-dark and new dark-bright solitons

Cosmology in the laboratory: An analogy between hyperbolic metamaterials and the Milne universe

Science.gov (United States)

Figueiredo, David; Moraes, Fernando; Fumeron, Sébastien; Berche, Bertrand

2017-11-01

This article shows that the compactified Milne universe geometry, a toy model for the big crunch/big bang transition, can be realized in hyperbolic metamaterials, a new class of nanoengineered systems which have recently found its way as an experimental playground for cosmological ideas. On one side, Klein-Gordon particles, as well as tachyons, are used as probes of the Milne geometry. On the other side, the propagation of light in two versions of a liquid crystal-based metamaterial provides the analogy. It is shown that ray and wave optics in the metamaterial mimic, respectively, the classical trajectories and wave function propagation, of the Milne probes, leading to the exciting perspective of realizing experimental tests of particle tunneling through the cosmic singularity, for instance.

Transition from complete synchronization to spatio-temporal chaos in coupled chaotic systems with nonhyperbolic and hyperbolic attractors

Science.gov (United States)

Rybalova, Elena; Semenova, Nadezhda; Strelkova, Galina; Anishchenko, Vadim

2017-06-01

We study the transition from coherence (complete synchronization) to incoherence (spatio-temporal chaos) in ensembles of nonlocally coupled chaotic maps with nonhyperbolic and hyperbolic attractors. As basic models of a partial element we use the Henon map and the Lozi map. We show that the transition to incoherence in a ring of coupled Henon maps occurs through the appearance of phase and amplitude chimera states. An ensemble of coupled Lozi maps demonstrates the coherence-incoherence transition via solitary states and no chimera states are observed in this case.

A high-order finite-volume method for hyperbolic conservation laws on locally-refined grids

Energy Technology Data Exchange (ETDEWEB)

McCorquodale, Peter; Colella, Phillip

2011-01-28

We present a fourth-order accurate finite-volume method for solving time-dependent hyperbolic systems of conservation laws on Cartesian grids with multiple levels of refinement. The underlying method is a generalization of that in [5] to nonlinear systems, and is based on using fourth-order accurate quadratures for computing fluxes on faces, combined with fourth-order accurate Runge?Kutta discretization in time. To interpolate boundary conditions at refinement boundaries, we interpolate in time in a manner consistent with the individual stages of the Runge-Kutta method, and interpolate in space by solving a least-squares problem over a neighborhood of each target cell for the coefficients of a cubic polynomial. The method also uses a variation on the extremum-preserving limiter in [8], as well as slope flattening and a fourth-order accurate artificial viscosity for strong shocks. We show that the resulting method is fourth-order accurate for smooth solutions, and is robust in the presence of complex combinations of shocks and smooth flows.

Computing with high-resolution upwind schemes for hyperbolic equations

International Nuclear Information System (INIS)

Chakravarthy, S.R.; Osher, S.; California Univ., Los Angeles)

1985-01-01

Computational aspects of modern high-resolution upwind finite-difference schemes for hyperbolic systems of conservation laws are examined. An operational unification is demonstrated for constructing a wide class of flux-difference-split and flux-split schemes based on the design principles underlying total variation diminishing (TVD) schemes. Consideration is also given to TVD scheme design by preprocessing, the extension of preprocessing and postprocessing approaches to general control volumes, the removal of expansion shocks and glitches, relaxation methods for implicit TVD schemes, and a new family of high-accuracy TVD schemes. 21 references

Six-month exenatide improves HOMA hyperbolic product in type 2 diabetic patients mostly by enhancing beta-cell function rather than insulin sensitivity.

Science.gov (United States)

Preumont, V; Hermans, M-P; Brichard, S; Buysschaert, M

2010-09-01

This study aimed to determine whether or not the improvement of glycaemic control with 6-month exenatide therapy in type 2 diabetic patients with secondary failure to combined oral therapy is related to amelioration of β-cell function and/or insulin sensitivity and their combined product. Thirty-three patients with type 2 diabetes were investigated. Their β-cell function and insulin sensitivity were measured using Homoeostasis Model Assessment [HOMA-B, HOMA-S and HOMA hyperbolic product (BxS)]. Additional endpoints included changes in weight, HbA(1c) and plasma adiponectin, as well as baseline clinical and biological characteristics, as potential predictors of HbA(1c) response. After 6 months, unadjusted HOMA-B increased from 33 ± 24% to 43 ± 23% (P=0.0210), whereas there was no significant change in HOMA-S (from 58 ± 35% to 61 ± 40%). The hyperbolic product increased by a relative 70% (from 15 ± 7% to 22 ± 15%; P=0.0055). Body mass index decreased from 32.2 ± 5.1 kg/m(2) to 31.0 ± 4.8 kg/m(2) (PHOMA-B and hyperbolic product over a 6-month treatment period with no overall change in insulin sensitivity, despite weight loss. Thus, improved β-cell function rather than increased insulin sensitivity accounts for the bulk of HbA(1c) reduction following 6 months of exenatide treatment. Copyright © 2010 Elsevier Masson SAS. All rights reserved.

Tangent hyperbolic circular frequency diverse array radars

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Sarah Saeed

2016-03-01

Full Text Available Frequency diverse array (FDA with uniform frequency offset (UFO has been in spot light of research for past few years. Not much attention has been devoted to non-UFOs in FDA. This study investigates tangent hyperbolic (TH function for frequency offset selection scheme in circular FDAs (CFDAs. Investigation reveals a three-dimensional single-maximum beampattern, which promises to enhance system detection capability and signal-to-interference plus noise ratio. Furthermore, by utilising the versatility of TH function, a highly configurable type array system is achieved, where beampatterns of three different configurations of FDA can be generated, just by adjusting a single function parameter. This study further examines the utility of the proposed TH-CFDA in some practical radar scenarios.

Formation mechanism of a basin of attraction for passive dynamic walking induced by intrinsic hyperbolicity

Science.gov (United States)

Aoi, Shinya; Tsuchiya, Kazuo; Kokubu, Hiroshi

2016-01-01

Passive dynamic walking is a useful model for investigating the mechanical functions of the body that produce energy-efficient walking. The basin of attraction is very small and thin, and it has a fractal-like shape; this explains the difficulty in producing stable passive dynamic walking. The underlying mechanism that produces these geometric characteristics was not known. In this paper, we consider this from the viewpoint of dynamical systems theory, and we use the simplest walking model to clarify the mechanism that forms the basin of attraction for passive dynamic walking. We show that the intrinsic saddle-type hyperbolicity of the upright equilibrium point in the governing dynamics plays an important role in the geometrical characteristics of the basin of attraction; this contributes to our understanding of the stability mechanism of bipedal walking. PMID:27436971

A Novel Modified Algorithm with Reduced Complexity LDPC Code Decoder

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Song Yang

2014-10-01

Full Text Available A novel efficient decoding algorithm reduced the sum-product algorithm (SPA Complexity with LPDC code is proposed. Base on the hyperbolic tangent rule, modified the Check node update with two horizontal process, which have similar calculation, Motivated by the finding that sun- min (MS algorithm reduce the complexity reducing the approximation error in the horizontal process, simplify the information weight small part. Compared with the exiting approximations, the proposed method is less computational complexity than SPA algorithm. Simulation results show that the author algorithm can achieve performance very close SPA.

Quantum and classical properties of some billiards on the hyperbolic plane

International Nuclear Information System (INIS)

Schmit, C.

1991-01-01

Some 'experimental' results are given on the quantal spectrum of some billiards on two-dimensional manifolds of constant negative curvature. It is shown that the use of the Selberg trace formula may bring some interesting new results on the properties of the classical motion. Some new (and quite unexpected) results are presented about the quantal spectrum of the octagon on the hyperbolic plane. (K.A.) 8 refs.; 17 figs.; 2 tabs

Ray equations of a weak shock in a hyperbolic system of ...

Indian Academy of Sciences (India)

differential form of this system of conservation laws is a hyperbolic system of partial differential equations. A(u)ut + B(α)(u)uxα = 0,. (1.3) where. A(u) = 〈∇u,H〉 and B(α)(u) = 〈∇u, F(α)〉,. (1.4) and we use the summation convention that a repeated symbol in subscripts and super- scripts in a term will mean summation over the ...

Why plankton modellers should reconsider using rectangular hyperbolic (Michaelis-Menten, Monod descriptions of predator-prey interactions

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Kevin John Flynn

2016-09-01

Full Text Available Rectangular hyperbolic type 2 (RHt2; Michaelis-Menten or Monod -like functions are commonly used to describe predation kinetics in plankton models, either alone or together with a prey selectivity algorithm deploying the same half-saturation constant for all prey types referenced to external prey biomass abundance. We present an analysis that indicates that such descriptions are liable to give outputs that are not plausible according to encounter theory. This is especially so for multi-prey type applications or where changes are made to the maximum feeding rate during a simulation. The RHt2 approach also gives no or limited potential for descriptions of events such as true de-selection of prey, effects of turbulence on encounters, or changes in grazer motility with satiation. We present an alternative, which carries minimal parameterisation effort and computational cost, linking allometric algorithms relating prey abundance and encounter rates to a prey-selection function controlled by satiation. The resultant Satiation-Controlled-Encounter-Based (SCEB function provides a flexible construct describing numeric predator-prey interactions with biomass-feedback control of grazing. The SCEB function includes an attack component similar to that in the Holling disk equation but SCEB differs in having only a single (satiation-based handling constant and an explicit maximum grazing rate. We argue that there is no justification for continuing to deploy RHt2 functions to describe plankton predator-prey interactions.

Elliptic–hyperbolic partial differential equations a mini-course in geometric and quasilinear methods

CERN Document Server

Otway, Thomas H

2015-01-01

This text is a concise introduction to the partial differential equations which change from elliptic to hyperbolic type across a smooth hypersurface of their domain. These are becoming increasingly important in diverse sub-fields of both applied mathematics and engineering, for example:   • The heating of fusion plasmas by electromagnetic waves • The behaviour of light near a caustic • Extremal surfaces in the space of special relativity • The formation of rapids; transonic and multiphase fluid flow • The dynamics of certain models for elastic structures • The shape of industrial surfaces such as windshields and airfoils • Pathologies of traffic flow • Harmonic fields in extended projective space   They also arise in models for the early universe, for cosmic acceleration, and for possible violation of causality in the interiors of certain compact stars. Within the past 25 years, they have become central to the isometric embedding of Riemannian manifolds and the prescription of Gauss curvatur...

On the asymptotic behavior of complex earthquakes and Teichmüller disks

DEFF Research Database (Denmark)

Gupta, Subhojoy

2015-01-01

Given a hyperbolic surface and a simple closed geodesic on it, complex-twists along the curve produce a holomorphic family of deformations in Teichmuller space, degenerating to the Riemann surface where it is pinched. We show there is a corresponding Teichmuller disk such that the two are strongl...

On the automorphisms of foliations defined by complex linear vectorfields

International Nuclear Information System (INIS)

Shahshahani, S.

1989-04-01

We study biholomorphisms of C n that preserve the foliation associated to a complex linear vector fields. It is shown that for hyperbolic Poincare vector fields the only such biholomorphisms are linear. Nonlinear biholomorphisms emerge in the presence of resonance among the eigenvalues of the system. A complete classification is given in dimension 2. (author). 8 refs, 1 fig

Nonlocal optical effects on the Goos–Hänchen shifts at multilayered hyperbolic metamaterials

International Nuclear Information System (INIS)

Chen, Chih-Wei; Bian, Tingting; Chiang, Hai-Pang; Leung, P T

2016-01-01

The lateral beam shift of light incident on a multilayered hyperbolic metamaterial (HMM) is investigated using a theoretical model which emphasizes the nonlocal optical response of the indefinite material. By applying an effective local response theory formulated recently in the literature, it is found that nonlocal effects only affect p polarized light in this Goos–Hänchen (GH) shift of the incident beam; leading to a blue-shifted peak for positive shifts at high frequencies and red-shifted dip for negative shifts at low frequencies in the GH shift spectrum. An account for the observed phenomenon is given by referring to the ‘Brewster condition’ for the reflected wave from the HMM. This observation thus provides a relatively direct probe for the nonlocal response of the HMM. (paper)

Hyperbolic Cosine–Exponentiated Exponential Lifetime Distribution and its Application in Reliability

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Omid Kharazmi

2017-02-01

Full Text Available Recently, Kharazmi and Saadatinik (2016 introduced a new family of lifetime distributions called hyperbolic cosine – F (HCF distribution. In the present paper, it is focused on a special case of HCF family with exponentiated exponential distribution as a baseline distribution (HCEE. Various properties of the proposed distribution including explicit expressions for the moments, quantiles, mode, moment generating function, failure rate function, mean residual lifetime, order statistics and expression of the entropy are derived. Estimating parameters of HCEE distribution are obtained by eight estimation methods: maximum likelihood, Bayesian, maximum product of spacings, parametric bootstrap, non-parametric bootstrap, percentile, least-squares and weighted least-squares. A simulation study is conducted to examine the bias, mean square error of the maximum likelihood estimators. Finally, one real data set has been analyzed for illustrative purposes and it is observed that the proposed model fits better than Weibull, gamma and generalized exponential distributions.

Light propagation in a magneto-optical hyperbolic biaxial crystal

Science.gov (United States)

Kuznetsov, Evgeniy V.; Merzlikin, Alexander M.

2017-12-01

The light propagation through a magneto-optical hyperbolic biaxial crystal is investigated. Magnetization of the structure results in splitting and reconnection of an isofrequency near the self-intersection point and thus it leads to the disappearance of conical refraction in a crystal. In its turn the isofrequency splitting leads to band gap opening and makes it possible to steer the beam. These effects allow to control the light propagation by means of an external magnetostatic field. The Poynting's vector distribution in the crystal is calculated by means of a Fourier transform in order to demonstrate the aforementioned effects.

Gupta-Bleuler Quantization of the Maxwell Field in Globally Hyperbolic Space-Times

Science.gov (United States)

Finster, Felix; Strohmaier, Alexander

2015-08-01

We give a complete framework for the Gupta-Bleuler quantization of the free electromagnetic field on globally hyperbolic space-times. We describe one-particle structures that give rise to states satisfying the microlocal spectrum condition. The field algebras in the so-called Gupta-Bleuler representations satisfy the time-slice axiom, and the corresponding vacuum states satisfy the microlocal spectrum condition. We also give an explicit construction of ground states on ultrastatic space-times. Unlike previous constructions, our method does not require a spectral gap or the absence of zero modes. The only requirement, the absence of zero-resonance states, is shown to be stable under compact perturbations of topology and metric. Usual deformation arguments based on the time-slice axiom then lead to a construction of Gupta-Bleuler representations on a large class of globally hyperbolic space-times. As usual, the field algebra is represented on an indefinite inner product space, in which the physical states form a positive semi-definite subspace. Gauge transformations are incorporated in such a way that the field can be coupled perturbatively to a Dirac field. Our approach does not require any topological restrictions on the underlying space-time.

An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws

Science.gov (United States)

Borges, Rafael; Carmona, Monique; Costa, Bruno; Don, Wai Sun

2008-03-01

In this article we develop an improved version of the classical fifth-order weighted essentially non-oscillatory finite difference scheme of [G.S. Jiang, C.W. Shu, Efficient implementation of weighted ENO schemes, J. Comput. Phys. 126 (1996) 202-228] (WENO-JS) for hyperbolic conservation laws. Through the novel use of a linear combination of the low order smoothness indicators already present in the framework of WENO-JS, a new smoothness indicator of higher order is devised and new non-oscillatory weights are built, providing a new WENO scheme (WENO-Z) with less dissipation and higher resolution than the classical WENO. This new scheme generates solutions that are sharp as the ones of the mapped WENO scheme (WENO-M) of Henrick et al. [A.K. Henrick, T.D. Aslam, J.M. Powers, Mapped weighted essentially non-oscillatory schemes: achieving optimal order near critical points, J. Comput. Phys. 207 (2005) 542-567], however with a 25% reduction in CPU costs, since no mapping is necessary. We also provide a detailed analysis of the convergence of the WENO-Z scheme at critical points of smooth solutions and show that the solution enhancements of WENO-Z and WENO-M at problems with shocks comes from their ability to assign substantially larger weights to discontinuous stencils than the WENO-JS scheme, not from their superior order of convergence at critical points. Numerical solutions of the linear advection of discontinuous functions and nonlinear hyperbolic conservation laws as the one dimensional Euler equations with Riemann initial value problems, the Mach 3 shock-density wave interaction and the blastwave problems are compared with the ones generated by the WENO-JS and WENO-M schemes. The good performance of the WENO-Z scheme is also demonstrated in the simulation of two dimensional problems as the shock-vortex interaction and a Mach 4.46 Richtmyer-Meshkov Instability (RMI) modeled via the two dimensional Euler equations.

Analytic smoothing effect for the cubic hyperbolic Schrodinger equation in two space dimensions

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Gaku Hoshino

2016-01-01

Full Text Available We study the Cauchy problem for the cubic hyperbolic Schrodinger equation in two space dimensions. We prove existence of analytic global solutions for sufficiently small and exponential decaying data. The method of proof depends on the generalized Leibniz rule for the generator of pseudo-conformal transform acting on pseudo-conformally invariant nonlinearity.

On a second order of accuracy stable difference scheme for the solution of a source identification problem for hyperbolic-parabolic equations

Science.gov (United States)

Ashyralyyeva, Maral; Ashyraliyev, Maksat

2016-08-01

In the present paper, a second order of accuracy difference scheme for the approximate solution of a source identification problem for hyperbolic-parabolic equations is constructed. Theorem on stability estimates for the solution of this difference scheme and their first and second order difference derivatives is presented. In applications, this abstract result permits us to obtain the stability estimates for the solutions of difference schemes for approximate solutions of two source identification problems for hyperbolic-parabolic equations.

A boundary value problem for a third order hyperbolic equation with degeneration of order inside the domain

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Ruzanna Kh. Makaova

2017-12-01

Full Text Available In this paper we study the boundary value problem for a degenerating third order equation of hyperbolic type in a mixed domain. The equation under consideration in the positive part of the domain coincides with the Hallaire equation, which is a pseudoparabolic type equation. Moreover, in the negative part of the domain it coincides with a degenerating hyperbolic equation of the first kind, the particular case of the Bitsadze–Lykov equation. The existence and uniqueness theorem for the solution is proved. The uniqueness of the solution to the problem is proved with the Tricomi method. Using the functional relationships of the positive and negative parts of the domain on the degeneration line, we arrive at the convolution type Volterra integral equation of the 2nd kind with respect to the desired solution by a derivative trace. With the Laplace transform method, we obtain the solution of the integral equation in its explicit form. At last, the solution to the problem under study is written out explicitly as the solution of the second boundary-value problem in the positive part of the domain for the Hallaire equation and as the solution to the Cauchy problem in the negative part of the domain for a degenerate hyperbolic equation of the first kind.

Multi-time-scale heat transfer modeling of turbid tissues exposed to short-pulsed irradiations.

Science.gov (United States)

Kim, Kyunghan; Guo, Zhixiong

2007-05-01

A combined hyperbolic radiation and conduction heat transfer model is developed to simulate multi-time-scale heat transfer in turbid tissues exposed to short-pulsed irradiations. An initial temperature response of a tissue to an ultrashort pulse irradiation is analyzed by the volume-average method in combination with the transient discrete ordinates method for modeling the ultrafast radiation heat transfer. This response is found to reach pseudo steady state within 1 ns for the considered tissues. The single pulse result is then utilized to obtain the temperature response to pulse train irradiation at the microsecond/millisecond time scales. After that, the temperature field is predicted by the hyperbolic heat conduction model which is solved by the MacCormack's scheme with error terms correction. Finally, the hyperbolic conduction is compared with the traditional parabolic heat diffusion model. It is found that the maximum local temperatures are larger in the hyperbolic prediction than the parabolic prediction. In the modeled dermis tissue, a 7% non-dimensional temperature increase is found. After about 10 thermal relaxation times, thermal waves fade away and the predictions between the hyperbolic and parabolic models are consistent.

Complex dynamics of an archetypal self-excited SD oscillator driven by moving belt friction

International Nuclear Information System (INIS)

Li Zhi-Xin; Cao Qing-Jie; Alain, Léger

2016-01-01

We propose an archetypal self-excited system driven by moving belt friction, which is constructed with the smooth and discontinuous (SD) oscillator proposed by the Cao et al. and the classical moving belt. The moving belt friction is modeled as the Coulomb friction to formulate the mathematical model of the proposed self-excited SD oscillator. The equilibrium states of the unperturbed system are obtained to show the complex equilibrium bifurcations. Phase portraits are depicted to present the hyperbolic structure transition, the multiple stick regions, and the friction-induced asymmetry phenomena. The numerical simulations are carried out to demonstrate the friction-induced vibration of multiple stick-slip phenomena and the stick-slip chaos in the perturbed self-excited system. The results presented here provide an opportunity for us to get insight into the mechanism of the complex friction-induced nonlinear dynamics in mechanical engineering and geography. (paper)

Front tracking for hyperbolic conservation laws

CERN Document Server

Holden, Helge

2002-01-01

Hyperbolic conservation laws are central in the theory of nonlinear partial differential equations and in science and technology. The reader is given a self-contained presentation using front tracking, which is also a numerical method. The multidimensional scalar case and the case of systems on the line are treated in detail. A chapter on finite differences is included. "It is already one of the few best digests on this topic. The present book is an excellent compromise between theory and practice. Students will appreciate the lively and accurate style." D. Serre, MathSciNet "I have read the book with great pleasure, and I can recommend it to experts as well as students. It can also be used for reliable and very exciting basis for a one-semester graduate course." S. Noelle, Book review, German Math. Soc. "Making it an ideal first book for the theory of nonlinear partial differential equations...an excellent reference for a graduate course on nonlinear conservation laws." M. Laforest, Comp. Phys. Comm.

Weak linear degeneracy and lifespan of classical solutions for first order quasilinear hyperbolic systems

International Nuclear Information System (INIS)

Li Tatsien

1994-01-01

By means of the concept of the weak linear degeneracy, one gets the global existence and the sharp estimate of the lifespan of C 1 solutions to the Cauchy problem for general first order quasilinear hyperbolic systems with small initial data with compact support. (author). 23 refs, 1 fig

CIP - a new numerical solver for general nonlinear hyperbolic equations in multi-dimension

International Nuclear Information System (INIS)

Yabe, Takashi; Takewaki, Hideaki.

1986-12-01

A new method CIP (Cubic-Interpolated Pseudo-particle) to solve hyperbolic equations is proposed. The method gives a stable and less diffusive result for square wave propagation compared with FCT (Flux-Corrected Transport) and a better result for propagation of a sine wave with a discontinuity. The scheme is extended to nonlinear and multi-dimensional problems. (orig.) [de

Modeling Complex Time Limits

Directory of Open Access Journals (Sweden)

Oleg Svatos

2013-01-01

Full Text Available In this paper we analyze complexity of time limits we can find especially in regulated processes of public administration. First we review the most popular process modeling languages. There is defined an example scenario based on the current Czech legislature which is then captured in discussed process modeling languages. Analysis shows that the contemporary process modeling languages support capturing of the time limit only partially. This causes troubles to analysts and unnecessary complexity of the models. Upon unsatisfying results of the contemporary process modeling languages we analyze the complexity of the time limits in greater detail and outline lifecycles of a time limit using the multiple dynamic generalizations pattern. As an alternative to the popular process modeling languages there is presented PSD process modeling language, which supports the defined lifecycles of a time limit natively and therefore allows keeping the models simple and easy to understand.

Modeling Complex Systems

CERN Document Server

Boccara, Nino

2010-01-01

Modeling Complex Systems, 2nd Edition, explores the process of modeling complex systems, providing examples from such diverse fields as ecology, epidemiology, sociology, seismology, and economics. It illustrates how models of complex systems are built and provides indispensable mathematical tools for studying their dynamics. This vital introductory text is useful for advanced undergraduate students in various scientific disciplines, and serves as an important reference book for graduate students and young researchers. This enhanced second edition includes: . -recent research results and bibliographic references -extra footnotes which provide biographical information on cited scientists who have made significant contributions to the field -new and improved worked-out examples to aid a student’s comprehension of the content -exercises to challenge the reader and complement the material Nino Boccara is also the author of Essentials of Mathematica: With Applications to Mathematics and Physics (Springer, 2007).

Computational modeling for fluid flow and interfacial transport

CERN Document Server

Shyy, Wei

2006-01-01

Practical applications and examples highlight this treatment of computational modeling for handling complex flowfields. A reference for researchers and graduate students of many different backgrounds, it also functions as a text for learning essential computation elements.Drawing upon his own research, the author addresses both macroscopic and microscopic features. He begins his three-part treatment with a survey of the basic concepts of finite difference schemes for solving parabolic, elliptic, and hyperbolic partial differential equations. The second part concerns issues related to computati

Metric Characterizations of Superreflexivity in Terms of Word Hyperbolic Groups and Finite Graphs

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Ostrovskii Mikhail

2014-01-01

Full Text Available We show that superreflexivity can be characterized in terms of bilipschitz embeddability of word hyperbolic groups.We compare characterizations of superrefiexivity in terms of diamond graphs and binary trees.We show that there exist sequences of series-parallel graphs of increasing topological complexitywhich admit uniformly bilipschitz embeddings into a Hilbert space, and thus do not characterize superrefiexivity.

Mixed problems for linear symmetric hyperbolic systems with characteristic boundary conditions

International Nuclear Information System (INIS)

Secchi, P.

1994-01-01

We consider the initial-boundary value problem for symmetric hyperbolic systems with characteristic boundary of constant multiplicity. In the linear case we give some results about the existence of regular solutions in suitable functions spaces which take in account the loss of regularity in the normal direction to the characteristic boundary. We also consider the equations of ideal magneto-hydrodynamics under perfectly conducting wall boundary conditions and give some results about the solvability of such mixed problem. (author). 16 refs

Modeling Complex Systems

International Nuclear Information System (INIS)

Schreckenberg, M

2004-01-01

This book by Nino Boccara presents a compilation of model systems commonly termed as 'complex'. It starts with a definition of the systems under consideration and how to build up a model to describe the complex dynamics. The subsequent chapters are devoted to various categories of mean-field type models (differential and recurrence equations, chaos) and of agent-based models (cellular automata, networks and power-law distributions). Each chapter is supplemented by a number of exercises and their solutions. The table of contents looks a little arbitrary but the author took the most prominent model systems investigated over the years (and up until now there has been no unified theory covering the various aspects of complex dynamics). The model systems are explained by looking at a number of applications in various fields. The book is written as a textbook for interested students as well as serving as a comprehensive reference for experts. It is an ideal source for topics to be presented in a lecture on dynamics of complex systems. This is the first book on this 'wide' topic and I have long awaited such a book (in fact I planned to write it myself but this is much better than I could ever have written it!). Only section 6 on cellular automata is a little too limited to the author's point of view and one would have expected more about the famous Domany-Kinzel model (and more accurate citation!). In my opinion this is one of the best textbooks published during the last decade and even experts can learn a lot from it. Hopefully there will be an actualization after, say, five years since this field is growing so quickly. The price is too high for students but this, unfortunately, is the normal case today. Nevertheless I think it will be a great success! (book review)

Code Samples Used for Complexity and Control

Science.gov (United States)

Ivancevic, Vladimir G.; Reid, Darryn J.

2015-11-01

The following sections are included: * MathematicaⓇ Code * Generic Chaotic Simulator * Vector Differential Operators * NLS Explorer * 2C++ Code * C++ Lambda Functions for Real Calculus * Accelerometer Data Processor * Simple Predictor-Corrector Integrator * Solving the BVP with the Shooting Method * Linear Hyperbolic PDE Solver * Linear Elliptic PDE Solver * Method of Lines for a Set of the NLS Equations * C# Code * Iterative Equation Solver * Simulated Annealing: A Function Minimum * Simple Nonlinear Dynamics * Nonlinear Pendulum Simulator * Lagrangian Dynamics Simulator * Complex-Valued Crowd Attractor Dynamics * Freeform Fortran Code * Lorenz Attractor Simulator * Complex Lorenz Attractor * Simple SGE Soliton * Complex Signal Presentation * Gaussian Wave Packet * Hermitian Matrices * Euclidean L2-Norm * Vector/Matrix Operations * Plain C-Code: Levenberg-Marquardt Optimizer * Free Basic Code: 2D Crowd Dynamics with 3000 Agents

Metrical and dynamical aspects in complex analysis

CERN Document Server

2017-01-01

The central theme of this reference book is the metric geometry of complex analysis in several variables. Bridging a gap in the current literature, the text focuses on the fine behavior of the Kobayashi metric of complex manifolds and its relationships to dynamical systems, hyperbolicity in the sense of Gromov and operator theory, all very active areas of research. The modern points of view expressed in these notes, collected here for the first time, will be of interest to academics working in the fields of several complex variables and metric geometry. The different topics are treated coherently and include expository presentations of the relevant tools, techniques and objects, which will be particularly useful for graduate and PhD students specializing in the area.

On problems with displacement in boundary conditions for hyperbolic equation

Directory of Open Access Journals (Sweden)

Elena A. Utkina

2016-03-01

Full Text Available We consider three problems for hyperbolic equation on a plane in the characteristic domain. In these problems at least one of the conditions of the Goursat problem is replaced by nonlocal condition on the relevant characteristic. Non-local conditions are the linear combinations of the normal derivatives at points on opposite characteristics. In case of replacement of one condition we solve the problem by reduction to the Goursat problem for which it exists and is unique. To find the unknown Goursat condition author receives the integral equation, rewrite it in operational form and finds its unique solvability cases. To prove the unique solvability of the equation, the author shows the continuous linear operator and the fact, that some degree of the resulting operator is a contraction mapping. It is known that in this case the required Goursat condition can be written as Neumann series. We considered in detail only one of the tasks, but for both the unique solvability theorems are formulated. If the two conditions are changed, the uniqueness of the solution on the assumption that it exists, is proved by the method of a priori estimates. For this purpose, the inner product and the norm in $L_2$ are used. As a result, the conditions were obtained for the coefficients of a hyperbolic equation that ensure the uniqueness of the solution. An example is given, confirming that these conditions are essential. Namely, constructed an equation whose coefficients do not satisfy the conditions of the last theorem, given the conditions on the characteristics and nontrivial solution is built.

Analysis and Adaptive Synchronization of Two Novel Chaotic Systems with Hyperbolic Sinusoidal and Cosinusoidal Nonlinearity and Unknown Parameters

Directory of Open Access Journals (Sweden)

S. Vaidyanathan

2013-09-01

Full Text Available This research work describes the modelling of two novel 3-D chaotic systems, the first with a hyperbolic sinusoidal nonlinearity and two quadratic nonlinearities (denoted as system (A and the second with a hyperbolic cosinusoidal nonlinearity and two quadratic nonlinearities (denoted as system (B. In this work, a detailed qualitative analysis of the novel chaotic systems (A and (B has been presented, and the Lyapunov exponents and Kaplan-Yorke dimension of these chaotic systems have been obtained. It is found that the maximal Lyapunov exponent (MLE for the novel chaotic systems (A and (B has a large value, viz. for the system (A and for the system (B. Thus, both the novel chaotic systems (A and (B display strong chaotic behaviour. This research work also discusses the problem of finding adaptive controllers for the global chaos synchronization of identical chaotic systems (A, identical chaotic systems (B and nonidentical chaotic systems (A and (B with unknown system parameters. The adaptive controllers for achieving global chaos synchronization of the novel chaotic systems (A and (B have been derived using adaptive control theory and Lyapunov stability theory. MATLAB simulations have been shown to illustrate the novel chaotic systems (A and (B, and also the adaptive synchronization results derived for the novel chaotic systems (A and (B.

Effects of hyperbolic rotation in Minkowski space on the modeling of plasma accelerators in a Lorentz boosted frame

International Nuclear Information System (INIS)

Vay, J.-L.; Geddes, C. G. R.; Cormier-Michel, E.; Grote, D. P.

2011-01-01

The effects of hyperbolic rotation in Minkowski space resulting from the use of Lorentz boosted frames of calculation on laser propagation in plasmas are analyzed. Selection of a boost frame at the laser group velocity is shown to alter the laser spectrum, allowing the use of higher boost velocities. The technique is applied to simulations of laser driven plasma wakefield accelerators, which promise much smaller machines and whose development requires detailed simulations that challenge or exceed current capabilities. Speedups approaching the theoretical optima are demonstrated, producing the first direct simulations of stages up to 1 TeV. This is made possible by a million times speedup thanks to a frame boost with a relativistic factor γ b as high as 1300, taking advantage of the rotation to mitigate an instability that limited previous work.

Dynamics in stationary, non-globally hyperbolic spacetimes

Energy Technology Data Exchange (ETDEWEB)

Seggev, Itai [Enrico Fermi Institute and Department of Physics, University of Chicago, 5640 S Ellis Avenue, Chicago, IL 60637 (United States)

2004-06-07

Classically, the dynamics of a scalar field in a non-globally hyperbolic spacetime is ill-posed. Previously, a prescription was given for defining dynamics in static spacetimes in terms of a second-order operator acting on a Hilbert space defined on static slices. The present work extends this result by giving a similar prescription for defining dynamics in stationary spacetimes obeying certain mild assumptions. The prescription is defined in terms of a first-order operator acting on a different Hilbert space from that used in the static prescription. It preserves the important properties of the earlier prescription: the formal solution agrees with the Cauchy evolution within the domain of dependence, and smooth data of compact support always give rise to smooth solutions. In the static case, the first-order formalism agrees with the second-order formalism (using specifically the Friedrichs extension). Applications to field quantization are also discussed.

Control of Hyperbolic Heat Transfer Mechanisms Application to the Distributed Concentrated Solar Collectors

KAUST Repository

Elmetennani, Shahrazed

2017-04-01

This dissertation addresses the flow control problem in hyperbolic heat transfer mechanisms. It raises in concentrated distributed solar collectors to enhance their production efficiency under the unpredictable variations of the solar energy and the external disturbances. These factors which are either locally measured (the solar irradiance) or inaccessible for measurement (the collectors’ cleanliness) affect the source term of the distributed model and represent a major difficulty for the control design. Moreover, the temperature in the collector can only be measured at the boundaries. In this dissertation, we propose new adaptive control approaches to provide the adequate level of heat while coping with the unpredictable varying disturbances. First, we design model based control strategies for a better efficiency, in terms of accuracy and response time, with a relatively reduced complexity. Second, we enhance the controllers with on-line adaptation laws to continuously update the efficient value of the external conditions. In this study, we approach the control problem using both, the infinite dimensional model (late lumping) and a finite dimensional approximate representation (early lumping). For the early lumping approach, we introduce a new reduced order bilinear approximate model for system analysis and control design. This approximate state representation is then used to derive a nonlinear state feedback resorting to Lyapunov stability theory. To compensate for the external disturbances and the approximation uncertainties, an adaptive controller is developed based on a phenomenological representation of the system dynamics. For the late lumping approach, we propose two PDE based controllers by stabilization of the reference tracking error distributed profile. The control laws are explicitly defined as functions of the available measurement. The first one is obtained using a direct approach for error stabilization while the second one is derived through a

Blow-up Mechanism of Classical Solutions to Quasilinear Hyperbolic Systems in the Critical Case

Institute of Scientific and Technical Information of China (English)

无

2006-01-01

This paper deals with the blow-up phenomenon, particularly, the geometric blow-up mechanism, of classical solutions to the Cauchy problem for quasilinear hyperbolic systems in the critical case. We prove that it is still the envelope of the same family of characteristics which yields the blowup of classical solutions to the Cauchy problem in the critical case.

Particle resonance in the Dirac equation in the presence of a delta interaction and a perturbative hyperbolic potential

International Nuclear Information System (INIS)

Villalba, Victor M.; Gonzalez-Diaz, Luis A.

2009-01-01

We show that the energy spectrum of the one-dimensional Dirac equation, in the presence of an attractive vectorial delta potential, exhibits a resonant behavior when one includes an asymptotically spatially vanishing weak electric field associated with a hyperbolic tangent potential. We solve the Dirac equation in terms of Gauss hyper-geometric functions and show explicitly how the resonant behavior depends on the strength of the electric field evaluated at the support of the point interaction. We derive an approximate expression for the value of the resonances and compare the results calculated for the hyperbolic potential with those obtained for a linear perturbative potential. Finally, we characterize the resonances with the help of the phase shift and the Wigner delay time. (orig.)

A comparison of hyperbolic solvers for ideal and real gas flows

Directory of Open Access Journals (Sweden)

R. M. L. Coelho

2006-09-01

Full Text Available Classical and recent numerical schemes for solving hyperbolic conservation laws were analyzed for computational efficiency and application to nonideal gas flows. The Roe-Pike approximate Riemann solver with entropy correction, the Harten second-order scheme and the extension of the Roe-Pike method to second-order by the MUSCL strategy were compared for one-dimensional flows of an ideal gas. These methods require the so-called Roe's average state, which is frequently difficult and sometimes impossible to obtain. Other methods that do not require the average state are best suited for complex equations of state. Of these, the VFRoe, AUSM+ and Hybrid Lax-Friedrich-Lax-Wendroff methods were compared for one-dimensional compressible flows of a Van der Waals gas. All methods were evaluated regarding their accuracy for given mesh sizes and their computational cost for a given solution accuracy. It was shown that, even though they require more floating points and indirect addressing operations per time step, for a given time interval for integration the second-order methods are less-time consuming than the first-order methods for a required accuracy. It was also shown that AUSM+ and VFRoe are the most accurate methods and that AUSM+ is much faster than the others, and is thus recommended for nonideal one-phase gas flows.

Optimized difference schemes for multidimensional hyperbolic partial differential equations

Directory of Open Access Journals (Sweden)

Adrian Sescu

2009-04-01

Full Text Available In numerical solutions to hyperbolic partial differential equations in multidimensions, in addition to dispersion and dissipation errors, there is a grid-related error (referred to as isotropy error or numerical anisotropy that affects the directional dependence of the wave propagation. Difference schemes are mostly analyzed and optimized in one dimension, wherein the anisotropy correction may not be effective enough. In this work, optimized multidimensional difference schemes with arbitrary order of accuracy are designed to have improved isotropy compared to conventional schemes. The derivation is performed based on Taylor series expansion and Fourier analysis. The schemes are restricted to equally-spaced Cartesian grids, so the generalized curvilinear transformation method and Cartesian grid methods are good candidates.

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.

Hyperbolically Patterned 3D Graphene Metamaterial with Negative Poisson's Ratio and Superelasticity.

Science.gov (United States)

Zhang, Qiangqiang; Xu, Xiang; Lin, Dong; Chen, Wenli; Xiong, Guoping; Yu, Yikang; Fisher, Timothy S; Li, Hui

2016-03-16

A hyperbolically patterned 3D graphene metamaterial (GM) with negative Poisson's ratio and superelasticity is highlighted. It is synthesized by a modified hydrothermal approach and subsequent oriented freeze-casting strategy. GM presents a tunable Poisson's ratio by adjusting the structural porosity, macroscopic aspect ratio (L/D), and freeze-casting conditions. Such a GM suggests promising applications as soft actuators, sensors, robust shock absorbers, and environmental remediation. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Nonparametric Bayesian Modeling of Complex Networks

DEFF Research Database (Denmark)

Schmidt, Mikkel Nørgaard; Mørup, Morten

2013-01-01

an infinite mixture model as running example, we go through the steps of deriving the model as an infinite limit of a finite parametric model, inferring the model parameters by Markov chain Monte Carlo, and checking the model?s fit and predictive performance. We explain how advanced nonparametric models......Modeling structure in complex networks using Bayesian nonparametrics makes it possible to specify flexible model structures and infer the adequate model complexity from the observed data. This article provides a gentle introduction to nonparametric Bayesian modeling of complex networks: Using...

Clinical Complexity in Medicine: A Measurement Model of Task and Patient Complexity.

Science.gov (United States)

Islam, R; Weir, C; Del Fiol, G

2016-01-01

Complexity in medicine needs to be reduced to simple components in a way that is comprehensible to researchers and clinicians. Few studies in the current literature propose a measurement model that addresses both task and patient complexity in medicine. The objective of this paper is to develop an integrated approach to understand and measure clinical complexity by incorporating both task and patient complexity components focusing on the infectious disease domain. The measurement model was adapted and modified for the healthcare domain. Three clinical infectious disease teams were observed, audio-recorded and transcribed. Each team included an infectious diseases expert, one infectious diseases fellow, one physician assistant and one pharmacy resident fellow. The transcripts were parsed and the authors independently coded complexity attributes. This baseline measurement model of clinical complexity was modified in an initial set of coding processes and further validated in a consensus-based iterative process that included several meetings and email discussions by three clinical experts from diverse backgrounds from the Department of Biomedical Informatics at the University of Utah. Inter-rater reliability was calculated using Cohen's kappa. The proposed clinical complexity model consists of two separate components. The first is a clinical task complexity model with 13 clinical complexity-contributing factors and 7 dimensions. The second is the patient complexity model with 11 complexity-contributing factors and 5 dimensions. The measurement model for complexity encompassing both task and patient complexity will be a valuable resource for future researchers and industry to measure and understand complexity in healthcare.

Weak asymptotic solution for a non-strictly hyperbolic system of conservation laws-II

Directory of Open Access Journals (Sweden)

Manas Ranjan Sahoo

2016-04-01

Full Text Available In this article we introduce a concept of entropy weak asymptotic solution for a system of conservation laws and construct the same for a prolonged system of conservation laws which is highly non-strictly hyperbolic. This is first done for Riemann type initial data by introducing $\\delta,\\delta',\\delta''$ waves along a discontinuity curve and then for general initial data by piecing together the Riemann solutions.

Complex matrix model duality

International Nuclear Information System (INIS)

Brown, T.W.

2010-11-01

The same complex matrix model calculates both tachyon scattering for the c=1 non-critical string at the self-dual radius and certain correlation functions of half-BPS operators in N=4 super- Yang-Mills. It is dual to another complex matrix model where the couplings of the first model are encoded in the Kontsevich-like variables of the second. The duality between the theories is mirrored by the duality of their Feynman diagrams. Analogously to the Hermitian Kontsevich- Penner model, the correlation functions of the second model can be written as sums over discrete points in subspaces of the moduli space of punctured Riemann surfaces. (orig.)

Complex matrix model duality

Energy Technology Data Exchange (ETDEWEB)

Brown, T.W.

2010-11-15

The same complex matrix model calculates both tachyon scattering for the c=1 non-critical string at the self-dual radius and certain correlation functions of half-BPS operators in N=4 super- Yang-Mills. It is dual to another complex matrix model where the couplings of the first model are encoded in the Kontsevich-like variables of the second. The duality between the theories is mirrored by the duality of their Feynman diagrams. Analogously to the Hermitian Kontsevich- Penner model, the correlation functions of the second model can be written as sums over discrete points in subspaces of the moduli space of punctured Riemann surfaces. (orig.)

Distinguished hyperbolic trajectories in time-dependent fluid flows: analytical and computational approach for velocity fields defined as data sets

Directory of Open Access Journals (Sweden)

K. Ide

2002-01-01

Full Text Available In this paper we develop analytical and numerical methods for finding special hyperbolic trajectories that govern geometry of Lagrangian structures in time-dependent vector fields. The vector fields (or velocity fields may have arbitrary time dependence and be realized only as data sets over finite time intervals, where space and time are discretized. While the notion of a hyperbolic trajectory is central to dynamical systems theory, much of the theoretical developments for Lagrangian transport proceed under the assumption that such a special hyperbolic trajectory exists. This brings in new mathematical issues that must be addressed in order for Lagrangian transport theory to be applicable in practice, i.e. how to determine whether or not such a trajectory exists and, if it does exist, how to identify it in a sequence of instantaneous velocity fields. We address these issues by developing the notion of a distinguished hyperbolic trajectory (DHT. We develop an existence criteria for certain classes of DHTs in general time-dependent velocity fields, based on the time evolution of Eulerian structures that are observed in individual instantaneous fields over the entire time interval of the data set. We demonstrate the concept of DHTs in inhomogeneous (or "forced" time-dependent linear systems and develop a theory and analytical formula for computing DHTs. Throughout this work the notion of linearization is very important. This is not surprising since hyperbolicity is a "linearized" notion. To extend the analytical formula to more general nonlinear time-dependent velocity fields, we develop a series of coordinate transforms including a type of linearization that is not typically used in dynamical systems theory. We refer to it as Eulerian linearization, which is related to the frame independence of DHTs, as opposed to the Lagrangian linearization, which is typical in dynamical systems theory, which is used in the computation of Lyapunov exponents. We

BOUNDARY VALUE PROBLEM FOR A LOADED EQUATION ELLIPTIC-HYPERBOLIC TYPE IN A DOUBLY CONNECTED DOMAIN

Directory of Open Access Journals (Sweden)

O.Kh. Abdullaev

2014-06-01

Full Text Available We study the existence and uniqueness of the solution of one boundary value problem for the loaded elliptic-hyperbolic equation of the second order with two lines of change of type in double-connected domain. Similar results have been received by D.M.Kuryhazov, when investigated domain is one-connected.

An Interactive Analysis of Hyperboles in a British TV Series: Implications For EFL Classes

Science.gov (United States)

Sert, Olcay

2008-01-01

This paper, part of an ongoing study on the analysis of hyperboles in a British TV series, reports findings drawing upon a 90,000 word corpus. The findings are compared to the ones from CANCODE (McCarthy and Carter 2004), a five-million word corpus of spontaneous speech, in order to identify similarities between the two. The analysis showed that…

Spherical CR geometry and Dehn surgery

CERN Document Server

Schwarz, Richard Evan

2007-01-01

This book proves an analogue of William Thurston's celebrated hyperbolic Dehn surgery theorem in the context of complex hyperbolic discrete groups, and then derives two main geometric consequences from it. The first is the construction of large numbers of closed real hyperbolic 3-manifolds which bound complex hyperbolic orbifolds--the only known examples of closed manifolds that simultaneously have these two kinds of geometric structures. The second is a complete understanding of the structure of complex hyperbolic reflection triangle groups in cases where the angle is small. In an accessible

Numerical simulation of idealized front motion in neutral and stratified atmosphere with a hyperbolic system of equations

Science.gov (United States)

Yudin, M. S.

2017-11-01

In the present paper, stratification effects on surface pressure in the propagation of an atmospheric gravity current (cold front) over flat terrain are estimated with a non-hydrostatic finite-difference model of atmospheric dynamics. Artificial compressibility is introduced into the model in order to make its equations hyperbolic. For comparison with available simulation data, the physical processes under study are assumed to be adiabatic. The influence of orography is also eliminated. The front surface is explicitly described by a special equation. A time filter is used to suppress the non-physical oscillations. The results of simulations of surface pressure under neutral and stable stratification are presented. Under stable stratification the front moves faster and shows an abrupt pressure jump at the point of observation. This fact is in accordance with observations and the present-day theory of atmospheric fronts.

Simulation in Complex Modelling

DEFF Research Database (Denmark)

Nicholas, Paul; Ramsgaard Thomsen, Mette; Tamke, Martin

2017-01-01

This paper will discuss the role of simulation in extended architectural design modelling. As a framing paper, the aim is to present and discuss the role of integrated design simulation and feedback between design and simulation in a series of projects under the Complex Modelling framework. Complex...... performance, engage with high degrees of interdependency and allow the emergence of design agency and feedback between the multiple scales of architectural construction. This paper presents examples for integrated design simulation from a series of projects including Lace Wall, A Bridge Too Far and Inflated...... Restraint developed for the research exhibition Complex Modelling, Meldahls Smedie Gallery, Copenhagen in 2016. Where the direct project aims and outcomes have been reported elsewhere, the aim for this paper is to discuss overarching strategies for working with design integrated simulation....

Source term boundary adaptive estimation in a first-order 1D hyperbolic PDE: Application to a one loop solar collector through

KAUST Repository

Mechhoud, Sarra

2016-08-04

In this paper, boundary adaptive estimation of solar radiation in a solar collector plant is investigated. The solar collector is described by a 1D first-order hyperbolic partial differential equation where the solar radiation models the source term and only boundary measurements are available. Using boundary injection, the estimator is developed in the Lyapunov approach and consists of a combination of a state observer and a parameter adaptation law which guarantee the asymptotic convergence of the state and parameter estimation errors. Simulation results are provided to illustrate the performance of the proposed identifier.

High-Order Wave Propagation Algorithms for Hyperbolic Systems

KAUST Repository

Ketcheson, David I.

2013-01-22

We present a finite volume method that is applicable to hyperbolic PDEs including spatially varying and semilinear nonconservative systems. The spatial discretization, like that of the well-known Clawpack software, is based on solving Riemann problems and calculating fluctuations (not fluxes). The implementation employs weighted essentially nonoscillatory reconstruction in space and strong stability preserving Runge--Kutta integration in time. The method can be extended to arbitrarily high order of accuracy and allows a well-balanced implementation for capturing solutions of balance laws near steady state. This well-balancing is achieved through the $f$-wave Riemann solver and a novel wave-slope WENO reconstruction procedure. The wide applicability and advantageous properties of the method are demonstrated through numerical examples, including problems in nonconservative form, problems with spatially varying fluxes, and problems involving near-equilibrium solutions of balance laws.

Optical absorption of hyperbolic metamaterial with stochastic surfaces

DEFF Research Database (Denmark)

Liu, Jingjing; Naik, Gururaj V.; Ishii, Satoshi

2014-01-01

We investigate the absorption properties of planar hyperbolic metamaterials (HMMs) consisting of metal-dielectric multilayers, which support propagating plane waves with anomalously large wavevectors and high photonic-density-of-states over a broad bandwidth. An interface formed by depositing...... indium-tin-oxide nanoparticles on an HMM surface scatters light into the high-k propagating modes of the metamaterial and reduces reflection. We compare the reflection and absorption from an HMM with the nanoparticle cover layer versus those of a metal film with the same thickness also covered...... with the nanoparticles. It is predicted that the super absorption properties of HMM show up when exceedingly large amounts of high-k modes are excited by strong plasmonic resonances. In the case that the coupling interface is formed by non-resonance scatterers, there is almost the same enhancement in the absorption...

Metamaterial Model of Tachyonic Dark Energy

Directory of Open Access Journals (Sweden)

Igor I. Smolyaninov

2014-02-01

Full Text Available Dark energy with negative pressure and positive energy density is believed to be responsible for the accelerated expansion of the universe. Quite a few theoretical models of dark energy are based on tachyonic fields interacting with itself and normal (bradyonic matter. Here, we propose an experimental model of tachyonic dark energy based on hyperbolic metamaterials. Wave equation describing propagation of extraordinary light inside hyperbolic metamaterials exhibits 2 + 1 dimensional Lorentz symmetry. The role of time in the corresponding effective 3D Minkowski spacetime is played by the spatial coordinate aligned with the optical axis of the metamaterial. Nonlinear optical Kerr effect bends this spacetime resulting in effective gravitational force between extraordinary photons. We demonstrate that this model has a self-interacting tachyonic sector having negative effective pressure and positive effective energy density. Moreover, a composite multilayer SiC-Si hyperbolic metamaterial exhibits closely separated tachyonic and bradyonic sectors in the long wavelength infrared range. This system may be used as a laboratory model of inflation and late time acceleration of the universe.

Method of construction of the Riemann function for a second-order hyperbolic equation

Science.gov (United States)

Aksenov, A. V.

2017-12-01

A linear hyperbolic equation of the second order in two independent variables is considered. The Riemann function of the adjoint equation is shown to be invariant with respect to the fundamental solutions transformation group. Symmetries and symmetries of fundamental solutions of the Euler-Poisson-Darboux equation are found. The Riemann function is constructed with the aid of fundamental solutions symmetries. Examples of the application of the algorithm for constructing Riemann function are given.

Plasmon analysis and homogenization in plane layered photonic crystals and hyperbolic metamaterials

Energy Technology Data Exchange (ETDEWEB)

Davidovich, M. V., E-mail: davidovichmv@info.sgu.ru [Saratov State University (Russian Federation)

2016-12-15

Dispersion equations are obtained and analysis and homogenization are carried out in periodic and quasiperiodic plane layered structures consisting of alternating dielectric layers, metal and dielectric layers, as well as graphene sheets and dielectric (SiO{sub 2}) layers. Situations are considered when these structures acquire the properties of hyperbolic metamaterials (HMMs), i.e., materials the real parts of whose effective permittivity tensor have opposite signs. It is shown that the application of solely dielectric layers is more promising in the context of reducing losses.

Modeling complexes of modeled proteins.

Science.gov (United States)

Anishchenko, Ivan; Kundrotas, Petras J; Vakser, Ilya A

2017-03-01

Structural characterization of proteins is essential for understanding life processes at the molecular level. However, only a fraction of known proteins have experimentally determined structures. This fraction is even smaller for protein-protein complexes. Thus, structural modeling of protein-protein interactions (docking) primarily has to rely on modeled structures of the individual proteins, which typically are less accurate than the experimentally determined ones. Such "double" modeling is the Grand Challenge of structural reconstruction of the interactome. Yet it remains so far largely untested in a systematic way. We present a comprehensive validation of template-based and free docking on a set of 165 complexes, where each protein model has six levels of structural accuracy, from 1 to 6 Å C α RMSD. Many template-based docking predictions fall into acceptable quality category, according to the CAPRI criteria, even for highly inaccurate proteins (5-6 Å RMSD), although the number of such models (and, consequently, the docking success rate) drops significantly for models with RMSD > 4 Å. The results show that the existing docking methodologies can be successfully applied to protein models with a broad range of structural accuracy, and the template-based docking is much less sensitive to inaccuracies of protein models than the free docking. Proteins 2017; 85:470-478. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Model Predictive Control of Mineral Column Flotation Process

Directory of Open Access Journals (Sweden)

Yahui Tian

2018-06-01

Full Text Available Column flotation is an efficient method commonly used in the mineral industry to separate useful minerals from ores of low grade and complex mineral composition. Its main purpose is to achieve maximum recovery while ensuring desired product grade. This work addresses a model predictive control design for a mineral column flotation process modeled by a set of nonlinear coupled heterodirectional hyperbolic partial differential equations (PDEs and ordinary differential equations (ODEs, which accounts for the interconnection of well-stirred regions represented by continuous stirred tank reactors (CSTRs and transport systems given by heterodirectional hyperbolic PDEs, with these two regions combined through the PDEs’ boundaries. The model predictive control considers both optimality of the process operations and naturally present input and state/output constraints. For the discrete controller design, spatially varying steady-state profiles are obtained by linearizing the coupled ODE–PDE model, and then the discrete system is obtained by using the Cayley–Tustin time discretization transformation without any spatial discretization and/or without model reduction. The model predictive controller is designed by solving an optimization problem with input and state/output constraints as well as input disturbance to minimize the objective function, which leads to an online-solvable finite constrained quadratic regulator problem. Finally, the controller performance to keep the output at the steady state within the constraint range is demonstrated by simulation studies, and it is concluded that the optimal control scheme presented in this work makes this flotation process more efficient.

The Split Coefficient Matrix method for hyperbolic systems of gasdynamic equations

Science.gov (United States)

Chakravarthy, S. R.; Anderson, D. A.; Salas, M. D.

1980-01-01

The Split Coefficient Matrix (SCM) finite difference method for solving hyperbolic systems of equations is presented. This new method is based on the mathematical theory of characteristics. The development of the method from characteristic theory is presented. Boundary point calculation procedures consistent with the SCM method used at interior points are explained. The split coefficient matrices that define the method for steady supersonic and unsteady inviscid flows are given for several examples. The SCM method is used to compute several flow fields to demonstrate its accuracy and versatility. The similarities and differences between the SCM method and the lambda-scheme are discussed.

Dynamics in non-globally-hyperbolic static spacetimes: III. Anti-de Sitter spacetime

International Nuclear Information System (INIS)

Ishibashi, Akihiro; Wald, Robert M

2004-01-01

In recent years, there has been considerable interest in theories formulated in anti-de Sitter (AdS) spacetime. However, AdS spacetime fails to be globally hyperbolic, so a classical field satisfying a hyperbolic wave equation on AdS spacetime need not have a well-defined dynamics. Nevertheless, AdS spacetime is static, so the possible rules of dynamics for a field satisfying a linear wave equation are constrained by our previous general analysis-given in paper II-where it was shown that the possible choices of dynamics correspond to choices of positive, self-adjoint extensions of a certain differential operator, A. In the present paper, we reduce the analysis of electromagnetic and gravitational perturbations in AdS spacetime to scalar wave equations. We then apply our general results to analyse the possible dynamics of scalar, electromagnetic and gravitational perturbations in AdS spacetime. In AdS spacetime, the freedom (if any) in choosing self-adjoint extensions of A corresponds to the freedom (if any) in choosing suitable boundary conditions at infinity, so our analysis determines all the possible boundary conditions that can be imposed at infinity. In particular, we show that other boundary conditions besides the Dirichlet and Neumann conditions may be possible, depending on the value of the effective mass for scalar field perturbations, and depending on the number of spacetime dimensions and type of mode for electromagnetic and gravitational perturbations

Spectral approach to homogenization of hyperbolic equations with periodic coefficients

Science.gov (United States)

Dorodnyi, M. A.; Suslina, T. A.

2018-06-01

In L2 (Rd ;Cn), we consider selfadjoint strongly elliptic second order differential operators Aε with periodic coefficients depending on x / ε, ε > 0. We study the behavior of the operators cos ⁡ (Aε1/2 τ) and Aε-1/2 sin ⁡ (Aε1/2 τ), τ ∈ R, for small ε. Approximations for these operators in the (Hs →L2)-operator norm with a suitable s are obtained. The results are used to study the behavior of the solution vε of the Cauchy problem for the hyperbolic equation ∂τ2 vε = -Aεvε + F. General results are applied to the acoustics equation and the system of elasticity theory.

Effects of nonlocal response on the density of states of hyperbolic metamaterials

DEFF Research Database (Denmark)

Yan, Wei; Wubs, Martijn; Mortensen, N. Asger

2012-01-01

. By expanding the Green function in a plane-wave basis and using the transfer matrix method to calculate the reflection coefficients, we study the local density of states (LDOS) of hyperbolic metamaterials. We show that the nonlocal response of the electron gas in the metal removes the singularity of both...... radiative and non-radiative local density of states, and also sets up a finite maximal value. We also briefly discuss the effects of the nonlocal response on other plasmonic structures, such as a metallic semi-infinite substrate and a metallic slab....

Wideband absorption in one dimensional photonic crystal with graphene-based hyperbolic metamaterials

Science.gov (United States)

Kang, Yongqiang; Liu, Hongmei

2018-02-01

A broadband absorber which was proposed by one dimensional photonic crystal (1DPC) containing graphene-based hyperbolic metamaterials (GHMM) is theoretically investigated. For TM mode, it was demonstrated to absorb roughly 90% of all available electromagnetic waves at a 14 THz absorption bandwidth at normal incidence. The absorption bandwidth was affected by Fermi energy and thickness of dielectric layer. When the incident angle was increased, the absorption value decreased, and the absorption band had a gradual blue shift. These findings have potential applications for designing broadband optoelectronic devices at mid-infrared and THz frequency range.

Solutions of hyperbolic equations with the CIP-BS method

International Nuclear Information System (INIS)

Utsumi, Takayuki; Koga, James; Yamagiwa, Mitsuru; Yabe, Takashi; Aoki, Takayuki

2004-01-01

In this paper, we show that a new numerical method, the Constrained Interpolation Profile - Basis Set (CIP-BS) method, can solve general hyperbolic equations efficiently. This method uses a simple polynomial basis set that is easily extendable to any desired higher-order accuracy. The interpolating profile is chosen so that the subgrid scale solution approaches the local real solution owing to the constraints from the spatial derivatives of the master equations. Then, introducing scalar products, the linear and nonlinear partial differential equations are uniquely reduced to the ordinary differential equations for values and spatial derivatives at the grid points. The method gives stable, less diffusive, and accurate results. It is successfully applied to the continuity equation, the Burgers equation, the Korteweg-de Vries equation, and one-dimensional shock tube problems. (author)

Hyperbolic projections of siemens 3d-mlc leaf paths

International Nuclear Information System (INIS)

Menzies, N.

2004-01-01

Full text: The Siemens Primus linear accelerator has the option of being fitted with a multi-leaf collimator (3D-MLC) that is marketed as having 'double focus', to achieve a constant dose penumbra for all leaf settings. This is achieved by moving the leaves through arcs (similar to some conventional collimator jaws), as well as shaping the leaf side-faces as divergent planes from the x-ray source. One consequence of the mechanical design of the 3D-MLC is that as individual leaves are moved, their projections from the light / x-ray source to the treatment plane follow paths that are hyperbolic, as shown in the figure below. (The eccentricity of the hyperbola is a function of leaf number / distance from centre.) The trajectories of the MLC leaves were modelled (in a spreadsheet) using geometrical projections of the MLC leaves to the treatment plane, with construction details provided in Siemens documentation. The results were checked against the image of the leaf in the linac light field. This problem belongs to the class of conic sections in mathematics, where the intersection of a plane with both nappes of a double right circular cone results in a hyperbola. The good agreement between the model and the light field image provided confirmation of the MLC construction details. AS/NZS 4434.1:1996 (reproduced from IEC 976:1989) provides specifications for maximum deviation from orthogonality of adjacent edges, which can be interpreted for MLC collimators to parallelism of the direction of leaf travel and the adjacent collimator edge (e.g. Elekta ATS). However for the Siemens 'double focused' MLC, it is demonstrated that the geometrical construction of the MLC militates against the leaf image being used for this kind of test. It is also demonstrated that at last one commercial treatment planning system models the Siemens leaf trajectories linearly. The clinical significance of the error in this model is shown to be negligible. Copyright (2004) Australasian College of

Conformal and covariant Z4 formulation of the Einstein equations: Strongly hyperbolic first-order reduction and solution with discontinuous Galerkin schemes

Science.gov (United States)

Dumbser, Michael; Guercilena, Federico; Köppel, Sven; Rezzolla, Luciano; Zanotti, Olindo

2018-04-01

We present a strongly hyperbolic first-order formulation of the Einstein equations based on the conformal and covariant Z4 system (CCZ4) with constraint-violation damping, which we refer to as FO-CCZ4. As CCZ4, this formulation combines the advantages of a conformal and traceless formulation, with the suppression of constraint violations given by the damping terms, but being first order in time and space, it is particularly suited for a discontinuous Galerkin (DG) implementation. The strongly hyperbolic first-order formulation has been obtained by making careful use of first and second-order ordering constraints. A proof of strong hyperbolicity is given for a selected choice of standard gauges via an analytical computation of the entire eigenstructure of the FO-CCZ4 system. The resulting governing partial differential equations system is written in nonconservative form and requires the evolution of 58 unknowns. A key feature of our formulation is that the first-order CCZ4 system decouples into a set of pure ordinary differential equations and a reduced hyperbolic system of partial differential equations that contains only linearly degenerate fields. We implement FO-CCZ4 in a high-order path-conservative arbitrary-high-order-method-using-derivatives (ADER)-DG scheme with adaptive mesh refinement and local time-stepping, supplemented with a third-order ADER-WENO subcell finite-volume limiter in order to deal with singularities arising with black holes. We validate the correctness of the formulation through a series of standard tests in vacuum, performed in one, two and three spatial dimensions, and also present preliminary results on the evolution of binary black-hole systems. To the best of our knowledge, these are the first successful three-dimensional simulations of moving punctures carried out with high-order DG schemes using a first-order formulation of the Einstein equations.

Model complexity control for hydrologic prediction

NARCIS (Netherlands)

Schoups, G.; Van de Giesen, N.C.; Savenije, H.H.G.

2008-01-01

A common concern in hydrologic modeling is overparameterization of complex models given limited and noisy data. This leads to problems of parameter nonuniqueness and equifinality, which may negatively affect prediction uncertainties. A systematic way of controlling model complexity is therefore

The Role of the Element Rhodium in the Hyperbolic Law of the Periodic Table of Elements

Directory of Open Access Journals (Sweden)

Albert Khazan

2008-07-01

Full Text Available The role of the element rhodium as an independent affirmation of calculations by the Hyperbolic Law and validity of all its relations is shown herein. The deviation in calculation by this method of the atomic mass of heaviest element is 0.0024%, and its coefficient of scaling 0.001-0.005%.

Hyperbolic theory of relativistic conformal dissipative fluids

Science.gov (United States)

Lehner, Luis; Reula, Oscar A.; Rubio, Marcelo E.

2018-01-01

We develop a complete description of the class of conformal relativistic dissipative fluids of divergence form, following the formalism described in [R. Geroch and L. Lindblom, Phys. Rev. D 41, 1855 (1990), 10.1103/PhysRevD.41.1855, S. Pennisi, Some considerations on a non linear approach to extended thermodynamics and in Proceedings of Symposium of Kinetic Theory and Extended Thermodynamics, Bologna, 1987.]. This type of theory is fully described in terms of evolution variables whose dynamics are governed by total divergence-type conservation laws. Specifically, we give a characterization of the whole family of conformal fluids in terms of a single master scalar function defined up to second-order corrections in dissipative effects, which we explicitly find in general form. This allows us to identify the equilibrium states of the theory and derive constitutive relations and a Fourier-like law for the corresponding first-order theory heat flux. Finally, we show that among this class of theories—and near equilibrium configurations—there exist symmetric hyperbolic ones, implying that for them one can define well-posed initial value problems.

Probing low-energy hyperbolic polaritons in van der Waals crystals with an electron microscope

KAUST Repository

Govyadinov, Alexander A.

2017-07-14

Van der Waals materials exhibit intriguing structural, electronic, and photonic properties. Electron energy loss spectroscopy within scanning transmission electron microscopy allows for nanoscale mapping of such properties. However, its detection is typically limited to energy losses in the eV range-too large for probing low-energy excitations such as phonons or mid-infrared plasmons. Here, we adapt a conventional instrument to probe energy loss down to 100 meV, and map phononic states in hexagonal boron nitride, a representative van der Waals material. The boron nitride spectra depend on the flake thickness and on the distance of the electron beam to the flake edges. To explain these observations, we developed a classical response theory that describes the interaction of fast electrons with (anisotropic) van der Waals slabs, revealing that the electron energy loss is dominated by excitation of hyperbolic phonon polaritons, and not of bulk phonons as often reported. Thus, our work is of fundamental importance for interpreting future low-energy loss spectra of van der Waals materials.Here the authors adapt a STEM-EELS system to probe energy loss down to 100 meV, and apply it to map phononic states in hexagonal boron nitride, revealing that the electron loss is dominated by hyperbolic phonon polaritons.

Probing low-energy hyperbolic polaritons in van der Waals crystals with an electron microscope.

Science.gov (United States)

Govyadinov, Alexander A; Konečná, Andrea; Chuvilin, Andrey; Vélez, Saül; Dolado, Irene; Nikitin, Alexey Y; Lopatin, Sergei; Casanova, Fèlix; Hueso, Luis E; Aizpurua, Javier; Hillenbrand, Rainer

2017-07-21

Van der Waals materials exhibit intriguing structural, electronic, and photonic properties. Electron energy loss spectroscopy within scanning transmission electron microscopy allows for nanoscale mapping of such properties. However, its detection is typically limited to energy losses in the eV range-too large for probing low-energy excitations such as phonons or mid-infrared plasmons. Here, we adapt a conventional instrument to probe energy loss down to 100 meV, and map phononic states in hexagonal boron nitride, a representative van der Waals material. The boron nitride spectra depend on the flake thickness and on the distance of the electron beam to the flake edges. To explain these observations, we developed a classical response theory that describes the interaction of fast electrons with (anisotropic) van der Waals slabs, revealing that the electron energy loss is dominated by excitation of hyperbolic phonon polaritons, and not of bulk phonons as often reported. Thus, our work is of fundamental importance for interpreting future low-energy loss spectra of van der Waals materials.Here the authors adapt a STEM-EELS system to probe energy loss down to 100 meV, and apply it to map phononic states in hexagonal boron nitride, revealing that the electron loss is dominated by hyperbolic phonon polaritons.

Probing low-energy hyperbolic polaritons in van der Waals crystals with an electron microscope

KAUST Repository

Govyadinov, Alexander A.; Konečná , Andrea; Chuvilin, Andrey; Vé lez, Saü l; Dolado, Irene; Nikitin, Alexey Y.; Lopatin, Sergei; Casanova, Fè lix; Hueso, Luis E.; Aizpurua, Javier; Hillenbrand, Rainer

2017-01-01

Van der Waals materials exhibit intriguing structural, electronic, and photonic properties. Electron energy loss spectroscopy within scanning transmission electron microscopy allows for nanoscale mapping of such properties. However, its detection is typically limited to energy losses in the eV range-too large for probing low-energy excitations such as phonons or mid-infrared plasmons. Here, we adapt a conventional instrument to probe energy loss down to 100 meV, and map phononic states in hexagonal boron nitride, a representative van der Waals material. The boron nitride spectra depend on the flake thickness and on the distance of the electron beam to the flake edges. To explain these observations, we developed a classical response theory that describes the interaction of fast electrons with (anisotropic) van der Waals slabs, revealing that the electron energy loss is dominated by excitation of hyperbolic phonon polaritons, and not of bulk phonons as often reported. Thus, our work is of fundamental importance for interpreting future low-energy loss spectra of van der Waals materials.Here the authors adapt a STEM-EELS system to probe energy loss down to 100 meV, and apply it to map phononic states in hexagonal boron nitride, revealing that the electron loss is dominated by hyperbolic phonon polaritons.

Generalized Roe's numerical scheme for a two-fluid model

International Nuclear Information System (INIS)

Toumi, I.; Raymond, P.

1993-01-01

This paper is devoted to a mathematical and numerical study of a six equation two-fluid model. We will prove that the model is strictly hyperbolic due to the inclusion of the virtual mass force term in the phasic momentum equations. The two-fluid model is naturally written under a nonconservative form. To solve the nonlinear Riemann problem for this nonconservative hyperbolic system, a generalized Roe's approximate Riemann solver, is used, based on a linearization of the nonconservative terms. A Godunov type numerical scheme is built, using this approximate Riemann solver. 10 refs., 5 figs,

The structure of spectral problems and geometry: hyperbolic surfaces in E sup 3

CERN Document Server

Cieslinski, J L

2003-01-01

Working in the framework of Sym's soliton surfaces approach we point out that some simple assumptions about the structure of linear (spectral) problems of the theory of solitons lead uniquely to the geometry of some special immersions. In this paper we consider general su(2) spectral problems. Under some very weak assumptions they turn out to be associated with hyperbolic surfaces (surfaces of negative Gaussian curvature) immersed in three-dimensional Euclidean space, and especially with the so-called Bianchi surfaces.

Optimal control of coupled parabolic-hyperbolic non-autonomous PDEs: infinite-dimensional state-space approach

Science.gov (United States)

Aksikas, I.; Moghadam, A. Alizadeh; Forbes, J. F.

2018-04-01

This paper deals with the design of an optimal state-feedback linear-quadratic (LQ) controller for a system of coupled parabolic-hypebolic non-autonomous partial differential equations (PDEs). The infinite-dimensional state space representation and the corresponding operator Riccati differential equation are used to solve the control problem. Dynamical properties of the coupled system of interest are analysed to guarantee the existence and uniqueness of the solution of the LQ-optimal control problem and also to guarantee the exponential stability of the closed-loop system. Thanks to the eigenvalues and eigenfunctions of the parabolic operator and also the fact that the hyperbolic-associated operator Riccati differential equation can be converted to a scalar Riccati PDE, an algorithm to solve the LQ control problem has been presented. The results are applied to a non-isothermal packed-bed catalytic reactor. The LQ optimal controller designed in the early portion of the paper is implemented for the original non-linear model. Numerical simulations are performed to show the controller performances.

Multifaceted Modelling of Complex Business Enterprises.

Science.gov (United States)

Chakraborty, Subrata; Mengersen, Kerrie; Fidge, Colin; Ma, Lin; Lassen, David

2015-01-01

We formalise and present a new generic multifaceted complex system approach for modelling complex business enterprises. Our method has a strong focus on integrating the various data types available in an enterprise which represent the diverse perspectives of various stakeholders. We explain the challenges faced and define a novel approach to converting diverse data types into usable Bayesian probability forms. The data types that can be integrated include historic data, survey data, and management planning data, expert knowledge and incomplete data. The structural complexities of the complex system modelling process, based on various decision contexts, are also explained along with a solution. This new application of complex system models as a management tool for decision making is demonstrated using a railway transport case study. The case study demonstrates how the new approach can be utilised to develop a customised decision support model for a specific enterprise. Various decision scenarios are also provided to illustrate the versatility of the decision model at different phases of enterprise operations such as planning and control.

Multifaceted Modelling of Complex Business Enterprises

Science.gov (United States)

2015-01-01

We formalise and present a new generic multifaceted complex system approach for modelling complex business enterprises. Our method has a strong focus on integrating the various data types available in an enterprise which represent the diverse perspectives of various stakeholders. We explain the challenges faced and define a novel approach to converting diverse data types into usable Bayesian probability forms. The data types that can be integrated include historic data, survey data, and management planning data, expert knowledge and incomplete data. The structural complexities of the complex system modelling process, based on various decision contexts, are also explained along with a solution. This new application of complex system models as a management tool for decision making is demonstrated using a railway transport case study. The case study demonstrates how the new approach can be utilised to develop a customised decision support model for a specific enterprise. Various decision scenarios are also provided to illustrate the versatility of the decision model at different phases of enterprise operations such as planning and control. PMID:26247591

Localization of supersymmetric field theories on non-compact hyperbolic three-manifolds

Energy Technology Data Exchange (ETDEWEB)

Assel, Benjamin; Martelli, Dario; Murthy, Sameer; Yokoyama, Daisuke [Department of Mathematics, King’s College London,The Strand, London WC2R 2LS (United Kingdom)

2017-03-17

We study supersymmetric gauge theories with an R-symmetry, defined on non-compact, hyperbolic, Riemannian three-manifolds, focusing on the case of a supersymmetry-preserving quotient of Euclidean AdS{sub 3}. We compute the exact partition function in these theories, using the method of localization, thus reducing the problem to the computation of one-loop determinants around a supersymmetric locus. We evaluate the one-loop determinants employing three different techniques: an index theorem, the method of pairing of eigenvalues, and the heat kernel method. Along the way, we discuss aspects of supersymmetry in manifolds with a conformal boundary, including supersymmetric actions and boundary conditions.

Geometry through history Euclidean, hyperbolic, and projective geometries

CERN Document Server

Dillon, Meighan I

2018-01-01

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

Complex magnetic monopoles, geometric phases and quantum evolution in the vicinity of diabolic and exceptional points

International Nuclear Information System (INIS)

Nesterov, Alexander I; Aceves de la Cruz, F

2008-01-01

We consider the geometric phase and quantum tunneling in the vicinity of diabolic and exceptional points. We show that the geometric phase associated with the degeneracy points is defined by the flux of complex magnetic monopoles. In the limit of weak coupling, the leading contribution to the real part of the geometric phase is given by the flux of the Dirac monopole plus a quadrupole term, and the expansion of the imaginary part starts with a dipole-like field. For a two-level system governed by a generic non-Hermitian Hamiltonian, we derive a formula to compute the non-adiabatic, complex, geometric phase by integrating over the complex Bloch sphere. We apply our results to study a dissipative two-level system driven by a periodic electromagnetic field and show that, in the vicinity of the exceptional point, the complex geometric phase behaves like a step-function. Studying the tunneling process near and at the exceptional point, we find two different regimes: coherent and incoherent. The coherent regime is characterized by Rabi oscillations, with a one-sheeted hyperbolic monopole emerging in this region of the parameters. The two-sheeted hyperbolic monopole is associated with the incoherent regime. We show that the dissipation results in a series of pulses in the complex geometric phase which disappear when the dissipation dies out. Such a strong coupling effect of the environment is beyond the conventional adiabatic treatment of the Berry phase

Proof of concept of an artificial muscle: theoretical model, numerical model, and hardware experiment.

Science.gov (United States)

Haeufle, D F B; Günther, M; Blickhan, R; Schmitt, S

2011-01-01

Recently, the hyperbolic Hill-type force-velocity relation was derived from basic physical components. It was shown that a contractile element CE consisting of a mechanical energy source (active element AE), a parallel damper element (PDE), and a serial element (SE) exhibits operating points with hyperbolic force-velocity dependency. In this paper, the contraction dynamics of this CE concept were analyzed in a numerical simulation of quick release experiments against different loads. A hyperbolic force-velocity relation was found. The results correspond to measurements of the contraction dynamics of a technical prototype. Deviations from the theoretical prediction could partly be explained by the low stiffness of the SE, which was modeled analog to the metal spring in the hardware prototype. The numerical model and hardware prototype together, are a proof of this CE concept and can be seen as a well-founded starting point for the development of Hill-type artificial muscles. This opens up new vistas for the technical realization of natural movements with rehabilitation devices. © 2011 IEEE

Computation of Quasiperiodic Normally Hyperbolic Invariant Tori: Rigorous Results

Science.gov (United States)

Canadell, Marta; Haro, Àlex

2017-12-01

The development of efficient methods for detecting quasiperiodic oscillations and computing the corresponding invariant tori is a subject of great importance in dynamical systems and their applications in science and engineering. In this paper, we prove the convergence of a new Newton-like method for computing quasiperiodic normally hyperbolic invariant tori carrying quasiperiodic motion in smooth families of real-analytic dynamical systems. The main result is stated as an a posteriori KAM-like theorem that allows controlling the inner dynamics on the torus with appropriate detuning parameters, in order to obtain a prescribed quasiperiodic motion. The Newton-like method leads to several fast and efficient computational algorithms, which are discussed and tested in a companion paper (Canadell and Haro in J Nonlinear Sci, 2017. doi: 10.1007/s00332-017-9388-z), in which new mechanisms of breakdown are presented.

Attractors in complex networks

Science.gov (United States)

Rodrigues, Alexandre A. P.

2017-10-01

In the framework of the generalized Lotka-Volterra model, solutions representing multispecies sequential competition can be predictable with high probability. In this paper, we show that it occurs because the corresponding "heteroclinic channel" forms part of an attractor. We prove that, generically, in an attracting heteroclinic network involving a finite number of hyperbolic and non-resonant saddle-equilibria whose linearization has only real eigenvalues, the connections corresponding to the most positive expanding eigenvalues form part of an attractor (observable in numerical simulations).

Effect of metallic and hyperbolic metamaterial surfaces on electric and magnetic dipole emission transitions

DEFF Research Database (Denmark)

Ni, X.; Naik, G. V.; Kildishev, A. V.

2011-01-01

Spontaneous emission patterns of electric and magnetic dipoles on different metallic surfaces and a hyperbolic metamaterial (HMM) surface were simulated using the dyadic Green’s function technique. The theoretical approach was verified by experimental results obtained by measuring angular......-dependent emission spectra of europium ions on top of different films. The results show the modified behavior of electric and magnetic dipoles on metallic and HMM surfaces. The results of numerical calculations agree well with experimental data....

Modelling the structure of complex networks

DEFF Research Database (Denmark)

Herlau, Tue

networks has been independently studied as mathematical objects in their own right. As such, there has been both an increased demand for statistical methods for complex networks as well as a quickly growing mathematical literature on the subject. In this dissertation we explore aspects of modelling complex....... The next chapters will treat some of the various symmetries, representer theorems and probabilistic structures often deployed in the modelling complex networks, the construction of sampling methods and various network models. The introductory chapters will serve to provide context for the included written...

Toward a Definition of Complexity for Quantum Field Theory States.

Science.gov (United States)

Chapman, Shira; Heller, Michal P; Marrochio, Hugo; Pastawski, Fernando

2018-03-23

We investigate notions of complexity of states in continuous many-body quantum systems. We focus on Gaussian states which include ground states of free quantum field theories and their approximations encountered in the context of the continuous version of the multiscale entanglement renormalization ansatz. Our proposal for quantifying state complexity is based on the Fubini-Study metric. It leads to counting the number of applications of each gate (infinitesimal generator) in the transformation, subject to a state-dependent metric. We minimize the defined complexity with respect to momentum-preserving quadratic generators which form su(1,1) algebras. On the manifold of Gaussian states generated by these operations, the Fubini-Study metric factorizes into hyperbolic planes with minimal complexity circuits reducing to known geodesics. Despite working with quantum field theories far outside the regime where Einstein gravity duals exist, we find striking similarities between our results and those of holographic complexity proposals.

Updating the debate on model complexity

Science.gov (United States)

Simmons, Craig T.; Hunt, Randall J.

2012-01-01

As scientists who are trying to understand a complex natural world that cannot be fully characterized in the field, how can we best inform the society in which we live? This founding context was addressed in a special session, “Complexity in Modeling: How Much is Too Much?” convened at the 2011 Geological Society of America Annual Meeting. The session had a variety of thought-provoking presentations—ranging from philosophy to cost-benefit analyses—and provided some areas of broad agreement that were not evident in discussions of the topic in 1998 (Hunt and Zheng, 1999). The session began with a short introduction during which model complexity was framed borrowing from an economic concept, the Law of Diminishing Returns, and an example of enjoyment derived by eating ice cream. Initially, there is increasing satisfaction gained from eating more ice cream, to a point where the gain in satisfaction starts to decrease, ending at a point when the eater sees no value in eating more ice cream. A traditional view of model complexity is similar—understanding gained from modeling can actually decrease if models become unnecessarily complex. However, oversimplified models—those that omit important aspects of the problem needed to make a good prediction—can also limit and confound our understanding. Thus, the goal of all modeling is to find the “sweet spot” of model sophistication—regardless of whether complexity was added sequentially to an overly simple model or collapsed from an initial highly parameterized framework that uses mathematics and statistics to attain an optimum (e.g., Hunt et al., 2007). Thus, holistic parsimony is attained, incorporating “as simple as possible,” as well as the equally important corollary “but no simpler.”

Acoustically-driven surface and hyperbolic plasmon-phonon polaritons in graphene/h-BN heterostructures on piezoelectric substrates

Science.gov (United States)

Fandan, R.; Pedrós, J.; Schiefele, J.; Boscá, A.; Martínez, J.; Calle, F.

2018-05-01

Surface plasmon polaritons in graphene couple strongly to surface phonons in polar substrates leading to hybridized surface plasmon-phonon polaritons (SPPPs). We demonstrate that a surface acoustic wave (SAW) can be used to launch propagating SPPPs in graphene/h-BN heterostructures on a piezoelectric substrate like AlN, where the SAW-induced surface modulation acts as a dynamic diffraction grating. The efficiency of the light coupling is greatly enhanced by the introduction of the h-BN film as compared to the bare graphene/AlN system. The h-BN interlayer not only significantly changes the dispersion of the SPPPs but also enhances their lifetime. The strengthening of the SPPPs is shown to be related to both the higher carrier mobility induced in graphene and the coupling with h-BN and AlN surface phonons. In addition to surface phonons, hyperbolic phonons polaritons (HPPs) appear in the case of multilayer h-BN films leading to hybridized hyperbolic plasmon-phonon polaritons (HPPPs) that are also mediated by the SAW. These results pave the way for engineering SAW-based graphene/h-BN plasmonic devices and metamaterials covering the mid-IR to THz range.

On the possibility of superluminal energy propagation in a hyperbolic metamaterial of metal-dielectric layers

Directory of Open Access Journals (Sweden)

Pi-Gang Luan

2018-01-01

Full Text Available The energy propagation of electromagnetic fields in the effective medium of a one-dimensional photonic crystal consisting of dielectric and metallic layers is investigated. We show that the medium behaves like Drude and Lorentz medium, respectively, when the electric field is parallel and perpendicular to the layers. For arbitrary time-varying electromagnetic fields in this medium, the energy density formula is derived. We prove rigorously that the group velocity of any propagating mode obeying the hyperbolic dispersion must be slower than the speed of light in vacuum, taking into account the frequency dependence of the permittivity tensor. That is, it is not possible to have superluminal propagation in this dispersive hyperbolic medium consisting of real dielectric and metallic material layers. The propagation velocity of a wave packet is also studied numerically. This packet velocity is very close to the velocity of the propagating mode having the central frequency and central wave vector of the wave packet. When the frequency spread of the wave packet is not narrow enough, small discrepancy between these two velocities manifests, which is caused by the non-penetration effect of the evanescent modes. This work reveals that no superluminal phenomenon can happen in a dispersive anisotropic metamaterial medium made of real materials.

Energy spectra of the hyperbolic and second Poeschl-Teller like potentials solved by new exact quantization rule

International Nuclear Information System (INIS)

Dong Shihai; Gonzalez-Cisneros, A.

2008-01-01

A new exact quantization rule simplifies the calculation of the energy levels for the exactly solvable quantum system. In this work we calculate the energy levels of the Schroedinger equation with the hyperbolic potential by this quantization rule. The corresponding eigenfunction is also derived for completeness. The second Poeschl-Teller like potential case is also carried out

The Rôle of the Element Rhodium in the Hyperbolic Law of the Periodic Table of Elements

Directory of Open Access Journals (Sweden)

Khazan A.

2008-07-01

Full Text Available The role of the element rhodium as an independent affirmation of calculations by the Hyperbolic Law and validity of all its relations is shown herein. The deviation in cal- culation by this method of the atomic mass of heaviest element is 0.0024%, and its coefficient of scaling 0.001–0.005%

Explicit finite difference predictor and convex corrector with applications to hyperbolic partial differential equations

Science.gov (United States)

Dey, C.; Dey, S. K.

1983-01-01

An explicit finite difference scheme consisting of a predictor and a corrector has been developed and applied to solve some hyperbolic partial differential equations (PDEs). The corrector is a convex-type function which is applied at each time level and at each mesh point. It consists of a parameter which may be estimated such that for larger time steps the algorithm should remain stable and generate a fast speed of convergence to the steady-state solution. Some examples have been given.

Optimal boundary control and boundary stabilization of hyperbolic systems

CERN Document Server

Gugat, Martin

2015-01-01

This brief considers recent results on optimal control and stabilization of systems governed by hyperbolic partial differential equations, specifically those in which the control action takes place at the boundary.  The wave equation is used as a typical example of a linear system, through which the author explores initial boundary value problems, concepts of exact controllability, optimal exact control, and boundary stabilization.  Nonlinear systems are also covered, with the Korteweg-de Vries and Burgers Equations serving as standard examples.  To keep the presentation as accessible as possible, the author uses the case of a system with a state that is defined on a finite space interval, so that there are only two boundary points where the system can be controlled.  Graduate and post-graduate students as well as researchers in the field will find this to be an accessible introduction to problems of optimal control and stabilization.

Optimal control for parabolic-hyperbolic system with time delay

International Nuclear Information System (INIS)

Kowalewski, A.

1985-07-01

In this paper we consider an optimal control problem for a system described by a linear partial differential equation of the parabolic-hyperbolic type with time delay in the state. The right-hand side of this equation and the initial conditions are not continuous functions usually, but they are measurable functions belonging to L 2 or Lsup(infinity) spaces. Therefore, the solution of this equation is given by a certain Sobolev space. The time delay in the state is constant, but it can be also a function of time. The control time T is fixed in our problem. Making use of the Milutin-Dubovicki theorem, necessary and sufficient conditions of optimality with the quadratic performance functional and constrained control are derived for the Dirichlet problem. The flow chart of the algorithm which can be used in the numerical solving of certain optimization problems for distributed systems is also presented. (author)

Topological vertex, string amplitudes and spectral functions of hyperbolic geometry

Energy Technology Data Exchange (ETDEWEB)

Guimaraes, M.E.X.; Rosa, T.O. [Universidade Federal Fluminense, Instituto de Fisica, Av. Gal. Milton Tavares de Souza, s/n, CEP 24210-346, Niteroi, RJ (Brazil); Luna, R.M. [Universidade Estadual de Londrina, Departamento de Fisica, Caixa Postal 6001, Londrina, Parana (Brazil)

2014-05-15

We discuss the homological aspects of the connection between quantum string generating function and the formal power series associated to the dimensions of chains and homologies of suitable Lie algebras. Our analysis can be considered as a new straightforward application of the machinery of modular forms and spectral functions (with values in the congruence subgroup of SL(2,Z)) to the partition functions of Lagrangian branes, refined vertex and open string partition functions, represented by means of formal power series that encode Lie algebra properties. The common feature in our examples lies in the modular properties of the characters of certain representations of the pertinent affine Lie algebras and in the role of Selberg-type spectral functions of a hyperbolic three-geometry associated with q-series in the computation of the string amplitudes. (orig.)

A chaotic jerk system with non-hyperbolic equilibrium: Dynamics, effect of time delay and circuit realisation

Science.gov (United States)

Rajagopal, Karthikeyan; Pham, Viet-Thanh; Tahir, Fadhil Rahma; Akgul, Akif; Abdolmohammadi, Hamid Reza; Jafari, Sajad

2018-04-01

The literature on chaos has highlighted several chaotic systems with special features. In this work, a novel chaotic jerk system with non-hyperbolic equilibrium is proposed. The dynamics of this new system is revealed through equilibrium analysis, phase portrait, bifurcation diagram and Lyapunov exponents. In addition, we investigate the time-delay effects on the proposed system. Realisation of such a system is presented to verify its feasibility.

Preliminary Results on the Gravitational Slingshot Effect and the Population of Hyperbolic Meteoroids at Earth

Science.gov (United States)

Wiegert, P. A.

2011-01-01

Interstellar meteoroids, solid particles arriving from outside our Solar System, are not easily distinguished from local meteoroids. A velocity above the escape velocity of the Sun is often used as an indicator of a possible interstellar origin. We demonstrate that the gravitational slingshot effect, resulting from the passage of local meteoroid near a planet, can produce hyperbolic meteoroids at the Earth s orbit with excess velocities comparable to those expected of interstellar meteoroids.

Hyperbolic heat conduction, effective temperature, and third law for nonequilibrium systems with heat flux

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Sobolev, S. L.

2018-02-01

Some analogies between different nonequilibrium heat conduction models, particularly random walk, the discrete variable model, and the Boltzmann transport equation with the single relaxation time approximation, have been discussed. We show that, under an assumption of a finite value of the heat carrier velocity, these models lead to the hyperbolic heat conduction equation and the modified Fourier law with relaxation term. Corresponding effective temperature and entropy have been introduced and analyzed. It has been demonstrated that the effective temperature, defined as a geometric mean of the kinetic temperatures of the heat carriers moving in opposite directions, acts as a criterion for thermalization and is a nonlinear function of the kinetic temperature and heat flux. It is shown that, under highly nonequilibrium conditions when the heat flux tends to its maximum possible value, the effective temperature, heat capacity, and local entropy go to zero even at a nonzero equilibrium temperature. This provides a possible generalization of the third law to nonequilibrium situations. Analogies and differences between the proposed effective temperature and some other definitions of a temperature in nonequilibrium state, particularly for active systems, disordered semiconductors under electric field, and adiabatic gas flow, have been shown and discussed. Illustrative examples of the behavior of the effective temperature and entropy during nonequilibrium heat conduction in a monatomic gas and a strong shockwave have been analyzed.

Analytical Solution of Dirac Equation for q-Deformed Hyperbolic Manning-Rosen Potential in D Dimensions using SUSY QM and its Thermodynamics Application

International Nuclear Information System (INIS)

Cari, C; Suparmi, A; Yunianto, M; Pratiwi, B N

2016-01-01

The Dirac equation of q-deformed hyperbolic Manning Rosen potential in D dimension was solved by using Supersymmetric Quantum Mechanics (SUSY QM). The D dimensional relativistic energy spectra were obtained by using SUSY QM and shape invariant properties and D dimensional wave functions of q-deformed hyperbolic Manning Rosen potential were obtained by using the SUSY raising and lowering operators. In the nonrelativistic limit, the relativistic energy spectra for exact spin symmetry case reduced into nonrelativistic energy spectra and so for the wave functions. In the classical regime, the partition function, the vibrational specific heat, and the vibrational mean energy of some diatomic molecules were calculated from the non-relativistic energy spectra with the help of error function and imaginary error function. (paper)

Toward a Definition of Complexity for Quantum Field Theory States

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Chapman, Shira; Heller, Michal P.; Marrochio, Hugo; Pastawski, Fernando

2018-03-01

We investigate notions of complexity of states in continuous many-body quantum systems. We focus on Gaussian states which include ground states of free quantum field theories and their approximations encountered in the context of the continuous version of the multiscale entanglement renormalization ansatz. Our proposal for quantifying state complexity is based on the Fubini-Study metric. It leads to counting the number of applications of each gate (infinitesimal generator) in the transformation, subject to a state-dependent metric. We minimize the defined complexity with respect to momentum-preserving quadratic generators which form s u (1 ,1 ) algebras. On the manifold of Gaussian states generated by these operations, the Fubini-Study metric factorizes into hyperbolic planes with minimal complexity circuits reducing to known geodesics. Despite working with quantum field theories far outside the regime where Einstein gravity duals exist, we find striking similarities between our results and those of holographic complexity proposals.

Physical properties of scalar and spinor field states with the Rindler-Milne (hyperbolic) symmetry

International Nuclear Information System (INIS)

Ritus, V.I.

2001-01-01

It is shown that right and left combinations of the positive- and negative-frequency hyperbolically symmetric solutions of the Klein-Fock-Gordon equation possess an everywhere timelike current density vector with a definite Lorentz-invariant sing of the charge density, and similar combinations of solutions to the Dirac equation possess the energy-momentum tensor with everywhere real eigenvalues and a definite Lorentz-invariant sing of the energy density. These right and left modes, just as their ±-frequency components, are eigenfunctions of the Lorentz generator [ru

THREE-POINT BACKWARD FINITE DIFFERENCE METHOD FOR SOLVING A SYSTEM OF MIXED HYPERBOLIC-PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS. (R825549C019)

Science.gov (United States)

A three-point backward finite-difference method has been derived for a system of mixed hyperbolic¯¯parabolic (convection¯¯diffusion) partial differential equations (mixed PDEs). The method resorts to the three-point backward differenci...

Complexity, Modeling, and Natural Resource Management

Directory of Open Access Journals (Sweden)

Paul Cilliers

2013-09-01

Full Text Available This paper contends that natural resource management (NRM issues are, by their very nature, complex and that both scientists and managers in this broad field will benefit from a theoretical understanding of complex systems. It starts off by presenting the core features of a view of complexity that not only deals with the limits to our understanding, but also points toward a responsible and motivating position. Everything we do involves explicit or implicit modeling, and as we can never have comprehensive access to any complex system, we need to be aware both of what we leave out as we model and of the implications of the choice of our modeling framework. One vantage point is never sufficient, as complexity necessarily implies that multiple (independent conceptualizations are needed to engage the system adequately. We use two South African cases as examples of complex systems - restricting the case narratives mainly to the biophysical domain associated with NRM issues - that make the point that even the behavior of the biophysical subsystems themselves are already complex. From the insights into complex systems discussed in the first part of the paper and the lessons emerging from the way these cases have been dealt with in reality, we extract five interrelated generic principles for practicing science and management in complex NRM environments. These principles are then further elucidated using four further South African case studies - organized as two contrasting pairs - and now focusing on the more difficult organizational and social side, comparing the human organizational endeavors in managing such systems.

The necessary and sufficient conditions of the optimality for hyperbolic systems with non-differentiable performance functional

International Nuclear Information System (INIS)

Kowalewski, A.

1982-11-01

In this paper an optimal control problem with non-differentiable cost function for distributed parameter system is solved. As an example an optimal control problem for system described by a linear partial differential of hyperbolic type with the Neuman's boundary condition is considered. By use of the Milutin-Dubovicki method, necessary and sufficient conditions of optimality with non-differentiable performance functional and constrained control are derived for Neuman's problem. (author)

Sutherland models for complex reflection groups

International Nuclear Information System (INIS)

Crampe, N.; Young, C.A.S.

2008-01-01

There are known to be integrable Sutherland models associated to every real root system, or, which is almost equivalent, to every real reflection group. Real reflection groups are special cases of complex reflection groups. In this paper we associate certain integrable Sutherland models to the classical family of complex reflection groups. Internal degrees of freedom are introduced, defining dynamical spin chains, and the freezing limit taken to obtain static chains of Haldane-Shastry type. By considering the relation of these models to the usual BC N case, we are led to systems with both real and complex reflection groups as symmetries. We demonstrate their integrability by means of new Dunkl operators, associated to wreath products of dihedral groups

Mathematical and numerical methods for the nonlinear hyperbolic propagation problem: d2GAMMA/dt2 = d/dz [dGAMMA/dt dGAMMA/dz

International Nuclear Information System (INIS)

Stanco, L.; Vaccaro, V.G.; Funk, U.; Krueger, U.; Mika, K.; Wuestefeld, G.

1982-03-01

In the first part of this report a physical model is presented, which describes the deforming of a bunch in a storage ring influenced only by its own space charge field. A system of two differential equations for the density and the momentum of the particles is set up, which is independent of any special machine parameter. Due to the sign of the inductance of the chamber walls and the sign of the dispersion of the revolution frequency, we distinguish between a de-bunching and a self-bunching situation. The de-bunching corresponds to a nonlinear hyperbolic propagation problem well-known in gas dynamics, and the self-bunching to a nonlinear elliptic initial value problem. The second part deals with a mathematical and numerical treatment of an approximate equation for the hyperbolic case. For this nonlinear second order partial differential equation we first present three particular integrals: the solution by separating the variables, the similarity solution, and the solution for a parabolic initial distribution of the density. For a more realistic initial condition, we must resort to other methods: Results are obtained in three different ways, first from a highly accurate Taylor series expansion, second from a common finite difference method, and thirdly from the numerical method of characteristics. The appearance of a shock discontinuity is furthermore established in each of these cases. (orig.)

Enhanced spin Hall effect of tunneling light in hyperbolic metamaterial waveguide.

Science.gov (United States)

Tang, Tingting; Li, Chaoyang; Luo, Li

2016-08-01

Giant enhancement of spin Hall effect of tunneling light (SHETL) is theoretically proposed in a frustrated total internal reflection (FTIR) structure with hyperbolic metamaterial (HMM). We calculate the transverse shift of right-circularly polarized light in a SiO2-air-HMM-air-SiO2 waveguide and analyze the physical mechanism of the enhanced SHETL. The HMM anisotropy can greatly increase the transverse shift of polarized light even though HMM loss might reduce it. Compared with transverse shift of transmitted light through a single HMM slab with ZnAlO/ZnO multilayer, the maximum transverse shift of tunneling light through a FTIR structure with identical HMM can be significantly enlarged by more than three times which reaches -38 μm without any amplification method.

The hyperbolic chemical bond: Fourier analysis of ground and first excited state potential energy curves of HX (X = H-Ne).

Science.gov (United States)

Harrison, John A

2008-09-04

RHF/aug-cc-pVnZ, UHF/aug-cc-pVnZ, and QCISD/aug-cc-pVnZ, n = 2-5, potential energy curves of H2 X (1) summation g (+) are analyzed by Fourier transform methods after transformation to a new coordinate system via an inverse hyperbolic cosine coordinate mapping. The Fourier frequency domain spectra are interpreted in terms of underlying mathematical behavior giving rise to distinctive features. There is a clear difference between the underlying mathematical nature of the potential energy curves calculated at the HF and full-CI levels. The method is particularly suited to the analysis of potential energy curves obtained at the highest levels of theory because the Fourier spectra are observed to be of a compact nature, with the envelope of the Fourier frequency coefficients decaying in magnitude in an exponential manner. The finite number of Fourier coefficients required to describe the CI curves allows for an optimum sampling strategy to be developed, corresponding to that required for exponential and geometric convergence. The underlying random numerical noise due to the finite convergence criterion is also a clearly identifiable feature in the Fourier spectrum. The methodology is applied to the analysis of MRCI potential energy curves for the ground and first excited states of HX (X = H-Ne). All potential energy curves exhibit structure in the Fourier spectrum consistent with the existence of resonances. The compact nature of the Fourier spectra following the inverse hyperbolic cosine coordinate mapping is highly suggestive that there is some advantage in viewing the chemical bond as having an underlying hyperbolic nature.

Predictive Surface Complexation Modeling

Energy Technology Data Exchange (ETDEWEB)

Sverjensky, Dimitri A. [Johns Hopkins Univ., Baltimore, MD (United States). Dept. of Earth and Planetary Sciences

2016-11-29

Surface complexation plays an important role in the equilibria and kinetics of processes controlling the compositions of soilwaters and groundwaters, the fate of contaminants in groundwaters, and the subsurface storage of CO₂ and nuclear waste. Over the last several decades, many dozens of individual experimental studies have addressed aspects of surface complexation that have contributed to an increased understanding of its role in natural systems. However, there has been no previous attempt to develop a model of surface complexation that can be used to link all the experimental studies in order to place them on a predictive basis. Overall, my research has successfully integrated the results of the work of many experimentalists published over several decades. For the first time in studies of the geochemistry of the mineral-water interface, a practical predictive capability for modeling has become available. The predictive correlations developed in my research now enable extrapolations of experimental studies to provide estimates of surface chemistry for systems not yet studied experimentally and for natural and anthropogenically perturbed systems.

Are Model Transferability And Complexity Antithetical? Insights From Validation of a Variable-Complexity Empirical Snow Model in Space and Time

Science.gov (United States)

Lute, A. C.; Luce, Charles H.

2017-11-01

The related challenges of predictions in ungauged basins and predictions in ungauged climates point to the need to develop environmental models that are transferable across both space and time. Hydrologic modeling has historically focused on modelling one or only a few basins using highly parameterized conceptual or physically based models. However, model parameters and structures have been shown to change significantly when calibrated to new basins or time periods, suggesting that model complexity and model transferability may be antithetical. Empirical space-for-time models provide a framework within which to assess model transferability and any tradeoff with model complexity. Using 497 SNOTEL sites in the western U.S., we develop space-for-time models of April 1 SWE and Snow Residence Time based on mean winter temperature and cumulative winter precipitation. The transferability of the models to new conditions (in both space and time) is assessed using non-random cross-validation tests with consideration of the influence of model complexity on transferability. As others have noted, the algorithmic empirical models transfer best when minimal extrapolation in input variables is required. Temporal split-sample validations use pseudoreplicated samples, resulting in the selection of overly complex models, which has implications for the design of hydrologic model validation tests. Finally, we show that low to moderate complexity models transfer most successfully to new conditions in space and time, providing empirical confirmation of the parsimony principal.

Structural stability of Riemann solutions for strictly hyperbolic systems with three piecewise constant states

Directory of Open Access Journals (Sweden)

Xuefeng Wei

2016-12-01

Full Text Available This article concerns the wave interaction problem for a strictly hyperbolic system of conservation laws whose Riemann solutions involve delta shock waves. To cover all situations, the global solutions are constructed when the initial data are taken as three piecewise constant states. It is shown that the Riemann solutions are stable with respect to a specific small perturbation of the Riemann initial data. In addition, some interesting nonlinear phenomena are captured during the process of constructing the solutions, such as the generation and decomposition of delta shock waves.

Lipschitz stability for an inverse hyperbolic problem of determining two coefficients by a finite number of observations

Science.gov (United States)

Beilina, L.; Cristofol, M.; Li, S.; Yamamoto, M.

2018-01-01

We consider an inverse problem of reconstructing two spatially varying coefficients in an acoustic equation of hyperbolic type using interior data of solutions with suitable choices of initial condition. Using a Carleman estimate, we prove Lipschitz stability estimates which ensure unique reconstruction of both coefficients. Our theoretical results are justified by numerical studies on the reconstruction of two unknown coefficients using noisy backscattered data.

Special Issue: Very large eddy simulation. Issue Edited by Dimitris Drikakis.Copyright © 2002 John Wiley & Sons, Ltd.Save Title to My ProfileSet E-Mail Alert Previous Issue | Next Issue > Full Issue Listing-->Volume 39, Issue 9, Pages 763-864(30 July 2002)Research ArticleEmbedded turbulence model in numerical methods for hyperbolic conservation laws

Science.gov (United States)

Drikakis, D.

2002-07-01

The paper describes the use of numerical methods for hyperbolic conservation laws as an embedded turbulence modelling approach. Different Godunov-type schemes are utilized in computations of Burgers' turbulence and a two-dimensional mixing layer. The schemes include a total variation diminishing, characteristic-based scheme which is developed in this paper using the flux limiter approach. The embedded turbulence modelling property of the above methods is demonstrated through coarsely resolved large eddy simulations with and without subgrid scale models. Copyright

Parallel hyperbolic PDE simulation on clusters: Cell versus GPU

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Rostrup, Scott; De Sterck, Hans

2010-12-01

Increasingly, high-performance computing is looking towards data-parallel computational devices to enhance computational performance. Two technologies that have received significant attention are IBM's Cell Processor and NVIDIA's CUDA programming model for graphics processing unit (GPU) computing. In this paper we investigate the acceleration of parallel hyperbolic partial differential equation simulation on structured grids with explicit time integration on clusters with Cell and GPU backends. The message passing interface (MPI) is used for communication between nodes at the coarsest level of parallelism. Optimizations of the simulation code at the several finer levels of parallelism that the data-parallel devices provide are described in terms of data layout, data flow and data-parallel instructions. Optimized Cell and GPU performance are compared with reference code performance on a single x86 central processing unit (CPU) core in single and double precision. We further compare the CPU, Cell and GPU platforms on a chip-to-chip basis, and compare performance on single cluster nodes with two CPUs, two Cell processors or two GPUs in a shared memory configuration (without MPI). We finally compare performance on clusters with 32 CPUs, 32 Cell processors, and 32 GPUs using MPI. Our GPU cluster results use NVIDIA Tesla GPUs with GT200 architecture, but some preliminary results on recently introduced NVIDIA GPUs with the next-generation Fermi architecture are also included. This paper provides computational scientists and engineers who are considering porting their codes to accelerator environments with insight into how structured grid based explicit algorithms can be optimized for clusters with Cell and GPU accelerators. It also provides insight into the speed-up that may be gained on current and future accelerator architectures for this class of applications. Program summaryProgram title: SWsolver Catalogue identifier: AEGY_v1_0 Program summary URL

Modeling Musical Complexity: Commentary on Eerola (2016

Directory of Open Access Journals (Sweden)

Joshua Albrecht

2016-07-01

Full Text Available In his paper, "Expectancy violation and information-theoretic models of melodic complexity," Eerola compares a number of models that correlate musical features of monophonic melodies with participant ratings of perceived melodic complexity. He finds that fairly strong results can be achieved using several different approaches to modeling perceived melodic complexity. The data used in this study are gathered from several previously published studies that use widely different types of melodies, including isochronous folk melodies, isochronous 12-tone rows, and rhythmically complex African folk melodies. This commentary first briefly reviews the article's method and main findings, then suggests a rethinking of the theoretical framework of the study. Finally, some of the methodological issues of the study are discussed.

Sensitivity of Velocity Picking on 4th Order Non Hyperbolic Move out Correction

International Nuclear Information System (INIS)

Enuma, C.; Hope, R.; Idoko, P.

2003-01-01

Long offset processing has become the standard for TotaFinaElf in the Deep Offshore Nigeria. The advantage of having longer offsets are numerous; higher fold of coverage, improved S/N improved AVA analysis, less multiple contamination etc. A key element in successful long offset processing is the higher order velocity picking. In classical processing of seismic data with standard 2nd order terms for NMO correction, and outer mute at approximately 27 degrees, not to include non flattened events is required. By applying 3 terms 4th order anisotropic non hyperbolic corrections, angles out to 50-60 degrees may be flattened and can be very useful. Typically in modern 3D seismic data processing velocities are picked every 1km or 0.5km. a test was carried out to study the effect of the lateral velocity pick spacing required to properly flatten events at longer offsets. The evaluation of the test w3as carried out by loading all the CMP gathers along the line on a workstation as a 3D so that the flatness on pre-stack could be studied. The analysis showed that for 2nd order NMO 0.5km spacing is adequate to properly interpolate and flatten events at all CMP gathers along the line. However it was shown that for more advanced processing, such as the 4th order anisotropic three terms non hyperbolic velocity corrections, a more dense lateral velocity picking would be advantageous in terms of flattening of reflections. This presentation show how important long offset processing is and especially the importance of velocity picking

Multidimensional Riemann problem with self-similar internal structure - part III - a multidimensional analogue of the HLLI Riemann solver for conservative hyperbolic systems

Science.gov (United States)

Balsara, Dinshaw S.; Nkonga, Boniface

2017-10-01

Just as the quality of a one-dimensional approximate Riemann solver is improved by the inclusion of internal sub-structure, the quality of a multidimensional Riemann solver is also similarly improved. Such multidimensional Riemann problems arise when multiple states come together at the vertex of a mesh. The interaction of the resulting one-dimensional Riemann problems gives rise to a strongly-interacting state. We wish to endow this strongly-interacting state with physically-motivated sub-structure. The fastest way of endowing such sub-structure consists of making a multidimensional extension of the HLLI Riemann solver for hyperbolic conservation laws. Presenting such a multidimensional analogue of the HLLI Riemann solver with linear sub-structure for use on structured meshes is the goal of this work. The multidimensional MuSIC Riemann solver documented here is universal in the sense that it can be applied to any hyperbolic conservation law. The multidimensional Riemann solver is made to be consistent with constraints that emerge naturally from the Galerkin projection of the self-similar states within the wave model. When the full eigenstructure in both directions is used in the present Riemann solver, it becomes a complete Riemann solver in a multidimensional sense. I.e., all the intermediate waves are represented in the multidimensional wave model. The work also presents, for the very first time, an important analysis of the dissipation characteristics of multidimensional Riemann solvers. The present Riemann solver results in the most efficient implementation of a multidimensional Riemann solver with sub-structure. Because it preserves stationary linearly degenerate waves, it might also help with well-balancing. Implementation-related details are presented in pointwise fashion for the one-dimensional HLLI Riemann solver as well as the multidimensional MuSIC Riemann solver.

Design of high-gain, wideband antenna using microwave hyperbolic metasurface

Energy Technology Data Exchange (ETDEWEB)

Zhao, Yan, E-mail: yan.z@chula.ac.th [International School of Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok 10330 (Thailand)

2016-05-15

In this work, we apply hyperbolic metasurfaces (HMSs) to design high-gain and wideband antennas. It is shown that HMSs formed by a single layer of split-ring resonators (SRRs) can be excited to generate highly directive beams. In particular, we suggest two types of the SRR-HMS: a capacitively loaded SRR (CLSRR)-HMS and a substrate-backed double SRR (DSRR)-HMS. Both configurations ensure that the periodicity of the structures is sufficiently small for satisfying the effective medium theory. For the antenna design, we propose a two-layer-stacked configuration for the 2.4 GHz frequency band based on the DSRR-HMS excited by a folded monopole. Measurement results confirm numerical simulations and demonstrate that an antenna gain of more than 5 dBi can be obtained for the frequency range of 2.1 - 2.6 GHz, with a maximum gain of 7.8 dBi at 2.4 GHz.

The effects of model and data complexity on predictions from species distributions models

DEFF Research Database (Denmark)

García-Callejas, David; Bastos, Miguel

2016-01-01

How complex does a model need to be to provide useful predictions is a matter of continuous debate across environmental sciences. In the species distributions modelling literature, studies have demonstrated that more complex models tend to provide better fits. However, studies have also shown...... that predictive performance does not always increase with complexity. Testing of species distributions models is challenging because independent data for testing are often lacking, but a more general problem is that model complexity has never been formally described in such studies. Here, we systematically...

A Primer for Model Selection: The Decisive Role of Model Complexity

Science.gov (United States)

Höge, Marvin; Wöhling, Thomas; Nowak, Wolfgang

2018-03-01

Selecting a "best" model among several competing candidate models poses an often encountered problem in water resources modeling (and other disciplines which employ models). For a modeler, the best model fulfills a certain purpose best (e.g., flood prediction), which is typically assessed by comparing model simulations to data (e.g., stream flow). Model selection methods find the "best" trade-off between good fit with data and model complexity. In this context, the interpretations of model complexity implied by different model selection methods are crucial, because they represent different underlying goals of modeling. Over the last decades, numerous model selection criteria have been proposed, but modelers who primarily want to apply a model selection criterion often face a lack of guidance for choosing the right criterion that matches their goal. We propose a classification scheme for model selection criteria that helps to find the right criterion for a specific goal, i.e., which employs the correct complexity interpretation. We identify four model selection classes which seek to achieve high predictive density, low predictive error, high model probability, or shortest compression of data. These goals can be achieved by following either nonconsistent or consistent model selection and by either incorporating a Bayesian parameter prior or not. We allocate commonly used criteria to these four classes, analyze how they represent model complexity and what this means for the model selection task. Finally, we provide guidance on choosing the right type of criteria for specific model selection tasks. (A quick guide through all key points is given at the end of the introduction.)

Plasmonic Lithography Utilizing Epsilon Near Zero Hyperbolic Metamaterial.

Science.gov (United States)

Chen, Xi; Zhang, Cheng; Yang, Fan; Liang, Gaofeng; Li, Qiaochu; Guo, L Jay

2017-10-24

In this work, a special hyperbolic metamaterial (HMM) metamaterial is investigated for plasmonic lithography of period reduction patterns. It is a type II HMM (ϵ ∥ 0) whose tangential component of the permittivity ϵ ∥ is close to zero. Due to the high anisotropy of the type II epsilon-near-zero (ENZ) HMM, only one plasmonic mode can propagate horizontally with low loss in a waveguide system with ENZ HMM as its core. This work takes the advantage of a type II ENZ HMM composed of aluminum/aluminum oxide films and the associated unusual mode to expose a photoresist layer in a specially designed lithography system. Periodic patterns with a half pitch of 58.3 nm were achieved due to the interference of third-order diffracted light of the grating. The lines were 1/6 of the mask with a period of 700 nm and ∼1/7 of the wavelength of the incident light. Moreover, the theoretical analyses performed are widely applicable to structures made of different materials such as silver as well as systems working at deep ultraviolet wavelengths including 193, 248, and 365 nm.

A Relation Between the Eikonal Equation Associated to a Potential Energy Surface and a Hyperbolic Wave Equation.

Science.gov (United States)

Bofill, Josep Maria; Quapp, Wolfgang; Caballero, Marc

2012-12-11

The potential energy surface (PES) of a molecule can be decomposed into equipotential hypersurfaces. We show in this article that the hypersurfaces are the wave fronts of a certain hyperbolic partial differential equation, a wave equation. It is connected with the gradient lines, or the steepest descent, or the steepest ascent lines of the PES. The energy seen as a reaction coordinate plays the central role in this treatment.

Enhanced spontaneous emission from the inside of a multilayer hyperbolic metamaterial (presentation video)

Science.gov (United States)

Ferrari, Lorenzo; Lu, Dylan; Lepage, Dominic; Liu, Zhaowei

2014-09-01

We study the spontaneous emission enhancement inside a hyperbolic metamaterial, composed of a periodic stack of silver and silicon layers. After showing that the decay rate outside the multilayer can be spectrally altered via the metallic filling ratio, we embed the source within the individual silicon layers, and predict a 3-fold increase of the Purcell factor with respect to its outer value. Then we include the emitter in a polymethyl-methacrylate (PMMA) layer, and extract the plasmonic modes by means of a triangular and a rectangular grating, obtaining respectively a 10-fold and 6-fold enhancement in the power emitted into the far-field.

Epidemic modeling in complex realities.

Science.gov (United States)

Colizza, Vittoria; Barthélemy, Marc; Barrat, Alain; Vespignani, Alessandro

2007-04-01

In our global world, the increasing complexity of social relations and transport infrastructures are key factors in the spread of epidemics. In recent years, the increasing availability of computer power has enabled both to obtain reliable data allowing one to quantify the complexity of the networks on which epidemics may propagate and to envision computational tools able to tackle the analysis of such propagation phenomena. These advances have put in evidence the limits of homogeneous assumptions and simple spatial diffusion approaches, and stimulated the inclusion of complex features and heterogeneities relevant in the description of epidemic diffusion. In this paper, we review recent progresses that integrate complex systems and networks analysis with epidemic modelling and focus on the impact of the various complex features of real systems on the dynamics of epidemic spreading.

The Kuramoto model in complex networks

Science.gov (United States)

Rodrigues, Francisco A.; Peron, Thomas K. DM.; Ji, Peng; Kurths, Jürgen

2016-01-01

Synchronization of an ensemble of oscillators is an emergent phenomenon present in several complex systems, ranging from social and physical to biological and technological systems. The most successful approach to describe how coherent behavior emerges in these complex systems is given by the paradigmatic Kuramoto model. This model has been traditionally studied in complete graphs. However, besides being intrinsically dynamical, complex systems present very heterogeneous structure, which can be represented as complex networks. This report is dedicated to review main contributions in the field of synchronization in networks of Kuramoto oscillators. In particular, we provide an overview of the impact of network patterns on the local and global dynamics of coupled phase oscillators. We cover many relevant topics, which encompass a description of the most used analytical approaches and the analysis of several numerical results. Furthermore, we discuss recent developments on variations of the Kuramoto model in networks, including the presence of noise and inertia. The rich potential for applications is discussed for special fields in engineering, neuroscience, physics and Earth science. Finally, we conclude by discussing problems that remain open after the last decade of intensive research on the Kuramoto model and point out some promising directions for future research.

A boundary value approach for solving three-dimensional elliptic and hyperbolic partial differential equations.

Science.gov (United States)

Biala, T A; Jator, S N

2015-01-01

In this article, the boundary value method is applied to solve three dimensional elliptic and hyperbolic partial differential equations. The partial derivatives with respect to two of the spatial variables (y, z) are discretized using finite difference approximations to obtain a large system of ordinary differential equations (ODEs) in the third spatial variable (x). Using interpolation and collocation techniques, a continuous scheme is developed and used to obtain discrete methods which are applied via the Block unification approach to obtain approximations to the resulting large system of ODEs. Several test problems are investigated to elucidate the solution process.

A fast computing method to distinguish the hyperbolic trajectory of an non-autonomous system

Science.gov (United States)

Jia, Meng; Fan, Yang-Yu; Tian, Wei-Jian

2011-03-01

Attempting to find a fast computing method to DHT (distinguished hyperbolic trajectory), this study first proves that the errors of the stable DHT can be ignored in normal direction when they are computed as the trajectories extend. This conclusion means that the stable flow with perturbation will approach to the real trajectory as it extends over time. Based on this theory and combined with the improved DHT computing method, this paper reports a new fast computing method to DHT, which magnifies the DHT computing speed without decreasing its accuracy. Project supported by the National Natural Science Foundation of China (Grant No. 60872159).

A fast computing method to distinguish the hyperbolic trajectory of an non-autonomous system

International Nuclear Information System (INIS)

Jia Meng; Fan Yang-Yu; Tian Wei-Jian

2011-01-01

Attempting to find a fast computing method to DHT (distinguished hyperbolic trajectory), this study first proves that the errors of the stable DHT can be ignored in normal direction when they are computed as the trajectories extend. This conclusion means that the stable flow with perturbation will approach to the real trajectory as it extends over time. Based on this theory and combined with the improved DHT computing method, this paper reports a new fast computing method to DHT, which magnifies the DHT computing speed without decreasing its accuracy. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

Gravitational wave bursts from Primordial Black Hole hyperbolic encounters

CERN Document Server

Garcia-Bellido, Juan

2017-01-01

We propose that Gravitational Wave (GW) bursts with millisecond durations can be explained by the GW emission from the hyperbolic encounters of Primordial Black Holes in dense clusters. These bursts are single events, with the bulk of the released energy happening during the closest approach, and emitted in frequencies within the AdvLIGO sensitivity range. We provide expressions for the shape of the GW emission in terms of the peak frequency and amplitude, and estimate the rates of these events for a variety of mass and velocity configurations. We study the regions of parameter space that will allow detection by both AdvLIGO and, in the future, LISA. We find for realistic configurations, with total mass M∼60 M⊙, relative velocities v∼0.01c, and impact parameters b∼10−3 AU, for AdvLIGO an expected event rate is O(10) events/yr/Gpc^3 with millisecond durations. For LISA, the typical duration is in the range of minutes to hours and the event-rate is O(10^3) events/yr/Gpc^3 for both 10^3 M⊙ IMBH and 1...

The physics of communicability in complex networks

International Nuclear Information System (INIS)

Estrada, Ernesto; Hatano, Naomichi; Benzi, Michele

2012-01-01

A fundamental problem in the study of complex networks is to provide quantitative measures of correlation and information flow between different parts of a system. To this end, several notions of communicability have been introduced and applied to a wide variety of real-world networks in recent years. Several such communicability functions are reviewed in this paper. It is emphasized that communication and correlation in networks can take place through many more routes than the shortest paths, a fact that may not have been sufficiently appreciated in previously proposed correlation measures. In contrast to these, the communicability measures reviewed in this paper are defined by taking into account all possible routes between two nodes, assigning smaller weights to longer ones. This point of view naturally leads to the definition of communicability in terms of matrix functions, such as the exponential, resolvent, and hyperbolic functions, in which the matrix argument is either the adjacency matrix or the graph Laplacian associated with the network. Considerable insight on communicability can be gained by modeling a network as a system of oscillators and deriving physical interpretations, both classical and quantum-mechanical, of various communicability functions. Applications of communicability measures to the analysis of complex systems are illustrated on a variety of biological, physical and social networks. The last part of the paper is devoted to a review of the notion of locality in complex networks and to computational aspects that by exploiting sparsity can greatly reduce the computational efforts for the calculation of communicability functions for large networks.

Geometry and dynamics in Gromov hyperbolic metric spaces with an emphasis on non-proper settings

CERN Document Server

Das, Tushar; Urbański, Mariusz

2016-01-01

This book presents the foundations of the theory of groups and semigroups acting isometrically on Gromov hyperbolic metric spaces. Particular emphasis is paid to the geometry of their limit sets and on behavior not found in the proper setting. The authors provide a number of examples of groups which exhibit a wide range of phenomena not to be found in the finite-dimensional theory. The book contains both introductory material to help beginners as well as new research results, and closes with a list of attractive unsolved problems.

Linking Complexity and Sustainability Theories: Implications for Modeling Sustainability Transitions

Directory of Open Access Journals (Sweden)

Camaren Peter

2014-03-01

Full Text Available In this paper, we deploy a complexity theory as the foundation for integration of different theoretical approaches to sustainability and develop a rationale for a complexity-based framework for modeling transitions to sustainability. We propose a framework based on a comparison of complex systems’ properties that characterize the different theories that deal with transitions to sustainability. We argue that adopting a complexity theory based approach for modeling transitions requires going beyond deterministic frameworks; by adopting a probabilistic, integrative, inclusive and adaptive approach that can support transitions. We also illustrate how this complexity-based modeling framework can be implemented; i.e., how it can be used to select modeling techniques that address particular properties of complex systems that we need to understand in order to model transitions to sustainability. In doing so, we establish a complexity-based approach towards modeling sustainability transitions that caters for the broad range of complex systems’ properties that are required to model transitions to sustainability.

Carleman estimates and applications to inverse problems for hyperbolic systems

CERN Document Server

Bellassoued, Mourad

2017-01-01

This book is a self-contained account of the method based on Carleman estimates for inverse problems of determining spatially varying functions of differential equations of the hyperbolic type by non-overdetermining data of solutions. The formulation is different from that of Dirichlet-to-Neumann maps and can often prove the global uniqueness and Lipschitz stability even with a single measurement. These types of inverse problems include coefficient inverse problems of determining physical parameters in inhomogeneous media that appear in many applications related to electromagnetism, elasticity, and related phenomena. Although the methodology was created in 1981 by Bukhgeim and Klibanov, its comprehensive development has been accomplished only recently. In spite of the wide applicability of the method, there are few monographs focusing on combined accounts of Carleman estimates and applications to inverse problems. The aim in this book is to fill that gap. The basic tool is Carleman estimates, the theory of wh...

Complexity-aware simple modeling.

Science.gov (United States)

Gómez-Schiavon, Mariana; El-Samad, Hana

2018-02-26

Mathematical models continue to be essential for deepening our understanding of biology. On one extreme, simple or small-scale models help delineate general biological principles. However, the parsimony of detail in these models as well as their assumption of modularity and insulation make them inaccurate for describing quantitative features. On the other extreme, large-scale and detailed models can quantitatively recapitulate a phenotype of interest, but have to rely on many unknown parameters, making them often difficult to parse mechanistically and to use for extracting general principles. We discuss some examples of a new approach-complexity-aware simple modeling-that can bridge the gap between the small-scale and large-scale approaches. Copyright © 2018 Elsevier Ltd. All rights reserved.

Computational models of complex systems

CERN Document Server

Dabbaghian, Vahid

2014-01-01

Computational and mathematical models provide us with the opportunities to investigate the complexities of real world problems. They allow us to apply our best analytical methods to define problems in a clearly mathematical manner and exhaustively test our solutions before committing expensive resources. This is made possible by assuming parameter(s) in a bounded environment, allowing for controllable experimentation, not always possible in live scenarios. For example, simulation of computational models allows the testing of theories in a manner that is both fundamentally deductive and experimental in nature. The main ingredients for such research ideas come from multiple disciplines and the importance of interdisciplinary research is well recognized by the scientific community. This book provides a window to the novel endeavours of the research communities to present their works by highlighting the value of computational modelling as a research tool when investigating complex systems. We hope that the reader...

Comparing spatial grain-size trends inferred from textural parameters using percentile statistical parameters and those based on the log-hyperbolic method

DEFF Research Database (Denmark)

Bartholdy, Jesper; Christiansen, C.; Pedersen, Jørn Bjarke Torp

2007-01-01

The Folk&Ward (F&W) and the log-hyperbolic methods are applied to a small - and easy to overlook - number of typical sand sized grain-size distributions from the Danish Wadden Sea. The sand originates from the same source, and the pattern of change in the grain-size distributions is, therefore...

Existence conditions for bulk large-wavevector waves in metal-dielectric and graphene-dielectric multilayer hyperbolic metamaterials

DEFF Research Database (Denmark)

Zhukovsky, Sergei; Andryieuski, Andrei; Lavrinenko, Andrei

2014-01-01

We theoretically investigate general existence conditions for broadband bulk large-wavevector (high-k) propagating waves (such as volume plasmon polaritons in hyperbolic metamaterials) in arbitrary subwavelength periodic multilayers structures. Treating the elementary excitation in the unit cell...... of the structure as a generalized resonance pole of reflection coefficient and using Bloch's theorem, we derive analytical expressions for the band of large-wavevector propagating solutions. We apply our formalism to determine the high-k band existence in two important cases: the well-known metal-dielectric...

Elements of complexity in subsurface modeling, exemplified with three case studies

Energy Technology Data Exchange (ETDEWEB)

Freedman, Vicky L. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Truex, Michael J. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Rockhold, Mark [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Bacon, Diana H. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Freshley, Mark D. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Wellman, Dawn M. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

2017-04-03

There are complexity elements to consider when applying subsurface flow and transport models to support environmental analyses. Modelers balance the benefits and costs of modeling along the spectrum of complexity, taking into account the attributes of more simple models (e.g., lower cost, faster execution, easier to explain, less mechanistic) and the attributes of more complex models (higher cost, slower execution, harder to explain, more mechanistic and technically defensible). In this paper, modeling complexity is examined with respect to considering this balance. The discussion of modeling complexity is organized into three primary elements: 1) modeling approach, 2) description of process, and 3) description of heterogeneity. Three examples are used to examine these complexity elements. Two of the examples use simulations generated from a complex model to develop simpler models for efficient use in model applications. The first example is designed to support performance evaluation of soil vapor extraction remediation in terms of groundwater protection. The second example investigates the importance of simulating different categories of geochemical reactions for carbon sequestration and selecting appropriate simplifications for use in evaluating sequestration scenarios. In the third example, the modeling history for a uranium-contaminated site demonstrates that conservative parameter estimates were inadequate surrogates for complex, critical processes and there is discussion on the selection of more appropriate model complexity for this application. All three examples highlight how complexity considerations are essential to create scientifically defensible models that achieve a balance between model simplification and complexity.

Design and implementation of an interface supporting information navigation tasks using hyperbolic visualization technique

International Nuclear Information System (INIS)

Lee, J. K.; Choi, I. K.; Jun, S. H.; Park, K. O.; Seo, Y. S.; Seo, S. M.; Koo, I. S.; Jang, M. H.

2001-01-01

Visualization techniques can be used to support operator's information navigation tasks on the system especially consisting of an enormous volume of information, such as operating information display system and computerized operating procedure system in advanced control room of nuclear power plants. By offering an easy understanding environment of hierarchially structured information, these techniques can reduce the operator's supplementary navigation task load. As a result of that, operators can pay more attention on the primary tasks and ultimately improve the cognitive task performance, in this thesis, an interface was designed and implemented using hyperbolic visualization technique, which is expected to be applied as a means of optimizing operator's information navigation tasks

Geometrically motivated hyperbolic coordinate conditions for numerical relativity: Analysis, issues and implementations

International Nuclear Information System (INIS)

Bona, Carles; Lehner, Luis; Palenzuela-Luque, Carlos

2005-01-01

We study the implications of adopting hyperbolic-driver coordinate conditions motivated by geometrical considerations. In particular, conditions that minimize the rate of change of the metric variables. We analyze the properties of the resulting system of equations and their effect when implementing excision techniques. We find that commonly used coordinate conditions lead to a characteristic structure at the excision surface where some modes are not of outflow type with respect to any excision boundary chosen inside the horizon. Thus, boundary conditions are required for these modes. Unfortunately, the specification of these conditions is a delicate issue as the outflow modes involve both gauge and main variables. As an alternative to these driver equations, we examine conditions derived from extremizing a scalar constructed from Killing's equation and present specific numerical examples

Cumulative complexity: a functional, patient-centered model of patient complexity can improve research and practice.

Science.gov (United States)

Shippee, Nathan D; Shah, Nilay D; May, Carl R; Mair, Frances S; Montori, Victor M

2012-10-01

To design a functional, patient-centered model of patient complexity with practical applicability to analytic design and clinical practice. Existing literature on patient complexity has mainly identified its components descriptively and in isolation, lacking clarity as to their combined functions in disrupting care or to how complexity changes over time. The authors developed a cumulative complexity model, which integrates existing literature and emphasizes how clinical and social factors accumulate and interact to complicate patient care. A narrative literature review is used to explicate the model. The model emphasizes a core, patient-level mechanism whereby complicating factors impact care and outcomes: the balance between patient workload of demands and patient capacity to address demands. Workload encompasses the demands on the patient's time and energy, including demands of treatment, self-care, and life in general. Capacity concerns ability to handle work (e.g., functional morbidity, financial/social resources, literacy). Workload-capacity imbalances comprise the mechanism driving patient complexity. Treatment and illness burdens serve as feedback loops, linking negative outcomes to further imbalances, such that complexity may accumulate over time. With its components largely supported by existing literature, the model has implications for analytic design, clinical epidemiology, and clinical practice. Copyright © 2012 Elsevier Inc. All rights reserved.

A highly sensitive multiplasmonic sensor using hyperbolic chiral sculptured thin films

Science.gov (United States)

Abbas, Farhat; Faryad, Muhammad

2017-11-01

Surface plasmon-polariton (SPP) waves guided by an interface of a metal and a hyperbolic chiral sculptured thin film (STF) were theoretically investigated for optical sensing of an analyte. The chiral STF was infiltrated with the analyte to be sensed, and the resulting change in the incidence angle of excitation of the SPP waves in the prism-coupled configuration was computed. The results indicated the potential of this configuration for a plasmonic sensor with sensitivity up to 6000 degrees per refractive index units of the infiltrating fluid in the angular investigation scheme, with multiple SPP waves of the same frequency but different phase speeds, spatial profiles, and sensitivities. The enhancement in the sensitivity is attributed to the high field strength of the SPP waves near the interface. A multiplasmonic sensor is advantageous because of its potential for higher confidence in the measurement of the same analyte.

On spin and matrix models in the complex plane

International Nuclear Information System (INIS)

Damgaard, P.H.; Heller, U.M.

1993-01-01

We describe various aspects of statistical mechanics defined in the complex temperature or coupling-constant plane. Using exactly solvable models, we analyse such aspects as renormalization group flows in the complex plane, the distribution of partition function zeros, and the question of new coupling-constant symmetries of complex-plane spin models. The double-scaling form of matrix models is shown to be exactly equivalent to finite-size scaling of two-dimensional spin systems. This is used to show that the string susceptibility exponents derived from matrix models can be obtained numerically with very high accuracy from the scaling of finite-N partition function zeros in the complex plane. (orig.)

Deterministic ripple-spreading model for complex networks.

Science.gov (United States)

Hu, Xiao-Bing; Wang, Ming; Leeson, Mark S; Hines, Evor L; Di Paolo, Ezequiel

2011-04-01

This paper proposes a deterministic complex network model, which is inspired by the natural ripple-spreading phenomenon. The motivations and main advantages of the model are the following: (i) The establishment of many real-world networks is a dynamic process, where it is often observed that the influence of a few local events spreads out through nodes, and then largely determines the final network topology. Obviously, this dynamic process involves many spatial and temporal factors. By simulating the natural ripple-spreading process, this paper reports a very natural way to set up a spatial and temporal model for such complex networks. (ii) Existing relevant network models are all stochastic models, i.e., with a given input, they cannot output a unique topology. Differently, the proposed ripple-spreading model can uniquely determine the final network topology, and at the same time, the stochastic feature of complex networks is captured by randomly initializing ripple-spreading related parameters. (iii) The proposed model can use an easily manageable number of ripple-spreading related parameters to precisely describe a network topology, which is more memory efficient when compared with traditional adjacency matrix or similar memory-expensive data structures. (iv) The ripple-spreading model has a very good potential for both extensions and applications.

Modeling OPC complexity for design for manufacturability

Science.gov (United States)

Gupta, Puneet; Kahng, Andrew B.; Muddu, Swamy; Nakagawa, Sam; Park, Chul-Hong

2005-11-01

Increasing design complexity in sub-90nm designs results in increased mask complexity and cost. Resolution enhancement techniques (RET) such as assist feature addition, phase shifting (attenuated PSM) and aggressive optical proximity correction (OPC) help in preserving feature fidelity in silicon but increase mask complexity and cost. Data volume increase with rise in mask complexity is becoming prohibitive for manufacturing. Mask cost is determined by mask write time and mask inspection time, which are directly related to the complexity of features printed on the mask. Aggressive RET increase complexity by adding assist features and by modifying existing features. Passing design intent to OPC has been identified as a solution for reducing mask complexity and cost in several recent works. The goal of design-aware OPC is to relax OPC tolerances of layout features to minimize mask cost, without sacrificing parametric yield. To convey optimal OPC tolerances for manufacturing, design optimization should drive OPC tolerance optimization using models of mask cost for devices and wires. Design optimization should be aware of impact of OPC correction levels on mask cost and performance of the design. This work introduces mask cost characterization (MCC) that quantifies OPC complexity, measured in terms of fracture count of the mask, for different OPC tolerances. MCC with different OPC tolerances is a critical step in linking design and manufacturing. In this paper, we present a MCC methodology that provides models of fracture count of standard cells and wire patterns for use in design optimization. MCC cannot be performed by designers as they do not have access to foundry OPC recipes and RET tools. To build a fracture count model, we perform OPC and fracturing on a limited set of standard cells and wire configurations with all tolerance combinations. Separately, we identify the characteristics of the layout that impact fracture count. Based on the fracture count (FC) data

Selberg trace formula for bordered Riemann surfaces: Hyperbolic, elliptic and parabolic conjugacy classes, and determinants of Maass-Laplacians

International Nuclear Information System (INIS)

Bolte, J.

1992-08-01

The Selberg trace formula for automorphic forms of weight m ε- Z, on bordered Riemann surfaces is developed. The trace formula is formulated for arbitrary Fuchsian groups of the first kind which include hyperbolic, elliptic and parabolic conjugacy classes. In the case of compact bordered Riemann surfaces we can explicitly evaluate determinants of Maass-Laplacians for both Dirichlet and Neumann boundary-conditions, respectively. Some implications for the open bosonic string theory are mentioned. (orig.)

Dynamics of compressible gas-liquid flows with a stiff density ratio

International Nuclear Information System (INIS)

Cortes, Julien

1999-01-01

This work is devoted to the study of transient two-phase flows when the ratio of the two densities is stiff. At first, we review briefly some of the basic principles about two-phase flow, hyperbolicity and the finite volume method. Then we develop a perturbation method, based on the stiffness of the density ratio, to examine the Eigen-structure of two-fluid models. Indeed, in such models, complex phasic interactions yield a complex Eigen-structure which may raise numerous problems in simulations. We show that our approach provides a convenient frame to study the hyperbolicity of such models. At this stage, advanced numerical tests are computed showing the efficiency of our approach in the context of unstructured multidimensional meshes. Our tests are validated for non-equilibrium flows using experimental data or through mesh refinements. At last, we use the scaling of the densities to analyse how momentum is transferred between phases in the context of bubbly flows. We study the relevance of a stiff relaxation term related to the ratio of the densities using linear stability properties and Chapman-Enskog expansions. Our results and some numerical computations tends to show that such a system is apparently well-posed despite being 'weakly' hyperbolic. (author) [fr

Efficient, Broadband and Wide-Angle Hot-Electron Transduction using Metal-Semiconductor Hyperbolic Metamaterials

KAUST Repository

Sakhdari, Maryam

2016-05-20

Hot-electron devices are emerging as promising candidates for the transduction of optical radiation into electrical current, as they enable photodetection and solar/infrared energy harvesting at sub-bandgap wavelengths. Nevertheless, poor photoconversion quantum yields and low bandwidth pose fundamental challenge to fascinating applications of hot-electron optoelectronics. Based on a novel hyperbolic metamaterial (HMM) structure, we theoretically propose a vertically-integrated hot-electron device that can efficiently couple plasmonic excitations into electron flows, with an external quantum efficiency approaching the physical limit. Further, this metamaterial-based device can have a broadband and omnidirectional response at infrared and visible wavelengths. We believe that these findings may shed some light on designing practical devices for energy-efficient photodetection and energy harvesting beyond the bandgap spectral limit.

Modeling heterogeneous populations of thermostatically controlled loads using diffusion-advection PDEs

DEFF Research Database (Denmark)

Moura, Scott; Ruiz, Victor; Bendtsen, Jan Dimon

2013-01-01

This paper focuses on developing a partial differential equation (PDE)-based model and parameter identification scheme for heterogeneous populations of thermostatically controlled loads (TCLs). First, a coupled two-state hyperbolic PDE model for homogenous TCL populations is derived. This model i...

From surface to volume plasmons in hyperbolic metamaterials: General existence conditions for bulk high-k waves in metal-dielectric and graphene-dielectric multilayers

DEFF Research Database (Denmark)

Zhukovsky, Sergei; Andryieuski, Andrei; Sipe, John E.

2014-01-01

-dielectric and recently introduced graphene-dielectric stacks. We confirm that short-range surface plasmons in thin metal layers can give rise to hyperbolic metamaterial properties and demonstrate that long-range surface plasmons cannot. We also show that graphene-dielectric multilayers tend to support high- k waves...

Modeling the Structure and Complexity of Engineering Routine Design Problems

NARCIS (Netherlands)

Jauregui Becker, Juan Manuel; Wits, Wessel Willems; van Houten, Frederikus J.A.M.

2011-01-01

This paper proposes a model to structure routine design problems as well as a model of its design complexity. The idea is that having a proper model of the structure of such problems enables understanding its complexity, and likewise, a proper understanding of its complexity enables the development

Orienteering in Knowledge Spaces: The Hyperbolic Geometry of Wikipedia Mathematics

Science.gov (United States)

Leibon, Gregory; Rockmore, Daniel N.

2013-01-01

In this paper we show how the coupling of the notion of a network with directions with the adaptation of the four-point probe from materials testing gives rise to a natural geometry on such networks. This four-point probe geometry shares many of the properties of hyperbolic geometry wherein the network directions take the place of the sphere at infinity, enabling a navigation of the network in terms of pairs of directions: the geodesic through a pair of points is oriented from one direction to another direction, the pair of which are uniquely determined. We illustrate this in the interesting example of the pages of Wikipedia devoted to Mathematics, or “The MathWiki.” The applicability of these ideas extends beyond Wikipedia to provide a natural framework for visual search and to prescribe a natural mode of navigation for any kind of “knowledge space” in which higher order concepts aggregate various instances of information. Other examples would include genre or author organization of cultural objects such as books, movies, documents or even merchandise in an online store. PMID:23844017

Orienteering in knowledge spaces: the hyperbolic geometry of Wikipedia Mathematics.

Directory of Open Access Journals (Sweden)

Gregory Leibon

Full Text Available In this paper we show how the coupling of the notion of a network with directions with the adaptation of the four-point probe from materials testing gives rise to a natural geometry on such networks. This four-point probe geometry shares many of the properties of hyperbolic geometry wherein the network directions take the place of the sphere at infinity, enabling a navigation of the network in terms of pairs of directions: the geodesic through a pair of points is oriented from one direction to another direction, the pair of which are uniquely determined. We illustrate this in the interesting example of the pages of Wikipedia devoted to Mathematics, or "The MathWiki." The applicability of these ideas extends beyond Wikipedia to provide a natural framework for visual search and to prescribe a natural mode of navigation for any kind of "knowledge space" in which higher order concepts aggregate various instances of information. Other examples would include genre or author organization of cultural objects such as books, movies, documents or even merchandise in an online store.

Linear models of income patterns in consumer demand for foods and evaluation of its elasticity

Directory of Open Access Journals (Sweden)

Pavel Syrovátka

2005-01-01

Full Text Available The paper is focused on the use of the linear constructions for developing of Engel’s demand models in the field of the food-consumer demand. In the theoretical part of the paper, the linear approximations of this demand models are analysed on the bases of the linear interpolation. In the same part of this text, the hyperbolic elasticity function was defined for the linear Engel model. The behaviour of the hyperbolic elasticity function and its properties were consequently investigated too. The behaviour of the determined elasticity function was investigated according to the values of the intercept point and the direction parameter in the original linear Engel model. The obtained theoretical findings were tested using the real data of Czech Statistical Office. The developed linear Engel model was explicitly dynamised, because the achieved database was formed into the time series. With respect to the two variables definitions of the hyperbolic function in the theoretical part of the text, the determined dynamic model of the Engel demand for food was transformed into the form with parametric intercept point:ret* = At + 0.0946 · rmt*,where the values of absolute member are defined as:At = 1773.0973 + 9.3064 · t – 0.3023 · t2; (t = 1, 2, ... 32.The value of At in the parametric linear model of Engel consumer demand for food was during the observed period (1995–2002 always positive. Thus, the hyperbolic elasticity function achieved the elasticity coefficients from the interval:ηt ∈〈+0; +1.Within quantitative analysis of Engel demand for food in the Czech Republic during the given time period, it was founded, that income elasticity of food expenditures of the average Czech household was moved between +0.4080 and +0.4511. The Czech-household demand for food is thus income inelastic with the normal income reactions.

Vacuum inhomogeneous cosmological models

International Nuclear Information System (INIS)

Hanquin, J.-L.

1984-01-01

The author presents some results concerning the vacuum cosmological models which admit a 2-dimensional Abelian group of isometries: classifications of these space-times based on the topological nature of their space-like hypersurfaces and on their time evolution, analysis of the asymptotical behaviours at spatial infinity for hyperbolical models as well as in the neighbourhood of the singularity for the models possessing a time singularity during their evolution. (Auth.)

ASYMMETRIC PRICE TRANSMISSION MODELING: THE IMPORTANCE OF MODEL COMPLEXITY AND THE PERFORMANCE OF THE SELECTION CRITERIA

Directory of Open Access Journals (Sweden)

Henry de-Graft Acquah

2013-01-01

Full Text Available Information Criteria provides an attractive basis for selecting the best model from a set of competing asymmetric price transmission models or theories. However, little is understood about the sensitivity of the model selection methods to model complexity. This study therefore fits competing asymmetric price transmission models that differ in complexity to simulated data and evaluates the ability of the model selection methods to recover the true model. The results of Monte Carlo experimentation suggest that in general BIC, CAIC and DIC were superior to AIC when the true data generating process was the standard error correction model, whereas AIC was more successful when the true model was the complex error correction model. It is also shown that the model selection methods performed better in large samples for a complex asymmetric data generating process than with a standard asymmetric data generating process. Except for complex models, AIC's performance did not make substantial gains in recovery rates as sample size increased. The research findings demonstrate the influence of model complexity in asymmetric price transmission model comparison and selection.

Structural stability of solutions to the Riemann problem for a non-strictly hyperbolic system with flux approximation

Directory of Open Access Journals (Sweden)

Meina Sun

2016-05-01

Full Text Available We study the Riemann problem for a non-strictly hyperbolic system of conservation laws under the linear approximations of flux functions with three parameters. The approximated system also belongs to the type of triangular systems of conservation laws and this approximation does not change the structure of Riemann solutions to the original system. Furthermore, it is proven that the Riemann solutions to the approximated system converge to the corresponding ones to the original system as the perturbation parameter tends to zero.

Studying ventricular abnormalities in mild cognitive impairment with hyperbolic Ricci flow and tensor-based morphometry.

Science.gov (United States)

Shi, Jie; Stonnington, Cynthia M; Thompson, Paul M; Chen, Kewei; Gutman, Boris; Reschke, Cole; Baxter, Leslie C; Reiman, Eric M; Caselli, Richard J; Wang, Yalin

2015-01-01

Mild Cognitive Impairment (MCI) is a transitional stage between normal aging and dementia and people with MCI are at high risk of progression to dementia. MCI is attracting increasing attention, as it offers an opportunity to target the disease process during an early symptomatic stage. Structural magnetic resonance imaging (MRI) measures have been the mainstay of Alzheimer's disease (AD) imaging research, however, ventricular morphometry analysis remains challenging because of its complicated topological structure. Here we describe a novel ventricular morphometry system based on the hyperbolic Ricci flow method and tensor-based morphometry (TBM) statistics. Unlike prior ventricular surface parameterization methods, hyperbolic conformal parameterization is angle-preserving and does not have any singularities. Our system generates a one-to-one diffeomorphic mapping between ventricular surfaces with consistent boundary matching conditions. The TBM statistics encode a great deal of surface deformation information that could be inaccessible or overlooked by other methods. We applied our system to the baseline MRI scans of a set of MCI subjects from the Alzheimer's Disease Neuroimaging Initiative (ADNI: 71 MCI converters vs. 62 MCI stable). Although the combined ventricular area and volume features did not differ between the two groups, our fine-grained surface analysis revealed significant differences in the ventricular regions close to the temporal lobe and posterior cingulate, structures that are affected early in AD. Significant correlations were also detected between ventricular morphometry, neuropsychological measures, and a previously described imaging index based on fluorodeoxyglucose positron emission tomography (FDG-PET) scans. This novel ventricular morphometry method may offer a new and more sensitive approach to study preclinical and early symptomatic stage AD. Copyright © 2014 Elsevier Inc. All rights reserved.

Modelling of information processes management of educational complex

Directory of Open Access Journals (Sweden)

Оксана Николаевна Ромашкова

2014-12-01

Full Text Available This work concerns information model of the educational complex which includes several schools. A classification of educational complexes formed in Moscow is given. There are also a consideration of the existing organizational structure of the educational complex and a suggestion of matrix management structure. Basic management information processes of the educational complex were conceptualized.

Complex networks under dynamic repair model

Science.gov (United States)

Chaoqi, Fu; Ying, Wang; Kun, Zhao; Yangjun, Gao

2018-01-01

Invulnerability is not the only factor of importance when considering complex networks' security. It is also critical to have an effective and reasonable repair strategy. Existing research on network repair is confined to the static model. The dynamic model makes better use of the redundant capacity of repaired nodes and repairs the damaged network more efficiently than the static model; however, the dynamic repair model is complex and polytropic. In this paper, we construct a dynamic repair model and systematically describe the energy-transfer relationships between nodes in the repair process of the failure network. Nodes are divided into three types, corresponding to three structures. We find that the strong coupling structure is responsible for secondary failure of the repaired nodes and propose an algorithm that can select the most suitable targets (nodes or links) to repair the failure network with minimal cost. Two types of repair strategies are identified, with different effects under the two energy-transfer rules. The research results enable a more flexible approach to network repair.

Predictive modelling of complex agronomic and biological systems.

Science.gov (United States)

Keurentjes, Joost J B; Molenaar, Jaap; Zwaan, Bas J

2013-09-01

Biological systems are tremendously complex in their functioning and regulation. Studying the multifaceted behaviour and describing the performance of such complexity has challenged the scientific community for years. The reduction of real-world intricacy into simple descriptive models has therefore convinced many researchers of the usefulness of introducing mathematics into biological sciences. Predictive modelling takes such an approach another step further in that it takes advantage of existing knowledge to project the performance of a system in alternating scenarios. The ever growing amounts of available data generated by assessing biological systems at increasingly higher detail provide unique opportunities for future modelling and experiment design. Here we aim to provide an overview of the progress made in modelling over time and the currently prevalent approaches for iterative modelling cycles in modern biology. We will further argue for the importance of versatility in modelling approaches, including parameter estimation, model reduction and network reconstruction. Finally, we will discuss the difficulties in overcoming the mathematical interpretation of in vivo complexity and address some of the future challenges lying ahead. © 2013 John Wiley & Sons Ltd.

Does model performance improve with complexity? A case study with three hydrological models

Science.gov (United States)

Orth, Rene; Staudinger, Maria; Seneviratne, Sonia I.; Seibert, Jan; Zappa, Massimiliano

2015-04-01

In recent decades considerable progress has been made in climate model development. Following the massive increase in computational power, models became more sophisticated. At the same time also simple conceptual models have advanced. In this study we validate and compare three hydrological models of different complexity to investigate whether their performance varies accordingly. For this purpose we use runoff and also soil moisture measurements, which allow a truly independent validation, from several sites across Switzerland. The models are calibrated in similar ways with the same runoff data. Our results show that the more complex models HBV and PREVAH outperform the simple water balance model (SWBM) in case of runoff but not for soil moisture. Furthermore the most sophisticated PREVAH model shows an added value compared to the HBV model only in case of soil moisture. Focusing on extreme events we find generally improved performance of the SWBM during drought conditions and degraded agreement with observations during wet extremes. For the more complex models we find the opposite behavior, probably because they were primarily developed for prediction of runoff extremes. As expected given their complexity, HBV and PREVAH have more problems with over-fitting. All models show a tendency towards better performance in lower altitudes as opposed to (pre-) alpine sites. The results vary considerably across the investigated sites. In contrast, the different metrics we consider to estimate the agreement between models and observations lead to similar conclusions, indicating that the performance of the considered models is similar at different time scales as well as for anomalies and long-term means. We conclude that added complexity does not necessarily lead to improved performance of hydrological models, and that performance can vary greatly depending on the considered hydrological variable (e.g. runoff vs. soil moisture) or hydrological conditions (floods vs. droughts).