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
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.)
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...
Advanced Research Workshop on Nonlinear Hyperbolic Problems
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.
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.
Some problems on nonlinear hyperbolic equations and applications
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.
7th International Conference on Hyperbolic Problems Theory, Numerics, Applications
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...
Numerical methods for hyperbolic differential functional problems
Directory of Open Access Journals (Sweden)
Roman Ciarski
2008-01-01
Full Text Available The paper deals with the initial boundary value problem for quasilinear first order partial differential functional systems. A general class of difference methods for the problem is constructed. Theorems on the error estimate of approximate solutions for difference functional systems are presented. The convergence results are proved by means of consistency and stability arguments. A numerical example is given.
8th International Conference on Hyperbolic Problems : Theory, Numerics, Applications
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...
Carleman estimates and applications to inverse problems for hyperbolic systems
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...
Hyperbolic systems with analytic coefficients well-posedness of the Cauchy problem
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...
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.
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.
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.
First-Order Hyperbolic System Method for Time-Dependent Advection-Diffusion Problems
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
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,.
An inspection to the hyperbolic heat conduction problem in processed meat
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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.
BOUNDARY VALUE PROBLEM FOR A LOADED EQUATION ELLIPTIC-HYPERBOLIC TYPE IN A DOUBLY CONNECTED DOMAIN
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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.
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 ....
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
The structure of spectral problems and geometry: hyperbolic surfaces in E sup 3
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.
Integral geometry and inverse problems for hyperbolic equations
Romanov, V G
1974-01-01
There are currently many practical situations in which one wishes to determine the coefficients in an ordinary or partial differential equation from known functionals of its solution. These are often called "inverse problems of mathematical physics" and may be contrasted with problems in which an equation is given and one looks for its solution under initial and boundary conditions. Although inverse problems are often ill-posed in the classical sense, their practical importance is such that they may be considered among the pressing problems of current mathematical re search. A. N. Tihonov showed [82], [83] that there is a broad class of inverse problems for which a particular non-classical definition of well-posed ness is appropriate. This new definition requires that a solution be unique in a class of solutions belonging to a given subset M of a function space. The existence of a solution in this set is assumed a priori for some set of data. The classical requirement of continuous dependence of the solutio...
International Nuclear Information System (INIS)
Huang, C.-H.; Wu, H.-H.
2006-01-01
In the present study an inverse hyperbolic heat conduction problem is solved by the conjugate gradient method (CGM) in estimating the unknown boundary heat flux based on the boundary temperature measurements. Results obtained in this inverse problem will be justified based on the numerical experiments where three different heat flux distributions are to be determined. Results show that the inverse solutions can always be obtained with any arbitrary initial guesses of the boundary heat flux. Moreover, the drawbacks of the previous study for this similar inverse problem, such as (1) the inverse solution has phase error and (2) the inverse solution is sensitive to measurement error, can be avoided in the present algorithm. Finally, it is concluded that accurate boundary heat flux can be estimated in this study
The nonlocal problem for a hyperbolic equation with Bessel operator in a rectangular domain
Directory of Open Access Journals (Sweden)
Natalya V. Zaitseva
2016-12-01
Full Text Available We consider a boundary value problem for a hyperbolic equation with Bessel differential operator in a rectangular domain with integral nonlocal boundary value condition of the first kind. The equivalence between boundary value problem with integral nonlocal condition of the first kind and a local boundary value problem with mixed boundary conditions of the first and third kinds is proved. The existence and uniqueness of solution of the equivalent problem are established by means of the spectral method. At the uniqueness proof the completeness of the eigenfunction system of the spectral problem is used . At the existence proof the assessment of coefficients of series, the asymptotic formula for Bessel function of the first kind and asymptotic formula for eigenvalues are used. Sufficient conditions on the functions defining initial data of the problem are received. The solution of the problem is obtained in explicit form. The solution is obtained in the form of the Fourier–Bessel series. Its convergence is proved in the class of regular solutions.
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.
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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.
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.
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.
Hyperbolic partial differential equations
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
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.
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
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.)
Li, Yanning
2013-10-01
This article presents a new robust control framework for transportation problems in which the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a Hamilton-Jacobi equation, we pose the problem of controlling the state of the system on a network link, using boundary flow control, as a Linear Program. Unlike many previously investigated transportation control schemes, this method yields a globally optimal solution and is capable of handling shocks (i.e. discontinuities in the state of the system). We also demonstrate that the same framework can handle robust control problems, in which the uncontrollable components of the initial and boundary conditions are encoded in intervals on the right hand side of inequalities in the linear program. The lower bound of the interval which defines the smallest feasible solution set is used to solve the robust LP (or MILP if the objective function depends on boolean variables). Since this framework leverages the intrinsic properties of the Hamilton-Jacobi equation used to model the state of the system, it is extremely fast. Several examples are given to demonstrate the performance of the robust control solution and the trade-off between the robustness and the optimality. © 2013 IEEE.
Li, Yanning; Canepa, Edward S.; Claudel, Christian G.
2013-01-01
This article presents a new robust control framework for transportation problems in which the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a Hamilton-Jacobi equation, we pose the problem of controlling the state of the system on a network link, using boundary flow control, as a Linear Program. Unlike many previously investigated transportation control schemes, this method yields a globally optimal solution and is capable of handling shocks (i.e. discontinuities in the state of the system). We also demonstrate that the same framework can handle robust control problems, in which the uncontrollable components of the initial and boundary conditions are encoded in intervals on the right hand side of inequalities in the linear program. The lower bound of the interval which defines the smallest feasible solution set is used to solve the robust LP (or MILP if the objective function depends on boolean variables). Since this framework leverages the intrinsic properties of the Hamilton-Jacobi equation used to model the state of the system, it is extremely fast. Several examples are given to demonstrate the performance of the robust control solution and the trade-off between the robustness and the optimality. © 2013 IEEE.
Loss of hyperbolicity changes the number of wave groups in Riemann problems
Vítor Matos; Julio D. Silva; Dan Marchesin
2016-01-01
Themain goal of ourwork is to showthat there exists a class of 2×2 Riemann problems for which the solution comprises a singlewave group for an open set of initial conditions. This wave group comprises a 1-rarefaction joined to a 2-rarefaction, not by an intermediate state, but by a doubly characteristic shock, 1-left and 2-right characteristic. In order to ensure that perturbations of initial conditions do not destroy the adjacency of the waves, local transversality between a composite curve ...
Inverse Boundary Value Problem for Non-linear Hyperbolic Partial Differential Equations
Nakamura, Gen; Vashisth, Manmohan
2017-01-01
In this article we are concerned with an inverse boundary value problem for a non-linear wave equation of divergence form with space dimension $n\\geq 3$. This non-linear wave equation has a trivial solution, i.e. zero solution. By linearizing this equation at the trivial solution, we have the usual linear isotropic wave equation with the speed $\\sqrt{\\gamma(x)}$ at each point $x$ in a given spacial domain. For any small solution $u=u(t,x)$ of this non-linear equation, we have the linear isotr...
Balsara, Dinshaw S.; Dumbser, Michael
2015-04-01
Multidimensional Riemann solvers that have internal sub-structure in the strongly-interacting state have been formulated recently (D.S. Balsara (2012, 2014) [5,16]). Any multidimensional Riemann solver operates at the grid vertices and takes as its input all the states from its surrounding elements. It yields as its output an approximation of the strongly interacting state, as well as the numerical fluxes. The multidimensional Riemann problem produces a self-similar strongly-interacting state which is the result of several one-dimensional Riemann problems interacting with each other. To compute this strongly interacting state and its higher order moments we propose the use of a Galerkin-type formulation to compute the strongly interacting state and its higher order moments in terms of similarity variables. The use of substructure in the Riemann problem reduces numerical dissipation and, therefore, allows a better preservation of flow structures, like contact and shear waves. In this second part of a series of papers we describe how this technique is extended to unstructured triangular meshes. All necessary details for a practical computer code implementation are discussed. In particular, we explicitly present all the issues related to computational geometry. Because these Riemann solvers are Multidimensional and have Self-similar strongly-Interacting states that are obtained by Consistency with the conservation law, we call them MuSIC Riemann solvers. (A video introduction to multidimensional Riemann solvers is available on http://www.elsevier.com/xml/linking-roles/text/html". The MuSIC framework is sufficiently general to handle general nonlinear systems of hyperbolic conservation laws in multiple space dimensions. It can also accommodate all self-similar one-dimensional Riemann solvers and subsequently produces a multidimensional version of the same. In this paper we focus on unstructured triangular meshes. As examples of different systems of conservation laws we
Hyperbolicity of projective hypersurfaces
Diverio, Simone
2016-01-01
This book presents recent advances on Kobayashi hyperbolicity in complex geometry, especially in connection with projective hypersurfaces. This is a very active field, not least because of the fascinating relations with complex algebraic and arithmetic geometry. Foundational works of Serge Lang and Paul A. Vojta, among others, resulted in precise conjectures regarding the interplay of these research fields (e.g. existence of Zariski dense entire curves should correspond to the (potential) density of rational points). Perhaps one of the conjectures which generated most activity in Kobayashi hyperbolicity theory is the one formed by Kobayashi himself in 1970 which predicts that a very general projective hypersurface of degree large enough does not contain any (non-constant) entire curves. Since the seminal work of Green and Griffiths in 1979, later refined by J.-P. Demailly, J. Noguchi, Y.-T. Siu and others, it became clear that a possible general strategy to attack this problem was to look at particular algebr...
International Nuclear Information System (INIS)
Hung, Nguyen M
1999-01-01
An existence and uniqueness theorem for generalized solutions of the first initial-boundary-value problem for strongly hyperbolic systems in bounded domains is established. The question of estimates in Sobolev spaces of the derivatives with respect to time of the generalized solution is discussed. It is shown that the smoothness of generalized solutions with respect to time is independent of the structure of the boundary of the domain but depends on the coefficients of the right-hand side. Results on the smoothness of the generalized solution and its asymptotic behaviour in a neighbourhood of a conical boundary point are also obtained
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.)
International Nuclear Information System (INIS)
Panov, E Yu
1999-01-01
We consider a hyperbolic system of conservation laws on the space of symmetric second-order matrices. The right-hand side of this system contains the functional calculus operator f-bar(U) generated in the general case only by a continuous scalar function f(u). For these systems we define and describe the set of singular entropies, introduce the concept of generalized entropy solutions of the corresponding Cauchy problem, and investigate the properties of generalized entropy solutions. We define the class of strong generalized entropy solutions, in which the Cauchy problem has precisely one solution. We suggest a condition on the initial data under which any generalized entropy solution is strong, which implies its uniqueness. Under this condition we establish that the 'vanishing viscosity' method converges. An example shows that in the general case there can be more than one generalized entropy solution
International Nuclear Information System (INIS)
Panov, E Yu
2000-01-01
Many-dimensional non-strictly hyperbolic systems of conservation laws with a radially degenerate flux function are considered. For such systems the set of entropies is defined and described, the concept of generalized entropy solution of the Cauchy problem is introduced, and the properties of generalized entropy solutions are studied. The class of strong generalized entropy solutions is distinguished, in which the Cauchy problem in question is uniquely soluble. A condition on the initial data is described that ensures that the generalized entropy solution is strong and therefore unique. Under this condition the convergence of the 'vanishing viscosity' method is established. An example presented in the paper shows that a generalized entropy solution is not necessarily unique in the general case
Pettersson, Mass Per; Nordström, Jan
2015-01-01
This monograph presents computational techniques and numerical analysis to study conservation laws under uncertainty using the stochastic Galerkin formulation. With the continual growth of computer power, these methods are becoming increasingly popular as an alternative to more classical sampling-based techniques. The approach described in the text takes advantage of stochastic Galerkin projections applied to the original conservation laws to produce a large system of modified partial differential equations, the solutions to which directly provide a full statistical characterization of the effect of uncertainties. Polynomial Chaos Methods of Hyperbolic Partial Differential Equations focuses on the analysis of stochastic Galerkin systems obtained for linear and non-linear convection-diffusion equations and for a systems of conservation laws; a detailed well-posedness and accuracy analysis is presented to enable the design of robust and stable numerical methods. The exposition is restricted to one spatial dime...
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.
Geometry of hyperbolic monopoles
International Nuclear Information System (INIS)
Nash, C.
1986-01-01
The hyperbolic monopoles of Atiyah [M. F. Atiyah, Commun. Math. Phys. 93, 471 (1984); ''Magnetic monopoles in hyperbolic space,'' in Proceedings of the International Colloquium on Vector Bundles (Tata Institute, Bombay, 1984)] and Chakrabarti [A. Chakrabarti, J. Math. Phys. 27, 340 (1986)] are introduced and their geometric properties and relations to instantons and ordinary monopoles clarified. A key tool is the use of the ball model of hyperbolic space to construct and examine solutions
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...
Admissibility and hyperbolicity
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...
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.
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.
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.
Hyperbolic Metamaterials with Complex Geometry
DEFF Research Database (Denmark)
Lavrinenko, Andrei; Andryieuski, Andrei; Zhukovsky, Sergei
2016-01-01
We investigate new geometries of hyperbolic metamaterialssuch as highly corrugated structures, nanoparticle monolayer assemblies, super-structured or vertically arranged multilayersand nanopillars. All structures retain basic propertiesof hyperbolic metamaterials, but have functionality improved...
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)
Sources of hyperbolic geometry
Stillwell, John
1996-01-01
This book presents, for the first time in English, the papers of Beltrami, Klein, and Poincaré that brought hyperbolic geometry into the mainstream of mathematics. A recognition of Beltrami comparable to that given the pioneering works of Bolyai and Lobachevsky seems long overdue-not only because Beltrami rescued hyperbolic geometry from oblivion by proving it to be logically consistent, but because he gave it a concrete meaning (a model) that made hyperbolic geometry part of ordinary mathematics. The models subsequently discovered by Klein and Poincaré brought hyperbolic geometry even further down to earth and paved the way for the current explosion of activity in low-dimensional geometry and topology. By placing the works of these three mathematicians side by side and providing commentaries, this book gives the student, historian, or professional geometer a bird's-eye view of one of the great episodes in mathematics. The unified setting and historical context reveal the insights of Beltrami, Klein, and Po...
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.
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.
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...
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.
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
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
Uncertainty quantification for hyperbolic and kinetic equations
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.
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.
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.
Hyperbolic-symmetry vector fields.
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.
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.
Differentiable dynamical systems an introduction to structural stability and hyperbolicity
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...
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
Hyperbolic isometries of systolic complexes
DEFF Research Database (Denmark)
Prytula, Tomasz Pawel
The main topics of this thesis are the geometric features of systolic complexesarising from the actions of hyperbolic isometries. The thesis consists ofan introduction followed by two articles.Given a hyperbolic isometry h of a systolic complex X, our central theme isto study the minimal displace......The main topics of this thesis are the geometric features of systolic complexesarising from the actions of hyperbolic isometries. The thesis consists ofan introduction followed by two articles.Given a hyperbolic isometry h of a systolic complex X, our central theme isto study the minimal...... algebraic-topological features of systolic groups. In addition, we provide newexamples of systolic groups.In the first article we show that the minimal displacement set of a hyperbolicisometry of a systolic complex is quasi-isometric to the product of a tree andthe real line. We use this theorem...
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
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.
Quasilinear Hyperbolic Systems, Compressible Flows, and Waves
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
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.)
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.
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.
The Arabic Hyperbolic Pattern "Fa??al" in Two Recent Translations of the Qur'an
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…
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
The spectrum of hyperbolic surfaces
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...
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....
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
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
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)
Dynamics beyond uniform hyperbolicity a global geometric and probabilistic perspective
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.
Cognitive Procedures and Hyperbolic Discounting
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
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.
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)
Front tracking for hyperbolic conservation laws
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 ...
Directory of Open Access Journals (Sweden)
Hatem Mejjaoli
2008-12-01
Full Text Available We introduce and study the Dunkl symmetric systems. We prove the well-posedness results for the Cauchy problem for these systems. Eventually we describe the finite speed of it. Next the semi-linear Dunkl-wave equations are also studied.
Nonlinear hyperbolic waves in multidimensions
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...
Computation of Hyperbolic Structures in Knot Theory
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...
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
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 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....
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
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 Chaos A Physicist’s View
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.
The art and science of hyperbolic tessellations.
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.
Stability and boundary stabilization of 1-D hyperbolic systems
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...
Spectral theory of infinite-area hyperbolic surfaces
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 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.)
A Gyrovector Space Approach to Hyperbolic Geometry
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
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
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.
Electromagnetic ``black holes'' in hyperbolic metamaterials
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.
Hyperbolic theory of relativistic conformal dissipative fluids
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.
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.
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....
Hyperbolic conservation laws in continuum physics
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...
Hyperbolic metamaterial lens with hydrodynamic nonlocal response.
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.
Computing the Gromov hyperbolicity constant of a discrete metric space
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
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....
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
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...
Congruence Approximations for Entrophy Endowed Hyperbolic Systems
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.
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...
High-Order Wave Propagation Algorithms for Hyperbolic Systems
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.
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)
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)
Atomic disintegrations for partially hyperbolic diffeomorphisms
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
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)
The Hyperbolic Sine Cardinal and the Catenary
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…
Analytic smoothing effect for the cubic hyperbolic Schrodinger equation in two space dimensions
Directory of Open Access Journals (Sweden)
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.
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
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/
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.
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
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.
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.)
Extended Thermodynamics: a Theory of Symmetric Hyperbolic Field Equations
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.
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.
Near-perfect broadband absorption from hyperbolic metamaterial nanoparticles
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.
Optimal boundary control and boundary stabilization of hyperbolic systems
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.
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 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...
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....
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)
Hyperbolic metamaterial lens with hydrodynamic nonlocal response
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...
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
Discontinuous Galerkin Method for Hyperbolic Conservation Laws
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
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.
Representation of the contextual statistical model by hyperbolic amplitudes
International Nuclear Information System (INIS)
Khrennikov, Andrei
2005-01-01
We continue the development of a so-called contextual statistical model (here context has the meaning of a complex of physical conditions). It is shown that, besides contexts producing the conventional trigonometric cos-interference, there exist contexts producing the hyperbolic cos-interference. Starting with the corresponding interference formula of total probability we represent such contexts by hyperbolic probabilistic amplitudes or in the abstract formalism by normalized vectors of a hyperbolic analogue of the Hilbert space. There is obtained a hyperbolic Born's rule. Incompatible observables are represented by noncommutative operators. This paper can be considered as the first step towards hyperbolic quantum probability. We also discuss possibilities of experimental verification of hyperbolic quantum mechanics: in physics of elementary particles, string theory as well as in experiments with nonphysical systems, e.g., in psychology, cognitive sciences, and economy
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)
Spectral approach to homogenization of hyperbolic equations with periodic coefficients
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.
Geometry through history Euclidean, hyperbolic, and projective geometries
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...
Hyperbolic Rendezvous at Mars: Risk Assessments and Mitigation Strategies
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.
Considerations on the hyperbolic complex Klein-Gordon equation
International Nuclear Information System (INIS)
Ulrych, S.
2010-01-01
This article summarizes and consolidates investigations on hyperbolic complex numbers with respect to the Klein-Gordon equation for fermions and bosons. The hyperbolic complex numbers are applied in the sense that complex extensions of groups and algebras are performed not with the complex unit, but with the product of complex and hyperbolic unit. The modified complexification is the key ingredient for the theory. The Klein-Gordon equation is represented in this framework in the form of the first invariant of the Poincare group, the mass operator, in order to emphasize its geometric origin. The possibility of new interactions arising from hyperbolic complex gauge transformations is discussed.
Hyperbolic functions with configuration theorems and equivalent and equidecomposable figures
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 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.
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...
Hyperbolic statics in space-time
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...
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.
Holographic complexity of cold hyperbolic black holes
International Nuclear Information System (INIS)
Barbón, José L.F.; Martín-García, Javier
2015-01-01
AdS black holes with hyperbolic horizons provide strong-coupling descriptions of thermal CFT states on hyperboloids. The low-temperature limit of these systems is peculiar. In this note we show that, in addition to a large ground state degeneracy, these states also have an anomalously large holographic complexity, scaling logarithmically with the temperature. We speculate on whether this fact generalizes to other systems whose extreme infrared regime is formally controlled by Conformal Quantum Mechanics, such as various instances of near-extremal charged black holes.
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)
Computing the Gromov hyperbolicity of a discrete metric space
Fournier, Hervé
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
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...
Computing the Gromov hyperbolicity constant of a discrete metric space
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.
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.
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.
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...
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.
One-way spatial integration of hyperbolic equations
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.
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)
Tangent hyperbolic circular frequency diverse array radars
Directory of Open Access Journals (Sweden)
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.
Resonances for Obstacles in Hyperbolic Space
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.
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)
High-Order Hyperbolic Residual-Distribution Schemes on Arbitrary Triangular Grids
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.
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)
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)
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
Infrared hyperbolic metasurface based on nanostructured van der Waals materials
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.
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.
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.
Hyperbolic Plykin attractor can exist in neuron models
DEFF Research Database (Denmark)
Belykh, V.; Belykh, I.; Mosekilde, Erik
2005-01-01
Strange hyperbolic attractors are hard to find in real physical systems. This paper provides the first example of a realistic system, a canonical three-dimensional (3D) model of bursting neurons, that is likely to have a strange hyperbolic attractor. Using a geometrical approach to the study...... of the neuron model, we derive a flow-defined Poincare map giving ail accurate account of the system's dynamics. In a parameter region where the neuron system undergoes bifurcations causing transitions between tonic spiking and bursting, this two-dimensional map becomes a map of a disk with several periodic...... holes. A particular case is the map of a disk with three holes, matching the Plykin example of a planar hyperbolic attractor. The corresponding attractor of the 3D neuron model appears to be hyperbolic (this property is not verified in the present paper) and arises as a result of a two-loop (secondary...
Hyperbolicity measures democracy in real-world networks
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).
Ergodicity-breaking bifurcations and tunneling in hyperbolic transport models
Giona, M.; Brasiello, A.; Crescitelli, S.
2015-11-01
One of the main differences between parabolic transport, associated with Langevin equations driven by Wiener processes, and hyperbolic models related to generalized Kac equations driven by Poisson processes, is the occurrence in the latter of multiple stable invariant densities (Frobenius multiplicity) in certain regions of the parameter space. This phenomenon is associated with the occurrence in linear hyperbolic balance equations of a typical bifurcation, referred to as the ergodicity-breaking bifurcation, the properties of which are thoroughly analyzed.
Hyperbolic Discounting of the Far-Distant Future
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...
A note on sigular limits to hyperbolic systems
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.
The Kerr geometry, complex world lines and hyperbolic strings
International Nuclear Information System (INIS)
Burinskii, A.Ya.
1994-01-01
In the Lind-Newman representation the Kerr geometry is created by a source moving along an analytical complex world line. An equivalence of the complex world line and complex (hyperbolic) string is considered. Therefore the hyperbolic string may play the role of the complex source of the Kerr geometry. The Kerr solution with the complex string source acquires Regge behavior of the angular momentum. (orig.)
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...
Euler and Navier-Stokes equations on the hyperbolic plane.
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.
Euler and Navier–Stokes equations on the hyperbolic plane
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
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.
Perturbed Strong Stability Preserving Time-Stepping Methods For Hyperbolic PDEs
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
Hyperbolic phonon polaritons in hexagonal boron nitride (Conference Presentation)
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).
Hyperbole, abstract motion and spatial knowledge: sequential versus simultaneous scanning.
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.
Front tracking for hyperbolic conservation laws
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.
Computing the Gromov hyperbolicity of a discrete metric space
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 (2log2n)-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 mapping of complex networks based on community information
Wang, Zuxi; Li, Qingguang; Jin, Fengdong; Xiong, Wei; Wu, Yao
2016-08-01
To improve the hyperbolic mapping methods both in terms of accuracy and running time, a novel mapping method called Community and Hyperbolic Mapping (CHM) is proposed based on community information in this paper. Firstly, an index called Community Intimacy (CI) is presented to measure the adjacency relationship between the communities, based on which a community ordering algorithm is introduced. According to the proposed Community-Sector hypothesis, which supposes that most nodes of one community gather in a same sector in hyperbolic space, CHM maps the ordered communities into hyperbolic space, and then the angular coordinates of nodes are randomly initialized within the sector that they belong to. Therefore, all the network nodes are so far mapped to hyperbolic space, and then the initialized angular coordinates can be optimized by employing the information of all nodes, which can greatly improve the algorithm precision. By applying the proposed dual-layer angle sampling method in the optimization procedure, CHM reduces the time complexity to O(n2) . The experiments show that our algorithm outperforms the state-of-the-art methods.
Super-Coulombic atom-atom interactions in hyperbolic media
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.
Geometry and dynamics in Gromov hyperbolic metric spaces with an emphasis on non-proper settings
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.
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.
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.
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.
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.
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)
Origin of hyperbolicity in brain-to-brain coordination networks
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.
Parallel hyperbolic PDE simulation on clusters: Cell versus GPU
Rostrup, Scott; De Sterck, Hans
2010-12-01
:http://cpc.cs.qub.ac.uk/summaries/AEGY_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GPL v3 No. of lines in distributed program, including test data, etc.: 59 168 No. of bytes in distributed program, including test data, etc.: 453 409 Distribution format: tar.gz Programming language: C, CUDA Computer: Parallel Computing Clusters. Individual compute nodes may consist of x86 CPU, Cell processor, or x86 CPU with attached NVIDIA GPU accelerator. Operating system: Linux Has the code been vectorised or parallelized?: Yes. Tested on 1-128 x86 CPU cores, 1-32 Cell Processors, and 1-32 NVIDIA GPUs. RAM: Tested on Problems requiring up to 4 GB per compute node. Classification: 12 External routines: MPI, CUDA, IBM Cell SDK Nature of problem: MPI-parallel simulation of Shallow Water equations using high-resolution 2D hyperbolic equation solver on regular Cartesian grids for x86 CPU, Cell Processor, and NVIDIA GPU using CUDA. Solution method: SWsolver provides 3 implementations of a high-resolution 2D Shallow Water equation solver on regular Cartesian grids, for CPU, Cell Processor, and NVIDIA GPU. Each implementation uses MPI to divide work across a parallel computing cluster. Additional comments: Sub-program numdiff is used for the test run.
Diffusive instabilities in hyperbolic reaction-diffusion equations
Zemskov, Evgeny P.; Horsthemke, Werner
2016-03-01
We investigate two-variable reaction-diffusion systems of the hyperbolic type. A linear stability analysis is performed, and the conditions for diffusion-driven instabilities are derived. Two basic types of eigenvalues, real and complex, are described. Dispersion curves for both types of eigenvalues are plotted and their behavior is analyzed. The real case is related to the Turing instability, and the complex one corresponds to the wave instability. We emphasize the interesting feature that the wave instability in the hyperbolic equations occurs in two-variable systems, whereas in the parabolic case one needs three reaction-diffusion equations.
Right-angled polyhedra and hyperbolic 3-manifolds
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.
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.
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.
A Riemann problem with small viscosity and dispersion
Directory of Open Access Journals (Sweden)
Kayyunnapara Thomas Joseph
2006-09-01
Full Text Available In this paper we prove existence of global solutions to a hyperbolic system in elastodynamics, with small viscosity and dispersion terms and derive estimates uniform in the viscosity-dispersion parameters. By passing to the limit, we prove the existence of solution the Riemann problem for the hyperbolic system with arbitrary Riemann data.
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
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...
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
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
Figurative framing: Shaping public discourse through metaphor, hyperbole and irony
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
Hyperboles not turning to metaphors : How to explain audience cooperativeness?
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
Figurative framing : Shaping public discourse through metaphor, hyperbole and irony
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
Discontinuous Galerkin finite element methods for hyperbolic differential equations
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
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.
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.
Control of the hyperbolic dispersion of dielectrics by an ultrashort laser pulse
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.
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
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.
Global Classical Solutions for Partially Dissipative Hyperbolic System of Balance Laws
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.
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
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.
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.
Modeling and analysis of linear hyperbolic systems of balance laws
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...
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
Generalized heat-transport equations: parabolic and hyperbolic models
Rogolino, Patrizia; Kovács, Robert; Ván, Peter; Cimmelli, Vito Antonio
2018-03-01
We derive two different generalized heat-transport equations: the most general one, of the first order in time and second order in space, encompasses some well-known heat equations and describes the hyperbolic regime in the absence of nonlocal effects. Another, less general, of the second order in time and fourth order in space, is able to describe hyperbolic heat conduction also in the presence of nonlocal effects. We investigate the thermodynamic compatibility of both models by applying some generalizations of the classical Liu and Coleman-Noll procedures. In both cases, constitutive equations for the entropy and for the entropy flux are obtained. For the second model, we consider a heat-transport equation which includes nonlocal terms and study the resulting set of balance laws, proving that the corresponding thermal perturbations propagate with finite speed.
Low-dimensional geometry from euclidean surfaces to hyperbolic knots
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...
Clawpack: Building an open source ecosystem for solving hyperbolic PDEs
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.
Hyperbolic Conservation Laws and Related Analysis with Applications
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...
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.
Detecting topology in a nearly flat hyperbolic universe
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...
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
Testable Implications of Quasi-Hyperbolic and Exponential Time Discounting
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 and semi-parametric models in finance
Bingham, N. H.; Kiesel, Rüdiger
2001-02-01
The benchmark Black-Scholes-Merton model of mathematical finance is parametric, based on the normal/Gaussian distribution. Its principal parametric competitor, the hyperbolic model of Barndorff-Nielsen, Eberlein and others, is briefly discussed. Our main theme is the use of semi-parametric models, incorporating the mean vector and covariance matrix as in the Markowitz approach, plus a non-parametric part, a scalar function incorporating features such as tail-decay. Implementation is also briefly discussed.
Hyperbolic Cross Truncations for Stochastic Fourier Cosine Series
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
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 ...
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)
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
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.
Approximate Treatment of the Dirac Equation with Hyperbolic Potential Function
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.
A Combination Theorem for Convex Hyperbolic Manifolds, with Applications to Surfaces in 3-Manifolds
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...
The DSM-5: Hyperbole, Hope or Hypothesis?
Berk, Michael
2013-05-14
The furore preceding the release of the new edition of the Diagnostic and Statistical Manual of Mental Disorders (DSM-5) is in contrast to the incremental changes to several diagnostic categories, which are derived from new research since its predecessor's birth in 1990. While many of these changes are indeed controversial, they do reflect the intrinsic ambiguity of the extant literature. Additionally, this may be a mirror of the frustration of the field's limited progress, especially given the false hopes at the dawn of the "decade of the brain". In the absence of a coherent pathophysiology, the DSM remains no more than a set of consensus based operationalized adjectives, albeit with some degree of reliability. It does not cleave nature at its joints, nor does it aim to, but neither does alternate systems. The largest problem with the DSM system is how it's used; sometimes too loosely by clinicians, and too rigidly by regulators, insurers, lawyers and at times researchers, who afford it reference and deference disproportionate to its overt acknowledged limitations.
Covariant path integrals on hyperbolic surfaces
Schaefer, Joe
1997-11-01
DeWitt's covariant formulation of path integration [B. De Witt, "Dynamical theory in curved spaces. I. A review of the classical and quantum action principles," Rev. Mod. Phys. 29, 377-397 (1957)] has two practical advantages over the traditional methods of "lattice approximations;" there is no ordering problem, and classical symmetries are manifestly preserved at the quantum level. Applying the spectral theorem for unbounded self-adjoint operators, we provide a rigorous proof of the convergence of certain path integrals on Riemann surfaces of constant curvature -1. The Pauli-DeWitt curvature correction term arises, as in DeWitt's work. Introducing a Fuchsian group Γ of the first kind, and a continuous, bounded, Γ-automorphic potential V, we obtain a Feynman-Kac formula for the automorphic Schrödinger equation on the Riemann surface ΓH. We analyze the Wick rotation and prove the strong convergence of the so-called Feynman maps [K. D. Elworthy, Path Integration on Manifolds, Mathematical Aspects of Superspace, edited by Seifert, Clarke, and Rosenblum (Reidel, Boston, 1983), pp. 47-90] on a dense set of states. Finally, we give a new proof of some results in C. Grosche and F. Steiner, "The path integral on the Poincare upper half plane and for Liouville quantum mechanics," Phys. Lett. A 123, 319-328 (1987).
6j symbols for the modular double, quantum hyperbolic geometry, and supersymmetric gauge theories
Energy Technology Data Exchange (ETDEWEB)
Teschner, J.; Vartanov, G.S.
2012-02-15
We revisit the definition of the 6j-symbols from the modular double of U{sub q}(sl(2,R)), referred to as b-6j symbols. Our new results are (i) the identification of particularly natural normalization conditions, and (ii) new integral representations for this object. This is used to briefly discuss possible applications to quantum hyperbolic geometry, and to the study of certain supersymmetric gauge theories. We show, in particular, that the b-6j symbol has leading semiclassical asymptotics given by the volume of a non-ideal tetrahedron. We furthermore observe a close relation with the problem to quantize natural Darboux coordinates for moduli spaces of flat connections on Riemann surfaces related to the Fenchel-Nielsen coordinates. Our new integral representations finally indicate a possible interpretation of the b-6j symbols as partition functions of three-dimensional N=2 supersymmetric gauge theories. (orig.)
Observer-Based Bilinear Control of First-Order Hyperbolic PDEs: Application to the Solar Collector
Mechhoud, Sarra
2015-12-18
In this paper, we investigate the problem of bilinear control of a solar collector plant using the available boundary and solar irradiance measurements. The solar collector is described by a first-order 1D hyperbolic partial differential equation where the pump volumetric flow rate acts as the plant control input. By combining a boundary state observer and an internal energy-based control law, a nonlinear observer based feedback controller is proposed. With a feed-forward control term, the effect of the solar radiation is cancelled. Using the Lyapunov approach we prove that the proposed control guarantees the global exponential stability of both the plant and the tracking error. Simulation results are provided to illustrate the performance of the proposed method.
6j symbols for the modular double, quantum hyperbolic geometry, and supersymmetric gauge theories
International Nuclear Information System (INIS)
Teschner, J.; Vartanov, G.S.
2012-02-01
We revisit the definition of the 6j-symbols from the modular double of U q (sl(2,R)), referred to as b-6j symbols. Our new results are (i) the identification of particularly natural normalization conditions, and (ii) new integral representations for this object. This is used to briefly discuss possible applications to quantum hyperbolic geometry, and to the study of certain supersymmetric gauge theories. We show, in particular, that the b-6j symbol has leading semiclassical asymptotics given by the volume of a non-ideal tetrahedron. We furthermore observe a close relation with the problem to quantize natural Darboux coordinates for moduli spaces of flat connections on Riemann surfaces related to the Fenchel-Nielsen coordinates. Our new integral representations finally indicate a possible interpretation of the b-6j symbols as partition functions of three-dimensional N=2 supersymmetric gauge theories. (orig.)
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.
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
Fast computation of the Maslov index for hyperbolic linear systems with periodic coefficients
International Nuclear Information System (INIS)
Chardard, F; Dias, F; Bridges, T J
2006-01-01
The Maslov index is a topological property of periodic orbits of finite-dimensional Hamiltonian systems that is widely used in semiclassical quantization, quantum chaology, stability of waves and classical mechanics. The Maslov index is determined from the analysis of a linear Hamiltonian system with periodic coefficients. In this paper, a numerical scheme is devised to compute the Maslov index for hyperbolic linear systems when the phase space has a low dimension. The idea is to compute on the exterior algebra of the ambient vector space, where the Lagrangian subspace representing the unstable subspace is reduced to a line. When the exterior algebra is projectified the Lagrangian subspace always forms a closed loop. The idea is illustrated by application to Hamiltonian systems on a phase space of dimension 4. The theory is used to compute the Maslov index for the spectral problem associated with periodic solutions of the fifth-order Korteweg de Vries equation
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
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
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 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.)
Covariant path integrals on hyperbolic surfaces
International Nuclear Information System (INIS)
Schaefer, J.
1997-01-01
DeWitt close-quote s covariant formulation of path integration [B. De Witt, open-quotes Dynamical theory in curved spaces. I. A review of the classical and quantum action principles,close quotes Rev. Mod. Phys. 29, 377 endash 397 (1957)] has two practical advantages over the traditional methods of open-quotes lattice approximations;close quotes there is no ordering problem, and classical symmetries are manifestly preserved at the quantum level. Applying the spectral theorem for unbounded self-adjoint operators, we provide a rigorous proof of the convergence of certain path integrals on Riemann surfaces of constant curvature -1. The Pauli endash DeWitt curvature correction term arises, as in DeWitt close-quote s work. Introducing a Fuchsian group Γ of the first kind, and a continuous, bounded, Γ-automorphic potential V, we obtain a Feynman endash Kac formula for the automorphic Schroedinger equation on the Riemann surface Γ backslash H. We analyze the Wick rotation and prove the strong convergence of the so-called Feynman maps [K. D. Elworthy, Path Integration on Manifolds, Mathematical Aspects of Superspace, edited by Seifert, Clarke, and Rosenblum (Reidel, Boston, 1983), pp. 47 endash 90] on a dense set of states. Finally, we give a new proof of some results in C. Grosche and F. Steiner, open-quotes The path integral on the Poincare upper half plane and for Liouville quantum mechanics,close quotes Phys. Lett. A 123, 319 endash 328 (1987). copyright 1997 American Institute of Physics
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)
Nonlinear sigma models with compact hyperbolic target spaces
International Nuclear Information System (INIS)
Gubser, Steven; Saleem, Zain H.; Schoenholz, Samuel S.; Stoica, Bogdan; Stokes, James
2016-01-01
We explore the phase structure of nonlinear sigma models with target spaces corresponding to compact quotients of hyperbolic space, focusing on the case of a hyperbolic genus-2 Riemann surface. The continuum theory of these models can be approximated by a lattice spin system which we simulate using Monte Carlo methods. The target space possesses interesting geometric and topological properties which are reflected in novel features of the sigma model. In particular, we observe a topological phase transition at a critical temperature, above which vortices proliferate, reminiscent of the Kosterlitz-Thouless phase transition in the O(2) model V.L. Berezinskii, Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group II. Quantum systems, Sov. Phys. JETP 34 (1972) 610. J.M. Kosterlitz and D.J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C 6 (1973) 1181 [http://inspirehep.net/search?p=find+J+%22J.Phys.,C6,1181%22]. . Unlike in the O(2) case, there are many different types of vortices, suggesting a possible analogy to the Hagedorn treatment of statistical mechanics of a proliferating number of hadron species. Below the critical temperature the spins cluster around six special points in the target space known as Weierstrass points. The diversity of compact hyperbolic manifolds suggests that our model is only the simplest example of a broad class of statistical mechanical models whose main features can be understood essentially in geometric terms.
Nonlinear sigma models with compact hyperbolic target spaces
Energy Technology Data Exchange (ETDEWEB)
Gubser, Steven [Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544 (United States); Saleem, Zain H. [Department of Physics and Astronomy, University of Pennsylvania,Philadelphia, PA 19104 (United States); National Center for Physics, Quaid-e-Azam University Campus,Islamabad 4400 (Pakistan); Schoenholz, Samuel S. [Department of Physics and Astronomy, University of Pennsylvania,Philadelphia, PA 19104 (United States); Stoica, Bogdan [Walter Burke Institute for Theoretical Physics, California Institute of Technology,452-48, Pasadena, CA 91125 (United States); Stokes, James [Department of Physics and Astronomy, University of Pennsylvania,Philadelphia, PA 19104 (United States)
2016-06-23
We explore the phase structure of nonlinear sigma models with target spaces corresponding to compact quotients of hyperbolic space, focusing on the case of a hyperbolic genus-2 Riemann surface. The continuum theory of these models can be approximated by a lattice spin system which we simulate using Monte Carlo methods. The target space possesses interesting geometric and topological properties which are reflected in novel features of the sigma model. In particular, we observe a topological phase transition at a critical temperature, above which vortices proliferate, reminiscent of the Kosterlitz-Thouless phase transition in the O(2) model V.L. Berezinskii, Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group II. Quantum systems, Sov. Phys. JETP 34 (1972) 610. J.M. Kosterlitz and D.J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C 6 (1973) 1181 [http://inspirehep.net/search?p=find+J+%22J.Phys.,C6,1181%22]. . Unlike in the O(2) case, there are many different types of vortices, suggesting a possible analogy to the Hagedorn treatment of statistical mechanics of a proliferating number of hadron species. Below the critical temperature the spins cluster around six special points in the target space known as Weierstrass points. The diversity of compact hyperbolic manifolds suggests that our model is only the simplest example of a broad class of statistical mechanical models whose main features can be understood essentially in geometric terms.
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
Clawpack: building an open source ecosystem for solving hyperbolic PDEs
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.
Clawpack: building an open source ecosystem for solving hyperbolic PDEs
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.
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
Light propagation in a magneto-optical hyperbolic biaxial crystal
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.
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.
Directory of Open Access Journals (Sweden)
Navnit Jha
2014-04-01
Full Text Available An efficient numerical method based on quintic nonpolynomial spline basis and high order finite difference approximations has been presented. The scheme deals with the space containing hyperbolic and polynomial functions as spline basis. With the help of spline functions we derive consistency conditions and high order discretizations of the differential equation with the significant first order derivative. The error analysis of the new method is discussed briefly. The new method is analyzed for its efficiency using the physical problems. The order and accuracy of the proposed method have been analyzed in terms of maximum errors and root mean square errors.
Directory of Open Access Journals (Sweden)
Tommaso Ruggeri
2008-09-01
Full Text Available We discuss the different roles of the entropy principle in modern thermodynamics. We start with the approach of rational thermodynamics in which the entropy principle becomes a selection rule for physical constitutive equations. Then we discuss the entropy principle for selecting admissible discontinuous weak solutions and to symmetrize general systems of hyperbolic balance laws. A particular attention is given on the local and global well-posedness of the relative Cauchy problem for smooth solutions. Examples are given in the case of extended thermodynamics for rarefied gases and in the case of a multi-temperature mixture of fluids.
On the Growth of the Number of Hyperbolic Gravitational Instantons with respect to Volume
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.
Big Data Clustering via Community Detection and Hyperbolic Network Embedding in IoT Applications.
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.
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.
Exact boundary controllability of nodal profile for quasilinear hyperbolic systems
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...
On hyperbolic-dissipative systems of composite type
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.
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)
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.
Demonstrator of atmospheric reentry system with hyperbolic velocity—DASH
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.
Tuning subwavelength-structured focus in the hyperbolic metamaterials
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.
Non-Euclidean visibility problems
Indian Academy of Sciences (India)
FERNANDO CHAMIZO. Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spain. MS received 14 November 2005. Abstract. We consider the analog of visibility problems in hyperbolic plane (repre- sented by Poincaré half-plane model H), replacing the standard lattice Z ...
An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws
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.
Computation of Quasiperiodic Normally Hyperbolic Invariant Tori: Rigorous Results
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.
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.
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...
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.)
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.
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.
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.
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.
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)
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.
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.
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
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.
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...
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
Plasmonic Lithography Utilizing Epsilon Near Zero Hyperbolic Metamaterial.
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.
Gravitational wave bursts from Primordial Black Hole hyperbolic encounters
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...
Orienteering in Knowledge Spaces: The Hyperbolic Geometry of Wikipedia Mathematics
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.
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
Georlette, O; Gordon, J M
1994-07-01
Generalized nonimaging compound elliptical luminaires (CEL's) and compound hyperbolic luminaires (CHL's) are developed for pair-overlap illumination applications. A comprehensive analysis of CEL's and CHL's is presented. This includes the possibility of reflector truncation, as well as the extreme direction that spans the full range from positive to negative. Negative extreme direction devices have been overlooked in earlier studies and are shown to be well suited to illumination problems for which large cutoff angles are required. Flux maps can be calculated analytically without the need for computer ray tracing. It is demonstrated that, for a broad range of cutoff angles, adjacent pairs of CEL's and CHL's can generate highly uniform far-field illuminance while maintaining maximal lighting efficiency and excellent glare control. The trade-off between luminaire compactness and flux homogeneity is also illustrated. For V troughs, being a special case of CHL's and being well suited to simple, inexpensive fabri ation, we identify geometries that closely approach the performance characteristics of the optimized CEL's and CHL's.
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.
Hyperbolic Positioning with Antenna Arrays and Multi-Channel Pseudolite for Indoor Localization
Directory of Open Access Journals (Sweden)
Kenjirou Fujii
2015-09-01
Full Text Available A hyperbolic positioning method with antenna arrays consisting of proximately-located antennas and a multi-channel pseudolite is proposed in order to overcome the problems of indoor positioning with conventional pseudolites (ground-based GPS transmitters. A two-dimensional positioning experiment using actual devices is conducted. The experimental result shows that the positioning accuracy varies centimeter- to meter-level according to the geometric relation between the pseudolite antennas and the receiver. It also shows that the bias error of the carrier-phase difference observables is more serious than their random error. Based on the size of the bias error of carrier-phase difference that is inverse-calculated from the experimental result, three-dimensional positioning performance is evaluated by computer simulation. In addition, in the three-dimensional positioning scenario, an initial value convergence analysis of the non-linear least squares is conducted. Its result shows that initial values that can converge to a right position exist at least under the proposed antenna setup. The simulated values and evaluation methods introduced in this work can be applied to various antenna setups; therefore, by using them, positioning performance can be predicted in advance of installing an actual system.
Directory of Open Access Journals (Sweden)
R.K. Mohanty
2014-01-01
Full Text Available In this paper, we report new three level implicit super stable methods of order two in time and four in space for the solution of hyperbolic damped wave equations in one, two and three space dimensions subject to given appropriate initial and Dirichlet boundary conditions. We use uniform grid points both in time and space directions. Our methods behave like fourth order accurate, when grid size in time-direction is directly proportional to the square of grid size in space-direction. The proposed methods are super stable. The resulting system of algebraic equations is solved by the Gauss elimination method. We discuss new alternating direction implicit (ADI methods for two and three dimensional problems. Numerical results and the graphical representation of numerical solution are presented to illustrate the accuracy of the proposed methods.
A Gas-Kinetic Method for Hyperbolic-Elliptic Equations and Its Application in Two-Phase Fluid Flow
Xu, Kun
1999-01-01
A gas-kinetic method for the hyperbolic-elliptic equations is presented in this paper. In the mixed type system, the co-existence and the phase transition between liquid and gas are described by the van der Waals-type equation of state (EOS). Due to the unstable mechanism for a fluid in the elliptic region, interface between the liquid and gas can be kept sharp through the condensation and evaporation process to remove the "averaged" numerical fluid away from the elliptic region, and the interface thickness depends on the numerical diffusion and stiffness of the phase change. A few examples are presented in this paper for both phase transition and multifluid interface problems.
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)
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.
Theory of hyperbolic stratified nanostructures for surface-enhanced Raman scattering
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.
Policy Effects in Hyperbolic vs. Exponential Models of Consumption and Retirement.
Gustman, Alan L; Steinmeier, Thomas L
2012-06-01
This paper constructs a structural retirement model with hyperbolic preferences and uses it to estimate the effect of several potential Social Security policy changes. Estimated effects of policies are compared using two models, one with hyperbolic preferences and one with standard exponential preferences. Sophisticated hyperbolic discounters may accumulate substantial amounts of wealth for retirement. We find it is frequently difficult to distinguish empirically between models with the two types of preferences on the basis of asset accumulation paths or consumption paths around the period of retirement. Simulations suggest that, despite the much higher initial time preference rate, individuals with hyperbolic preferences may actually value a real annuity more than individuals with exponential preferences who have accumulated roughly equal amounts of assets. This appears to be especially true for individuals with relatively high time preference rates or who have low assets for whatever reason. This affects the tradeoff between current benefits and future benefits on which many of the retirement incentives of the Social Security system rest.Simulations involving increasing the early entitlement age and increasing the delayed retirement credit do not show a great deal of difference whether exponential or hyperbolic preferences are used, but simulations for eliminating the earnings test show a non-trivially greater effect when exponential preferences are used.
Elliptical, parabolic, and hyperbolic exchanges of energy in drag reducing plane Couette flows
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.
Inverse and Ill-posed Problems Theory and Applications
Kabanikhin, S I
2011-01-01
The text demonstrates the methods for proving the existence (if et all) and finding of inverse and ill-posed problems solutions in linear algebra, integral and operator equations, integral geometry, spectral inverse problems, and inverse scattering problems. It is given comprehensive background material for linear ill-posed problems and for coefficient inverse problems for hyperbolic, parabolic, and elliptic equations. A lot of examples for inverse problems from physics, geophysics, biology, medicine, and other areas of application of mathematics are included.
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.
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.
Some remarks on the topology of hyperbolic actions of Rn on n-manifolds
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.
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.
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.
Modified hyperbolic sine model for titanium dioxide-based memristive thin films
Abu Bakar, Raudah; Syahirah Kamarozaman, Nur; Fazlida Hanim Abdullah, Wan; Herman, Sukreen Hana
2018-03-01
Since the emergence of memristor as the newest fundamental circuit elements, studies on memristor modeling have been evolved. To date, the developed models were based on the linear model, linear ionic drift model using different window functions, tunnelling barrier model and hyperbolic-sine function based model. Although using hyperbolic-sine function model could predict the memristor electrical properties, the model was not well fitted to the experimental data. In order to improve the performance of the hyperbolic-sine function model, the state variable equation was modified. On the one hand, the addition of window function cannot provide an improved fitting. By multiplying the Yakopcic’s state variable model to Chang’s model on the other hand resulted in the closer agreement with the TiO2 thin film experimental data. The percentage error was approximately 2.15%.
Analytic Solutions and Resonant Solutions of Hyperbolic Partial Differential Equations
Wagenmaker, Timothy Roger
This dissertation contains two main subject areas. The first deals with solutions to the wave equation Du/Dt + a Du/Dx = 0, where D/Dt and D/Dx represent partial derivatives and a(t,x) is real valued. The question I studied, which arises in control theory, is whether solutions which are real analytic with respect to the time variable are dense in the space of all solutions. If a is real analytic in t and x, the Cauchy-Kovalevsky Theorem implies that the solutions real analytic in t and x are dense, since it suffices to approximate the initial data by polynomials. The same positive result is valid when a is continuously differentiable and independent of t. This is proved by regularization in time. The hypothesis that a is independent of t cannot be replaced by the weaker assumption that a is real analytic in t, even when it is infinitely smooth. I construct a(t,x) for which the solutions which are analytic in time are automatically periodic in time. In particular these solutions are not dense in the space of all solutions. The second area concerns the resonant interaction of oscillatory waves propagating in a compressible inviscid fluid. An asymptotic description given by Andrew Majda, Rodolfo Rosales, and Maria Schonbek (MRS) involves the genuinely nonlinear quasilinear hyperbolic system Du/Dt + D(uu/2)/Dt + v = 0, Dv/Dt - D(vv/2)/Dt - u = 0. They performed many numerical simulations which indicated that small amplitude solutions of this system tend to evade shock formation, and conjectured that "smooth initial data with a sufficiently small amplitude never develop shocks throughout a long time interval of integration.". I proved that for smooth periodic U(x), V(x) and initial data u(0,x) = epsilonU(x), v(0,x) = epsilonV(x), the solution is smooth for time at least constant times | ln epsilon| /epsilon. This is longer than the lifetime order 1/ epsilon of the solution to the decoupled Burgers equations. The decoupled equation describes nonresonant interaction of
Theory, Characterization and Applications of Infrared Hyperbolic Metamaterials
Fullager, Daniel B.
Hyperbolic Metamaterials (HMMs) are engineered structures capable of supporting lightmatter interactions that are not normally observed in naturally occuring material systems. These unusual responses are enabled by an enhancement of the photonic density of states (PDOS) in the material. The PDOS enhancement is a result of deliberately introduced anisotropy via a permittivity sign-change in HMM structures which increases the number and frequency spread of possible wave vectors that propagate in the material. Subwavelength structural features allow effective medium theories to be invoked to construct the k-space isofrequency quadratic curves that, for HMMs, result in the k-space isofrequency contour transitioning from being a bounded surface to an unbounded one. Since the PDOS is the integral of the differential volume between k-space contours, unbounded manifolds lead to the implication of an infinite or otherwise drastically enhanced PDOS. Since stored heat can be thought of as a set of non-radiative electromagnetic modes, in this dissertation we demonstrate that HMMs provide an ideal platform to attempt to modify the thermal/IR emissivity of a material. We also show that HMMs provide a platform for broadband plasmonic sensing. The advent of commercial two photon polymerization tools has enabled the rapid production of nano- and microstructures which can be used as scaffolds for directive infrared scatterers. We describe how such directive components can be used to address thermal management needs in vacuum environments in order to maximize radiative thermal transfer. In this context, the fundamental limitations of enhanced spon- taneous emission due to conjugate impedance matched scatterers are also explored. The HMM/conjugate scatterer system's performance is strongly correlated with the dielectric function of the negative permittivity component of the HMM. In order to fully understand the significance of these engineered materials, we examine in detail the
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
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.
Onto the stability analysis of hyperbolic secant-shaped Bose-Einstein condensate
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.
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)
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
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...
2012-09-03
27] introduced a new smoothness indicator, which removed the slight post- shock oscillations and improved the convergence . A Newton- iteration method... Gauss - Seidel algorithm for steady Euler equation on unstructured grids, Numer. Math. Theor. Meth. Appl., Vol. 1, pp. 92–112, (2008). [14] G.-S. Jiang...was adopted to solve the steady two dimensional Euler equations [10, 11, 13]. The matrix-free Squared Preconditioning is applied to a Newton iteration
Uniform approximations of Bernoulli and Euler polynomials in terms of hyperbolic functions
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
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...
Small universal cellular automata in hyperbolic spaces a collection of jewels
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...
Chaotic Dynamics in Smart Grid and Suppression Scheme via Generalized Fuzzy Hyperbolic Model
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
Exponential spreading and singular behavior of quantum dynamics near hyperbolic points.
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.
An Interactive Analysis of Hyperboles in a British TV Series: Implications For EFL Classes
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…
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.
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%.
Metric Characterizations of Superreflexivity in Terms of Word Hyperbolic Groups and Finite Graphs
Directory of Open Access Journals (Sweden)
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.
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
Metaphor, hyperbole, and irony: Uses in isolation and in combination in written discourse
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
The classical Stefan problem basic concepts, modelling and analysis
Gupta, SC
2003-01-01
This volume emphasises studies related toclassical Stefan problems. The term "Stefan problem" isgenerally used for heat transfer problems with phase-changes suchas from the liquid to the solid. Stefan problems have somecharacteristics that are typical of them, but certain problemsarising in fields such as mathematical physics and engineeringalso exhibit characteristics similar to them. The term``classical" distinguishes the formulation of these problems fromtheir weak formulation, in which the solution need not possessclassical derivatives. Under suitable assumptions, a weak solutioncould be as good as a classical solution. In hyperbolic Stefanproblems, the characteristic features of Stefan problems arepresent but unlike in Stefan problems, discontinuous solutions areallowed because of the hyperbolic nature of the heat equation. Thenumerical solutions of inverse Stefan problems, and the analysis ofdirect Stefan problems are so integrated that it is difficult todiscuss one without referring to the other. So no...
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.
A combined Preisach–Hyperbolic Tangent model for magnetic hysteresis of Terfenol-D
Energy Technology Data Exchange (ETDEWEB)
Talebian, Soheil [Department of Mechanical Engineering, Tarbiat Modares University, Tehran (Iran, Islamic Republic of); Hojjat, Yousef, E-mail: yhojjat@modares.ac.ir [Department of Mechanical Engineering, Tarbiat Modares University, Tehran (Iran, Islamic Republic of); Ghodsi, Mojtaba [Department of Mechanical and Industrial Engineering, Sultan Qaboos University, Muscat (Oman); Karafi, Mohammad Reza [Department of Mechanical Engineering, Tarbiat Modares University, Tehran (Iran, Islamic Republic of); Mirzamohammadi, Shahed [Department of Mechanical Engineering, Shahid Rajaee University, Tehran (Iran, Islamic Republic of)
2015-12-15
This study presents a new model using the combination of Preisach and Hyperbolic Tangent models, to predict the magnetic hysteresis of Terfenol-D at different frequencies. Initially, a proper experimental setup was fabricated and used to obtain different magnetic hysteresis curves of Terfenol-D; such as major, minor and reversal loops. Then, it was shown that the Hyperbolic Tangent model is precisely capable of modeling the magnetic hysteresis of the Terfenol-D for both rate-independent and rate-dependent cases. Empirical equations were proposed with respect to magnetic field frequency which can calculate the non-dimensional coefficients needed by the model. These empirical equations were validated at new frequencies of 100 Hz and 300 Hz. Finally, the new model was developed through the combination of Preisach and Hyperbolic Tangent models. In the combined model, analytical relations of the Hyperbolic Tangent model for the first order reversal loops determined the weighting function of the Preisach model. This model reduces the required experiments and errors due to numerical differentiations generally needed for characterization of the Preisach function. In addition, it can predict the rate-dependent hysteresis as well as rate-independent hysteresis. - Highlights: • Different hysteresis curves of Terfenol-D are experimentally obtained at 0–200 Hz. • A new model is presented using combination of Preisach and Hyperbolic Tangent models. • The model predicts both rate-independent and rate-dependent hystereses of Terfenol-D. • The analytical model reduces the numerical errors and number of required experiments.
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
Markov, A V; Korotaev, A V
2008-01-01
Among diverse models that are used to describe and interpret the changes in global biodiversity through the Phanerozoic, the exponential and logistic models (traditionally used in population biology) are the most popular. As we have recently demonstrated (Markov, Korotayev, 2007), the growth of the Phanerozoic marine biodiversity at genus level correlates better with the hyperbolic model (widely used in demography and macrosociology). Here we show that the hyperbolic model is also applicable to the Phanerozoic continental biota at genus and family levels, and to the marine biota at species, genus, and family levels. There are many common features in the evolutionary dynamics of the marine and continental biotas that imply similarity and common nature of the factors and mechanisms underlying the hyperbolic growth. Both marine and continental biotas are characterized by continuous growth of the mean longevity of taxa, by decreasing extinction and origination rates, by similar pattern of replacement of dominant groups, by stepwise accumulation of evolutionary stable, adaptable and "physiologically buffered" taxa with effective mechanisms of parental care, protection of early developmental stages, etc. At the beginning of the development of continental biota, the observed taxonomic diversity was substantially lower than that predicted by the hyperbolic model. We suggest that this is due, firstly, to the fact that, during the earliest stages of the continental biota evolution, the groups that are not preserved in the fossil record (such as soil bacteria, unicellular algae, lichens, etc.) played a fundamental role, and secondly, to the fact that the continental biota initially formed as a marginal portion of the marine biota, rather than a separate system. The hyperbolic dynamics is most prominent when both marine and continental biotas are considered together. This fact can be interpreted as a proof of the integrated nature of the biosphere. In the macrosociological
A Taylor weak-statement algorithm for hyperbolic conservation laws
Baker, A. J.; Kim, J. W.
1987-01-01
Finite element analysis, applied to computational fluid dynamics (CFD) problem classes, presents a formal procedure for establishing the ingredients of a discrete approximation numerical solution algorithm. A classical Galerkin weak-statement formulation, formed on a Taylor series extension of the conservation law system, is developed herein that embeds a set of parameters eligible for constraint according to specification of suitable norms. The derived family of Taylor weak statements is shown to contain, as special cases, over one dozen independently derived CFD algorithms published over the past several decades for the high speed flow problem class. A theoretical analysis is completed that facilitates direct qualitative comparisons. Numerical results for definitive linear and nonlinear test problems permit direct quantitative performance comparisons.
Dynamical zeta functions and dynamical determinants for hyperbolic maps a functional approach
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...
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
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)
Doubly stratified MHD tangent hyperbolic nanofluid flow due to permeable stretched cylinder
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.
Free vibration of laminated composite stiffened hyperbolic paraboloid shell panel with cutout
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.
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.
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.
Near-field radiative heat transfer between graphene-covered hyperbolic metamaterials
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.
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.
A graphene Zener-Klein transistor cooled by a hyperbolic substrate
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.
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.
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
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)
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.
Strong coupling of collection of emitters on hyperbolic meta-material
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.
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.
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
A mathematical framework for inverse wave problems in heterogeneous media
Blazek, K.D.; Stolk, C.; Symes, W.W.
2013-01-01
This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The coefficients of these time-dependent partial differential equations
Finite difference techniques for nonlinear hyperbolic conservation laws
International Nuclear Information System (INIS)
Sanders, R.
1985-01-01
The present study is concerned with numerical approximations to the initial value problem for nonlinear systems of conservative laws. Attention is given to the development of a class of conservation form finite difference schemes which are based on the finite volume method (i.e., the method of averages). These schemes do not fit into the classical framework of conservation form schemes discussed by Lax and Wendroff (1960). The finite volume schemes are specifically intended to approximate solutions of multidimensional problems in the absence of rectangular geometries. In addition, the development is reported of different schemes which utilize the finite volume approach for time discretization. Particular attention is given to local time discretization and moving spatial grids. 17 references
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.
Hyperbolically Patterned 3D Graphene Metamaterial with Negative Poisson's Ratio and Superelasticity.
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.
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
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.
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 ...
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.
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.
Coexistence of critical orbit types in sub-hyperbolic polynomial maps
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.
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.
Method of construction of the Riemann function for a second-order hyperbolic equation
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.
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....
Geometry in a dynamical system without space: Hyperbolic Geometry in Kuramoto Oscillator Systems
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.
Long-range propagation of plasmon and phonon polaritons in hyperbolic-metamaterial waveguides
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.
Dynamic hyperbolic geometry: building intuition and understanding mediated by a Euclidean model
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.
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.
International Nuclear Information System (INIS)
Yee, H.C.; Shinn, J.L.
1986-12-01
Some numerical aspects of finite-difference algorithms for nonlinear multidimensional hyperbolic conservation laws with stiff nonhomogenous (source) terms are discussed. If the stiffness is entirely dominated by the source term, a semi-implicit shock-capturing method is proposed provided that the Jacobian of the source terms possesses certain properties. The proposed semi-implicit method can be viewed as a variant of the Bussing and Murman point-implicit scheme with a more appropriate numerical dissipation for the computation of strong shock waves. However, if the stiffness is not solely dominated by the source terms, a fully implicit method would be a better choice. The situation is complicated by problems that are higher than one dimension, and the presence of stiff source terms further complicates the solution procedures for alternating direction implicit (ADI) methods. Several alternatives are discussed. The primary motivation for constructing these schemes was to address thermally and chemically nonequilibrium flows in the hypersonic regime. Due to the unique structure of the eigenvalues and eigenvectors for fluid flows of this type, the computation can be simplified, thus providing a more efficient solution procedure than one might have anticipated
International Nuclear Information System (INIS)
Yee, H.C.; Shinn, J.L.
1987-01-01
Some numerical aspects of finite-difference algorithms for nonlinear multidimensional hyperbolic conservation laws with stiff nonhomogeneous (source) terms are discussed. If the stiffness is entirely dominated by the source term, a semi-implicit shock-capturing method is proposed provided that the Jacobian of the source terms possesses certain properties. The proposed semi-implicit method can be viewed as a variant of the Bussing and Murman point-implicit scheme with a more appropriate numerical dissipation for the computation of strong shock waves. However, if the stiffness is not solely dominated by the source terms, a fully implicit method would be a better choice. The situation is complicated by problems that are higher than one dimension, and the presence of stiff source terms further complicates the solution procedures for alternating direction implicit (ADI) methods. Several alternatives are discussed. The primary motivation for constructing these schemes was to address thermally and chemically nonequilibrium flows in the hypersonic regime. Due to the unique structure of the eigenvalues and eigenvectors for fluid flows of this type, the computation can be simplified, thus providing a more efficient solution procedure than one might have anticipated. 46 references
Optimal consumption problem in the Vasicek model
Directory of Open Access Journals (Sweden)
Jakub Trybuła
2015-01-01
Full Text Available We consider the problem of an optimal consumption strategy on the infinite time horizon based on the hyperbolic absolute risk aversion utility when the interest rate is an Ornstein-Uhlenbeck process. Using the method of subsolution and supersolution we obtain the existence of solutions of the dynamic programming equation. We illustrate the paper with a numerical example of the optimal consumption strategy and the value function.
Hyperbolicity of the Nonlinear Models of Maxwell's Equations
Serre, Denis
. We consider the class of nonlinear models of electromagnetism that has been described by Coleman & Dill [7]. A model is completely determined by its energy density W(B,D). Viewing the electromagnetic field (B,D) as a 3×2 matrix, we show that polyconvexity of W implies the local well-posedness of the Cauchy problem within smooth functions of class Hs with s>1+d/2. The method follows that designed by Dafermos in his book [9] in the context of nonlinear elasticity. We use the fact that B×D is a (vectorial, non-convex) entropy, and we enlarge the system from 6 to 9 equations. The resulting system admits an entropy (actually the energy) that is convex. Since the energy conservation law does not derive from the system of conservation laws itself (Faraday's and Ampère's laws), but also needs the compatibility relations divB=divD=0 (the latter may be relaxed in order to take into account electric charges), the energy density is not an entropy in the classical sense. Thus the system cannot be symmetrized, strictly speaking. However, we show that the structure is close enough to symmetrizability, so that the standard estimates still hold true.
Global nonexistence results for a class of hyperbolic systems
Said-Houari, Belkacem
2011-12-01
Our concern in this paper is to prove blow-up results to the non-autonomous nonlinear system of wave equations utt-Δu=a(t,x)| v|p,vtt-Δv=b(t,x)|u|q,t>0, x∈RN in any space dimension. We show that a curve F̃(p,q)=0 depending on the space dimension, on the exponents p,q and on the behavior of the functions a(t,x) and b(t,x) exists, such that all nontrivial solutions to the above system blow-up in a finite time whenever F̃(p,q)>0. Our method of proof uses some estimates developed by Galaktionov and Pohozaev in [11] for a single non-autonomous wave equation enabling us to obtain a system of ordinary differential inequalities from which the desired result is derived. Our result generalizes some important results such as the ones in Del Santo et al. (1996) [12] and Galaktionov and Pohozaev (2003) [11]. The advantage here is that our result applies to a wide variety of problems. © 2011 Elsevier Ltd. All rights reserved.
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.
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)
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....
A fast computing method to distinguish the hyperbolic trajectory of an non-autonomous system
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)
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)
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.
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
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.
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.
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.
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
Wideband absorption in one dimensional photonic crystal with graphene-based hyperbolic metamaterials
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.
The Split Coefficient Matrix method for hyperbolic systems of gasdynamic equations
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.
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)
Out-of-plane heat transfer in van der Waals stacks through electron-hyperbolic phonon coupling
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.
Directory of Open Access Journals (Sweden)
Wubshet Ibrahim
Full Text Available This article presents the effect of thermal radiation on magnetohydrodynamic flow of tangent hyperbolic fluid with nanoparticle past an enlarging sheet with second order slip and convective boundary condition. Condition of zero normal flux of nanoparticles at the wall is used for the concentration boundary condition, which is the current topic that have yet to be studied extensively. The solution for the velocity, temperature and nanoparticle concentration is governed by parameters viz. power-law index (n, Weissenberg number We, Biot number Bi, Prandtl number Pr, velocity slip parameters δ and γ, Lewis number Le, Brownian motion parameter Nb and the thermophoresis parameter Nt. Similarity transformation is used to metamorphosed the governing non-linear boundary-value problem into coupled higher order non-linear ordinary differential equation. The succeeding equations were numerically solved using the function bvp4c from the matlab for different values of emerging parameters. Numerical results are deliberated through graphs and tables for velocity, temperature, concentration, the skin friction coefficient and local Nusselt number. The results designate that the skin friction coefficient Cf deplete as the values of Weissenberg number We, slip parameters γ and δ upturn and it rises as the values of power-law index n increase. The local Nusselt number -θ′(0 decreases as slip parameters γ and δ, radiation parameter Nr, Weissenberg number We, thermophoresis parameter Nt and power-law index n increase. However, the local Nusselt number increases as the Biot number Bi increase. Keywords: Tangent hyperbolic fluid, Second order slip flow, MHD, Convective boundary condition, Radiation effect, Passive control of nanoparticles
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
Hyperbolic umbilic caustics from oblate water drops with tilted illumination: Observations
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.
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
Probing low-energy hyperbolic polaritons in van der Waals crystals with an electron microscope.
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
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.
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.
On the Smooth Dependence of SRB Measures for Partially Hyperbolic Systems
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).
Gupta-Bleuler Quantization of the Maxwell Field in Globally Hyperbolic Space-Times
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.
Local bounds preserving stabilization for continuous Galerkin discretization of hyperbolic systems
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.
Probing low-energy hyperbolic polaritons in van der Waals crystals with an electron microscope
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.
A novel grid multiwing chaotic system with only non-hyperbolic equilibria
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.
Directory of Open Access Journals (Sweden)
Wang Xujing
2008-08-01
Full Text Available Abstract Background Insulin, the principal regulating hormone of blood glucose, is released through the bursting of the pancreatic islets. Increasing evidence indicates the importance of islet morphostructure in its function, and the need of a quantitative investigation. Recently we have studied this problem from the perspective of islet bursting of insulin, utilizing a new 3D hexagonal closest packing (HCP model of islet structure that we have developed. Quantitative non-linear dependence of islet function on its structure was found. In this study, we further investigate two key structural measures: the number of neighboring cells that each β-cell is coupled to, nc, and the coupling strength, gc. Results β-cell clusters of different sizes with number of β-cells nβ ranging from 1–343, nc from 0–12, and gc from 0–1000 pS, were simulated. Three functional measures of islet bursting characteristics – fraction of bursting β-cells fb, synchronization index λ, and bursting period Tb, were quantified. The results revealed a hyperbolic dependence on the combined effect of nc and gc. From this we propose to define a dimensionless cluster coupling index or CCI, as a composite measure for islet morphostructural integrity. We show that the robustness of islet oscillatory bursting depends on CCI, with all three functional measures fb, λ and Tb increasing monotonically with CCI when it is small, and plateau around CCI = 1. Conclusion CCI is a good islet function predictor. It has the potential of linking islet structure and function, and providing insight to identify therapeutic targets for the preservation and restoration of islet β-cell mass and function.
Waves in hyperbolic and double negative metamaterials including rogues and solitons
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
The topics here deal with some current progress in electromagnetic wave propagation in a family of substances known as metamaterials. To begin with, it is discussed how a pulse can develop a leading edge that steepens and it is emphasised that such self-steepening is an important inclusion within a metamaterial environment together with Raman scattering and third-order dispersion whenever very short pulses are being investigated. It is emphasised that the self-steepening parameter is highly metamaterial-driven compared to Raman scattering, which is associated with a coefficient of the same form whether a normal positive phase, or a metamaterial waveguide is the vehicle for any soliton propagation. It is also shown that the influence of magnetooptics provides a beautiful and important control mechanism for metamaterial devices and that, in the future, this feature will have a significant impact upon the design of data control systems for optical computing. A major objective is fulfiled by the investigations of the fascinating properties of hyperbolic media that exhibit asymmetry of supported modes due to the tilt of optical axes. This is a topic that really merits elaboration because structural and optical asymmetry in optical components that end up manipulating electromagnetic waves is now the foundation of how to operate some of the most successful devices in photonics and electronics. It is pointed out, in this context, that graphene is one of the most famous plasmonic media with very low losses. It is a two-dimensional material that makes the implementation of an effective-medium approximation more feasible. Nonlinear non-stationary diffraction in active planar anisotropic hyperbolic metamaterials is discussed in detail and two approaches are compared. One of them is based on the averaging over a unit cell, while the other one does not include sort of averaging. The formation and propagation of optical spatial solitons in hyperbolic metamaterials is also
The seismic reflection inverse problem
International Nuclear Information System (INIS)
Symes, W W
2009-01-01
The seismic reflection method seeks to extract maps of the Earth's sedimentary crust from transient near-surface recording of echoes, stimulated by explosions or other controlled sound sources positioned near the surface. Reasonably accurate models of seismic energy propagation take the form of hyperbolic systems of partial differential equations, in which the coefficients represent the spatial distribution of various mechanical characteristics of rock (density, stiffness, etc). Thus the fundamental problem of reflection seismology is an inverse problem in partial differential equations: to find the coefficients (or at least some of their properties) of a linear hyperbolic system, given the values of a family of solutions in some part of their domains. The exploration geophysics community has developed various methods for estimating the Earth's structure from seismic data and is also well aware of the inverse point of view. This article reviews mathematical developments in this subject over the last 25 years, to show how the mathematics has both illuminated innovations of practitioners and led to new directions in practice. Two themes naturally emerge: the importance of single scattering dominance and compensation for spectral incompleteness by spatial redundancy. (topical review)
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
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)
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.
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.
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%
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.
A highly sensitive multiplasmonic sensor using hyperbolic chiral sculptured thin films
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.
Chaotic Dynamics in Smart Grid and Suppression Scheme via Generalized Fuzzy Hyperbolic Model
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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.
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.
International Nuclear Information System (INIS)
Alabau-Boussouira, Fatiha
2005-01-01
This work is concerned with the stabilization of hyperbolic systems by a nonlinear feedback which can be localized on a part of the boundary or locally distributed. We show that general weighted integral inequalities together with convexity arguments allow us to produce a general semi-explicit formula which leads to decay rates of the energy in terms of the behavior of the nonlinear feedback close to the origin. This formula allows us to unify for instance the cases where the feedback has a polynomial growth at the origin, with the cases where it goes exponentially fast to zero at the origin. We also give three other significant examples of nonpolynomial growth at the origin. We also prove the optimality of our results for the one-dimensional wave equation with nonlinear boundary dissipation. The key property for obtaining our general energy decay formula is the understanding between convexity properties of an explicit function connected to the feedback and the dissipation of energy
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)
Kim, Sungryul; Yoo, Younghwan
2018-01-26
Medium Access Control (MAC) delay which occurs between the anchor node's transmissions is one of the error sources in underwater localization. In particular, in AUV localization, the MAC delay significantly degrades the ranging accuracy. The Cramer-Rao Low Bound (CRLB) definition theoretically proves that the MAC delay significantly degrades the localization performance. This paper proposes underwater localization combined with multiple access technology to decouple the localization performance from the MAC delay. Towards this goal, we adopt hyperbolic frequency modulation (HFM) signal that provides multiplexing based on its good property, high-temporal correlation. Owing to the multiplexing ability of the HFM signal, the anchor nodes can transmit packets without MAC delay, i.e., simultaneous transmission is possible. In addition, the simulation results show that the simultaneous transmission is not an optional communication scheme, but essential for the localization of mobile object in underwater.
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...
Enhanced spin Hall effect of tunneling light in hyperbolic metamaterial waveguide.
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.
A second-order iterative implicit-explicit hybrid scheme for hyperbolic systems of conservation laws
International Nuclear Information System (INIS)
Dai, Wenlong; Woodward, P.R.
1996-01-01
An iterative implicit-explicit hybrid scheme is proposed for hyperbolic systems of conservation laws. Each wave in a system may be implicitly, or explicitly, or partially implicitly and partially explicitly treated depending on its associated Courant number in each numerical cell, and the scheme is able to smoothly switch between implicit and explicit calculations. The scheme is of Godunov-type in both explicit and implicit regimes, is in a strict conservation form, and is accurate to second-order in both space and time for all Courant numbers. The computer code for the scheme is easy to vectorize. Multicolors proposed in this paper may reduce the number of iterations required to reach a converged solution by several orders for a large time step. The feature of the scheme is shown through numerical examples. 38 refs., 12 figs
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
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
International Nuclear Information System (INIS)
Shang Yadong
2008-01-01
The extended hyperbolic functions method for nonlinear wave equations is presented. Based on this method, we obtain a multiple exact explicit solutions for the nonlinear evolution equations which describe the resonance interaction between the long wave and the short wave. The solutions obtained in this paper include (a) the solitary wave solutions of bell-type for S and L, (b) the solitary wave solutions of kink-type for S and bell-type for L, (c) the solitary wave solutions of a compound of the bell-type and the kink-type for S and L, (d) the singular travelling wave solutions, (e) periodic travelling wave solutions of triangle function types, and solitary wave solutions of rational function types. The variety of structure to the exact solutions of the long-short wave equation is illustrated. The methods presented here can also be used to obtain exact solutions of nonlinear wave equations in n dimensions
A Synthesizable VHDL Model of the Exact Solution for Three-dimensional Hyperbolic Positioning System
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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.
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.
Energy Technology Data Exchange (ETDEWEB)
Keilacker, H; Becker, G; Ziegler, M; Gottschling, H D [Zentralinstitut fuer Diabetes, Karlsburg (German Democratic Republic)
1980-10-01
In order to handle all types of radioimmunoassay (RIA) calibration curves obtained in the authors' laboratory in the same way, they tried to find a non-linear expression for their regression which allows calibration curves with different degrees of curvature to be fitted. Considering the two boundary cases of the incubation protocol they derived a hyperbolic inverse regression function: x = a/sub 1/y + a/sub 0/ + asub(-1)y/sup -1/, where x is the total concentration of antigen, asub(i) are constants, and y is the specifically bound radioactivity. An RIA evaluation procedure based on this function is described providing a fitted inverse RIA calibration curve and some statistical quality parameters. The latter are of an order which is normal for RIA systems. There is an excellent agreement between fitted and experimentally obtained calibration curves having a different degree of curvature.
Cosmology in the laboratory: An analogy between hyperbolic metamaterials and the Milne universe
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.
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.
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.
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
Numerical models for differential problems
Quarteroni, Alfio
2017-01-01
In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods, and reduced basis methods. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, an...
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
1994-07-25
Astrophysik are investigated numerically. These collisions do not seem to Karl - Schwarzschild -str., 1, D-85470 Garching, Germany be elastic. On the other hand...Astrophysak, Departamento de Matemdtsca Aplscada y Astronomia Karl -Schwaarzschild-Str. i Universadad de Valencia 85740 Garching bes Munchen. Germany "E...the R-W metric to the empty space Schwarzschild metric, and since in this cae mass and momentum cannot cross the interface, (which in this case models
1988-01-01
e’l EIl-i1s Finlis t-riaigunires. in lIr(’larationi. [3] BIABA K., TABATA Ni.. On a conservattive upiwind finite element. scheme for convective...illproveliaeait11 1.o I-lie algonil i,, t.11vi midor rer.1i11 i’oii.it ions we Call prove HIint, lIii :tbove we~ak s’. hit ion satisli"s ent ropy coificjin for ny ci...propagates down the duct (Figs. 2e,f). It is believed, that the very high pressures and temperatures, which appear when the triple wave hits the walls
1988-07-08
Marcus and C. Baczynski), Computer Science Press, Rockville, Maryland, 1986. 3. An Introduction to Pascal and Precalculus , Computer Science Press...Science Press, Rockville, Maryland, 1986. 35. An Introduction to Pascal and Precalculus , Computer Science Press, Rockville, Maryland, 1986. 36
Geevers, Sjoerd; van der Vegt, J.J.W.
2017-01-01
We present sharp and sucient bounds for the interior penalty term and time step size to ensure stability of the symmetric interior penalty discontinuous Galerkin (SIPDG) method combined with an explicit time-stepping scheme. These conditions hold for generic meshes, including unstructured
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
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.)
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.)
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.
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.
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.
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.
EXISTENCE AND UNIQUENESS OF THE ENTROPY SOLUTION TO A NONLINEAR HYPERBOLIC EQUATION
Institute of Scientific and Technical Information of China (English)
R.EYMARD; T.Gallouёt; R.Herbin
1995-01-01
This work is concerned with the proof of the existence and uniqueness of the entropy weak solution to the following nonlinear hyperbolic equation: ut+div(vf(u)） = 0 in IRN×（0, T）, with initial data u(-, 0) = u0(-) in IRN, where u0 ∈ L∞（IRN) is a given function, v is a divergence-free bounded fnnction of class C1 from IRN × [0, T] to IRN, and f is a 5motion of class C1 from IR to IR. It also gives a result of convergence of a numerical scheme for the discretization of this equation. The authors first show the existence of a “process” solution (which generalizes the concept of entropy weak solutions, and can be obtained by passing to the limit of solutions ofthe numerical scheme). The uniqueness of this entropy process solution is then proven; it isalso proven that the entropy process solution is in fact an entropy weak solution. Hence the existence and uniqueness of the entropy weak solution are proven.
Directory of Open Access Journals (Sweden)
Laurendeau Christine
2009-01-01
Full Text Available A malicious insider in a wireless network may carry out a number of devastating attacks without fear of retribution, since the messages it broadcasts are authenticated with valid credentials such as a digital signature. In attributing an attack message to its perpetrator by localizing the signal source, we can make no presumptions regarding the type of radio equipment used by a malicious transmitter, including the transmitting power utilized to carry out an exploit. Hyperbolic position bounding (HPB provides a mechanism to probabilistically estimate the candidate location of an attack message's originator using received signal strength (RSS reports, without assuming knowledge of the transmitting power. We specialize the applicability of HPB into the realm of vehicular networks and provide alternate HPB algorithms to improve localization precision and computational efficiency. We extend HPB for tracking the consecutive locations of a mobile attacker. We evaluate the localization and tracking performance of HPB in a vehicular scenario featuring a variable number of receivers and a known navigational layout. We find that HPB can position a transmitting device within stipulated guidelines for emergency services localization accuracy.
Friedline, Terri; Masa, Rainier D; Chowa, Gina A N
2015-01-01
The natural log and categorical transformations commonly applied to wealth for meeting the statistical assumptions of research may not always be appropriate for adjusting for skewness given wealth's unique properties. Finding and applying appropriate transformations is becoming increasingly important as researchers consider wealth as a predictor of well-being. We present an alternative transformation-the inverse hyperbolic sine (IHS)-for simultaneously dealing with skewness and accounting for wealth's unique properties. Using the relationship between household wealth and youth's math achievement as an example, we apply the IHS transformation to wealth data from US and Ghanaian households. We also explore non-linearity and accumulation thresholds by combining IHS transformed wealth with splines. IHS transformed wealth relates to youth's math achievement similarly when compared to categorical and natural log transformations, indicating that it is a viable alternative to other transformations commonly used in research. Non-linear relationships and accumulation thresholds emerge that predict youth's math achievement when splines are incorporated. In US households, accumulating debt relates to decreases in math achievement whereas accumulating assets relates to increases in math achievement. In Ghanaian households, accumulating assets between the 25th and 50th percentiles relates to increases in youth's math achievement. Copyright © 2014 Elsevier Inc. All rights reserved.
The hidden hyperbolic geometry of international trade: World Trade Atlas 1870-2013.
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.
The hidden hyperbolic geometry of international trade: World Trade Atlas 1870–2013
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
Unsplit schemes for hyperbolic conservation laws with source terms in one space dimension
International Nuclear Information System (INIS)
Papalexandris, M.V.; Leonard, A.; Dimotakis, P.E.
1997-01-01
The present work is concerned with an application of the theory of characteristics to conservation laws with source terms in one space dimension, such as the Euler equations for reacting flows. Space-time paths are introduced on which the flow/chemistry equations decouple to a characteristic set of ODE's for the corresponding homogeneous laws, thus allowing the introduction of functions analogous to the Riemann invariants in classical theory. The geometry of these paths depends on the spatial gradients of the solution. This particular decomposition can be used in the design of efficient unsplit algorithms for the numerical integration of the equations. As a first step, these ideas are implemented for the case of a scalar conservation law with a nonlinear source term. The resulting algorithm belongs to the class of MUSCL-type, shock-capturing schemes. Its accuracy and robustness are checked through a series of tests. The stiffness of the source term is also studied. Then, the algorithm is generalized for a system of hyperbolic equations, namely the Euler equations for reacting flows. A numerical study of unstable detonations is performed. 57 refs
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)
Stress hormones predict hyperbolic time-discount rates six months later in adults.
Takahashi, Taiki; Shinada, Mizuho; Inukai, Keigo; Tanida, Shigehito; Takahashi, Chisato; Mifune, Nobuhiro; Takagishi, Haruto; Horita, Yutaka; Hashimoto, Hirofumi; Yokota, Kunihiro; Kameda, Tatsuya; Yamagishi, Toshio
2010-01-01
Stress hormones have been associated with temporal discounting. Although time-discount rate is shown to be stable over a long term, no study to date examines whether individual differences in stress hormones could predict individuals' time-discount rates in the relatively distant future (e.g., six month later), which is of interest in neuroeconomics of stress-addiction association. We assessed 87 participants' salivary stress hormone (cortisol, cortisone, and alpha-amylase) levels and hyperbolic discounting of delayed rewards consisting of three magnitudes, at the time-interval of six months. For salivary steroid assays, we employed a liquid chromatography/ mass spectroscopy (LC/MS) method. The correlations between the stress hormone levels and time-discount rates were examined. We observed that salivary alpha-amylase (sAA) levels were negatively associated with time-discount rates in never-smokers. Notably, salivary levels of stress steroids (i.e., cortisol and cortisone) negatively and positively related to time-discount rates in men and women, respectively, in never-smokers. Ever-smokers' discount rates were not predicted from these stress hormone levels. Individual differences in stress hormone levels predict impulsivity in temporal discounting in the future. There are sex differences in the effect of stress steroids on temporal discounting; while there was no sex defference in the relationship between sAA and temporal discounting.
Gong, Xiangbo; Feng, Fei; Jiao, Xuming; Wang, Shengchao
2017-10-01
Simultaneous seismic source separation, also known as deblending, is an essential process for blended acquisition. With the assumption that the blending noise is coherent in the common shot domain but is incoherent in other domains, traditional deblending methods are commonly performed in the common receiver, common midpoint or common offset domain. In this paper, we propose an improved apex-shifted hyperbolic radon transform (ASHRT) to deblend directly in the common shot domain. A time-axis stretch strategy named Stolt-stretch is introduced to overcome the limitation of the constant velocity assumption of Stolt-based operators. To improve the sparsity in the transform domain, a total variation (TV) norm inversion is implemented to enhance the energy convergence in the radon panel. Because of highly efficient Stolt migration and the demigration operator in the frequency-wavenumber domain, as well as the flexible geometry condition of the source-receiver, this approach is quite suitable for quality control (QC) during streamer acquisition. The synthetic and field examples demonstrate that our proposition is robust and efficient.
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.
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.
User's manual for the HYPGEN hyperbolic grid generator and the HGUI graphical user interface
Chan, William M.; Chiu, Ing-Tsau; Buning, Pieter G.
1993-01-01
The HYPGEN program is used to generate a 3-D volume grid over a user-supplied single-block surface grid. This is accomplished by solving the 3-D hyperbolic grid generation equations consisting of two orthogonality relations and one cell volume constraint. In this user manual, the required input files and parameters and output files are described. Guidelines on how to select the input parameters are given. Illustrated examples are provided showing a variety of topologies and geometries that can be treated. HYPGEN can be used in stand-alone mode as a batch program or it can be called from within a graphical user interface HGUI that runs on Silicon Graphics workstations. This user manual provides a description of the menus, buttons, sliders, and typein fields in HGUI for users to enter the parameters needed to run HYPGEN. Instructions are given on how to configure the interface to allow HYPGEN to run either locally or on a faster remote machine through the use of shell scripts on UNIX operating systems. The volume grid generated is copied back to the local machine for visualization using a built-in hook to PLOT3D.
Directory of Open Access Journals (Sweden)
M. Ali Abbas
2016-03-01
Full Text Available In this present analysis, three dimensional peristaltic flow of hyperbolic tangent fluid in a non-uniform channel has been investigated. We have considered that the pressure is uniform over the whole cross section and the interial effects have been neglected. For this purpose we consider laminar flow under the assumptions of long wavelength (λ→∞ and creeping flow (Re→0 approximations. The attained highly nonlinear equations are solved with the help of Homotopy perturbation method. The influence of various physical parameters of interest is demonstrated graphically for wall tension, mass characterization, damping nature of the wall, wall rigidity, wall elastance, aspect ratio and the Weissenberg number. In this present investigation we found that the magnitude of the velocity is maximum in the center of the channel whereas it is minimum near the walls. Stream lines are also drawn to discuss the trapping mechanism for all the physical parameters. Comparison has also been presented between Newtonian and non-Newtonian fluid.
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.
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.
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.
A Hyperbolic Ontology Visualization Tool for Model Application Programming Interface Documentation
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.
International Nuclear Information System (INIS)
Olson, T.S.; Hiscock, W.A.
1990-01-01
Stability and causality are studied for linear perturbations about equilibrium in Carter's ''regular'' theory of relativistic heat-conducting fluids. The ''regular'' theory, when linearized around an equilibrium state having vanishing expansion and shear, is shown to be equivalent to the inviscid limit of the linearized Israel-Stewart theory of relativistic dissipative fluids for a particular choice of the second-order coefficients β 1 and γ 2 . A set of stability conditions is determined for linear perturbations of a general inviscid Israel-Stewart fluid using a monotonically decreasing energy functional. It is shown that, as in the viscous case, stability implies that the characteristic velocities are subluminal and that perturbations obey hyperbolic equations. The converse theorem is also true. We then apply this analysis to a nonrelativistic Boltzmann gas and to a strongly degenerate free Fermi gas in the ''regular'' theory. Carter's ''regular'' theory is shown to be incapable of correctly describing the nonrelativistic Boltzmann gas and the degenerate Fermi gas (at all temperatures)
Contractive type non-self mappings on metric spaces of hyperbolic type
Ciric, Ljubomir B.
2006-05-01
Let (X,d) be a metric space of hyperbolic type and K a nonempty closed subset of X. In this paper we study a class of mappings from K into X (not necessarily self-mappings on K), which are defined by the contractive condition (2.1) below, and a class of pairs of mappings from K into X which satisfy the condition (2.28) below. We present fixed point and common fixed point theorems which are generalizations of the corresponding fixed point theorems of Ciric [L.B. Ciric, Quasi-contraction non-self mappings on Banach spaces, Bull. Acad. Serbe Sci. Arts 23 (1998) 25-31; L.B. Ciric, J.S. Ume, M.S. Khan, H.K.T. Pathak, On some non-self mappings, Math. Nachr. 251 (2003) 28-33], Rhoades [B.E. Rhoades, A fixed point theorem for some non-self mappings, Math. Japon. 23 (1978) 457-459] and many other authors. Some examples are presented to show that our results are genuine generalizations of known results from this area.
Directory of Open Access Journals (Sweden)
Vebil Yıldırım
2017-10-01
Full Text Available A broad parametric study is carried out to investigate the effects of both the inhomogeneity parameter, and a profile index of Stodola’s hyperbolic function on the static response of such structures subjected to both the inner and outer pressures. The investigation is based on the analytical formulas lately published by the author. The effects of those parameters on the variation of the radial displacement, the radial and hoop stresses are all graphically illustrated for an annulus pressurized at its both surfaces. It is observed that, especially, the variation of the hoop stress in radial coordinate is closely sensible to variation of those parameters. For the chosen problems it was observed that one of two materials whose Young’s modulus is higher than the other is better to locate at the inner surface of the disc having divergent profile to get reasonable maximum hoop stresses. However much smaller radial displacements may be obtained by using positive inhomogeneity indexes for all discs whose surfaces host a material whose Young’s modulus is smaller than the other. To reach a final decision, analytical formulas such as those used in the present study together with a failure criteria such as Von Mises and Tresca become indispensable means in a design process.
Qayyum, Sajid; Hayat, Tasawar; Shehzad, Sabir Ali; Alsaedi, Ahmed
2018-03-01
This article concentrates on the magnetohydrodynamic (MHD) stagnation point flow of tangent hyperbolic nanofluid in the presence of buoyancy forces. Flow analysis caused due to stretching surface. Characteristics of heat transfer are examined under the influence of thermal radiation and heat generation/absorption. Newtonian conditions for heat and mass transfer are employed. Nanofluid model includes Brownian motion and thermophoresis. The governing nonlinear partial differential systems of the problem are transformed into a systems of nonlinear ordinary differential equations through appropriate variables. Impact of embedded parameters on the velocity, temperature and nanoparticle concentration fields are presented graphically. Numerical computations are made to obtain the values of skin friction coefficient, local Nusselt and Sherwood numbers. It is concluded that velocity field enhances in the frame of mixed convection parameter while reverse situation is observed due to power law index. Effect of Brownian motion parameter on the temperature and heat transfer rate is quite reverse. Moreover impact of solutal conjugate parameter on the concentration and local Sherwood number is quite similar.
Bilyeu, David
This dissertation presents an extension of the Conservation Element Solution Element (CESE) method from second- to higher-order accuracy. The new method retains the favorable characteristics of the original second-order CESE scheme, including (i) the use of the space-time integral equation for conservation laws, (ii) a compact mesh stencil, (iii) the scheme will remain stable up to a CFL number of unity, (iv) a fully explicit, time-marching integration scheme, (v) true multidimensionality without using directional splitting, and (vi) the ability to handle two- and three-dimensional geometries by using unstructured meshes. This algorithm has been thoroughly tested in one, two and three spatial dimensions and has been shown to obtain the desired order of accuracy for solving both linear and non-linear hyperbolic partial differential equations. The scheme has also shown its ability to accurately resolve discontinuities in the solutions. Higher order unstructured methods such as the Discontinuous Galerkin (DG) method and the Spectral Volume (SV) methods have been developed for one-, two- and three-dimensional application. Although these schemes have seen extensive development and use, certain drawbacks of these methods have been well documented. For example, the explicit versions of these two methods have very stringent stability criteria. This stability criteria requires that the time step be reduced as the order of the solver increases, for a given simulation on a given mesh. The research presented in this dissertation builds upon the work of Chang, who developed a fourth-order CESE scheme to solve a scalar one-dimensional hyperbolic partial differential equation. The completed research has resulted in two key deliverables. The first is a detailed derivation of a high-order CESE methods on unstructured meshes for solving the conservation laws in two- and three-dimensional spaces. The second is the code implementation of these numerical methods in a computer code. For
One-dimensional inverse problems of mathematical physics
Lavrent'ev, M M; Yakhno, V G; Schulenberger, J R
1986-01-01
This monograph deals with the inverse problems of determining a variable coefficient and right side for hyperbolic and parabolic equations on the basis of known solutions at fixed points of space for all times. The problems are one-dimensional in nature since the desired coefficient of the equation is a function of only one coordinate, while the desired right side is a function only of time. The authors use methods based on the spectral theory of ordinary differential operators of second order and also methods which make it possible to reduce the investigation of the inverse problems to the in
Directory of Open Access Journals (Sweden)
Guo Chun Wen
2009-05-01
Full Text Available This article concerns the oblique derivative problems for second-order quasilinear degenerate equations of mixed type with several characteristic boundaries, which include the Tricomi problem as a special case. First we formulate the problem and obtain estimates of its solutions, then we show the existence of solutions by the successive iterations and the Leray-Schauder theorem. We use a complex analytic method: elliptic complex functions are used in the elliptic domain, and hyperbolic complex functions in the hyperbolic domain, such that second-order equations of mixed type with degenerate curve are reduced to the first order mixed complex equations with singular coefficients. An application of the complex analytic method, solves (1.1 below with $m=n=1$, $a=b=0$, which was posed as an open problem by Rassias.
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
Searching spectrum points of difference initial-boundary value problems with using GAS
International Nuclear Information System (INIS)
Mazepa, N.E.
1989-01-01
A new algorithm for searching spectrum points is proposed. The difference schemes which approximate systems of linear differential equations of hyperbolic type with constant coefficients and in one space dimension are considered. For important class of practiclas problems this algorithm reduces the hard spectrum calculation problem to the polynomial equation solution. For complicated analytic manipulations connected with realization of this algorithm the computation algebraic system REDUCE is used. 28 refs
Slow Integral Manifolds and Control Problems in Critical and Twice Critical Cases
International Nuclear Information System (INIS)
Sobolev, Vladimir
2016-01-01
We consider singularly perturbed differential systems in cases where the standard theory to establish a slow integral manifold existence does not work. The theory has traditionally dealt only with perturbation problems near normally hyperbolic manifold of singularities and this manifold is supposed to isolated. Applying transformations we reduce the original singularly perturbed problem to a regularized one such that the existence of slow integral manifolds can be established by means of the standard theory. We illustrate our approach by several examples. (paper)
Hyperbolicity and integral expression of the Lyapunov exponents for linear cocycles
Dai, Xiongping
Consider in this paper a linear skew-product system (θ,Θ) :T×W×R→W×R; (t,w,x)↦(tw,Θ(t,w)ṡx) where T=R or Z, and θ :(t,w)↦tw is a topological dynamical system on a compact metrizable space W, and where Θ(t,w)∈GL(n,R) satisfies the cocycle condition based on θ and is continuously differentiable in t if T=R. We show that 'semi λ-exponential dichotomy' of (θ,Θ) implies ' λ-exponential dichotomy.' Precisely, if Θ has no Lyapunov exponent λ and is almost uniformly λ-contracting along the λ-stable direction E(w;λ) and if dimE(w;λ) is constant a.e., then Θ is almost λ-exponentially dichotomous. To prove this, we first use Liao's spectrum theorem, which gives integral expression of the Lyapunov exponents, and then use the semi-uniform ergodic theorem by Sturman and Stark, which allows one to derive uniform estimates from nonuniform ones. As a consequence, we obtain the open-and-dense hyperbolicity of eventual GL(2,R)-cocycles based on a uniquely ergodic endomorphism, and of GL(2,R)-cocycles based on a uniquely ergodic equi-continuous endomorphism, respectively. On the other hand, in the sense of C-topology we obtain the density of SL(2,R)-cocycles having positive Lyapunov exponent based on a minimal subshift satisfying the Boshernitzan condition.
Zhang, Wen; Shi, Jie; Yu, Jun; Zhan, Liang; Thompson, Paul M.; Wang, Yalin
2017-01-01
In order to improve the preclinical diagnose of Alzheimer's disease (AD), there is a great deal of interest in analyzing the AD related brain structural changes with magnetic resonance image (MRI) analyses. As the major features, variation of the structural connectivity and the cortical surface morphometry provide different views of structural changes to determine whether AD is present on presymptomatic patients. However, the large scale tensor-valued information and relatively low imaging resolution in diffusion MRI (dMRI) have created huge challenges for analysis. In this paper, we propose a novel framework that improves dMRI analysis power by fusing cortical surface morphometry features from structural MRI (sMRI). We first compute the hyperbolic harmonic maps between cortical surfaces with the landmark constraints thus to precisely evaluate surface tensor-based morphometry. Meanwhile, the graph-based analysis of structural connectivity derived from dMRI is conducted. Next, we fuse these two features via the optimal mass transportation (OMT) and eventually the Wasserstein distance (WD) based single image index is computed as a potential clinical multimodality imaging score. We apply our framework to brain images of 20 AD patients and 20 matched healthy controls, randomly chosen from the Alzheimer's Disease Neuroimaging Initiative (AD-NI2) dataset. Our preliminary experimental results of group classification outperformed those of some other single dMRI-based features, such as regional hippocampal volume, mean scores of fractional anisotropy (FA) and mean axial (MD). The novel image fusion pipeline and simple imaging score of structural changes may benefit the preclinical AD and AD prevention research. PMID:28936280
Hyperbolic tangent variational approximation for interfacial profiles of binary polymer blends
International Nuclear Information System (INIS)
Lifschitz, M.; Freed, K.F.; Tang, H.
1995-01-01
Contemporary theories of binary polymer blend interfaces incorporate such features of real polymer blends as compressibility, local correlations, monomer structure, etc. However, these theories require complicated numerical schemes, and their solutions often cannot be interpreted in a physically clear fashion. We develop a variational formalism for computing interfacial properties of binary polymer blends based on a hyperbolic tangent representation for the interfaces. While such an analysis is straightforward in the incompressible limit, the extension to compressible binary blends requires two distinct width parameters and nontrivial analysis. When the profile width parameters are chosen to minimize the excess free energy of a phase separated binary blend, then the interfacial properties computed from our simplified interfacial theory closely match those computed with the much more sophisticated (and computationally intensive) treatments. Significant attention is devoted to describing the interfacial properties of blends in the regime intermediate between the strong and the weak segregation limits as well as to extrapolating between these limits. The extension of the square gradient theory to the Tang--Freed quartic approximation provides a more precise definition of the weak segregation limit, but the treatment is found to overestimate both the interfacial tension and width in the strong segregation limit. The width parameters for the different components of a strongly asymmetric compressible blend vary to a lesser extent than an asymptotic analysis in the bulk suggests. This finding indicates that the central portion of the profile contributes the most in the minimization of the excess free energy with respect to the variational width parameters. copyright 1995 American Institute of Physics
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...
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.
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...
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.
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.
International Nuclear Information System (INIS)
Cazenave, T.; Shatah, J.; Tahvildar-Zadeh, A.S.
1998-01-01
In this article we explore some of the connections between the theories of Yang-Mills fields, wave maps, and harmonic maps. It has been shown that the search for similarity solutions of wave maps leads to harmonic maps of the hyperbolic space. On the other hand, Glassey and Strauss have shown that the equations for an SO(3)-equivariant Yang-Mills connection on the Minkowski space R 3,1 with gauge group SU(2) reduce to a certain nonlinear wave equation, which we can now identify as a wave map on R 1,1 . More generally, we will here show the reduction under equivariance of a Yang-Mills system on the Minkowski space R n,1 to a wave map system on R n-2,1 in the specific case of SO(n) bundles with SO(n) symmetry. We then prove for odd n the existence of equivariant harmonic maps from the hyperbolic space H n that are smooth at the ideal boundary of H n , thus establishing the existence of similarity solutions for equivariant wave maps and Yang-Mills fields. As a consequence we show that for n ≥ 7, it is possible to have a wave map into a negatively curved target manifold that develops from smooth initial data and blows up in finite time, in sharp contrast to the elliptic case of harmonic maps. Finally we show how these singular solutions can be lifted to one dimension higher to produce singular travelling waves. (orig.)
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
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...
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...
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...
International Nuclear Information System (INIS)
Arauzo, Inmaculada; Campo, Antonio; Cortes, Cristobal
2005-01-01
This technical paper addresses an elementary analytic procedure for the approximate solution of the quasi-one-dimensional heat conduction equation (a generalized Bessel equation) that governs the temperature variation in annular fins of hyperbolic profile. This fin shape is of remarkable importance because its heat transfer performance is close to that of the annular fin of convex parabolic profile, the so-called optimal annular fin that is capable of delivering maximum heat transfer for a given volume of material [Zeitschrift des Vereines Deutscher Ingenieure 70 (1926) 885]. The salient feature of the analytic procedure developed here is that for realistic combinations of the two parameters: the enlarged Biot number and the normalized radii ratio, the truncated power series solutions embracing a moderate number of terms yields unprecedented results of excellent quality. The analytic results are conveniently presented in terms of the two primary quantities of interest in thermal design applications, namely the heat transfer rates and the tip temperature
Asiri, Sharefa M.; Elmetennani, Shahrazed; Laleg-Kirati, Taous-Meriem
2017-01-01
In this paper, an on-line estimation algorithm of the source term in a first order hyperbolic PDE is proposed. This equation describes heat transport dynamics in concentrated solar collectors where the source term represents the received energy. This energy depends on the solar irradiance intensity and the collector characteristics affected by the environmental changes. Control strategies are usually used to enhance the efficiency of heat production; however, these strategies often depend on the source term which is highly affected by the external working conditions. Hence, efficient source estimation methods are required. The proposed algorithm is based on modulating functions method where a moving horizon strategy is introduced. Numerical results are provided to illustrate the performance of the proposed estimator in open and closed loops.
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)
Energy Technology Data Exchange (ETDEWEB)
Suparmi, A., E-mail: soeparmi@staff.uns.ac.id; Cari, C., E-mail: cari@staff.uns.ac.id; Pratiwi, B. N., E-mail: namakubetanurpratiwi@gmail.com [Physics Department, Faculty of Mathematics and Science, Sebelas Maret University, Jl. Ir. Sutami 36A Kentingan Surakarta 57126 (Indonesia); Deta, U. A. [Physics Department, Faculty of Science and Mathematics Education and Teacher Training, Surabaya State University, Surabaya (Indonesia)
2016-02-08
The analytical solution of D-dimensional Dirac equation for hyperbolic tangent potential is investigated using Nikiforov-Uvarov method. In the case of spin symmetry the D dimensional Dirac equation reduces to the D dimensional Schrodinger equation. The D dimensional relativistic energy spectra are obtained from D dimensional relativistic energy eigen value equation by using Mat Lab software. The corresponding D dimensional radial wave functions are formulated in the form of generalized Jacobi polynomials. The thermodynamically properties of materials are generated from the non-relativistic energy eigen-values in the classical limit. In the non-relativistic limit, the relativistic energy equation reduces to the non-relativistic energy. The thermal quantities of the system, partition function and specific heat, are expressed in terms of error function and imaginary error function which are numerically calculated using Mat Lab software.
Asiri, Sharefa M.
2017-08-22
In this paper, an on-line estimation algorithm of the source term in a first order hyperbolic PDE is proposed. This equation describes heat transport dynamics in concentrated solar collectors where the source term represents the received energy. This energy depends on the solar irradiance intensity and the collector characteristics affected by the environmental changes. Control strategies are usually used to enhance the efficiency of heat production; however, these strategies often depend on the source term which is highly affected by the external working conditions. Hence, efficient source estimation methods are required. The proposed algorithm is based on modulating functions method where a moving horizon strategy is introduced. Numerical results are provided to illustrate the performance of the proposed estimator in open and closed loops.
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.
International Nuclear Information System (INIS)
Suparmi, A.; Cari, C.; Deta, U. A.; Handhika, J.
2016-01-01
The non-relativistic energies and wave functions of extended hyperbolic Scarf I plus separable non-central shape invariant potential in four dimensions are investigated using Supersymmetric Quantum Mechanics (SUSY QM) Approach. The three dimensional separable non-central shape invariant angular potential consists of trigonometric Scarf II, Manning Rosen and Poschl-Teller potentials. The four dimensional Schrodinger equation with separable shape invariant non-central potential is reduced into four one dimensional Schrodinger equations through variable separation method. By using SUSY QM, the non-relativistic energies and radial wave functions are obtained from radial Schrodinger equation, the orbital quantum numbers and angular wave functions are obtained from angular Schrodinger equations. The extended potential means there is perturbation terms in potential and cause the decrease in energy spectra of Scarf I potential. (paper)
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.
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.
Boscheri, Walter; Dumbser, Michael
2014-10-01
In this paper we present a new family of high order accurate Arbitrary-Lagrangian-Eulerian (ALE) one-step ADER-WENO finite volume schemes for the solution of nonlinear systems of conservative and non-conservative hyperbolic partial differential equations with stiff source terms on moving tetrahedral meshes in three space dimensions. A WENO reconstruction technique is used to achieve high order of accuracy in space, while an element-local space-time Discontinuous Galerkin finite element predictor on moving curved meshes is used to obtain a high order accurate one-step time discretization. Within the space-time predictor the physical element is mapped onto a reference element using a high order isoparametric approach, where the space-time basis and test functions are given by the Lagrange interpolation polynomials passing through a predefined set of space-time nodes. Since our algorithm is cell-centered, the final mesh motion is computed by using a suitable node solver algorithm. A rezoning step as well as a flattener strategy are used in some of the test problems to avoid mesh tangling or excessive element deformations that may occur when the computation involves strong shocks or shear waves. The ALE algorithm presented in this article belongs to the so-called direct ALE methods because the final Lagrangian finite volume scheme is based directly on a space-time conservation formulation of the governing PDE system, with the rezoned geometry taken already into account during the computation of the fluxes. We apply our new high order unstructured ALE schemes to the 3D Euler equations of compressible gas dynamics, for which a set of classical numerical test problems has been solved and for which convergence rates up to sixth order of accuracy in space and time have been obtained. We furthermore consider the equations of classical ideal magnetohydrodynamics (MHD) as well as the non-conservative seven-equation Baer-Nunziato model of compressible multi-phase flows with
... often, it could be a sign of a balance problem. Balance problems can make you feel unsteady. You may ... related injuries, such as a hip fracture. Some balance problems are due to problems in the inner ...
[Population problem, comprehension problem].
Tallon, F
1993-08-01
Overpopulation of developing countries in general, and Rwanda in particular, is not just their problem but a problem for developed countries as well. Rapid population growth is a key factor in the increase of poverty in sub-Saharan Africa. Population growth outstrips food production. Africa receives more and more foreign food, economic, and family planning aid each year. The Government of Rwanda encourages reduced population growth. Some people criticize it, but this criticism results in mortality and suffering. One must combat this ignorance, but attitudes change slowly. Some of these same people find the government's acceptance of family planning an invasion of their privacy. Others complain that rich countries do not have campaigns to reduce births, so why should Rwanda do so? The rate of schooling does not increase in Africa, even though the number of children in school increases, because of rapid population growth. Education is key to improvements in Africa's socioeconomic growth. Thus, Africa, is underpopulated in terms of potentiality but overpopulated in terms of reality, current conditions, and possibilities of overexploitation. Africa needs to invest in human resources. Families need to save, and to so, they must refrain from having many children. Africa should resist the temptation to waste, as rich countries do, and denounce it. Africa needs to become more independent of these countries, but structural adjustment plans, growing debt, and rapid population growth limit national independence. Food aid is a means for developed countries to dominate developing countries. Modernization through foreign aid has had some positive effects on developing countries (e.g., improved hygiene, mortality reduction), but these also sparked rapid population growth. Rwandan society is no longer traditional, but it is also not yet modern. A change in mentality to fewer births, better quality of life for living infants, better education, and less burden for women must occur