Analytic vortex solutions on compact hyperbolic surfaces
Maldonado, R
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.
Analytic vortex solutions on compact hyperbolic surfaces
Maldonado, Rafael; Manton, Nicholas S.
2015-06-01
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.
The homogeneous geometries of real hyperbolic space
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 ...
Nonlinear Sigma Models with Compact Hyperbolic Target Spaces
Gubser, Steven; Schoenholz, Samuel S; Stoica, Bogdan; Stokes, James
2015-01-01
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. 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 suggest...
Hyperbolic conservation laws and the compensated compactness method
Lu, Yunguang
2002-01-01
The method of compensated compactness as a technique for studying hyperbolic conservation laws is of fundamental importance in many branches of applied mathematics. Until now, however, most accounts of this method have been confined to research papers. Offering the first comprehensive treatment, Hyperbolic Conservation Laws and the Compensated Compactness Method gathers together into a single volume the essential ideas and developments.The authors begin with the fundamental theorems, then consider the Cauchy problem of the scalar equation, build a framework for L8 estimates of viscosity solutions, and introduce the Invariant Region Theory. The study then turns to methods for symmetric systems of two equations and two equations with quadratic flux, and the extension of these methods to the Le Roux system. After examining the system of polytropic gas dynamics (g-law), the authors first study two special systems of one-dimensional Euler equations, then consider the general Euler equations for one-dimensional com...
Nonlinear sigma models with compact hyperbolic target spaces
Gubser, Steven; Saleem, Zain H.; Schoenholz, Samuel S.; Stoica, Bogdan; Stokes, James
2016-06-01
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 [1, 2]. 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.
Kim, Inkang
2012-01-01
In this note, we study deformations of a non-uniform real hyperbolic lattice in quaternionic hyperbolic spaces. Specially we show that the representations of the fundamental group of the figure eight knot complement into PU(2,1) cannot be deformed in $PSp(2,1)$ out of PU(2,1) up to conjugacy.
Nonlinear sigma models with compact hyperbolic target spaces
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.
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).
Hyperbolicity Measures "Democracy" in Real-World Networks
Borassi, Michele; Caldarelli, Guido
2015-01-01
We analyze the hyperbolicity of real-world networks, a geometric quantity that measures if a space is negatively curved. In our interpretation, a network with small hyperbolicity is "aristocratic", because it contains a small set of vertices involved in many shortest paths, so that few elements "connect" the systems, while a network with large hyperbolicity has a more "democratic" structure with a larger number of crucial elements. We prove mathematically the soundness of this interpretation, and we derive its consequences by analyzing a large dataset of real-world networks. We confirm and improve previous results on hyperbolicity, and we analyze them in the light of our interpretation. Moreover, we study (for the first time in our knowledge) the hyperbolicity of the neighborhood of a given vertex. This allows to define an "influence area" for the vertices in the graph. We show that the influence area of the highest degree vertex is small in what we define "local" networks, like most social or peer-to-peer ne...
Zi-niu Wu
2003-01-01
For nonlinear hyperbolic problems, conservation of the numerical scheme is importantfor convergence to the correct weak solutions. In this paper the conservation of the well-known compact scheme up to fourth order of accuracy on a single and uniform grid isstudied, and a conservative interface treatment is derived for compact schemes on patchedgrids. For a pure initial value problem, the compact scheme is shown to be equivalent toa scheme in the usual conservative form. For the case of a mixed initial boundary valueproblem, the compact scheme is conservative only if the rounding errors are small enough.For a patched grid interface, a conservative interface condition useful for mesh refinementand for parallel computation is derived and its order of local accuracy is analyzed.
Localization of supersymmetric field theories on non-compact hyperbolic three-manifolds
Assel, Benjamin; Murthy, Sameer; Yokoyama, Daisuke
2016-01-01
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$_3$. 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.
Spherical Means in Annular Regions in the -Dimensional Real Hyperbolic Spaces
Rama Rawat; R K Srivastava
2011-08-01
Let $Z_{r,R}$ be the class of all continuous functions on the annulus $\\mathrm{Ann}(r,R)$ in the real hyperbolic space $\\mathbb{B}^n$ with spherical means $M_sf(x)=0$, whenever $s>0$ and $x\\in\\mathbb{B}^n$ are such that the sphere $S_s(x)\\subset\\mathrm{Ann}(r,R)$ and $B_r(o)\\subseteq B_s(x)$. In this article, we give a characterization for functions in $Z_{r,R}$. In the case =∞, this result gives a new proof of Helgason’s support theorem for spherical means in the real hyperbolic spaces.
Urabe, T
1995-01-01
We study the Gauss map and the dual variety of a real-analytic immersion of a connected compact real-analytic manifold into a sphere or into a hyperbolic space. The dual variety is defined to be the set of all normal directions of the immersion. First, we show that the image of the Gauss map characterizes the manifold. Also we show that the dual variety characterizes the manifold. Besides, duality of the second fundamental form and some results on degeneration are obtained. This LaTeX file is originally devided into the following 8 files: gauss_root.tex gauss1.tex gauss2.tex gauss3.tex gauss4.tex gauss5.tex gauss_bib.bib gauss_root.bbl. To submit to Algebraic Geometry E-prints, I write these 8 files continuously below.
TeV-scale gravity in Horava-Witten theory on a compact complex hyperbolic threefold
Austin, Chris
2007-01-01
The field equations and boundary conditions of Horava-Witten theory, compactified on a smooth compact quotient of CH^3, where CH^3 denotes the hyperbolic cousin of CP^3, are studied in the presence of Casimir energy density terms. If the Casimir energy densities near one boundary result in a certain constant of integration taking a value larger than around 10^5 in units of the d = 11 gravitational length, a form of thick pipe geometry is found that realizes TeV-scale gravity by the ADD mechanism, with that boundary becoming the inner surface of the thick pipe, where we live. Three alternative ways in which the outer surface of the thick pipe might be stabilized consistent with the observed value of the effective d = 4 cosmological constant are considered. In the first alternative, the outer surface is stabilized in the classical region and the constant of integration is fixed at around 10^{13} in units of the d = 11 gravitational length for consistency with the observed cosmological constant. In the second al...
Huynh, H. M.; Kunze, M.
2015-03-01
Physicists have argued that periodic orbit bunching leads to universal spectral fluctuations for chaotic quantum systems. To establish a more detailed mathematical understanding of this fact, it is first necessary to look more closely at the classical side of the problem and determine orbit pairs consisting of orbits which have similar actions. In this paper we consider the geodesic flow on compact factors of the hyperbolic plane as a classical chaotic system. We prove the existence of a periodic partner orbit for a given periodic orbit which has a small-angle self-crossing in configuration space which is a ‘2-encounter’ such configurations are called ‘Sieber-Richter pairs’ in physics literature. Furthermore, we derive an estimate for the action difference of the partners. In the second part of this paper (Huynh, submitted), an inductive argument is provided to deal with higher-order encounters.
Compact Sets without Converging Sequences in the Random Real Model
D. Fremlin
2007-10-01
Full Text Available It is shown that in the model obtained by adding any number of random reals to a model of CH, there is a compact Hausdorff space of weight w1 which contains no non-trivial converging sequences. It is shown that for certain spaces with noconverging sequences, the addition of random reals will not add any converging sequences.
Huynh, Minh Hien
2016-01-01
Physicists have argued that periodic orbit bunching leads to universal spectral fluctuations for chaotic quantum systems. To establish a more detailed mathematical understanding of this fact, it is first necessary to look more closely at the classical side of the problem and determine orbit pairs consisting of orbits which have similar actions. We specialize to the geodesic flow on compact factors of the hyperbolic plane as a classical chaotic system. The companion paper (Huynh and Kunze, 2015) proved the existence of a unique periodic partner orbit for a given periodic orbit with a small-angle self-crossing in configuration space that is a 2-encounter and derived an estimate for the action difference of the orbit pair. In this paper, we provide an inductive argument to deal with higher-order encounters: we prove that a given periodic orbit including an L-parallel encounter has (L - 1) ! - 1 partner orbits; we construct partner orbits and give estimates for the action differences between orbit pairs.
Weakly asymptotically hyperbolic manifolds
Allen, Paul T; Lee, John M; Allen, Iva Stavrov
2015-01-01
We introduce a class of "weakly asymptotically hyperbolic" geometries whose sectional curvatures tend to $-1$ and are $C^0$, but are not necessarily $C^1$, conformally compact. We subsequently investigate the rate at which curvature invariants decay at infinity, identifying a conformally invariant tensor which serves as an obstruction to "higher order decay" of the Riemann curvature operator. Finally, we establish Fredholm results for geometric elliptic operators, extending the work of Rafe Mazzeo and John M. Lee to this setting. As an application, we show that any weakly asymptotically hyperbolic metric is conformally related to a weakly asymptotically hyperbolic metric of constant negative curvature.
Compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions
Davood Alimohammadi
2014-10-01
Full Text Available We characterize compact composition operators on real Banachspaces of complex-valued bounded Lipschitz functions on metricspaces, not necessarily compact, with Lipschitz involutions anddetermine their spectra.
Trivalent expanders and hyperbolic surfaces
Ivrissimtzis, Ioannis; Vdovina, Alina
2012-01-01
We introduce a family of trivalent expanders which tessellate compact hyperbolic surfaces with large isometry groups. We compare this family with Platonic graphs and modifications of them and prove topological and spectral properties of these families.
Cantor-Type Sets in Hyperbolic Numbers
Balankin, A. S.; Bory-Reyes, J.; Luna-Elizarrarás, M. E.; Shapiro, M.
2016-12-01
The construction of the ternary Cantor set is generalized into the context of hyperbolic numbers. The partial order structure of hyperbolic numbers is revealed and the notion of hyperbolic interval is defined. This allows us to define a general framework of the fractal geometry on the hyperbolic plane. Three types of the hyperbolic analogues of the real Cantor set are identified. The complementary nature of the real Cantor dust and the real Sierpinski carpet on the hyperbolic plane are outlined. The relevance of these findings in the context of modern physics are briefly discussed.
A comparison of hyperbolic solvers for ideal and real gas flows
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.
Classical and quantum resonances for hyperbolic surfaces
Guillarmou, Colin; Hilgert, Joachim; Weich, Tobias
2016-01-01
For compact and for convex co-compact oriented hyperbolic surfaces, we prove an explicit correspondence between classical Ruelle resonant states and quantum resonant states, except at negative integers where the correspondence involves holomorphic sections of line bundles.
Gicquaud, Romain
2014-01-01
We construct solutions to the constraint equations in general relativity using the limit equation criterion introduced by Dahl, Humbert and the first author. We focus on solutions over compact 3-manifolds admitting a $\\bS^1$-symmetry group. When the quotient manifold has genus greater than 2, we obtain strong far from CMC results.
Charting the Real Four-Qubit Pauli Group via Ovoids of a Hyperbolic Quadric of PG(7,2)
Saniga, Metod; Pracna, Petr
2012-01-01
The geometry of the real four-qubit Pauli group, being embodied in the structure of the symplectic polar space W(7,2), is analyzed in terms of ovoids of a hyperbolic quadric of PG(7,2), the seven-dimensional projective space of order two. The quadric is selected in such a way that it contains all 135 symmetric elements of the group. Under such circumstances, the third element on the line defined by any two points of an ovoid is skew-symmetric, as is the nucleus of the conic defined by any three points of an ovoid. Each ovoid thus yields 36/84 elements of the former/latter type, accounting for all 120 skew-symmetric elements of the group. There are a number of notable types of ovoid-associated subgeometries of the group, of which we mention the following: a subset of 12 skew-symmetric elements lying on four mutually skew lines that span the whole ambient space, a subset of 15 symmetric elements that corresponds to two ovoids sharing three points, a subset of 19 symmetric elements generated by two ovoids on a c...
Real-time acquisition of compact volumetric maps
无
2006-01-01
Buildingcompact 3D maps of the environment models has become an important research topic. This paper presented an efficient stream decimation algorithm of massive meshes. The algorithm adapted the pre-processing step leading to lower in-core memory consumption. This algorithm is applied to reconstructing compact terrain with mobile robot, achieving satisfying results.
Poddubny, Alexander; Iorsh, Ivan; Belov, Pavel; Kivshar, Yuri
2013-12-01
Electromagnetic metamaterials, artificial media created by subwavelength structuring, are useful for engineering electromagnetic space and controlling light propagation. Such materials exhibit many unusual properties that are rarely or never observed in nature. They can be employed to realize useful functionalities in emerging metadevices based on light. Here, we review hyperbolic metamaterials -- one of the most unusual classes of electromagnetic metamaterials. They display hyperbolic (or indefinite) dispersion, which originates from one of the principal components of their electric or magnetic effective tensor having the opposite sign to the other two principal components. Such anisotropic structured materials exhibit distinctive properties, including strong enhancement of spontaneous emission, diverging density of states, negative refraction and enhanced superlensing effects.
Hyperbolicity of cycle spaces and automorphism groups of flag domains
Huckleberry, Alan
2010-01-01
If G_0 is a real form of a complex semisimple Lie group G and Z is compact G-homogeneous projective algebraic manifold, then G_0 has only finitely many orbits on Z. Complex analytic properties of open G_0-orbits D (flag domains) are studied. Schubert incidence-geometry is used to prove the Kobayashi hyperbolicity of certain cycle space components C_q(D). Using the hyperbolicity of C_q(D) and analyzing the action of Aut(D) on it, an exact description of Aut(D) is given. It is shown that, except in the easily understood case where D is holomorphically convex with a nontrivial Remmert reduction, it is a Lie group acting smoothly as a group of holomorphic transformations on D. With very few exceptions it is just G_0.
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...
Compact-like kink in a real electrical reaction-diffusion chain
Comte, J.C. [Laboratoire de Physiopathologie des Reseaux Neuronaux du Cycle Veille-Sommeil, CNRS UMR 5167, Faculte de Medecine Laennec 7, Rue Guillaume Paradin, 69372 Lyon Cedex 08 (France)]. E-mail: comtejc@sommeil.univ-lyon1.fr; Marquie, P. [Laboratoire d' Electronique, Informatique et Image (LE2i) UMR CNRS 5158, Aile des Sciences de l' Ingenieur, BP 47870, 21078 Dijon Cedex (France)
2006-07-15
We demonstrate experimentally the compact-like kinks existence in a real electrical reaction-diffusion chain. Our measures show that such entities are strictly localized and consequently present a finite spatial extent. We show equally that the kink velocity is threshold-dependent. A theoretical quantification of the critical coupling under which propagation fails is also achieved and reveals that nonlinear coupling leads to a propagation failure reduction.
Quasi-rigidity of hyperbolic 3-manifolds and scattering theory
Borthwick, D; Taylor, E; Borthwick, David; Rae, Alan Mc; Taylor, Edward
1996-01-01
Take two isomorphic convex co-compact co-infinite volume Kleinian groups, whose regular sets are diffeomorphic. The quotient of hyperbolic 3-space by these groups gives two hyperbolic 3-manifolds whose scattering operators may be compared. We prove that the operator norm of the difference between the scattering operators is small, then the groups are related by a coorespondingly small quasi-conformal deformation. This in turn implies that the two hyperbolic 3-manifolds are quasi-isometric.
A compact hybrid-multiplexed potentiostat for real-time electrochemical biosensing applications.
Ramfos, Ioannis; Vassiliadis, Nikolaos; Blionas, Spyridon; Efstathiou, Konstantinos; Fragoso, Alex; O'Sullivan, Ciara K; Birbas, Alexios
2013-09-15
The architecture and design of a compact, multichannel, hybrid-multiplexed potentiostat for performing electrochemical measurements on continuously-biased electrode arrays is presented. The proposed architecture utilises a combination of sequential and parallel measurements, to enable high performance whilst keeping the system low-cost and compact. The accuracy of the signal readout is maintained by following a special multiplexing approach, which ensures the continuous biasing of all the working electrodes of an array. After sampling the results, a digital calibration technique factors out errors from component inaccuracies. A prototype printed circuit board (PCB) was designed and built using off-the-shelf components for the real-time measurement of the amperometric signal of 48 electrodes. The operation and performance of the PCB was evaluated and characterised through a wide range of testing conditions, where it exhibited high linearity (R(2)>0.999) and a resolution of 400pA. The effectiveness of the proposed multiplexing scheme is demonstrated through electrochemical tests using KCl and [Fe(CN)6](3-) in KCl solutions. The applicability of the prototype multichannel potentiostat is also demonstrated using real biosensors, which were applied to the detection of IgA antibodies.
Hyperbolic positive mass theorem under modified energy condition
XIE NaQing
2008-01-01
We provide two new positive mass theorems under respective modified energy conditions allowing Too negative on some compact set for certain modified asymptotically hyperbolic manifolds. This work is analogous to Zhang's previous result for modified asymptotically fiat initial data sets.
Emergent Hyperbolic Network Geometry
Bianconi, Ginestra; Rahmede, Christoph
2017-02-01
A large variety of interacting complex systems are characterized by interactions occurring between more than two nodes. These systems are described by simplicial complexes. Simplicial complexes are formed by simplices (nodes, links, triangles, tetrahedra etc.) that have a natural geometric interpretation. As such simplicial complexes are widely used in quantum gravity approaches that involve a discretization of spacetime. Here, by extending our knowledge of growing complex networks to growing simplicial complexes we investigate the nature of the emergent geometry of complex networks and explore whether this geometry is hyperbolic. Specifically we show that an hyperbolic network geometry emerges spontaneously from models of growing simplicial complexes that are purely combinatorial. The statistical and geometrical properties of the growing simplicial complexes strongly depend on their dimensionality and display the major universal properties of real complex networks (scale-free degree distribution, small-world and communities) at the same time. Interestingly, when the network dynamics includes an heterogeneous fitness of the faces, the growing simplicial complex can undergo phase transitions that are reflected by relevant changes in the network geometry.
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…
Hyperbolicity in Median Graphs
José M Sigarreta
2013-11-01
If is a geodesic metric space and $x_1,x_2,x_3\\in X$, a geodesic triangle $T=\\{x_1,x_2,x_3\\}$ is the union of the three geodesics $[x_1 x_2],[x_2 x_3]$ and $[x_3 x_1]$ in . The space is -hyperbolic (in the Gromov sense) if any side of is contained in a -neighborhood of the union of the two other sides, for every geodesic triangle in . If is hyperbolic, we denote by () the sharp hyperbolicity constant of , i.e.,$(X)=\\inf\\{≥ 0: X \\quad\\text{is}\\quad -\\text{hyperbolic}\\}$. In this paper we study the hyperbolicity of median graphs and we also obtain some results about general hyperbolic graphs. In particular, we prove that a median graph is hyperbolic if and only if its bigons are thin.
Magnetic hyperbolic optical metamaterials.
Kruk, Sergey S; Wong, Zi Jing; Pshenay-Severin, Ekaterina; O'Brien, Kevin; Neshev, Dragomir N; Kivshar, Yuri S; Zhang, Xiang
2016-04-13
Strongly anisotropic media where the principal components of electric permittivity or magnetic permeability tensors have opposite signs are termed as hyperbolic media. Such media support propagating electromagnetic waves with extremely large wave vectors exhibiting unique optical properties. However, in all artificial and natural optical materials studied to date, the hyperbolic dispersion originates solely from the electric response. This restricts material functionality to one polarization of light and inhibits free-space impedance matching. Such restrictions can be overcome in media having components of opposite signs for both electric and magnetic tensors. Here we present the experimental demonstration of the magnetic hyperbolic dispersion in three-dimensional metamaterials. We measure metamaterial isofrequency contours and reveal the topological phase transition between the elliptic and hyperbolic dispersion. In the hyperbolic regime, we demonstrate the strong enhancement of thermal emission, which becomes directional, coherent and polarized. Our findings show the possibilities for realizing efficient impedance-matched hyperbolic media for unpolarized light.
Bifurcation of hyperbolic planforms
Chossat, Pascal; Faugeras, Olivier
2010-01-01
Motivated by a model for the perception of textures by the visual cortex in primates, we analyse the bifurcation of periodic patterns for nonlinear equations describing the state of a system defined on the space of structure tensors, when these equations are further invariant with respect to the isometries of this space. We show that the problem reduces to a bifurcation problem in the hyperbolic plane D (Poincar\\'e disc). We make use of the concept of periodic lattice in D to further reduce the problem to one on a compact Riemann surface D/T, where T is a cocompact, torsion-free Fuchsian group. The knowledge of the symmetry group of this surface allows to carry out the machinery of equivariant bifurcation theory. Solutions which generically bifurcate are called "H-planforms", by analogy with the "planforms" introduced for pattern formation in Euclidean space. This concept is applied to the case of an octagonal periodic pattern, where we are able to classify all possible H-planforms satisfying the hypotheses o...
The FirnCover Project - Real-time Monitoring of Greenland's Firn Compaction in a Changing Climate
MacFerrin, M. J.; Stevens, C.; Waddington, E. D.; Abdalati, W.
2015-12-01
An unavoidable source of uncertainty in altimetry-based mass balance assessments of ice sheets is the conversion from volume change into mass change. A primary component of this volume change is firn compaction, or the rate at which snow compresses into glacial ice. Firn densification models simulate this process, but model outputs vary widely, and Greenland's rapidly changing climate challenges many of the steady-state assumptions held in most of these models. Contemporary measurements of firn compaction rates are extremely sparse across Greenland in both time and space and are nonexistent in many large regions. Here we present initial results from Greenland's Firn Compaction Verification and Reconnaissance (FirnCover) Project, a network of real-time strain gauges at over thirty boreholes that continuously monitor compaction rates at eight locations in Greenland's accumulation zones, ranging from areas of heavy percolation to dry snow. Initial results from these stations indicate a strong seasonality in compaction, especially in regions where heavy melt and refreezing release latent heat into the firn column, a process that will intensify as melt increases across Greenland. We also discuss the substantial challenge of measuring firn compaction in regions of heterogeneous percolation, and other challenges encountered when validating firn models and monitoring contemporary mass changes of the Greenland ice sheet.
Lasing Action with Gold Nanorod Hyperbolic Metamaterials
Chandrasekar, Rohith; Meng, Xiangeng; Shalaginov, Mikhail Y; Lagutchev, Alexei; Kim, Young L; Wei, Alexander; Kildishev, Alexander V; Boltasseva, Alexandra; Shalaev, Vladimir M
2016-01-01
Coherent nanoscale photon sources are of paramount importance to achieving all-optical communication. Several nanolasers smaller than the diffraction limit have been theoretically proposed and experimentally demonstrated using plasmonic cavities to confine optical fields. Such compact cavities exhibit large Purcell factors, thereby enhancing spontaneous emission, which feeds into the lasing mode. However, most plasmonic nanolasers reported so far have employed resonant nanostructures and therefore had the lasing restricted to the proximity of the resonance wavelength. Here, we report on an approach based on gold nanorod hyperbolic metamaterials for lasing. Hyperbolic metamaterials provide broadband Purcell enhancement due to large photonic density of optical states, while also supporting surface plasmon modes to deliver optical feedback for lasing due to nonlocal effects in nanorod media. We experimentally demonstrate the advantage of hyperbolic metamaterials in achieving lasing action by its comparison with ...
Chen, Ying-ping; Chen, Chao-Hong
2010-01-01
An adaptive discretization method, called split-on-demand (SoD), enables estimation of distribution algorithms (EDAs) for discrete variables to solve continuous optimization problems. SoD randomly splits a continuous interval if the number of search points within the interval exceeds a threshold, which is decreased at every iteration. After the split operation, the nonempty intervals are assigned integer codes, and the search points are discretized accordingly. As an example of using SoD with EDAs, the integration of SoD and the extended compact genetic algorithm (ECGA) is presented and numerically examined. In this integration, we adopt a local search mechanism as an optional component of our back end optimization engine. As a result, the proposed framework can be considered as a memetic algorithm, and SoD can potentially be applied to other memetic algorithms. The numerical experiments consist of two parts: (1) a set of benchmark functions on which ECGA with SoD and ECGA with two well-known discretization methods: the fixed-height histogram (FHH) and the fixed-width histogram (FWH) are compared; (2) a real-world application, the economic dispatch problem, on which ECGA with SoD is compared to other methods. The experimental results indicate that SoD is a better discretization method to work with ECGA. Moreover, ECGA with SoD works quite well on the economic dispatch problem and delivers solutions better than the best known results obtained by other methods in existence.
Closure constraints for hyperbolic tetrahedra
Charles, Christoph
2015-01-01
We investigate the generalization of loop gravity's twisted geometries to a q-deformed gauge group. In the standard undeformed case, loop gravity is a formulation of general relativity as a diffeomorphism-invariant SU(2) gauge theory. Its classical states are graphs provided with algebraic data. In particular closure constraints at every node of the graph ensure their interpretation as twisted geometries. Dual to each node, one has a polyhedron embedded in flat space R^3. One then glues them allowing for both curvature and torsion. It was recently conjectured that q-deforming the gauge group SU(2) would allow to account for a non-vanishing cosmological constant Lambda, and in particular that deforming the loop gravity phase space with real parameter q>0 would lead to a generalization of twisted geometries to a hyperbolic curvature. Following this insight, we look for generalization of the closure constraints to the hyperbolic case. In particular, we introduce two new closure constraints for hyperbolic tetrahe...
Some hyperbolic three-manifolds that bound geometrically
KOLPAKOV, Alexander; Martelli, Bruno; Tschantz, Steven
2015-01-01
A closed connected hyperbolic $n$-manifold bounds geometrically if it is isometric to the geodesic boundary of a compact hyperbolic $(n+1)$-manifold. A. Reid and D. Long have shown by arithmetic methods the existence of infinitely many manifolds that bound geometrically in every dimension. We construct here infinitely many explicit examples in dimension $n=3$ using right-angled dodecahedra and $120$-cells and a simple colouring technique introduced by M. Davis and T. Januszkiewicz. Namely, fo...
The remains of a spinning, hyperbolic encounter
De Vittori, Lorenzo; Gupta, Anuradha; Jetzer, Philippe
2014-01-01
We review a recently proposed approach to construct gravitational wave (GW) polarization states of unbound spinning compact binaries. Through this rather simple method, we are able to include corrections due to the dominant order spin-orbit interactions, in the quadrupolar approximation and in a semi-analytic way. We invoke the 1.5 post-Newtonian (PN) accurate quasi-Keplerian parametrization for the radial part of the dynamics and impose its temporal evolution in the PN accurate polarization states equations. Further, we compute 1PN accurate amplitude corrections for the polarization states of non-spinning compact binaries on hyperbolic orbits. As an interesting application, we perform comparisons with previously available results for both the GW signals in the case of non-spinning binaries and the theoretical prediction for the amplitude of the memory effect on the metric after the hyperbolic passage.
Hyperbolic spaces are of strictly negative type
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....
On Invariant Decompositions, Dominated Splittings and Sectional-Hyperbolicity
Araujo, Vitor; Salgado, Luciana
2011-01-01
We obtain sufficient conditions for an invariant splitting over a compact invariant subset of a $C^1$ flow $X_t$ to be dominated. For a $C^1$ flow $X_t$ on a compact manifold $M$ and a compact invariant subset $\\Lambda$, with a continuous and $DX_t$-invariant splitting $E\\oplus F$ of the tangent bundle $T_\\Lambda M$ over $\\Lambda$, we consider the relation between weak forms of hyperbolicity along each subbundle and domination.
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
Compact Wireless BioMetric Monitoring and Real Time Processing System Project
National Aeronautics and Space Administration — BioWATCH is a modular ambulatory compact wireless biomedical data acquisition system. More specifically, it is a data acquisition unit for acquiring signals from...
Cuspidal discrete series for projective hyperbolic spaces
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 a...
Magnetic hyperbolic optical metamaterials
Kruk, Sergey S; Pshenay-Severin, Ekaterina; O'Brien, Kevin; Neshev, Dragomir N; Kivshar, Yuri S; Zhang, Xiang
2015-01-01
Strongly anisotropic media where the principal components of the electric permittivity and/or magnetic permeability tensor have opposite signs are termed as hyperbolic media. Such media support propagating electromagnetic waves with extremely large wavevectors, and therefore they exhibit unique optical properties. However in all artificial and natural optical structures studied to date the hyperbolic dispersion originates solely from their electric response. This restricts functionality of these materials for only one polarization of light and inhibits impedance matching with free space. Such restrictions can be overcome in media having components of opposite signs in both electric and magnetic tensors. Here we present the first experimental demonstration of the magnetic hyperbolic dispersion in three-dimensional metamaterials. We measure experimentally metamaterial's dispersion and trace the topological transition between the elliptic and hyperbolic regimes. We experimentally demonstrate that due to the uniq...
Existence for a class of discrete hyperbolic problems
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.
Stability and Convergence of Relaxation Schemes to Hyperbolic Balance Laws via a Wave Operator
Miroshnikov, Alexey; Trivisa, Konstantina
2014-01-01
This article deals with relaxation approximations of nonlinear systems of hyperbolic balance laws. We introduce a class of relaxation schemes and establish their stability and convergence to the solution of hyperbolic balance laws before the formation of shocks, provided that we are within the framework of the compensated compactness method. Our analysis treats systems of hyperbolic balance laws with source terms satisfying a special mechanism which induces weak dissipation in the spirit of D...
A Milnor-Wood inequality for complex hyperbolic lattices in quaternionic space
Garcia-Prada, Oscar
2010-01-01
We prove a Milnor-Wood inequality for representations of the fundamental group of a compact complex hyperbolic manifold in the group of isometries of quaternionic hyperbolic space. Of special interest is the case of equality, and its application to rigidity. We show that equality can only be achieved for totally geodesic representations, thereby establishing a global rigidity theorem for totally geodesic representations.
Gromov Hyperbolicity of Riemann Surfaces
José M. RODR(I)GUEZ; Eva TOUR(I)S
2007-01-01
We study the hyperbolicity in the Gromov sense of Riemann surfaces. We deduce the hyperbolicity of a surface from the hyperbolicity of its "building block components". We also prove the equivalence between the hyperbolicity of a Riemann surface and the hyperbolicity of some graph associated with it. These results clarify how the decomposition of a Riemann surface into Y-pieces and funnels affects the hyperbolicity of the surface. The results simplify the topology of the surface and allow us to obtain global results from local information.
On the Hyperbolicity of Large-Scale Networks
Kennedy, W Sean; Saniee, Iraj
2013-01-01
Through detailed analysis of scores of publicly available data sets corresponding to a wide range of large-scale networks, from communication and road networks to various forms of social networks, we explore a little-studied geometric characteristic of real-life networks, namely their hyperbolicity. In smooth geometry, hyperbolicity captures the notion of negative curvature; within the more abstract context of metric spaces, it can be generalized as d-hyperbolicity. This generalized definition can be applied to graphs, which we explore in this report. We provide strong evidence that communication and social networks exhibit this fundamental property, and through extensive computations we quantify the degree of hyperbolicity of each network in comparison to its diameter. By contrast, and as evidence of the validity of the methodology, applying the same methods to the road networks shows that they are not hyperbolic, which is as expected. Finally, we present practical computational means for detection of hyperb...
Hyperbolic Metamaterials with Complex Geometry
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...
Thermal hyperbolic metamaterials.
Guo, Yu; Jacob, Zubin
2013-06-17
We explore the near-field radiative thermal energy transfer properties of hyperbolic metamaterials. The presence of unique electromagnetic states in a broad bandwidth leads to super-planckian thermal energy transfer between metamaterials separated by a nano-gap. We consider practical phonon-polaritonic metamaterials for thermal engineering in the mid-infrared range and show that the effect exists in spite of the losses, absorption and finite unit cell size. For thermophotovoltaic energy conversion applications requiring energy transfer in the near-infrared range we introduce high temperature hyperbolic metamaterials based on plasmonic materials with a high melting point. Our work paves the way for practical high temperature radiative thermal energy transfer applications of hyperbolic metamaterials.
Luminescent hyperbolic metasurfaces
Smalley, J. S. T.; Vallini, F.; Montoya, S. A.; Ferrari, L.; Shahin, S.; Riley, C. T.; Kanté, B.; Fullerton, E. E.; Liu, Z.; Fainman, Y.
2017-01-01
When engineered on scales much smaller than the operating wavelength, metal-semiconductor nanostructures exhibit properties unobtainable in nature. Namely, a uniaxial optical metamaterial described by a hyperbolic dispersion relation can simultaneously behave as a reflective metal and an absorptive or emissive semiconductor for electromagnetic waves with orthogonal linear polarization states. Using an unconventional multilayer architecture, we demonstrate luminescent hyperbolic metasurfaces, wherein distributed semiconducting quantum wells display extreme absorption and emission polarization anisotropy. Through normally incident micro-photoluminescence measurements, we observe absorption anisotropies greater than a factor of 10 and degree-of-linear polarization of emission >0.9. We observe the modification of emission spectra and, by incorporating wavelength-scale gratings, show a controlled reduction of polarization anisotropy. We verify hyperbolic dispersion with numerical simulations that model the metasurface as a composite nanoscale structure and according to the effective medium approximation. Finally, we experimentally demonstrate >350% emission intensity enhancement relative to the bare semiconducting quantum wells.
Hyperbolic Resonances of Metasurface Cavities
Keene, David
2015-01-01
We propose a new class of optical resonator structures featuring one or two metasurface reflectors or metacavities and predict that such resonators support novel hyperbolic resonances. As an example of such resonances we introduce hyperbolic Tamm plasmons (HTPs) and hyperbolic Fabry-Perot resonances (HFPs). The hyperbolic optical modes feature low-loss incident power re-distribution over TM and TE polarization output channels, clover-leaf anisotropic dispersion, and other unique properties which are tunable and are useful for multiple applications.
Hyperbolic partial differential equations
Lax, Peter D
2006-01-01
The theory of hyperbolic equations is a large subject, and its applications are many: fluid dynamics and aerodynamics, the theory of elasticity, optics, electromagnetic waves, direct and inverse scattering, and the general theory of relativity. This book is an introduction to most facets of the theory and is an ideal text for a second-year graduate course on the subject. The first part deals with the basic theory: the relation of hyperbolicity to the finite propagation of signals, the concept and role of characteristic surfaces and rays, energy, and energy inequalities. The structure of soluti
Invariant Surfaces under Hyperbolic Translations in Hyperbolic Space
Mahmut Mak
2014-01-01
Full Text Available We consider hyperbolic rotation (G0, hyperbolic translation (G1, and horocyclic rotation (G2 groups in H3, which is called Minkowski model of hyperbolic space. Then, we investigate extrinsic differential geometry of invariant surfaces under subgroups of G0 in H3. Also, we give explicit parametrization of these invariant surfaces with respect to constant hyperbolic curvature of profile curves. Finally, we obtain some corollaries for flat and minimal invariant surfaces which are associated with de Sitter and hyperbolic shape operator in H3.
Hyperbolic positive mass theorem under modified energy condition
2008-01-01
We provide two new positive mass theorems under respective modified energy conditions allowing T00 negative on some compact set for certain modified asymptotically hyperbolic manifolds. This work is analogous to Zhang’s previous result for modified asymptotically ?at initial data sets.
Local topology in deformation spaces of hyperbolic 3-manifolds
Brock, Jeffrey F; Canary, Richard D; Minsky, Yair N
2009-01-01
We prove that the deformation space AH(M) of marked hyperbolic 3-manifolds homotopy equivalent to a fixed compact 3-manifold M with incompressible boundary is locally connected at minimally parabolic points. Moreover, spaces of Kleinian surface groups are locally connected at quasiconformally rigid points. Similar results are obtained for deformation spaces of acylindrical 3-manifolds and Bers slices.
Global Hyperbolicity and Completeness
Choquet-Bruhat, Y; Choquet-Bruhat, Yvonne; Cotsakis, Spiros
2002-01-01
We prove global hyperbolicity of spacetimes under generic regularity conditions on the metric. We then show that these spacetimes are timelike and null geodesically complete if the gradient of the lapse and the extrinsic curvature $K$ are integrable. This last condition is required only for the tracefree part of $K$ if the universe is expanding.
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...
Hyperbolic groupoids: definitions and duality
Nekrashevych, Volodymyr
2011-01-01
We define a notion of a hyperbolic groupoid (pseudogroup) generalizing actions of Gromov hyperbolic groups on their boundaries. We show that the boundary of a Gromov hyperbolic groupoid has a natural local product structure and that actions of hyperbolic groupoids on their boundaries can be described axiomatically as generalized Smale spaces (which we call Smale quasi-flows). The original groupoid is equivalent to the projection of the corresponding Smale quasi-flow onto the stable direction of the local product structure. The projection onto the unstable direction is called the dual of the groupoid. Examples of pairs of mutually dual hyperbolic groupoids and associated Smale quasi-flows are described.
A remark on geometric desingularization of a non-hyperbolic point using hyperbolic space
Kuehn, Christian
2016-06-01
A steady state (or equilibrium point) of a dynamical system is hyperbolic if the Jacobian at the steady state has no eigenvalues with zero real parts. In this case, the linearized system does qualitatively capture the dynamics in a small neighborhood of the hyperbolic steady state. However, one is often forced to consider non-hyperbolic steady states, for example in the context of bifurcation theory. A geometric technique to desingularize non-hyperbolic points is the blow-up method. The classical case of the method is motivated by desingularization techniques arising in algebraic geometry. The idea is to blow up the steady state to a sphere or a cylinder. In the blown-up space, one is then often able to gain additional hyperbolicity at steady states. The method has also turned out to be a key tool to desingularize multiple time scale dynamical systems with singularities. In this paper, we discuss an explicit example of the blow-up method where we replace the sphere in the blow-up by hyperbolic space. It is shown that the calculations work in the hyperbolic space case as for the spherical case. This approach may be even slightly more convenient if one wants to work with directional charts. Hence, it is demonstrated that the sphere should be viewed as an auxiliary object in the blow-up construction. Other smooth manifolds are also natural candidates to be inserted at steady states. Furthermore, we conjecture several problems where replacing the sphere could be particularly useful, i.e., in the context of singularities of geometric flows, for avoiding compactification, and generating 'interior' steady states.
Gualdesi, Lavinio
2017-04-01
Mooring lines in the Ocean might be seen as a pretty simple seamanlike activity. Connecting valuable scientific instrumentation to it transforms this simple activity into a sophisticated engineering support which needs to be accurately designed, developed, deployed, monitored and hopefully recovered with its precious load of scientific data. This work is an historical travel along the efforts carried out by scientists all over the world to successfully predict mooring line behaviour through both mathematical simulation and experimental verifications. It is at first glance unexpected how many factors one must observe to get closer and closer to a real ocean situation. Most models have dual applications for mooring lines and towed bodies lines equations. Numerous references are provided starting from the oldest one due to Isaac Newton. In his "Philosophiae Naturalis Principia Matematica" (1687) the English scientist, while discussing about the law of motion for bodies in resistant medium, is envisaging a hyperbolic fitting to the phenomenon including asymptotic behaviour in non-resistant media. A non-exhaustive set of mathematical simulations of the mooring lines trajectory prediction is listed hereunder to document how the subject has been under scientific focus over almost a century. Pode (1951) Prior personal computers diffusion a tabular form of calculus of cable geometry was used by generations of engineers keeping in mind the following limitations and approximations: tangential drag coefficients were assumed to be negligible. A steady current flow was assumed as in the towed configuration. Cchabra (1982) Finite Element Method that assumes an arbitrary deflection angle for the top first section and calculates equilibrium equations down to the sea floor iterating up to a compliant solution. Gualdesi (1987) ANAMOOR. A Fortran Program based on iterative methods above including experimental data from intensive mooring campaign. Database of experimental drag
On the stability of weakly hyperbolic invariant sets
Begun, N. A.; Pliss, V. A.; Sell, G. R.
2017-02-01
The dynamical object which we study is a compact invariant set with a suitable hyperbolic structure. Stability of weakly hyperbolic sets was studied by V. A. Pliss and G. R. Sell (see [1,2]). They assumed that the neutral, unstable and stable linear spaces of the corresponding linearized systems satisfy Lipschitz condition. They showed that if a perturbation is small, then the perturbed system has a weakly hyperbolic set KY, which is homeomorphic to the weakly hyperbolic set K of the initial system, close to K, and the dynamics on KY is close to the dynamics on K. At the same time, it is known that the Lipschitz property is too strong in the sense that the set of systems without this property is generic. Hence, there was a need to introduce new methods of studying stability of weakly hyperbolic sets without Lipschitz condition. These new methods appeared in [16-20]. They were based on the local coordinates introduced in [18] and the continuous on the whole weakly hyperbolic set coordinates introduced in [19]. In this paper we will show that even without Lipschitz condition there exists a continuous mapping h such that h (K) =KY.
A Real-time Image Processing with a Compact FPGA-based Architecture
Ridha Djemal
2005-01-01
Full Text Available This study have presented a filed programmable gate array implementation of a real time video smoothing algorithm. In comparison with smoothing video techniques like deblocking filters in H.264 or smoothing in JPEG2000, the proposed method is implemented in hardware and its computational cost and complexity are reduced where all pixel processing related to uncompressed video is done on the fly. Our proposed architecture tries to optimize the design of a modified version of the Nagao filter in order to make video smoothing with respect to real time constraints. This filter have to smooth video before applying an edge extraction approach for manufacturing process control. The proposed architecture based on the RC1000P-P Virtex prototyping Board is analyzed to gain an understanding of the relationships between algorithmic features and implementation cost. Experimental results indicate that using this prototyping board with optimized hardware architecture; we can deliver real-time performances and an improvement in the video quality. This filter is capable to process a real time video with a high resolution and deliver 30 images per second at 10 MHz clock cycle.
Zor, Kinga; Heiskanen, Arto; Caviglia, Claudia
2014-01-01
and electrochemical analysis platform with in-built fluid handling and detection, enabling complete cell based assays comprising on-line electrode cleaning, sterilization, surface functionalization, cell seeding, cultivation and electrochemical real-time monitoring of cellular dynamics. To demonstrate the versatility...
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...
Asymptotically hyperbolic connections
Fine, Joel; Krasnov, Kirill; Scarinci, Carlos
2015-01-01
General Relativity in 4 dimensions can be equivalently described as a dynamical theory of SO(3)-connections rather than metrics. We introduce the notion of asymptotically hyperbolic connections, and work out an analog of the Fefferman-Graham expansion in the language of connections. As in the metric setup, one can solve the arising "evolution" equations order by order in the expansion in powers of the radial coordinate. The solution in the connection setting is arguably simpler, and very straightforward algebraic manipulations allow one to see how the obstruction appears at third order in the expansion. Another interesting feature of the connection formulation is that the "counter terms" required in the computation of the renormalised volume all combine into the Chern-Simons functional of the restriction of the connection to the boundary. As the Chern-Simons invariant is only defined modulo large gauge transformations, the requirement that the path integral over asymptotically hyperbolic connections is well-d...
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...
A Penrose inequality for asymptotically locally hyperbolic graphs
de Lima, Levi Lopes
2013-01-01
We use the inverse mean curvature flow to prove a sharp Alexandrov-Fenchel-type inequality for a class of hypersurfaces in certain locally hyperbolic manifolds. As an application we derive an optimal Penrose inequality for asymptotically locally hyperbolic graphs in any dimension $n\\geq 3$. When the horizon has the topology of a compact surface of genus at least one, this provides an affirmative answer, for this class of initial data sets, to a question posed by Gibbons, Chru\\'sciel and Simon on the validity of a Penrose-type inequality for black hole solutions carrying a higher genus horizon.
Asymptotically hyperbolic connections
Fine, Joel; Herfray, Yannick; Krasnov, Kirill; Scarinci, Carlos
2016-09-01
General relativity in four-dimensions can be equivalently described as a dynamical theory of {SO}(3)˜ {SU}(2)-connections rather than metrics. We introduce the notion of asymptotically hyperbolic connections, and work out an analogue of the Fefferman-Graham expansion in the language of connections. As in the metric setup, one can solve the arising ‘evolution’ equations order by order in the expansion in powers of the radial coordinate. The solution in the connection setting is arguably simpler, and very straightforward algebraic manipulations allow one to see how the unconstrained by Einstein equations ‘stress-energy tensor’ appears at third order in the expansion. Another interesting feature of the connection formulation is that the ‘counter terms’ required in the computation of the renormalised volume all combine into the Chern-Simons functional of the restriction of the connection to the boundary. As the Chern-Simons invariant is only defined modulo large gauge transformations, the requirement that the path integral over asymptotically hyperbolic connections is well-defined requires the cosmological constant to be quantised. Finally, in the connection setting one can deform the 4D Einstein condition in an interesting way, and we show that asymptotically hyperbolic connection expansion is universal and valid for any of the deformed theories.
Hyperbolic Plykin attractor can exist in neuron models
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...
Emergent hyperbolic geometry of growing simplicial complexes
Bianconi, Ginestra
2016-01-01
A large variety of interacting complex systems, including brain functional networks, protein interactions and collaboration networks is characterized by interactions occurring between more than two nodes. These systems are described by simplicial complexes. Simplicial complexes are formed by simplices (nodes, links, triangles, tetrahedra etc.) that have a natural geometric interpretation. As such they are ideal structures to investigate the hidden geometry of complex networks and explore whether this geometry is hyperbolic. Here we show an hyperbolic network geometry emerges spontaneously from models of growing simplicial complexes. The statistical and geometrical properties of the growing simplicial complexes strongly depend on their dimensionality and display all the universal properties of real complex networks. Interestingly, when the network dynamics includes an heterogeneous fitness of the faces, the growing simplicial complex can undergo phase transitions that are reflected by dramatic changes in the n...
Two-Generator Free Kleinian Groups and Hyperbolic Displacements
Yuce, Ilker S
2009-01-01
The $\\log 3$ Theorem, proved by Culler and Shalen, states that every point in the hyperbolic 3-space is moved a distance at least $\\log 3$ by one of the non-commuting isometries $\\xi$ or $\\eta$ provided that $\\xi$ and $\\eta$ generate a torsion-free, discrete group which is not co-compact and contains no parabolic. This theorem lies in the foundation of many techniques that provide lower estimates for the volumes of orientable, closed hyperbolic 3-manifolds whose fundamental group has no 2-generator subgroup of finite index and, as a consequence, gives insights into the topological properties of these manifolds. In this paper, we show that every point in the hyperbolic 3-space is moved a distance at least $(1/2)\\log(5+3\\sqrt{2})$ by one of the isometries in $\\{\\xi,\\eta,\\xi\\eta\\}$ when $\\xi$ and $\\eta$ satisfy the conditions given in the $\\log 3$ Theorem.
On hyperbolic Bessel processes and beyond
Wisniewolski, Maciej
2011-01-01
We investigate distributions of hyperbolic Bessel processes. We find links between the hyperbolic cosinus of the hyperbolic Bessel processes and the functionals of geometric Brownian motion. We present an explicit formula of Laplace transform of hyperbolic cosinus of hyperbolic Bessel processes and some interesting different probabilistic representations of this Laplace transform. We express the one-dimensional distribution of hyperbolic Bessel process in terms of other, known and independent processes. We present some applications including a new proof of Bougerol's identity and it's generalization. We characterize the distribution of the process being hyperbolic sinus of hyperbolic Bessel processes.
Barbillon, Grégory; Biehs, Svend-Age; Ben-Abdallah, Philippe
2016-01-01
A thermal antenna is an electromagnetic source which emits in its surrounding, a spatially coherent field in the infrared frequency range. Usually, its emission pattern changes with the wavelength so that the heat flux it radiates is weakly directive. Here, we show that a class of hyperbolic materials, possesses a Brewster angle which is weakly dependent on the wavelength, so that they can radiate like a true thermal antenna with a highly directional heat flux. The realization of these sources could open a new avenue in the field of thermal management in far-field regime.
Evolutes of Hyperbolic Plane Curves
Shyuichi IZUMIYA; Dong He PEI; Takashi SANO; Erika TORII
2004-01-01
We define the notion of evolutes of curves in a hyperbolic plane and establish the relationships between singularities of these subjects and geometric invariants of curves under the action of the Lorentz group. We also describe how we can draw the picture of an evolute of a hyperbolic plane curve in the Poincar(e) disk.
Hyperbolic semi-adequate links
Futer, David; Kalfagianni, Efstratia; Purcell, Jessica S.
2013-01-01
We provide a diagrammatic criterion for semi-adequate links to be hyperbolic. We also give a conjectural description of the satellite structures of semi-adequate links. One application of our result is that the closures of sufficiently complicated positive braids are hyperbolic links.
Symbolic dynamics and hyperbolic groups
Coornaert, Michel
1993-01-01
Gromov's theory of hyperbolic groups have had a big impact in combinatorial group theory and has deep connections with many branches of mathematics suchdifferential geometry, representation theory, ergodic theory and dynamical systems. This book is an elaboration on some ideas of Gromov on hyperbolic spaces and hyperbolic groups in relation with symbolic dynamics. Particular attention is paid to the dynamical system defined by the action of a hyperbolic group on its boundary. The boundary is most oftenchaotic both as a topological space and as a dynamical system, and a description of this boundary and the action is given in terms of subshifts of finite type. The book is self-contained and includes two introductory chapters, one on Gromov's hyperbolic geometry and the other one on symbolic dynamics. It is intended for students and researchers in geometry and in dynamical systems, and can be used asthe basis for a graduate course on these subjects.
W. Q. Sun
2015-06-01
Full Text Available In this study, we report on the development of a compact lamp-based vacuum ultraviolet (VUV photoionization mass spectrometer (PIMS; hereafter referred to as VUV-PIMS in our laboratory; it is composed of a radio frequency-powered VUV lamp, a VUV photoionizer, an ion-immigration region, and a reflection time-of-flight mass spectrometer. By utilizing the novel photoionizer consisting of a photoionization cavity and a VUV light baffle, extremely low background noise was obtained. An ultrasensitive detection limit (2σ of 3 pptv was achieved for benzene after an acquisition time of 10 s. To examine its potential for application in real-time sample monitoring, the developed VUV-PIMS was employed for the continuous measurement of urban air for six days in Beijing, China. Strong signals of trace-level volatile organic compounds such as benzene and its alkylated derivatives were observed in the mass spectra. These initial experimental results reveal that the instrument can be used for the online monitoring of trace-level species in the atmosphere.
Mohammed, Mogtaba; Sango, Mamadou
2016-07-01
This paper deals with the homogenization of a linear hyperbolic stochastic partial differential equation (SPDE) with highly oscillating periodic coefficients. We use Tartar’s method of oscillating test functions and deep probabilistic compactness results due to Prokhorov and Skorokhod. We show that the sequence of solutions of the original problem converges in suitable topologies to the solution of a homogenized linear hyperbolic SPDE with constant coefficients. We also prove the convergence of the associated energies.
Roback, VIncent E.; Amzajerdian, Farzin; Brewster, Paul F.; Barnes, Bruce W.; Kempton, Kevin S.; Reisse, Robert A.; Bulyshev, Alexander E.
2013-01-01
A second generation, compact, real-time, air-cooled 3-D imaging Flash Lidar sensor system, developed from a number of cutting-edge components from industry and NASA, is lab characterized and helicopter flight tested under the Autonomous Precision Landing and Hazard Detection and Avoidance Technology (ALHAT) project. The ALHAT project is seeking to develop a guidance, navigation, and control (GN&C) and sensing system based on lidar technology capable of enabling safe, precise crewed or robotic landings in challenging terrain on planetary bodies under any ambient lighting conditions. The Flash Lidar incorporates a 3-D imaging video camera based on Indium-Gallium-Arsenide Avalanche Photo Diode and novel micro-electronic technology for a 128 x 128 pixel array operating at a video rate of 20 Hz, a high pulse-energy 1.06 µm Neodymium-doped: Yttrium Aluminum Garnet (Nd:YAG) laser, a remote laser safety termination system, high performance transmitter and receiver optics with one and five degrees field-of-view (FOV), enhanced onboard thermal control, as well as a compact and self-contained suite of support electronics housed in a single box and built around a PC-104 architecture to enable autonomous operations. The Flash Lidar was developed and then characterized at two NASA-Langley Research Center (LaRC) outdoor laser test range facilities both statically and dynamically, integrated with other ALHAT GN&C subsystems from partner organizations, and installed onto a Bell UH-1H Iroquois "Huey" helicopter at LaRC. The integrated system was flight tested at the NASA-Kennedy Space Center (KSC) on simulated lunar approach to a custom hazard field consisting of rocks, craters, hazardous slopes, and safe-sites near the Shuttle Landing Facility runway starting at slant ranges of 750 m. In order to evaluate different methods of achieving hazard detection, the lidar, in conjunction with the ALHAT hazard detection and GN&C system, operates in both a narrow 1deg FOV raster
Manton, Nicholas
2014-01-01
We construct a number of explicit examples of hyperbolic monopoles, with various charges and often with some platonic symmetry. The fields are obtained from instanton data in four-dimensional Euclidean space that are invariant under a circle action, and the monopole charge is equal to the instanton charge. A key ingredient is the identification of a new set of constraints on ADHM instanton data that are sufficient to ensure the circle invariance. Algebraic formulae for the Higgs field magnitude are given and from these we compute and illustrate the energy density of the monopoles. For particular monopoles, the explicit formulae provide a proof that the number of zeros of the Higgs field is greater than the monopole charge. We also present some one-parameter families of monopoles analogous to known scattering events for Euclidean monopoles within the geodesic approximation.
Hyperbolically Shaped Centrifugal Compressor
Romuald Puzyrewski; Pawel Flaszy(n)ski
2003-01-01
Starting from the classical centrifugal compressor, cone shaped in meridional cross section, two modifications are considered on the basis of results from 2D and 3D flow models. The first modification is the change of the meridional cross section to hyperbolically shaped channel. The second modification, proposed on the basis of 2D axisymmetric solution, concerns the shape of blading. On the strength of this solution the blades are formed as 3D shaped blades, coinciding with the recent tendency in 3D designs. Two aims were considered for the change of meridional compressor shape. The first was to remove the separation zone which appears as the flow tums from axial to radial direction. The second aim is to uniformize the flow at exit of impeller. These two goals were considered within the frame of 2D axisymmetric model. Replacing the cone shaped compressor by a hyperbolically shaped one, the separation at the corner was removed. The disc and shroud shape of the compressor was chosen in the way which satisfies the condition of most uniform flow at the compressor exit. The uniformity of exit flow from the rotor can be considered as the factor which influences the performance of the diffuser following the rotor. In the 2D model a family of stream surfaces of S1 type is given in order to find S2 surfaces which may be identified with the midblade surfaces of compressor blading. A computation of 3D type has been performed in order to establish the relations between 2D and 3D models in the calculation of flow parameters. In the presented example the 2D model appears as the inverse model which leads to 3D shape of blading whereas the 3D model has been used for the direct solution. In the presented example the confrontation of two models, 2D and 3D, leads to a better understanding of the application of these models to the design procedure.
Hyperbolic lattice-point counting and modular symbols
N. Petridis, Yiannis; Risager, Morten S.
2009-01-01
For a cocompact group $\\G$ of $\\slr$ we fix a real non-zero harmonic 1-form $\\alpha$. We study the asymptotics of the hyperbolic lattice-counting problem for $\\G$ under restrictions imposed by the modular symbols $\\modsym{\\gamma}{\\a}$. We prove that the normalized values of the modular symbols...
Ritt's theorem and the Heins map in hyperbolic complex manifolds
Marco; Abate; Filippo; Bracci
2005-01-01
Let X be a Kobayashi hyperbolic complex manifold, and assume that X does not contain compact complex submanifolds of positive dimension (e.g., X Stein). We shall prove the following generalization of Ritt's theorem: every holomorphic self-map f: X →X such that f(X) is relatively compact in X has a unique fixed point τ(f) ∈ X, which is attracting. Furthermore, we shall prove that τ(f) depends holomorphically on f in a suitable sense, generalizing results by Heins, Joseph-Kwack and the second author.
Hyperbolic Methods for Einstein's Equations
Reula Oscar
1998-01-01
Full Text Available I review evolutionary aspects of general relativity, in particular those related to the hyperbolic character of the field equations and to the applications or consequences that this property entails. I look at several approaches to obtaining symmetric hyperbolic systems of equations out of Einstein's equations by either removing some gauge freedoms from them, or by considering certain linear combinations of a subset of them.
Hyperbolically Discounted Temporal Difference Learning
Alexander, William H.; Brown, Joshua W.
2010-01-01
Hyperbolic discounting of future outcomes is widely observed to underlie choice behavior in animals. Additionally, recent studies (Kobayashi & Schultz, 2008) have reported that hyperbolic discounting is observed even in neural systems underlying choice. However, the most prevalent models of temporal discounting, such as temporal difference learning, assume that future outcomes are discounted exponentially. Exponential discounting has been preferred largely because it is able to be expressed r...
Abelian Duality on Globally Hyperbolic Spacetimes
Becker, Christian; Benini, Marco; Schenkel, Alexander; Szabo, Richard J.
2017-01-01
We study generalized electric/magnetic duality in Abelian gauge theory by combining techniques from locally covariant quantum field theory and Cheeger-Simons differential cohomology on the category of globally hyperbolic Lorentzian manifolds. Our approach generalizes previous treatments using the Hamiltonian formalism in a manifestly covariant way and without the assumption of compact Cauchy surfaces. We construct semi-classical configuration spaces and corresponding presymplectic Abelian groups of observables, which are quantized by the CCR-functor to the category of C*-algebras. We demonstrate explicitly how duality is implemented as a natural isomorphism between quantum field theories. We apply this formalism to develop a fully covariant quantum theory of self-dual fields.
Forced hyperbolic mean curvature flow
Mao, Jing
2012-01-01
In this paper, we investigate two hyperbolic flows obtained by adding forcing terms in direction of the position vector to the hyperbolic mean curvature flows in \\cite{klw,hdl}. For the first hyperbolic flow, as in \\cite{klw}, by using support function, we reduce it to a hyperbolic Monge-Amp$\\grave{\\rm{e}}$re equation successfully, leading to the short-time existence of the flow by the standard theory of hyperbolic partial differential equation. If the initial velocity is non-negative and the coefficient function of the forcing term is non-positive, we also show that there exists a class of initial velocities such that the solution of the flow exists only on a finite time interval $[0,T_{max})$, and the solution converges to a point or shocks and other propagating discontinuities are generated when $t\\rightarrow{T_{max}}$. These generalize the corresponding results in \\cite{klw}. For the second hyperbolic flow, as in \\cite{hdl}, we can prove the system of partial differential equations related to the flow is ...
Hitting spheres on hyperbolic spaces
Cammarota, Valentina
2011-01-01
For a hyperbolic Brownian motion on the Poincar\\'e half-plane $\\mathbb{H}^2$, starting from a point of hyperbolic coordinates $z=(\\eta, \\alpha)$ inside a hyperbolic disc $U$ of radius $\\bar{\\eta}$, we obtain the probability of hitting the boundary $\\partial U$ at the point $(\\bar \\eta,\\bar \\alpha)$. For $\\bar{\\eta} \\to \\infty$ we derive the asymptotic Cauchy hitting distribution on $\\partial \\mathbb{H}^2$ and for small values of $\\eta$ and $\\bar \\eta$ we obtain the classical Euclidean Poisson kernel. The exit probabilities $\\mathbb{P}_z\\{T_{\\eta_1}
Development of hyperbolic solution method for two fluids equation system
Lee, Sung Jae; Chang, Won Pyo
1997-07-01
Using the concept of surface tension thickness, the mathematical ill-posedness of the two fluids equation system can now be removed by splitting the pressure discontinuity of the two fluids interface. The bulk modulus L1 and L2 derived from the concept of surface tension thickness makes two fluids equation system hyperbolic type. The hyperbolic equation system has five complete sets of eigenvectors, each of which having real eigenvalues. Three sets of them represents the propagation speeds of the physical properties for individual flow regimes such as the dispersed, the slug, and the separated flows. The propagation characteristics of these eigenvalues have good agreements with both the experimental data and other theoretical results in two-phase mixture. The feature of the hyperbolic model allows to apply advanced numerical upwind technique such as Flux vector splitting (FVS) method. The numerical test show that the characteristics of equation system clearly classify all flow regimes. (author). 25 refs., 3 tabs., 20 figs.
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. PMID:28120826
Dayanga, Waduthanthree Thilina
Albert Einstein's general theory of relativity predicts the existence of gravitational waves (GWs). Direct detection of GWs will provide enormous amount of new information about physics, astronomy and cosmology. Scientists around the world are currently working towards the first direct detection of GWs. The global network of ground-based GW detectors are currently preparing for their first advanced detector Science runs. In this thesis we focus on detection of GWs from compact binary coalescence (CBC) systems. Ability to accurately model CBC GW waveforms makes them the most promising source for the first direct detection of GWs. In this thesis we try to address several challenges associated with detecting CBC signals buried in ground-based GW detector data for past and future searches. Data analysis techniques we employ to detect GW signals assume detector noise is Gaussian and stationary. However, in reality, detector data is neither Gaussian nor stationary. To estimate the performance loss due to these features, we compare the efficiencies of detecting CBC signals in simulated Gaussian and real data. Additionally, we also demonstrate the effectiveness of multi-detector signal based consistency tests such ad null-stream. Despite, non-Gaussian and non-stationary features of real detector data, with effective data quality studies and signal-based vetoes we can approach the performance of Gaussian and stationary data. As we are moving towards advanced detector era, it is important to be prepared for future CBC searches. In this thesis we investigate the performances of non-spinning binary black hole (BBH) searches in simulated Gaussian using advanced detector noise curves predicted for 2015--2016. In the same study, we analyze the GW detection probabilities of latest pN-NR hybrid waveforms submitted to second version of Numerical Injection Analysis (NINJA-2) project. The main motivation for this study is to understand the ability to detect realistic BBH signals of
Anomalous diffraction in hyperbolic materials
Alberucci, Alessandro; Boardman, Allan D; Assanto, Gaetano
2016-01-01
We demonstrate that light is subject to anomalous (i.e., negative) diffraction when propagating in the presence of hyperbolic dispersion. We show that light propagation in hyperbolic media resembles the dynamics of a quantum particle of negative mass moving in a two-dimensional potential. The negative effective mass implies time reversal if the medium is homogeneous. Such property paves the way to diffraction compensation, spatial analogue of dispersion compensating fibers in the temporal domain. At variance with materials exhibiting standard elliptic dispersion, in inhomogeneous hyperbolic materials light waves are pulled towards regions with a lower refractive index. In the presence of a Kerr-like optical response, bright (dark) solitons are supported by a negative (positive) nonlinearity.
Advanced fabrication of hyperbolic metamaterials
Shkondin, Evgeniy; Sukham, Johneph; Panah, Mohammad E. Aryaee; Takayama, Osamu; Malureanu, Radu; Jensen, Flemming; Lavrinenko, Andrei V.
2017-09-01
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 is expected to exhibit hyperbolic properties in the visible range. As the second approach we apply the atomic layer deposition technique to arrange vertical alignment of layers or pillars of heavily doped ZnO or TiN, which enables us to produce hyperbolic metamaterials for the near- and mid-infrared ranges.
Anomalous diffraction in hyperbolic materials
Alberucci, Alessandro; Jisha, Chandroth P.; Boardman, Allan D.; Assanto, Gaetano
2016-09-01
We demonstrate that light is subject to anomalous (i.e., negative) diffraction when propagating in the presence of hyperbolic dispersion. We show that light propagation in hyperbolic media resembles the dynamics of a quantum particle of negative mass moving in a two-dimensional potential. The negative effective mass implies time reversal if the medium is homogeneous. Such property paves the way to diffraction compensation, i.e., spatial analog of dispersion compensating fibers in the temporal domain. At variance with materials exhibiting standard elliptic dispersion, in inhomogeneous hyperbolic materials light waves are pulled towards regions with a lower refractive index. In the presence of a Kerr-like optical response, bright (dark) solitons are supported by a negative (positive) nonlinearity.
Exact Solutions for Einstein's Hyperbolic Geometric Flow
HE Chun-Lei
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.
DETERMINISTIC HOMOGENIZATION OF QUASILINEAR DAMPED HYPERBOLIC EQUATIONS
Gabriel Nguetseng; Hubert Nnang; Nils Svanstedt
2011-01-01
Deterministic homogenization is studied for quasilinear monotone hyperbolic problems with a linear damping term.It is shown by the sigma-convergence method that the sequence of solutions to a class of multi-scale highly oscillatory hyperbolic problems converges to the solution to a homogenized quasilinear hyperbolic problem.
Quasi-Hyperbolicity and Delay Semigroups
Shard Rastogi
2016-01-01
Full Text Available We study quasi-hyperbolicity of the delay semigroup associated with the equation u′(t=Bu(t+Φut, where ut is the history function and (B,D(B is the generator of a quasi-hyperbolic semigroup. We give conditions under which the associated solution semigroup of this equation generates a quasi-hyperbolic semigroup.
Exhibition of circular Bragg phenomenon by hyperbolic, dielectric, structurally chiral materials
Lakhtakia, Akhlesh
2014-01-01
The relative permittivity dyadic of a dielectric structurally chiral material (SCM) varies helicoidally along a fixed direction; in consequence, the SCM exhibits the circular Bragg phenomenon, which is the circular-polarization-selective reflection of light. The introduction of hyperbolicity in an SCM-by making either one or two but not all three eigenvalues of the relative permittivity dyadic acquire negative real parts-does not eliminate the circular Bragg phenomenon, but significantly alters the regime for its exhibition. Significantly wider circular-polarization-sensitive stopbands may be exhibited by hyperbolic SCMs in comparison to nonhyperbolic SCMs. Physical vapor deposition techniques appear to be suitable to fabricate hyperbolic SCMs.
A unified approach to finite-time hyperbolicity which extends finite-time Lyapunov exponents
Doan, T. S.; Karrasch, D.; Nguyen, T. Y.; Siegmund, S.
A hyperbolicity notion for linear differential equations x˙=A(t)x, t∈[t-,t+], is defined which unifies different existing notions like finite-time Lyapunov exponents (Haller, 2001, [13], Shadden et al., 2005, [24]), uniform or M-hyperbolicity (Haller, 2001, [13], Berger et al., 2009, [6]) and (t-,(t+-t-))-dichotomy (Rasmussen, 2010, [21]). Its relation to the dichotomy spectrum (Sacker and Sell, 1978, [23], Siegmund, 2002, [26]), D-hyperbolicity (Berger et al., 2009, [6]) and real parts of the eigenvalues (in case A is constant) is described. We prove a spectral theorem and provide an approximation result for the spectral intervals.
Nakasho Kazuhisa
2016-09-01
Full Text Available In this article, we mainly formalize in Mizar [2] the equivalence among a few compactness definitions of metric spaces, norm spaces, and the real line. In the first section, we formalized general topological properties of metric spaces. We discussed openness and closedness of subsets in metric spaces in terms of convergence of element sequences. In the second section, we firstly formalize the definition of sequentially compact, and then discuss the equivalence of compactness, countable compactness, sequential compactness, and totally boundedness with completeness in metric spaces.
Visible-frequency hyperbolic metasurface
High, Alexander A.; Devlin, Robert C.; Dibos, Alan; Polking, Mark; Wild, Dominik S.; Perczel, Janos; de Leon, Nathalie P.; Lukin, Mikhail D.; Park, Hongkun
2015-06-01
Metamaterials are artificial optical media composed of sub-wavelength metallic and dielectric building blocks that feature optical phenomena not present in naturally occurring materials. Although they can serve as the basis for unique optical devices that mould the flow of light in unconventional ways, three-dimensional metamaterials suffer from extreme propagation losses. Two-dimensional metamaterials (metasurfaces) such as hyperbolic metasurfaces for propagating surface plasmon polaritons have the potential to alleviate this problem. Because the surface plasmon polaritons are guided at a metal-dielectric interface (rather than passing through metallic components), these hyperbolic metasurfaces have been predicted to suffer much lower propagation loss while still exhibiting optical phenomena akin to those in three-dimensional metamaterials. Moreover, because of their planar nature, these devices enable the construction of integrated metamaterial circuits as well as easy coupling with other optoelectronic elements. Here we report the experimental realization of a visible-frequency hyperbolic metasurface using single-crystal silver nanostructures defined by lithographic and etching techniques. The resulting devices display the characteristic properties of metamaterials, such as negative refraction and diffraction-free propagation, with device performance greatly exceeding those of previous demonstrations. Moreover, hyperbolic metasurfaces exhibit strong, dispersion-dependent spin-orbit coupling, enabling polarization- and wavelength-dependent routeing of surface plasmon polaritons and two-dimensional chiral optical components. These results open the door to realizing integrated optical meta-circuits, with wide-ranging applications in areas from imaging and sensing to quantum optics and quantum information science.
Hyperbolic Formulation of General Relativity
Abrahams, A M; Choquet-Bruhat, Y; York, J W; Abrahams, Andrew; Anderson, Arlen; Choquet-Bruhat, Yvonne; York, James W.
1998-01-01
Two geometrical well-posed hyperbolic formulations of general relativity are described. One admits any time-slicing which preserves a generalized harmonic condition. The other admits arbitrary time-slicings. Both systems have only the physical characteristic speeds of zero and the speed of light.
Hyperbolic metamaterials: fundamentals and applications.
Shekhar, Prashant; Atkinson, Jonathan; Jacob, Zubin
2014-01-01
Metamaterials are nano-engineered media with designed properties beyond those available in nature with applications in all aspects of materials science. In particular, metamaterials have shown promise for next generation optical materials with electromagnetic responses that cannot be obtained from conventional media. We review the fundamental properties of metamaterials with hyperbolic dispersion and present the various applications where such media offer potential for transformative impact. These artificial materials support unique bulk electromagnetic states which can tailor light-matter interaction at the nanoscale. We present a unified view of practical approaches to achieve hyperbolic dispersion using thin film and nanowire structures. We also review current research in the field of hyperbolic metamaterials such as sub-wavelength imaging and broadband photonic density of states engineering. The review introduces the concepts central to the theory of hyperbolic media as well as nanofabrication and characterization details essential to experimentalists. Finally, we outline the challenges in the area and offer a set of directions for future work.
Nonlocal response of hyperbolic metasurfaces.
Correas-Serrano, D; Gomez-Diaz, J S; Tymchenko, M; Alù, A
2015-11-16
We analyze and model the nonlocal response of ultrathin hyperbolic metasurfaces (HMTSs) by applying an effective medium approach. We show that the intrinsic spatial dispersion in the materials employed to realize the metasurfaces imposes a wavenumber cutoff on the hyperbolic isofrequency contour, inversely proportional to the Fermi velocity, and we compare it with the cutoff arising from the structure granularity. In the particular case of HTMSs implemented by an array of graphene nanostrips, we find that graphene nonlocality can become the dominant mechanism that closes the hyperbolic contour - imposing a wavenumber cutoff at around 300k(0) - in realistic configurations with periodicity Lnonlocal response is mainly relevant in hyperbolic metasurfaces and metamaterials with periodicity below a few nm, being very weak in practical scenarios. In addition, we investigate how spatial dispersion affects the spontaneous emission rate of emitters located close to HMTSs. Our results establish an upper bound set by nonlocality to the maximum field confinement and light-matter interactions achievable in practical HMTSs, and may find application in the practical development of hyperlenses, sensors and on-chip networks.
Fractals with Hyperbolic Scators in 1 + 2 Dimensions
Fernández-Guasti, M.
2015-04-01
A nondistributive scator algebra in 1 + 2 dimensions is used to map the quadratic iteration. The hyperbolic numbers square bound set reveals a rich structure when taken into the three-dimensional (3D) hyperbolic scator space. Self-similar small copies of the larger set are obtained along the real axis. These self-similar sets are located at the same positions and have equivalent relative sizes as the small M-set copies found between the Myrberg-Feigenbaum (MF) point and -2 in the complex Mandelbrot set. Furthermore, these small copies are self similar 3D copies of the larger 3D bound set. The real roots of the respective polynomials exhibit basins of attraction in a 3D space. Slices of the 3D confined scator set, labeled {c2i0}{E}+1+2(s;x,y), are shown at different planes to give an approximate idea of the 3D objects highly complicated boundary.
Gromov Hyperbolicity in Cartesian Product Graphs
Junior Michel; José M Rodríguez; José M Sigarreta; María Villeta
2010-11-01
If is a geodesic metric space and $x_1,x_2,x_3\\in X$, a geodesic triangle $T=\\{x_1,x_2,x_3\\}$ is the union of the three geodesics $[x_1x_2], [x_2x_3]$ and $[x_3x_1]$ in . The space is -hyperbolic (in the Gromov sense) if any side of is contained in a -neighborhood of the union of the two other sides, for every geodesic triangle in . If is hyperbolic, we denote by () the sharp hyperbolicity constant of , i.e. $(X)=\\inf\\{≥ 0:X\\, \\text{is}-\\text{hyperbolic}\\}$. In this paper we characterize the product graphs 1 × 2 which are hyperbolic, in terms of 1 and 2: the product graph 1 × 2 is hyperbolic if and only if 1 is hyperbolic and 2 is bounded or 2 is hyperbolic and 1 is bounded. We also prove some sharp relations between the hyperbolicity constant of $1 × 2,(1),(2) and the diameters of 1 and 2 (and we find families of graphs for which the inequalities are attained). Furthermore, we obtain the precise value of the hyperbolicity constant for many product graphs.
Green function for hyperbolic media
Potemkin, Andrey S; Belov, Pavel A; Kivshar, Yuri S
2012-01-01
We revisit the problem of the electromagnetic Green function for homogeneous hyperbolic media, where longitudinal and transverse components of the dielectric permittivity tensor have different signs. We analyze the dipole emission patterns for both dipole orientations with respect to the symmetry axis and for different signs of dielectric constants, and show that the emission pattern is highly anisotropic and has a characteristic cross-like shape: the waves are propagating within a certain cone and are evanescent outside this cone. We demonstrate the coexistence of the cone-like pattern due to emission of the extraordinary TM-polarized waves and elliptical pattern due to emission of ordinary TE-polarized waves. We find a singular complex term in the Green function, proportional to the $\\delta-$function and governing the photonic density of states and Purcell effect in hyperbolic media.
Hyperbolic Metamaterials with Bragg Polaritons
Sedov, Evgeny S.; Iorsh, I. V.; Arakelian, S. M.; Alodjants, A. P.; Kavokin, Alexey
2015-06-01
We propose a novel mechanism for designing quantum hyperbolic metamaterials with the use of semiconductor Bragg mirrors containing periodically arranged quantum wells. The hyperbolic dispersion of exciton-polariton modes is realized near the top of the first allowed photonic miniband in such a structure which leads to the formation of exciton-polariton X waves. Exciton-light coupling provides a resonant nonlinearity which leads to nontrivial topologic solutions. We predict the formation of low amplitude spatially localized oscillatory structures: oscillons described by kink shaped solutions of the effective Ginzburg-Landau-Higgs equation. The oscillons have direct analogies in gravitational theory. We discuss implementation of exciton-polariton Higgs fields for the Schrödinger cat state generation.
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...
Bounds on Gromov Hyperbolicity Constant in Graphs
José M Rodríguez; José M Sigarreta
2012-02-01
If is a geodesic metric space and 1,2,3 $\\in$ , a geodesic triangle ={1,2,3} is the union of the three geodesics [1,2], [2,3] and [31] in . The space is -hyperbolic (in the Gromov sense) if any side of is contained in a -neighborhood of the union of two other sides, for every geodesic triangle in . If is hyperbolic, we denote by () the sharp hyperbolicity constant of , i.e. ()=$inf{$≥ 0$ : is -hyperbolic}. In this paper we relate the hyperbolicity constant of a graph with some known parameters of the graph, as its independence number, its maximum and minimum degree and its domination number. Furthermore, we compute explicitly the hyperbolicity constant of some class of product graphs.
Fourth order difference methods for hyperbolic IBVP's
Gustafsson, Bertil; Olsson, Pelle
1994-01-01
Fourth order difference approximations of initial-boundary value problems for hyperbolic partial differential equations are considered. We use the method of lines approach with both explicit and compact implicit difference operators in space. The explicit operator satisfies an energy estimate leading to strict stability. For the implicit operator we develop boundary conditions and give a complete proof of strong stability using the Laplace transform technique. We also present numerical experiments for the linear advection equation and Burgers' equation with discontinuities in the solution or in its derivative. The first equation is used for modeling contact discontinuities in fluid dynamics, the second one for modeling shocks and rarefaction waves. The time discretization is done with a third order Runge-Kutta TVD method. For solutions with discontinuities in the solution itself we add a filter based on second order viscosity. In case of the non-linear Burger's equation we use a flux splitting technique that results in an energy estimate for certain different approximations, in which case also an entropy condition is fulfilled. In particular we shall demonstrate that the unsplit conservative form produces a non-physical shock instead of the physically correct rarefaction wave. In the numerical experiments we compare our fourth order methods with a standard second order one and with a third order TVD-method. The results show that the fourth order methods are the only ones that give good results for all the considered test problems.
Height in Splittings of Hyperbolic Groups
Mahan Mitra
2004-02-01
Suppose is a hyperbolic subgroup of a hyperbolic group . Assume there exists > 0 such that the intersection of essentially distinct conjugates of is always finite. Further assume splits over with hyperbolic vertex and edge groups and the two inclusions of are quasi-isometric embeddings. Then is quasiconvex in . This answers a question of Swarup and provides a partial converse to the main theorem of [23].
Lyapunov type characterization of hyperbolic behavior
Barreira, Luis; Dragičević, Davor; Valls, Claudia
2017-09-01
We give a complete characterization of the uniform hyperbolicity and nonuniform hyperbolicity of a cocycle with values in the space of bounded linear operators acting on a Hilbert space in terms of the existence of appropriate quadratic forms. Our work unifies and extends many results in the literature by considering the general case of not necessarily invertible cocycles acting on a Hilbert space over an arbitrary invertible dynamics. As a nontrivial application of, we study the persistence of hyperbolicity under small linear perturbations.
Ahn Sung Hwan; Hong, B; Hong, S J; Ito, M; Kim, B I; Kim, J H; Kim, Y J; Kim, Y U; Koo, D G; Lee, H W; Lee, K B; Lee, K S; Lee, S J; Lim, J K; Moon, D H; Nam, S K; Park, S; Park, W J; Rhee, J T; Ryu, M S; Shim, H H; Sim, K S; Kang, T I
2005-01-01
We present the design and the test, results for a real-sized prototype resistive plate chamber by using cosmic-ray muons for the forward region of the Compact Muon Solenoid (CMS) experiment at the Large Hadron Collider (LHC). In particular, we investigate the effects of adding SF/sub 6/ to the gas mixture for the avalanche mode operation of a resistive plate chamber. A small fraction of SF/sub 6/ is very effective in suppressing streamer signals in a resistive plate chamber. The shapes of the muon detection efficiency and the muon cluster size remain similar, but are shifted to higher operating voltage by SF/sub 6/. The noise cluster rate and size are not influenced by SF/sub 6/.
Renormalization group equation for f (R ) gravity on hyperbolic spaces
Falls, Kevin; Ohta, Nobuyoshi
2016-10-01
We derive the flow equation for the gravitational effective average action in an f (R ) truncation on hyperbolic spacetimes using the exponential parametrization of the metric. In contrast to previous works on compact spaces, we are able to evaluate traces exactly using the optimized cutoff. This reveals in particular that all modes can be integrated out for a finite value of the cutoff due to a gap in the spectrum of the Laplacian, leading to the effective action. Studying polynomial solutions, we find poorer convergence than has been found on compact spacetimes even though at small curvature the equations only differ in the treatment of certain modes. In the vicinity of an asymptotically free fixed point, we find the universal beta function for the R2 coupling and compute the corresponding effective action which involves an R2log (R2) quantum correction.
A Remark on Contact Hypersurfaces of a Complex Hyperbolic Space
许志才
1993-01-01
A differentiable manifold is said to be contact if it admits a linear functional f on the tangent bundle satisfying f∧ (df)n-1≠0.This remark obtain the following the classification:Let M be a complete connected contact hyper-surface of CH2(-4),then M is congruent to one of the following:(i) A tube of redius r>0 around a totally geodesic,totally real hyperbolic space form H2(-1);(ii)A tube of radius r>0 around a totally geodesic complex hyperbolic space form CH1(-4);(iii)A geodesic hypersphere of radius r>0,or(iv)A horosphere.
Laplace-Type Semi-Invariants for a System of Two Linear Hyperbolic Equations by Complex Methods
F. M. Mahomed
2011-01-01
Full Text Available In 1773 Laplace obtained two fundamental semi-invariants, called Laplace invariants, for scalar linear hyperbolic partial differential equations (PDEs in two independent variables. He utilized this in his integration theory for such equations. Recently, Tsaousi and Sophocleous studied semi-invariants for systems of two linear hyperbolic PDEs in two independent variables. Separately, by splitting a complex scalar ordinary differential equation (ODE into its real and imaginary parts PDEs for two functions of two variables were obtained and their symmetry structure studied. In this work we revisit semi-invariants under equivalence transformations of the dependent variables for systems of two linear hyperbolic PDEs in two independent variables when such systems correspond to scalar complex linear hyperbolic equations in two independent variables, using the above-mentioned splitting procedure. The semi-invariants under linear changes of the dependent variables deduced for this class of hyperbolic linear systems correspond to the complex semi-invariants of the complex scalar linear (1+1 hyperbolic equation. We show that the adjoint factorization corresponds precisely to the complex splitting. We also study the reductions and the inverse problem when such systems of two linear hyperbolic PDEs arise from a linear complex hyperbolic PDE. Examples are given to show the application of this approach.
Paths of algebraic hyperbolic curves
Ya-juan LI; Li-zheng LU; Guo-zhao WANG
2008-01-01
Cubic algebraic hyperbolic (AH) Bezier curves and AH spline curves are defined with a positive parameter α in the space spanned by {1, t, sinht, cosht}. Modifying the value of α yields a family of AH Bezier or spline curves with the family parameter α. For a fixed point on the original curve, it will move on a defined curve called "path of AH curve" (AH Bezier and AH spline curves) when α changes. We describe the geometric effects of the paths and give a method to specify a curve passing through a given point.
Intelligent compaction theory of high roller compacted concrete dam
Liu Donghai
2012-01-01
The concept and realization process of intelligent compaction for the construction of high roller compacted concrete dam were presented, as well as the theory of monitoring and intelligent feedback control. Based on the real-time analysis of the compaction index, a multiple regression model of the dam compactness was established and a realime estimation method of compaction quality for the entire work area of roller compacted concrete dam was proposed finally. The adaptive adjustment of the roiling process parameters was achieved, with the speed, the exciting force, the roller pass and the compaction thickness meeting the standards during the whole construction process. As a result, the compaction quality and construction efficiency can be improved. The research provides a new way for the construction quality control of roller compacted concrete dam.
Adriana NASTASE
2015-12-01
Full Text Available A comparison of the behaviours of the elliptic with those of hyperbolic quadratic algebraic equations (QAEs with free and linear variable coefficients, in vicinity of their critical surfaces is made. The critic values of the elliptic and hyperbolic QAEs with variables coefficients are obtained by can-celling their great determinant. If only the free term of a QAE is variable from -∞ to + ∞ and the QAE are two-dimensional, an elliptic QAE is represented by coaxial ellipses, which decrease in size and collapse in their common centre. A hyperbolic QAE is represented by coaxial hyperbolas, which approach their asymptotes, degenerate in them, jump over them and go away from them. The real solutions of hyperbolic QAEs exist for all the values of free term and for elliptic QAE, if the value of the free term is greater than the critical one, the real solutions of elliptic QAEs do no longer exist. If, additionally, also the free term is variable, critical parabolas occur, if a plane of coefficients is used. The real solutions for elliptic QAE collapse along their critical parabola and do not exist inside of it. The hyperbolic QAE is represented by coaxial hyperbolas which degenerate in their asymptotes and jump over them along their critical parabola.
A Novel Hyperbolization Procedure for The Two-Phase Six-Equation Flow Model
Samet Y. Kadioglu; Robert Nourgaliev; Nam Dinh
2011-10-01
We introduce a novel approach for the hyperbolization of the well-known two-phase six equation flow model. The six-equation model has been frequently used in many two-phase flow applications such as bubbly fluid flows in nuclear reactors. One major drawback of this model is that it can be arbitrarily non-hyperbolic resulting in difficulties such as numerical instability issues. Non-hyperbolic behavior can be associated with complex eigenvalues that correspond to characteristic matrix of the system. Complex eigenvalues are often due to certain flow parameter choices such as the definition of inter-facial pressure terms. In our method, we prevent the characteristic matrix receiving complex eigenvalues by fine tuning the inter-facial pressure terms with an iterative procedure. In this way, the characteristic matrix possesses all real eigenvalues meaning that the characteristic wave speeds are all real therefore the overall two-phase flowmodel becomes hyperbolic. The main advantage of this is that one can apply less diffusive highly accurate high resolution numerical schemes that often rely on explicit calculations of real eigenvalues. We note that existing non-hyperbolic models are discretized mainly based on low order highly dissipative numerical techniques in order to avoid stability issues.
Building systems from simple hyperbolic ones
Zwart, H.; Le Gorrec, Y.; Maschke, B.
2016-01-01
In this article we introduce a technique that derives from the existence and uniqueness of solutions to a simple hyperbolic partial differential equation (p.d.e.) the existence and uniqueness of solutions to hyperbolic and parabolic p.d.e.’s. Among others, we show that starting with an impedance pas
Building systems from simple hyperbolic ones
Zwart, Heiko J.; Le Gorrec, Y.; Maschke, B.
In this article we introduce a technique that derives from the existence and uniqueness of solutions to a simple hyperbolic partial differential equation (p.d.e.) the existence and uniqueness of solutions to hyperbolic and parabolic p.d.e.’s. Among others, we show that starting with an impedance
Plasmonic waveguides cladded by hyperbolic metamaterials
Ishii, Satoshi; Shalaginov, Mikhail Y.; Babicheva, Viktoriia E.
2014-01-01
Strongly anisotropic media with hyperbolic dispersion can be used for claddings of plasmonic waveguides (PWs). In order to analyze the fundamental properties of such waveguides, we analytically study 1D waveguides arranged from a hyperbolic metamaterial (HMM) in a HMM-Insulator-HMM (HIH) structure...
IMPLEMENTATIONS AND PRACTICAL APPLICATIONS OF HYPERBOLIC METAMATERIALS
A. V. Shchelokova
2014-03-01
Full Text Available The paper presents a review on hyperbolic metamaterials which are normally described by the permittivity and permeability tensors with the components of the opposite sign. Therefore, the hyperbolic metamaterials have the hyperbolic isofrequency surfaces in the wave vector space. It leads to a number of unusual properties, such as the negative refraction, the diverging density of photonic states, ultra-high rate of spontaneous emission and increasing of subwavelength fields. The presence of the unique properties mentioned above makes the concept of hyperbolic metamaterials promising for research in modern science and explains the attempts of research groups around the world to realize structures with hyperbolic isofrequency curve suitable for applications in different frequency ranges. Hyperbolic metamaterials realized as layered metal-dielectric structures, arrays of nanowires, graphene layers, as well as artificial transmission lines are considered in the paper. Possible practical applications of hyperbolic metamaterials are described including hyperlens able to increase the nanoscale objects; wire mediums applied for spectroscopy to improve the resolution and increasing the distance to the object being scanned. Hyperbolic metamaterials are noted to be extremely promising for applications in nanophotonics, including single-photon generation, sensing and photovoltaics.
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.
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.
Hyperbolic monopoles, JNR data and spectral curves
Bolognesi, Stefano; Sutcliffe, Paul
2014-01-01
A large class of explicit hyperbolic monopole solutions can be obtained from JNR instanton data, if the curvature of hyperbolic space is suitably tuned. Here we provide explicit formulae for both the monopole spectral curve and its rational map in terms of JNR data. Examples with platonic symmetry are presented, together with some one-parameter families with cyclic and dihedral symmetries. These families include hyperbolic analogues of geodesics that describe symmetric monopole scatterings in Euclidean space and we illustrate the results with energy density isosurfaces. There is a metric on the moduli space of hyperbolic monopoles, defined using the abelian connection on the boundary of hyperbolic space, and we provide a simple integral formula for this metric on the space of JNR data.
Super-Coulombic atom-atom interactions in hyperbolic media
Cortes, Cristian L
2016-01-01
Dipole-dipole interactions which govern phenomena like cooperative Lamb shifts, superradiant decay rates, Van der Waals forces, as well as 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 (QED) 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 and propose practical implementations with phonon-polaritonic hexagonal boron nitride in the infrared spectral range and plasmonic super-lattice structures in the visible range. Our work paves the way for the control of cold atoms in hyperbolic media and the study of many-body atomic states where optical phonons mediate qua...
Scaling of clusters near discontinuous percolation transitions in hyperbolic networks.
Singh, Vijay; Boettcher, Stefan
2014-07-01
We investigate the onset of the discontinuous percolation transition in small-world hyperbolic networks by studying the systems-size scaling of the typical largest cluster approaching the transition, p ↗ p(c). To this end, we determine the average size of the largest cluster 〈s(max)〉 ∼ N(Ψ(p)) in the thermodynamic limit using real-space renormalization of cluster-generating functions for bond and site percolation in several models of hyperbolic networks that provide exact results. We determine that all our models conform to the recently predicted behavior regarding the growth of the largest cluster, which found diverging, albeit subextensive, clusters spanning the system with finite probability well below p(c) and at most quadratic corrections to unity in Ψ(p) for p ↗ p(c). Our study suggests a large universality in the cluster formation on small-world hyperbolic networks and the potential for an alternative mechanism in the cluster formation dynamics at the onset of discontinuous percolation transitions.
Observability estimate and state observation problems for stochastic hyperbolic equations
2013-01-01
In this paper, we derive a boundary and an internal observability inequality for stochastic hyperbolic equations with nonsmooth lower order terms. The required inequalities are obtained by global Carleman estimate for stochastic hyperbolic equations. By these inequalities, we study a state observation problem for stochastic hyperbolic equations. As a consequence, we also establish a unique continuation property for stochastic hyperbolic equations.
Analytic torsion versus Reidemeister torsion on hyperbolic 3-manifolds with cusps
Pfaff, Jonathan
2012-01-01
For a non-compact hyperbolic 3-manifold with cusps we prove an explicit formula that relates the regularized analytic torsion associated to the even symmetric powers of the standard representation of SL_2(C) to the corresponding Reidemeister torsion. Our proof rests on an expression of the analytic torsion in terms of special values of Ruelle zeta functions as well as on recent work of Pere Menal-Ferrer and Joan Porti.
Hyperbolic billiards of pure D=4 supergravities
Henneaux, M; Henneaux, Marc; Julia, Bernard
2003-01-01
We compute the billiards that emerge in the Belinskii-Khalatnikov-Lifshitz (BKL) limit for all pure supergravities in D=4 spacetime dimensions, as well as for D=4, N=4 supergravities coupled to k (N=4) Maxwell supermultiplets. We find that just as for the cases N=0 and N=8 investigated previously, these billiards can be identified with the fundamental Weyl chambers of hyperbolic Kac-Moody algebras. Hence, the dynamics is chaotic in the BKL limit. A new feature arises, however, which is that the relevant Kac-Moody algebra can be the Lorentzian extension of a twisted affine Kac-Moody algebra, while the N=0 and N=8 cases are untwisted. This occurs for N=5, N=3 and N=2. An understanding of this property is provided by showing that the data relevant for determining the billiards are the restricted root system and the maximal split subalgebra of the finite-dimensional real symmetry algebra characterizing the toroidal reduction to D=3 spacetime dimensions. To summarize: split symmetry controls chaos.
Hyperbolic Divergence Cleaning for SPH
Tricco, Terrence S
2012-01-01
We present SPH formulations of Dedner et al's hyperbolic/parabolic divergence cleaning scheme for magnetic and velocity fields. Our implementation preserves the conservation properties of SPH which is important for stability. This is achieved by deriving an energy term for the Psi field, and imposing energy conservation on the cleaning subsystem of equations. This necessitates use of conjugate operators for divB and gradPsi in the numerical equations. For both the magnetic and velocity fields, the average divergence error in the system is reduced by an order of magnitude with our cleaning algorithm. Divergence errors in SPMHD are maintained to < 1%, even for realistic 3D applications with a corresponding gain in numerical stability. Density errors for an oscillating elliptic water drop using weakly compressible SPH are reduced by a factor of two.
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
Hyperbolic Structures and the Stickiness Effect
周济林; 周礼勇; 孙义燧
2002-01-01
The stickiness effect of invariant tori in the phase space is widely studied, and extended to the slow-down of orbital diffusion due to some other invariant sets, such as Cantori, island-chains and hyperbolic periodic orbits.We report on two models in which hyperbolic periodic orbits show the stickiness effect. We discuss the generalized stickiness effects caused by different invariant sets. We believe that the main cause of the generalized stickiness effects is the hyperbolic structures in the phase space of the dynamical systems.
Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces
Dahmani, F; Osin, D
2017-01-01
The authors introduce and study the notions of hyperbolically embedded and very rotating families of subgroups. The former notion can be thought of as a generalization of the peripheral structure of a relatively hyperbolic group, while the latter one provides a natural framework for developing a geometric version of small cancellation theory. Examples of such families naturally occur in groups acting on hyperbolic spaces including hyperbolic and relatively hyperbolic groups, mapping class groups, Out(F_n), and the Cremona group. Other examples can be found among groups acting geometrically on CAT(0) spaces, fundamental groups of graphs of groups, etc. The authors obtain a number of general results about rotating families and hyperbolically embedded subgroups; although their technique applies to a wide class of groups, it is capable of producing new results even for well-studied particular classes. For instance, the authors solve two open problems about mapping class groups, and obtain some results which are n...
Magnetic hyperbolic metamaterial of high-index nanowires
Mirmoosa, M. S.; Kosulnikov, S. Yu.; Simovski, C. R.
2016-08-01
We show that the axial component of the magnetic permeability tensor is resonant for a wire medium consisting of high-index epsilon-positive nanowires, and its real part changes the sign at a certain frequency. At this frequency the medium experiences the topological phase transition between the elliptic and hyperbolic type of dispersion. We show that the transition regime is characterized by an extremely strong dependence of the permeability on the wave vector. This implies very high density of electromagnetic states that results in the filamentary pattern and noticeable Purcell factor for a transversely oriented magnetic dipole.
Gauss images of hyperbolic cusps with convex polyhedral boundary
Fillastre, François
2009-01-01
We prove that a 3--dimensional hyperbolic cusp with convex polyhedral boundary is uniquely determined by its Gauss image. Furthermore, any spherical metric on the torus with cone singularities of negative curvature and all closed contractible geodesics of length greater than $2\\pi$ is the metric of the Gauss image of some convex polyhedral cusp. This result is an analog of the Rivin-Hodgson theorem characterizing compact convex hyperbolic polyhedra in terms of their Gauss images. The proof uses a variational method. Namely, a cusp with a given Gauss image is identified with a critical point of a functional on the space of cusps with cone-type singularities along a family of half-lines. The functional is shown to be concave and to attain maximum at an interior point of its domain. As a byproduct, we prove rigidity statements with respect to the Gauss image for cusps with or without cone-type singularities. In a special case, our theorem is equivalent to existence of a circle pattern on the torus, with prescrib...
Non-local in time perturbations of linear hyperbolic PDEs
Lechner, Gandalf
2013-01-01
Linear Integro-differential equations of the form $(D+\\lambda W)f=0$ are studied, where $D$ is a normal or prenormal hyperbolic differential operator on $\\mathbb{R}^n$, $\\lambda\\in\\mathbb{C}$ is a coupling constant, and $W$ is a regular integral operator with compactly supported kernel. In particular, $W$ can be non-local in time, so that a Hamiltonian formulation is not possible. It is shown that for sufficiently small $|\\lambda|$, the hyperbolic character of $D$ is essentially preserved. Unique advanced/retarded fundamental solutions are constructed by means of a convergent expansion in $\\lambda$, and the solution spaces are analyzed. It is shown that the acausal behavior of the solutions is well-controlled, but the Cauchy problem is ill-posed in general. Nonetheless, a scattering operator can be calculated which describes the effect of $W$ on the space of solutions of $D$. It is also described how these structures occur in the context of wave or Dirac equations on noncommutative deformations of Minkowski s...
Penrose type inequalities for asymptotically hyperbolic graphs
Dahl, Mattias; Sakovich, Anna
2013-01-01
In this paper we study asymptotically hyperbolic manifolds given as graphs of asymptotically constant functions over hyperbolic space $\\bH^n$. The graphs are considered as subsets of $\\bH^{n+1}$ and carry the induced metric. For such manifolds the scalar curvature appears in the divergence of a 1-form involving the integrand for the asymptotically hyperbolic mass. Integrating this divergence we estimate the mass by an integral over an inner boundary. In case the inner boundary satisfies a convexity condition this can in turn be estimated in terms of the area of the inner boundary. The resulting estimates are similar to the conjectured Penrose inequality for asymptotically hyperbolic manifolds. The work presented here is inspired by Lam's article concerning the asymptotically Euclidean case.
Rothe's method to semilinear hyperbolic integrodifferential equations
D. Bahaguna
1990-01-01
Full Text Available In this paper we consider an application of Rothe's method to abstract semi-linear hyperbolic integrodifferential equations in Hilbert spaces. With the aid of Rothe's method we establish the existence of a unique strong solution.
Covariant Hyperbolization of Force-free Electrodynamics
Carrasco, Federico
2016-01-01
Force-Free Flectrodynamics (FFE) is a non-linear system of equations modeling the evolution of the electromagnetic field, in the presence of a magnetically dominated relativistic plasma. This configuration arises on several astrophysical scenarios, which represent exciting laboratories to understand physics in extreme regimes. We show that this system, when restricted to the correct constraint submanifold, is symmetric hyperbolic. In numerical applications is not feasible to keep the system in that submanifold, and so, it is necessary to analyze its structure first in the tangent space of that submanifold and then in a whole neighborhood of it. As already shown by Pfeiffer, a direct (or naive) formulation of this system (in the whole tangent space) results in a weakly hyperbolic system of evolution equations for which well-possednes for the initial value formulation does not follows. Using the generalized symmetric hyperbolic formalism due to Geroch, we introduce here a covariant hyperbolization for the FFE s...
Infinitesimal Lyapunov functions and singular-hyperbolicity
Araujo, Vitor
2012-01-01
We present an extension of the notion of infinitesimal Lyapunov function to singular flows on three-dimensional manifolds, and show how this technique provides a characterization of partially hyperbolic structures for invariant sets for such flows, and also of singular-hyperbolicity. In the absence of singularities, we can also rephrase uniform hyperbolicity with the language of infinitesimal Lyapunov functions. These conditions are expressed using the vector field X and its space derivative DX together with an infinitesimal Lyapunov function only and are reduced to checking that a certain symmetric operator is positive definite on the trapping region: we show how to express partial hyperbolicity using only the interplay between the infinitesimal generator X of the flow X_t, its derivative DX and the infinitesimal Lyapunov function.
Model Reduction for Complex Hyperbolic Networks
Himpe, Christian; Ohlberger, Mario
2013-01-01
We recently introduced the joint gramian for combined state and parameter reduction [C. Himpe and M. Ohlberger. Cross-Gramian Based Combined State and Parameter Reduction for Large-Scale Control Systems. arXiv:1302.0634, 2013], which is applied in this work to reduce a parametrized linear time-varying control system modeling a hyperbolic network. The reduction encompasses the dimension of nodes and parameters of the underlying control system. Networks with a hyperbolic structure have many app...
Absorbing Boundary Conditions for Hyperbolic Systems
Matthias Ehrhardt
2010-01-01
This paper deals with absorbing boundary conditions for hyperbolic systems in one and two space dimensions. We prove the strict well-posedness of the resulting initial boundary value problem in 1D. Afterwards we establish the GKS-stability of the corresponding Lax-Wendroff-type finite difference scheme. Hereby, we have to extend the classical proofs, since the (discretized) absorbing boundary conditions do not fit the standard form of boundary conditions for hyperbolic systems.
Hyperbolic differential operators and related problems
Ancona, Vincenzo
2003-01-01
Presenting research from more than 30 international authorities, this reference provides a complete arsenal of tools and theorems to analyze systems of hyperbolic partial differential equations. The authors investigate a wide variety of problems in areas such as thermodynamics, electromagnetics, fluid dynamics, differential geometry, and topology. Renewing thought in the field of mathematical physics, Hyperbolic Differential Operators defines the notion of pseudosymmetry for matrix symbols of order zero as well as the notion of time function. Surpassing previously published material on the top
Hyperbolicity of semigroups and Fourier multipliers
Latushkin, Yuri; Shvidkoy, Roman
2001-01-01
We present a characterization of hyperbolicity for strongly continuous semigroups on Banach spaces in terms of Fourier multiplier properties of the resolvent of the generator. Hyperbolicity with respect to classical solutions is also considered. Our approach unifies and simplifies the M. Kaashoek-- S. Verduyn Lunel theory and multiplier-type results previously obtained by S. Clark, M. Hieber, S. Montgomery-Smith, F. R\\"{a}biger, T. Randolph, and L. Weis.
Exhibition of circular Bragg phenomenon by hyperbolic, dielectric, structurally chiral materials
Lakhtakia, Akhlesh
2013-01-01
The relative permittivity dyadic of a dielectric structurally chiral material (SCM) varies helicoidally along a fixed direction; in consequence, the SCM exhibits the circular Bragg phenomenon, which is the circular-polarization-selective reflection of light. The introduction of hyperbolicity in an SCM---by making either one or two but not all three eigenvalues of the relative permittivity dyadic acquire negative real parts---does not eliminate the circular Bragg phenomenon, but significantly alters the regime for its exhibition. Physical vapor deposition techniques appear to be suitable to fabricate hyperbolic SCMs.
Shu, Chi-Wang
1992-01-01
The present treatment of elliptic regions via hyperbolic flux-splitting and high order methods proposes a flux splitting in which the corresponding Jacobians have real and positive/negative eigenvalues. While resembling the flux splitting used in hyperbolic systems, the present generalization of such splitting to elliptic regions allows the handling of mixed-type systems in a unified and heuristically stable fashion. The van der Waals fluid-dynamics equation is used. Convergence with good resolution to weak solutions for various Riemann problems are observed.
Discretizing singular point sources in hyperbolic wave propagation problems
Petersson, N. Anders; O'Reilly, Ossian; Sjögreen, Björn; Bydlon, Samuel
2016-09-01
We develop high order accurate source discretizations for hyperbolic wave propagation problems in first order formulation that are discretized by finite difference schemes. By studying the Fourier series expansions of the source discretization and the finite difference operator, we derive sufficient conditions for achieving design accuracy in the numerical solution. Only half of the conditions in Fourier space can be satisfied through moment conditions on the source discretization, and we develop smoothness conditions for satisfying the remaining accuracy conditions. The resulting source discretization has compact support in physical space, and is spread over as many grid points as the number of moment and smoothness conditions. In numerical experiments we demonstrate high order of accuracy in the numerical solution of the 1-D advection equation (both in the interior and near a boundary), the 3-D elastic wave equation, and the 3-D linearized Euler equations.
Dynamics in stationary, non-globally hyperbolic spacetimes
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.
Chiral Hyperbolic Metamaterial as A Robust Photonic Topological Insulator
Gao, Wenlong; Yang, Biao; Liu, Fu; Fang, Fengzhou; Li, Jensen; Zhang, Shuang
2014-01-01
Topological insulators represent a new phase of matter which remain insulating for bulk electron transport while supporting protected one-way edge states. Recently it has been shown that the concept of topological order can also be transferred to photonic systems. Thus far however, photonic topological insulators have been realized almost exclusively in periodic structures where the specific connection between lattice symmetry and the band structure plays a critical role. Here we demonstrate robust photonic topological order in a homogenous medium described by only a few effective electromagnetic parameters, and not requiring the presence of an external magnetic field. By combining hyperbolicity and chirality, we show that a topologically nontrivial gap appears between the equi-frequency surfaces which support one-way edge states. The effective medium approach towards topological insulation paves the way for highly compact one-way transportation of electromagnetic waves in integrated photonic circuits.
Toward optical sensing with hyperbolic metamaterials
Mackay, Tom G.
2015-06-01
A possible means of optical sensing, based on a porous hyperbolic material that is infiltrated by a fluid containing an analyte to be sensed, was theoretically investigated. The sensing mechanism relies on the observation that extraordinary plane waves propagate in the infiltrated hyperbolic material only in directions enclosed by a cone aligned with the optic axis of the infiltrated hyperbolic material. The angle this cone subtends to the plane perpendicular to the optic axis is θc. The sensitivity of θc to changes in the refractive index of the infiltrating fluid, namely nb, was explored; also considered were the permittivity parameters and porosity of the hyperbolic material, as well as the shape and size of its pores. Sensitivity was gauged by the derivative dθc/dnb. In parametric numerical studies, values of dθc/dnb in excess of 500 deg per refractive index unit were computed, depending upon the constitutive parameters of the porous hyperbolic material and infiltrating fluid and the nature of the porosity. In particular, it was observed that exceeding large values of dθc/dnb could be attained as the negative-valued eigenvalue of the infiltrated hyperbolic material approached zero.
Hyperbolic metamaterials: Novel physics and applications
Smolyaninov, Igor I.; Smolyaninova, Vera N.
2017-10-01
Hyperbolic metamaterials were originally introduced to overcome the diffraction limit of optical imaging. Soon thereafter it was realized that hyperbolic metamaterials demonstrate a number of novel phenomena resulting from the broadband singular behavior of their density of photonic states. These novel phenomena and applications include super resolution imaging, new stealth technologies, enhanced quantum-electrodynamic effects, thermal hyperconductivity, superconductivity, and interesting gravitation theory analogues. Here we briefly review typical material systems, which exhibit hyperbolic behavior and outline important novel applications of hyperbolic metamaterials. In particular, we will describe recent imaging experiments with plasmonic metamaterials and novel VCSEL geometries, in which the Bragg mirrors may be engineered in such a way that they exhibit hyperbolic metamaterial properties in the long wavelength infrared range, so that they may be used to efficiently remove excess heat from the laser cavity. We will also discuss potential applications of three-dimensional self-assembled photonic hypercrystals, which are based on cobalt ferrofluids in external magnetic field. This system bypasses 3D nanofabrication issues, which typically limit metamaterial applications. Photonic hypercrystals combine the most interesting features of hyperbolic metamaterials and photonic crystals.
Hyperbolic phonon polaritons in hexagonal boron nitride
Dai, Siyuan
2015-03-01
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 [Science, 343, 1125-1129 (2014)]. Additionally, we carried out the modification of hyperbolic response in heterostructures comprised of a mononlayer graphene deposited on hBN. 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 imaging and focusing using a slab of hBN.
Wilce, A
2004-01-01
We initiate a study of topological orthoalgebras (TOAs), concentrating on the compact case. Examples of TOAs include topological orthomodular lattices, and also the projection lattice of a Hilbert space. As the latter example illustrates, a lattice-ordered TOA need not be a topological lattice. However, we show that a compact Boolean TOA is a topological Boolean algebra. Using this, we prove that any compact regular TOA is atomistic, and has a compact center. We prove also that any compact TOA with isolated 0 is of finite height. We then focus on stably ordered TOAs: those in which the upper-set generated by an open set is open. These include both topological orthomodular lattices and interval orthoalgebras -- in particular, projection lattices. We show that the topology of a compact stably-ordered TOA with isolated 0 is determined by that of of its space of atoms.
Towards optical sensing with hyperbolic metamaterials
Mackay, Tom G
2015-01-01
A possible means of optical sensing, based on a porous hyperbolic material which is infiltrated by a fluid containing an analyte to be sensed, was investigated theoretically. The sensing mechanism relies on the observation that extraordinary plane waves propagate in the infiltrated hyperbolic material only in directions enclosed by a cone aligned with the optic axis of the infiltrated hyperbolic material. The angle this cone subtends to the plane perpendicular to the optic axis is $\\theta_c$. The sensitivity of $\\theta_c$ to changes in refractive index of the infiltrating fluid, namely $n_b$, was explored; also considered were the permittivity parameters and porosity of the hyperbolic material, as well as the shape and size of its pores. Sensitivity was gauged by the derivative $d \\theta_c / d n_b$. In parametric numerical studies, values of $d \\theta_c / d n_b$ in excess of 500 degrees per refractive index unit were computed, depending upon the constitutive parameters of the porous hyperbolic material and in...
IDENTIFICATION PECULIARITIES OF HYPERBOLE AND EUPHEMISMS
E. A. Kupriianycheva
2016-01-01
Full Text Available The article represents a research carried out within a cognitive-discursive paradigm of modern linguistics. The study represents an attempt to develop a method for hyperbole and euphemism identification as special cases of a metaphor. The Authors of article use the following determinations of tropes. Hyperbole is an expression that is more extreme than justified given its ontological referent [1, p. 163]. Euphemiya (greek eu – "good", phemi – "say" are the mitigations promoting effect indirect names substitutes of terrible, shameful or odious which brought to life by moral or religious motives [2]. As a basis for new method we use the Hyperbole Identification Procedure developed by research group from Vrije Universiteit Amsterdam under the leadership of G. Steen. The detailed analysis of hyperbolization and euphemization allows revealing and describing specifics of processes. The amplification of the existing sign is characteristic of the hyperbolization. The lexical unit with negative meaning becomes more expressional with additional negative connotations. The positive sign amplifies with addition of new positive meanings. In the euphemiya the positive connotations mitigate the negative meaning of lexical unit; sometimes it is possible full replacement negative on positive.
Analysis of laboratory compaction methods of roller compacted concrete
Trtík, Tomáš; Chylík, Roman; Bílý, Petr; Fládr, Josef
2017-09-01
Roller-Compacted Concrete (RCC) is an ordinary concrete poured and compacted with machines typically used for laying of asphalt road layers. One of the problems connected with this technology is preparation of representative samples in the laboratory. The aim of this work was to analyse two methods of preparation of RCC laboratory samples with bulk density as the comparative parameter. The first method used dynamic compaction by pneumatic hammer. The second method of compaction had a static character. The specimens were loaded by precisely defined force in laboratory loading machine to create the same conditions as during static rolling (in the Czech Republic, only static rolling is commonly used). Bulk densities obtained by the two compaction methods were compared with core drills extracted from real RCC structure. The results have shown that the samples produced by pneumatic hammer tend to overestimate the bulk density of the material. For both compaction methods, immediate bearing index test was performed to verify the quality of compaction. A fundamental difference between static and dynamic compaction was identified. In static compaction, initial resistance to penetration of the mandrel was higher, after exceeding certain limit the resistance was constant. This means that the samples were well compacted just on the surface. Specimens made by pneumatic hammer actively resisted throughout the test, the whole volume was uniformly compacted.
Curvature-based Hyperbolic Systems for General Relativity
Choquet-Bruhat, Y; Anderson, A; Choquet-Bruhat, Yvonne; York, James W.; Anderson, Arlen
1998-01-01
We review curvature-based hyperbolic forms of the evolution part of the Cauchy problem of General Relativity that we have obtained recently. We emphasize first order symmetrizable hyperbolic systems possessing only physical characteristics.
Multilayer cladding with hyperbolic dispersion for plasmonic waveguides
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....
Brane charges and Chern Simons invariants of hyperbolic spaces, with cosmological applications
Bytsenko, Andrei A.; Elizalde, Emilio
2006-05-01
We discuss methods of K-theory associated with hyperbolic orbifolds and valid for the description of Chern morphisms and brane charges. Such methods of K-theory are applied to compute D-brane charges, which are identified with elements of Grothendick K-groups, and for manifolds with horizons, spaces that naturally arise as the near-horizon of black brane geometries. In de Sitter spaces, these solutions break supersymmetry, and do not describe universes with zero cosmological constant. Here we pay attention to real hyperbolic spaces, and we examine associated Chern classes and brane charges using methods of K-theory and spectral theory of differential operators related to real hyperbolic spaces. An argument in favour of hyperbolic geometries in the treatment of the contributions to the vacuum persistence amplitude in QFT is given. All those are to be viewed as the proper mathematical structures underlying QFT with relevant backgrounds and boundary conditions in string cosmology. Invited contribution to the 7th Int. Workshop on Quantum Field Theory under the Influence of External Conditions, QFEXT'05 (Barcelona, 5 9 Sept. 2005).
Purcell effect in Hyperbolic Metamaterial Resonators
Slobozhanyuk, Alexey P; Powell, David A; Iorsh, Ivan; Shalin, Alexander S; Segovia, Paulina; Krasavin, Alexey V; Wurtz, Gregory A; Podolskiy, Viktor A; Belov, Pavel A; Zayats, Anatoly V
2015-01-01
The radiation dynamics of optical emitters can be manipulated by properly designed material structures providing high local density of photonic states, a phenomenon often referred to as the Purcell effect. Plasmonic nanorod metamaterials with hyperbolic dispersion of electromagnetic modes are believed to deliver a significant Purcell enhancement with both broadband and non-resonant nature. Here, we have investigated finite-size cavities formed by nanorod metamaterials and shown that the main mechanism of the Purcell effect in these hyperbolic resonators originates from the cavity hyperbolic modes, which in a microscopic description stem from the interacting cylindrical surface plasmon modes of the finite number of nanorods forming the cavity. It is found that emitters polarized perpendicular to the nanorods exhibit strong decay rate enhancement, which is predominantly influenced by the rod length. We demonstrate that this enhancement originates from Fabry-Perot modes of the metamaterial cavity. The Purcell fa...
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.
Domain Decomposition Methods for Hyperbolic Problems
Pravir Dutt; Subir Singh Lamba
2009-04-01
In this paper a method is developed for solving hyperbolic initial boundary value problems in one space dimension using domain decomposition, which can be extended to problems in several space dimensions. We minimize a functional which is the sum of squares of the 2 norms of the residuals and a term which is the sum of the squares of the 2 norms of the jumps in the function across interdomain boundaries. To make the problem well posed the interdomain boundaries are made to move back and forth at alternate time steps with sufficiently high speed. We construct parallel preconditioners and obtain error estimates for the method. The Schwarz waveform relaxation method is often employed to solve hyperbolic problems using domain decomposition but this technique faces difficulties if the system becomes characteristic at the inter-element boundaries. By making the inter-element boundaries move faster than the fastest wave speed associated with the hyperbolic system we are able to overcome this problem.
Broad-band acoustic hyperbolic metamaterial
Shen, Chen; Sui, Ni; Wang, Wenqi; Cummer, Steven A; Jing, Yun
2015-01-01
Acoustic metamaterials (AMMs) are engineered materials, made from subwavelength structures, that exhibit useful or unusual constitutive properties. There has been intense research interest in AMMs since its first realization in 2000 by Liu et al. A number of functionalities and applications have been proposed and achieved using AMMs. Hyperbolic metamaterials are one of the most important types of metamaterials due to their extreme anisotropy and numerous possible applications, including negative refraction, backward waves, spatial filtering, and subwavelength imaging. Although the importance of acoustic hyperbolic metamaterials (AHMMs) as a tool for achieving full control of acoustic waves is substantial, the realization of a broad-band and truly hyperbolic AMM has not been reported so far. Here, we demonstrate the design and experimental characterization of a broadband AHMM that operates between 1.0 kHz and 2.5 kHz.
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...
Near-Field Heat Transfer between Multilayer Hyperbolic Metamaterials
Biehs, Svend-Age; Ben-Abdallah, Philippe
2017-02-01
We review the near-field radiative heat flux between hyperbolic materials focusing on multilayer hyperbolic meta-materials. We discuss the formation of the hyperbolic bands, the impact of ordering of the multilayer slabs, as well as the impact of the first single layer on the heat transfer. Furthermore, we compare the contribution of surface modes to that of hyperbolic modes. Finally, we also compare the exact results with predictions from effective medium theory.
Near-field heat transfer between multilayer hyperbolic metamaterials
Biehs, Svend-Age [Oldenburg Univ. (Germany). Inst. fuer Physik; Ben-Abdallah, Philippe [Univ. Paris-Sud 11, Palaiseau (France). Lab. Charles Fabry; Univ. Sherbrooke, PQ (Canada). Dept. of Mechanical Engineering
2017-05-01
We review the near-field radiative heat flux between hyperbolic materials focusing on multilayer hyperbolic meta-materials. We discuss the formation of the hyperbolic bands, the impact of ordering of the multilayer slabs, as well as the impact of the first single layer on the heat transfer. Furthermore, we compare the contribution of surface modes to that of hyperbolic modes. Finally, we also compare the exact results with predictions from effective medium theory.
The Green's Functions of the Boundaries at Infinity of the Hyperbolic 3-Manifolds
Heydarpour, Majid
2009-01-01
The work is motivated by a result of Manin, which relates the Arakelov Green function on a compact Riemann surface to configurations of geodesics in a 3-dimensional hyperbolic handlebody with Schottky uniformization, having the Riemann surface as conformal boundary at infinity. A natural question is to what extent the result of Manin can be generalized to cases where, instead of dealing with a single Riemann surface, one has several Riemann surfaces whose union is the boundary of a hyperbolic 3-manifold, uniformized no longer by a Schottky group, but by a Fuchsian, quasi-Fuchsian, or more general Kleinian group. We have considered this question in this work and obtained several partial results that contribute towards constructing an analog of Manin's result in this more general context.
The Green’s functions of the boundaries at infinity of the hyperbolic 3-manifolds
Heydarpour, Majid
2012-04-01
The work is motivated by a result of Manin in [1], which relates the Arakelov Green's function on a compact Riemann surface to configurations of geodesics in a 3-dimensional hyperbolic handlebody with Schottky uniformization, having the Riemann surface as a conformal boundary at infinity. A natural question is to what extent the result of Manin can be generalized to cases where, instead of dealing with a single Riemann surface, one has several Riemann surfaces whose union is the boundary of a hyperbolic 3-manifold, uniformized no longer by a Schottky group, but by a Fuchsian, quasi-Fuchsian, or more general Kleinian group. We have considered this question in this work and obtained several partial results that contribute towards constructing an analog of Manin's result in this more general context.
BPS Wilson loops in N=4 SYM: Examples on hyperbolic submanifolds of space-time
Branding, Volker
2009-01-01
In this paper we present a family of supersymmetric Wilson loops of N=4 supersymmetric Yang-Mills theory in Minkowski space. Our examples focus on curves restricted to hyperbolic submanifolds, H_3 and H_2, of space-time. Generically they preserve two supercharges, but in special cases more, including a case which has not been discussed before, of the hyperbolic line, conformal to the straight line and circle, which is half-BPS. We discuss some general properties of these Wilson loops and their string duals and study special examples in more detail. Generically the string duals propagate on a complexification of AdS_5 x S^5 and in some specific examples the compact sphere is effectively replaced by a de-Sitter space.
Hamiltonian Optics of Hyperbolic Polaritons in Nanogranules.
Sun, Zhiyuan; Gutiérrez-Rubio, Á; Basov, D N; Fogler, M M
2015-07-08
Semiclassical quantization rules and numerical calculations are applied to study polariton modes of materials whose permittivity tensor has principal values of opposite sign (so-called hyperbolic materials). The spectra of volume- and surface-confined polaritons are computed for spheroidal nanogranules of hexagonal boron nitride, a natural hyperbolic crystal. The field distribution created by polaritons excited by an external dipole source is predicted to exhibit raylike patterns due to classical periodic orbits. Near-field infrared imaging and Purcell-factor measurements are suggested to test these predictions.
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.
Hyperbolic metamaterials based on Bragg polariton structures
Sedov, E. S.; Charukhchyan, M. V.; Arakelyan, S. M.; Alodzhants, A. P.; Lee, R.-K.; Kavokin, A. V.
2016-07-01
A new hyperbolic metamaterial based on a modified semiconductor Bragg mirror structure with embedded periodically arranged quantum wells is proposed. It is shown that exciton polaritons in this material feature hyperbolic dispersion in the vicinity of the second photonic band gap. Exciton-photon interaction brings about resonant nonlinearity leading to the emergence of nontrivial topological polaritonic states. The formation of spatially localized breather-type structures (oscillons) representing kink-shaped solutions of the effective Ginzburg-Landau-Higgs equation slightly oscillating along one spatial direction is predicted.
Generalised hyperbolicity in conical space-times
Vickers, J A
2000-01-01
Solutions of the wave equation in a space-time containing a thin cosmic string are examined in the context of non-linear generalised functions. Existence and uniqueness of solutions to the wave equation in the Colombeau algebra G is established for a conical space-time and this solution is shown to be associated to a distributional solution. A concept of generalised hyperbolicity, based on test fields, can be defined for such singular space-times and it is shown that a conical space-time is G-hyperbolic.
Hyperbolicity of the complement of plane algebraic curves
Dethloff, G E; Dethloff, Gerd; Schumacher, Georeg
1993-01-01
The paper is a contribution of the conjecture of Kobayashi that the complement o f a generic plain curve of degree at least five is hyperbolic. The main result is that the complement of a generic configuration of three quadr ics is hyperbolic and hyperbolically embedded as well as the complement of two q uadrics and a line.
The hyperbolic factor: A measure of time inconsistency
K.I.M. Rohde (Kirsten)
2010-01-01
textabstractMany studies have found that discounting is hyperbolic rather than constant. Hyperbolic discounting induces time-inconsistent behavior and is becoming increasingly popular in economic applications. Most studies that provide evidence in favor of hyperbolic discounting either are merely
The hyperbolic factor: A measure of time inconsistency
K.I.M. Rohde (Kirsten)
2010-01-01
textabstractMany studies have found that discounting is hyperbolic rather than constant. Hyperbolic discounting induces time-inconsistent behavior and is becoming increasingly popular in economic applications. Most studies that provide evidence in favor of hyperbolic discounting either are merely qu
Monotone method for nonlinear nonlocal hyperbolic problems
Azmy S. Ackleh
2003-02-01
Full Text Available We present recent results concerning the application of the monotone method for studying existence and uniqueness of solutions to general first-order nonlinear nonlocal hyperbolic problems. The limitations of comparison principles for such nonlocal problems are discussed. To overcome these limitations, we introduce new definitions for upper and lower solutions.
Hyperbolic L2-modules with Reproducing Kernels
David EELPODE; Frank SOMMEN
2006-01-01
Abstract In this paper, the Dirac operator on the Klein model for the hyperbolic space is considered. A function space containing L2-functions on the sphere Sm-1 in (R)m, which are boundary values of solutions for this operator, is defined, and it is proved that this gives rise to a Hilbert module with a reproducing kernel.
Hyperbolic spaces in Teichm\\"uller spaces
Leininger, Christopher J
2011-01-01
We prove, for any n, that there is a closed connected orientable surface S so that the hyperbolic space H^n almost-isometrically embeds into the Teichm\\"uller space of S, with quasi-convex image lying in the thick part. As a consequence, H^n quasi-isometrically embeds in the curve complex of S.
KAWA lecture notes on complex hyperbolic geometry
Rousseau, Erwan
2016-01-01
These lecture notes are based on a mini-course given at the fifth KAWA Winter School on March 24-29, 2014 at CIRM, Marseille. They provide an introduction to hyperbolicity of complex algebraic varieties namely the geometry of entire curves, and a description of some recent developments.
Mass Law Predicts Hyperbolic Hypoxic Ventilatory Response
Severinghaus, John W.
The hyperbolic hypoxic ventilatory response vs PaO2, HVRp, is interpreted as relecting a mass hyperbolic relationship of cytochrome PcO2 to cytochrome potential Ec, offset 32 torr by the constant diffusion gradient between arterial blood and cytochrome in CB at its constant metabolic rate dot VO_2 . Ec is taken to be a linear function of redox reduction and CB ventilatory drive. As Ec rises in hypoxia, the absolute potentials of each step in the citric acid cycle rises equally while the potential drop across each step remains constant because flux rate remains constant. A hypothetic HVRs ( dot VE vs SaO2) response curve computed from these assumptions is strikingly non linear. A hypothetic HVRp calculated from an assumed linear HVRs cannot be fit to the observed hyperbolic increase of ventilation in response to isocapnic hypoxia at PO2 less than 40 torr. The incompatibility of these results suggest that in future studies HVRs will not be found to be linear, especially below 80% SaO2 and HVRp will fail to be accurately hyperbolic.
Exactly integrable hyperbolic equations of Liouville type
Zhiber, A V [Institute of Mechanics, Ufa Centre of the Russian Academy of Sciences, Ufa (Russian Federation); Sokolov, Vladimir V [Centre for Non-linear Studies Landau Institute for Theoretical Physics, Moscow (Russian Federation)
2001-02-28
This is a survey of the authors' results concerning non-linear hyperbolic equations of Liouville type. The definition is based on the condition that the chain of Laplace invariants of the linearized equation be two-way finite. New results include a procedure for finding the general solution and a solution of the classification problem for Liouville type equations.
Volume of a doubly truncated hyperbolic tetrahedron
Kolpakov, Alexander
2012-01-01
The present paper regards the volume function of a doubly truncated hyperbolic tetrahedron. Starting from the previous results of J. Murakami, U. Yano and A. Ushijima, we have developed a unified approach to expressing the volume in different geometric cases by dilogarithm functions and to treat properly the many analytic strata of the latter. Finally, several numeric examples are given.
On the hyperbolicity condition in linear elasticity
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.
Approximation properties of fine hyperbolic graphs
Benyin Fu
2016-05-01
In this paper, we propose a definition of approximation property which is called the metric invariant translation approximation property for a countable discrete metric space. Moreover, we use the techniques of Ozawa’s to prove that a fine hyperbolic graph has the metric invariant translation approximation property.
Exhibition of circular Bragg phenomenon by hyperbolic, dielectric, structurally chiral materials
Lakhtakia, Akhlesh
2013-01-01
The relative permittivity dyadic of a dielectric structurally chiral material (SCM) varies helicoidally along a fixed direction; in consequence, the SCM exhibits the circular Bragg phenomenon, which is the circular-polarization-selective reflection of light. The introduction of hyperbolicity in an SCM---by making either one or two but not all three eigenvalues of the relative permittivity dyadic acquire negative real parts---does not eliminate the circular Bragg phenomenon, but significantly ...
On the Cauchy problem of a 2 times 2 system of nonstrictly hyperbolic conservation laws
Kan, P.T.
1989-01-01
Global existence for a 2 {times} 2 system of nonstrictly hyperbolic conservation law is established for data of arbitrary bounded variation. This result is obtained by proving a convergence theorem for the method of artificial viscosity applied to this system of conservation law. For this purpose, the method of compensated compactness and an analysis of the entropy functions are used. This system under consideration is a special case of a canonical class of 2 {times} 2 systems of conservation laws with quadratic flux functions possessing an isolated umbilic point (point of coinciding wave speeds where strict hyperbolicity fails) at the origin of the state space. These systems arise as model equations to equations used in oil reservoir simulations. Their wave curves and Riemann problem solutions are known to exhibit complexities not seen in any strictly hyperbolic systems. In this thesis, besides establishing global existence for a special system in the canonical class, general properties of a subclass are also investigated. The geometry of rarefaction wave curves are analytically studied and Riemann invariants are constructed. An L{sup {infinity}} bound (independent of the viscosity) for the solutions of the corresponding viscous systems are obtained. Also studied is the monotonicity properties of the wave speeds in the Riemann invariant plane.
Tunable VO2/Au hyperbolic metamaterial
Prayakarao, S.; Mendoza, B.; Devine, A.; Kyaw, C.; van Dover, R. B.; Liberman, V.; Noginov, M. A.
2016-08-01
Vanadium dioxide (VO2) is known to have a semiconductor-to-metal phase transition at ˜68 °C. Therefore, it can be used as a tunable component of an active metamaterial. The lamellar metamaterial studied in this work is composed of subwavelength VO2 and Au layers and is designed to undergo a temperature controlled transition from the optical hyperbolic phase to the metallic phase. VO2 films and VO2/Au lamellar metamaterial stacks have been fabricated and studied in electrical conductivity and optical (transmission and reflection) experiments. The observed temperature-dependent changes in the reflection and transmission spectra of the metamaterials and VO2 thin films are in a good qualitative agreement with theoretical predictions. The demonstrated optical hyperbolic-to-metallic phase transition is a unique physical phenomenon with the potential to enable advanced control of light-matter interactions.
Unknotting tunnels in hyperbolic 3-manifolds
Adams, Colin
2012-01-01
An unknotting tunnel in a 3-manifold with boundary is a properly embedded arc, the complement of an open neighborhood of which is a handlebody. A geodesic with endpoints on the cusp boundary of a hyperbolic 3-manifold and perpendicular to the cusp boundary is called a vertical geodesic. Given a vertical geodesic in a hyperbolic 3-manifold M, we find sufficient conditions for it to be an unknotting tunnel. In particular, if the vertical geodesic corresponds to a 4-bracelet, 5-bracelet or 6-bracelet in the universal cover and has short enough length, it must be an unknotting tunnel. Furthermore, we consider a vertical geodesic that satisfies the elder sibling property, which means that in the universal cover, every horoball except the one centered at infinity is connected to a larger horoball by a lift of the vertical geodesic. Such a vertical geodesic with length less than ln(2) is then shown to be an unknotting tunnel.
Is the Bianchi identity always hyperbolic?
Rácz, István
2014-01-01
We consider $n+1$ dimensional smooth Riemannian and Lorentzian spaces satisfying Einstein's equations. The base manifold is assumed to be smoothly foliated by a one-parameter family of hypersurfaces. In both cases---likewise it is usually done in the Lorentzian case---Einstein's equations may be split into `Hamiltonian' and `momentum' constraints and a `reduced' set of field equations. It is shown that regardless whether the primary space is Riemannian or Lorentzian whenever the foliating hypersurfaces are Riemannian the `Hamiltonian' and `momentum' type expressions are subject to a subsidiary first order symmetric hyperbolic system. Since this subsidiary system is linear and homogeneous in the `Hamiltonian' and `momentum' type expressions the hyperbolicity of the system implies that in both cases the solutions to the `reduced' set of field equations are also solutions to the full set of equations provided that the constraints hold on one of the hypersurfaces foliating the base manifold.
Hyperbolic metamaterial lens with hydrodynamic nonlocal response
Yan, Wei; Mortensen, N. Asger; Wubs, Martijn
2013-01-01
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......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...
Design of hyperbolic metamaterials by genetic algorithm
Goforth, Ian A.; Alisafaee, Hossein; Fullager, Daniel B.; Rosenbury, Chris; Fiddy, Michael A.
2014-09-01
We explain the design of one dimensional Hyperbolic Metamaterials (HMM) using a genetic algorithm (GA) and provide sample applications including the realization of negative refraction. The design method is a powerful optimization approach to find the optimal performance of such structures, which "naturally" finds HMM structures that are globally optimized for specific applications. We explain how a fitness function can be incorporated into the GA for different metamaterial properties.
Hyperbolic conservation laws and numerical methods
Leveque, Randall J.
1990-01-01
The mathematical structure of hyperbolic systems and the scalar equation case of conservation laws are discussed. Linear, nonlinear systems and the Riemann problem for the Euler equations are also studied. The numerical methods for conservation laws are presented in a nonstandard manner which leads to large time steps generalizations and computations on irregular grids. The solution of conservation laws with stiff source terms is examined.
On hyperbolic fixed points in ultrametric dynamics
Lindahl, Karl-Olof; 10.1134/S2070046610030052
2011-01-01
Let K be a complete ultrametric field. We give lower and upper bounds for the size of linearization discs for power series over K near hyperbolic fixed points. These estimates are maximal in the sense that there exist examples where these estimates give the exact size of the corresponding linearization disc. In particular, at repelling fixed points, the linearization disc is equal to the maximal disc on which the power series is injective.
Studies in the Hyperbolic Circle Problem
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...... distribution for certain integral versions of it. Finally we describe what results can be obtained by application of fractional calculus, especially fractional integration to small order, to the problem....
Mapped tent pitching schemes for hyperbolic systems
Gopalakrishnan, J; Schöberl, J.; Wintersteiger, C.
2016-01-01
A spacetime domain can be progressively meshed by tent shaped objects. Numerical methods for solving hyperbolic systems using such tent meshes to advance in time have been proposed previously. Such schemes have the ability to advance in time by different amounts at different spatial locations. This paper explores a technique by which standard discretizations, including explicit time stepping, can be used within tent-shaped spacetime domains. The technique transforms the equations within a spa...
Accuracy property of certain hyperbolic difference schemes
Hicks, D.L.; Madsen, M.M.
1976-12-01
An accuracy property called the CFL1 property is shared by several successful difference schemes. It appears to be a property at least as important as the property of higher-order accuracy for hyperbolic difference schemes when weak solutions (e.g., shocks) are sought. Investigation of this property leads to suggestions of ways to improve the accuracy in such wavecodes as WONDY, CHARTD, and THREEDY. 10 figures.
Modular realizations of hyperbolic Weyl groups
Kleinschmidt, Axel; Palmkvist, Jakob
2010-01-01
We study the recently discovered isomorphisms between hyperbolic Weyl groups and unfamiliar modular groups. These modular groups are defined over integer domains in normed division algebras, and we focus on the cases involving quaternions and octonions. We outline how to construct and analyse automorphic forms for these groups; their structure depends on the underlying arithmetic properties of the integer domains. We also give a new realization of the Weyl group W(E8) in terms of unit octavians and their automorphism group.
Remarks on the notion of global hyperbolicity
Sánchez, Miguel
2007-01-01
Global hyperbolicity is a classical and well-known concept, which lies in the core of General Relativity. Here we discuss briefly five approaches to this concept. They yield different definitions which become natural in diverse contexts: the initial value problem, singularity theorems, existence of maximizing causal geodesics, possibility to split globally the spacetime, causal boundaries. The neat formulation and definitive equivalence between these definitions have been completed only recently. A very brief summary is presented.
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.
Einstein's Equations and Equivalent Hyperbolic Dynamical Systems
Anderson, A; York, J W; Anderson, Arlen; Choquet-Bruhat, Yvonne
1999-01-01
We discuss several explicitly causal hyperbolic formulations of Einstein's dynamical 3+1 equations in a coherent way, emphasizing throughout the fundamental role of the ``slicing function,'' $\\alpha$---the quantity that relates the lapse $N$ to the determinant of the spatial metric $\\bar{g}$ through $N = \\bar{g}^{1/2} \\alpha$. The slicing function allows us to demonstrate explicitly that every foliation of spacetime by spatial time-slices can be used in conjunction with the causal hyperbolic forms of the dynamical Einstein equations. Specifically, the slicing function plays an essential role (1) in a clearer form of the canonical action principle and Hamiltonian dynamics for gravity and leads to a recasting (2) of the Bianchi identities evolution of the gravitational constraints in vacuum, and also (3) of evolution of the energy and momentum components of the stress tensor in the presence of matter, (4) in an explicit rendering of four hyperbolic formulations of Einstein's equations with only physical charact...
Conformal plasmonic and hyperbolic metamaterials (Conference Presentation)
Riley, Conor T.; Smalley, Joseph S. T.; Fainman, Yeshaiahu; Sirbuly, Donald J.; Liu, Zhaowei
2016-09-01
The majority of plasmonic and metamaterials research utilizes noble metals such as gold and silver which commonly operate in the visible region. However, these materials are not well suited for many applications due to their low melting temperature and polarization response at longer wavelengths. A viable alternative is aluminum doped zinc oxide (AZO); a high melting point, low loss, visibly transparent conducting oxide which can be tuned to show strong plasmonic behavior in the near-infrared region. Due to it's ultrahigh conformality, atomic layer deposition (ALD) is a powerful tool for the fabrication of the nanoscale features necessary for many nanoplasmonic and optical metamaterials. Despite many attempts, high quality, low loss AZO has not been achieved with carrier concentrations high enough to support plasmonic behavior at the important telecommunication wavelengths (ca. 1550 nm) by ALD. Here, we present a simple process for synthesizing high carrier concentration, thin film AZO with low losses via ALD that match the highest quality films created by all other methods. We show that this material is tunable by thermal treatment conditions, altering aluminum concentration, and changing buffer layer thickness. The use of this process is demonstrated by creating hyperbolic metamaterials with both a multilayer and embedded nanowire geometry. Hyperbolic dispersion is proven by negative refraction and numerical calculations in agreement with the effective medium approximation. This paves the way for fabricating high quality hyperbolic metamaterial coatings on high aspect ratio nanostructures that cannot be created by any other method.
Arithmetic and Hyperbolic Structures in String Theory
Persson, Daniel
2010-01-01
This monograph is an updated and extended version of the author's PhD thesis. It consists of an introductory text followed by two separate parts which are loosely related but may be read independently of each other. In Part I we analyze certain hyperbolic structures arising when studying gravity in the vicinity of a spacelike singularity (the "BKL-limit"). In this limit, spatial points decouple and the dynamics exhibits ultralocal behaviour which may be described in terms of a (possibly chaotic) hyperbolic billiard. In all supergravities arising as low-energy limits of string theory or M-theory, the billiard dynamics takes place within the fundamental Weyl chambers of certain hyperbolic Kac-Moody algebras, suggesting that these algebras generate hidden infinite-dimensional symmetries of the theory. Part II of the thesis is devoted to a study of how (U-)dualities in string theory provide powerful constraints on perturbative and non-perturbative quantum corrections. These dualities are described by certain arit...
Global attractors for damped abstract nonlinear hyperbolic systems
Pinter, Gabriella Agnes
1997-12-01
This dissertation is concerned with the long time dynamics of a class of damped abstract hyperbolic systems that arise in the study of certain smart material structures, namely elastomers. The term smart material refers to a material capable of both sensing and responding actively to outside excitation. These properties make smart materials a prime canditate for actuation and sensing in next generation control systems. However, modeling and numerically simulating their behavior poses several difficulties. In this work we consider a model for elastomers developed by H. T. Banks, N. J. Lybeck, B. C. Munoz, L. C. Yanyo, formulate this model as an abstract evolution system, and study the long time behavior of its solutions. We remark that the question of existence and uniqueness of solutions for this class of systems is a challenging problem and was only recently solved by H. T. Banks, D. S. Gilliam and V. I. Shubov. Concerning the long time dynamics of the problem, we first prove that the system generates a weak dynamical system, and possesses a weak global attractor. Our main result is the existence of a "strong" dynamical system which has a compact global attractor. With the help of a Lyapunov function we are able to characterize the structure of this attractor. We also give a theorem that guarantees the stability of the global attractor with respect to varying parameters in the system. Our last result concerns the uniform differentiability of the dynamical system.
Fourth-Order Difference Methods for Hyperbolic IBVPs
Gustafsson, Bertil; Olsson, Pelle
1995-03-01
In this paper we consider fourth-order difference approximations of initial-boundary value problems for hyperbolic partial differential equations. We use the method of lines approach with both explicit and compact implicit difference operators in space. The explicit operator satisfies an energy estimate leading to strict stability. For the implicit operator we develop boundary conditions and give a complete proof of strong stability using the Laplace transform technique. We also present numerical experiments for the linear advection equation and Burgers' equation with discontinuities in the solution or in its derivative. The first equation is used for modeling contact discontinuities in fluid dynamics; the second one is used for modeling shocks and rarefaction waves. The time discretization is done with a third-order Runge-Kutta TVD method. For solutions with discontinuities in the solution itself we add a filter based on second-order viscosity. In case of the non-linear Burgers' equation we use a flux splitting technique that results in an energy estimate for certain difference approximations, in which case also an entropy condition is fulfilled. In particular we shall demonstrate that the unsplit conservative form produces a non-physical shock instead of the physically correct rarefaction wave. In the numerical experiments we compare our fourth-order methods with a standard second-order one and with a third-order TVD method. The results show that the fourth-order methods are the only ones that give good results for all the considered test problems.
Gupta, Anshu; Austin, John; Davis, Sierra; Harris, Michael; Reklaitis, Gintaras
2015-05-01
Control of particulate processes is hard to achieve because of the ease with which powders tend to segregate. Thus, proper sensing methods must be employed to ensure content uniformity during operation. The role of sensing schemes becomes even more critical while operating the process continuously as measurements are essential for implementation of feedback control (Austin et al. 2013. J Pharm Sci 102(6):1895-1904; Austin et al. 2014. Anal Chim Acta 819:82-93). A microwave sensor was developed and shown to be effective in online measurement of active pharmaceutical ingredient (API) concentration in a powder blend. During powder transport and hopper storage before processing, powder blends may segregate and cause quality deviations in the subsequent tableting operation. Therefore, it is critical to know the API concentration in the ribbons as the content uniformity is fixed once the ribbon is processed. In this study, a novel microwave sensor was developed that could provide measurement of a roller compacted ribbon's API concentration online, along with its density and moisture content. The results indicate that this microwave sensor is capable of increased accuracy compared with a commercially available near-IR probe for the determination of content uniformity and density in roller compacted ribbons online. © 2015 Wiley Periodicals, Inc. and the American Pharmacists Association.
Second-order hyperbolic Fuchsian systems. General theory
Beyer, Florian; LeFloch, Philippe G.
2010-01-01
We introduce a class of singular partial differential equations, the second-order hyperbolic Fuchsian systems, and we investigate the associated initial value problem when data are imposed on the singularity. First of all, we analyze a class of equations in which hyperbolicity is not assumed and we construct asymptotic solutions of arbitrary order. Second, for the proposed class of second-order hyperbolic Fuchsian systems, we establish the existence of solutions with prescribed asymptotic beh...
Notes on holonomy matrices of hyperbolic 3-manifolds with cusps
Fukui, Fumitaka
2013-01-01
In this paper, we give a method to construct holonomy matrices of hyperbolic 3-manifolds by extending the known method of hyperbolic 2-manifolds. It enables us to consider hyperbolic 3-manifolds with nontrivial holonomies. We apply our method to an ideal tetrahedron and succeed in making the holonomies nontrivial. We also derive the partition function of the ideal tetrahedron with nontrivial holonomies by using the duality proposed by Dimofte, Gaiotto and Gukov.
Renormalization Group Equation for $f(R)$ gravity on hyperbolic spaces
Falls, Kevin
2016-01-01
We derive the flow equation for the gravitational effective average action in an $f(R)$ truncation on hyperbolic spacetimes using the exponential parametrization of the metric. In contrast to previous works on compact spaces, we are able to evaluate traces exactly using the optimised cutoff. This reveals in particular that all modes can be integrated out for a finite value of the cutoff due to a gap in the spectrum of the Laplacian, leading to the effective action. Studying polynomial solutions, we find poorer convergence than has been found on compact spacetimes even though at small curvature the equations only differ in the treatment of certain modes. In the vicinity of an asymptotically free fixed point, we find the universal beta function for the $R^2$ coupling and compute the corresponding effective action which involves an $R^2 \\log R$ quantum correction.
Bluemich, Bernhard; Haber-Pohlmeier, Sabina; Zia, Wasif [RWTH Aachen Univ. (Germany). Inst. fuer Technische und Makromolekulare Chemie (ITMC)
2014-06-01
Nuclear Magnetic Resonance (NMR) spectroscopy is the most popular method for chemists to analyze molecular structures, while Magnetic Resonance Imaging (MRI) is a non-invasive diagnostic tool for medical doctors that provides high-contrast images of biological tissue. In both applications, the sample (or patient) is positioned inside a large, superconducting magnet to magnetize the atomic nuclei. Interrogating radio-frequency pulses result in frequency spectra that provide the chemist with molecular information, the medical doctor with anatomic images, and materials scientist with NMR relaxation parameters. Recent advances in magnet technology have led to a variety of small permanent magnets to allow compact and low-cost instruments. The goal of this book is to provide an introduction to the practical use of compact NMR at a level nearly as basic as the operation of a smart phone.
Bazeia, D; Marques, M A; Menezes, R; Zafalan, I
2016-01-01
We study a family of Maxwell-Higgs models, described by the inclusion of a function of the scalar field that represent generalized magnetic permeability. We search for vortex configurations which obey first-order differential equations that solve the equations of motion. We first deal with the asymptotic behavior of the field configurations, and then implement a numerical study of the solutions, the energy density and the magnetic field. We work with the generalized permeability having distinct profiles, giving rise to new models, and we investigate how the vortices behave, compared with the solutions of the corresponding standard models. In particular, we show how to build compact vortices, that is, vortex solutions with the energy density and magnetic field vanishing outside a compact region of the plane.
Bazeia, D.; Losano, L.; Marques, M.A.; Zafalan, I. [Universidade Federal da Paraiba, Departamento de Fisica, Joao Pessoa, PB (Brazil); Menezes, R. [Universidade Federal da Paraiba, Departamento de Ciencias Exatas, Rio Tinto, PB (Brazil); Universidade Federal de Campina Grande, Departamento de Fisica, Campina Grande, PB (Brazil)
2017-02-15
We study a family of Maxwell-Higgs models, described by the inclusion of a function of the scalar field that represent generalized magnetic permeability. We search for vortex configurations which obey first-order differential equations that solve the equations of motion. We first deal with the asymptotic behavior of the field configurations, and then implement a numerical study of the solutions, the energy density and the magnetic field. We work with the generalized permeability having distinct profiles, giving rise to new models, and we investigate how the vortices behave, compared with the solutions of the corresponding standard models. In particular, we show how to build compact vortices, that is, vortex solutions with the energy density and magnetic field vanishing outside a compact region of the plane. (orig.)
Considerations on the hyperbolic complex Klein-Gordon equation
Ulrych, S
2010-01-01
The 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 Poincar\\'e 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
Nonreciprocity and one-way topological transitions in hyperbolic metamaterials
Leviyev, A.; Stein, B.; Christofi, A.; Galfsky, T.; Krishnamoorthy, H.; Kuskovsky, I. L.; Menon, V.; Khanikaev, A. B.
2017-07-01
Control of the electromagnetic waves in nano-scale structured materials is crucial to the development of next generation photonic circuits and devices. In this context, hyperbolic metamaterials, where elliptical isofrequency surfaces are morphed into surfaces with exotic hyperbolic topologies when the structure parameters are tuned, have shown unprecedented control over light propagation and interaction. Here we show that such topological transitions can be even more unusual when the hyperbolic metamaterial is endowed with nonreciprocity. Judicious design of metamaterials with reduced spatial symmetries, together with the breaking of time-reversal symmetry through magnetization, is shown to result in nonreciprocal dispersion and one-way topological phase transitions in hyperbolic metamaterials.
Hyperbolic neighborhoods as organizers of finite-time exponential stretching
Balasuriya, Sanjeeva; Ouellette, Nicholas
2016-11-01
Hyperbolic points and their unsteady generalization, hyperbolic trajectories, drive the exponential stretching that is the hallmark of nonlinear and chaotic flow. Typical experimental and observational velocity data is unsteady and available only over a finite time interval, and in such situations hyperbolic trajectories will move around in the flow, and may lose their hyperbolicity at times. Here we introduce a way to determine their region of influence, which we term a hyperbolic neighborhood, which marks fluid elements whose dynamics are instantaneously dominated by the hyperbolic trajectory. We establish, using both theoretical arguments and numerical verification from model and experimental data, that the hyperbolic neighborhoods profoundly impact Lagrangian stretching experienced by fluid elements. In particular, we show that fluid elements traversing a flow experience exponential boosts in stretching while within these time-varying regions, that greater residence time within hyperbolic neighborhoods is directly correlated to larger Finite-Time Lyapunov Exponent (FTLE) values, and that FTLE diagnostics are reliable only when the hyperbolic neighborhoods have a geometrical structure which is regular in a specific sense. Future Fellowship Grant FT130100484 from the Australian Research Council (SB), and a Terman Faculty Fellowship from Stanford University (NO).
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.
Complex hyperbolic (3,3,n)-triangle groups.
Parker, John R.; Wang, Jieyan; Xie, Baohua
2016-01-01
Let p,q,rp,q,r be positive integers. Complex hyperbolic (p,q,r)(p,q,r) triangle groups are representations of the hyperbolic (p,q,r)(p,q,r) reflection triangle group to the holomorphic isometry group of complex hyperbolic space H2CHℂ2, where the generators fix complex lines. In this paper, we obtain all the discrete and faithful complex hyperbolic (3,3,n)(3,3,n) triangle groups for n≥4n≥4. Our result solves a conjecture of Schwartz in the case when p=q=3p=q=3.
Time machines with the compactly determined Cauchy horizon
Krasnikov, S
2014-01-01
The building of a time machine, if possible at all, requires the relevant regions of spacetime to be compact (that is, physically speaking, free from sources of unpredictability such as infinities and singularities). Motivated by this argument we consider the spacetimes with the compactly determined Cauchy horizons (CDCHs), the defining property of which is the compactness of $\\overline{J^-(\\EuScript U)}\\cap J^+(\\EuScript S_0)$, where $\\EuScript U$ is an open subset of the Cauchy horizon and $\\EuScript S_0$ is a Cauchy surface of the initial globally hyperbolic region $\\ingh$. The following two facts are established: 1) $\\ingh$ has no globally hyperbolic maximal extension. This means that by shaping appropriately a precompact portion of a globally hyperbolic region one can \\emph{force} the Universe to produce either a closed causal curve, or a quasiregular singularity, whichever it abhors less; 2) Before a CDCH is formed a null geodesic appears which infinitely approaches the horizon returning again and again...
Barbu, Catalin
2010-01-01
Hyperbolic Geometry appeared in the first half of the 19th century as an attempt to understand Euclid's axiomatic basis of Geometry. It is also known as a type of non-Euclidean Geometry, being in many respects similar to Euclidean Geometry.
Geometry in the large and hyperbolic chaos
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.
Hyperbolic Unit Groups and Quaternion Algebras
S O Juriaans; I B S Passi; A C Souza Filho
2009-02-01
We classify the quadratic extensions $K=\\mathbb{Q}[\\sqrt{d}]$ and the finite groups for which the group ring $\\mathfrak{o}_K[G]$ of over the ring $\\mathfrak{o}_K$ of integers of has the property that the group $\\mathcal{U}_1(\\mathfrak{o}_K[G])$ of units of augmentation 1 is hyperbolic. We also construct units in the $\\mathbb{Z}$-order $\\mathcal{H}(\\mathfrak{o}_K)$ of the quaternion algebra $\\mathcal{H}(K)=\\left\\frac{-1,-1}{k}(\\right)$, when it is a division algebra.
Hypersurfaces of constant curvature in Hyperbolic space
Guan, Bo
2010-01-01
We show that for a very general and natural class of curvature functions, the problem of finding a complete strictly convex hypersurface satisfying f({\\kappa}) = {\\sigma} over (0,1) with a prescribed asymptotic boundary {\\Gamma} at infinity has at least one solution which is a "vertical graph" over the interior (or the exterior) of {\\Gamma}. There is uniqueness for a certain subclass of these curvature functions and as {\\sigma} varies between 0 and 1, these hypersurfaces foliate the two components of the complement of the hyperbolic convex hull of {\\Gamma}.
Hyperbolic heat equation in Kaluza's magnetohydrodynamics
Sandoval-Villalbazo, A; García-Perciante, A L
2006-01-01
This paper shows that a hyperbolic equation for heat conduction can be obtained directly using the tenets of linear irreversible thermodynamics in the context of the five dimensional space-time metric originally proposed by T. Kaluza back in 1922. The associated speed of propagation is slightly lower than the speed of light by a factor inversely proportional to the specific charge of the fluid element. Moreover, consistency with the second law of thermodynamics is achieved. Possible implications in the context of physics of clusters of galaxies of this result are briefly discussed.
Hyperbolicity of Scalar Tensor Theories of Gravity
Salgado, Marcelo; Alcubierre, Miguel; Núñez, Dario
2008-01-01
Two first order strongly hyperbolic formulations of scalar tensor theories of gravity (STT) allowing non-minimal couplings (Jordan frame) are presented along the lines of the 3+1 decomposition of spacetime. One is based on the Bona-Masso formulation while the other one employs a conformal decomposition similar to that of Baumgarte-Shapiro-Shibata-Nakamura. A modified Bona-Masso slicing condition adapted to the STT is proposed for the analysis. This study confirms that STT posses a well posed Cauchy problem even when formulated in the Jordan frame.
Spatial Mode Selective Waveguide with Hyperbolic Cladding
Tang, Y; Xu, M; Bäumer, S; Adam, A J L; Urbach, H P
2016-01-01
Hyperbolic Meta-Materials~(HMMs) are anisotropic materials with permittivity tensor that has both positive and negative eigenvalues. Here we report that by using a type II HMM as cladding material, a waveguide which only supports higher order modes can be achieved, while the lower order modes become leaky and are absorbed in the HMM cladding. This counter intuitive property can lead to novel application in optical communication and photonic integrated circuit. The loss in our HMM-Insulator-HMM~(HIH) waveguide is smaller than that of similar guided mode in a Metal-Insulator-Metal~(MIM) waveguide.
True thermal antenna with hyperbolic metamaterials
Barbillon, Grégory; Sakat, Emilie; Hugonin, Jean-Paul; Biehs, Svend-Age; Ben-Abdallah, Philippe
2017-09-01
A thermal antenna is an electromagnetic source which emits in its surrounding, a spatially coherent field in the infrared frequency range. Usually, its emission pattern changes with the wavelength so that the heat flux it radiates is weakly directive. Here, we show that a class of hyperbolic materials, possesses a Brewster angle which is weakly dependent on the wavelength, so that they can radiate like a true thermal antenna with a highly directional heat flux. The realization of these sources could open a new avenue in the field of thermal management in far-field regime.
Hyperbolic statics in space-time
Pavlov, Dmitry
2015-01-01
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 a fine balance between causal and geometric space-time characteristics (the two regularizations concordance).
Plasmonic waveguides with hyperbolic multilayer cladding
Babicheva, Viktoriia E; Ishii, Satoshi; Boltasseva, Alexandra; Kildishev, Alexander V
2014-01-01
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 homogenization, we calculate the resonant eigenmodes of the finite-width cladding layers, and find agreement with the resonant features in the dispersion of the cladded waveguides. We show that at the resonant widths, the propagating modes of the waveguides are coupled to the cladding eigenmodes and hence, are strongly absorbed. By avoiding the resonant widths in the design of the actual waveguides, the strong absorption can be eliminated.
Giant Compton Shifts in Hyperbolic Metamaterial
Iorsh, Ivan; Ginzburg, Pavel; Belov, Pavel; Kivshar, Yuri
2014-01-01
We study the Compton scattering of light by free electrons inside a hyperbolic medium. We demonstrate that the unconventional dispersion and local density of states of the electromagnetic modes in such media can lead to a giant Compton shift and dramatic enhancement of the scattering cross section. We develop an universal approach for the study of coupled multi-photon processes in nanostructured media and derive the spectral intensity function of the scattered radiation for realistic metamaterial structures. We predict the Compton shift of the order of a few meVs for the infrared spectrum that is at least one order of magnitude larger than the Compton shift in any other system.
An Internal Observability Estimate for Stochastic Hyperbolic Equations
2015-01-01
This paper is addressed to establishing an internal observability estimate for some linear stochastic hyperbolic equations. The key is to establish a new global Carleman estimate for forward stochastic hyperbolic equations in the $L^2$-space. Different from the deterministic case, a delicate analysis of the adaptedness for some stochastic processes is required in the stochastic setting.
Positive mass and Penrose type inequalities for asymptotically hyperbolic hypersurfaces
de Lima, Levi Lopes
2012-01-01
We establish versions of the Positive Mass and Penrose inequalities for a class of asymptotically hyperbolic hypersurfaces. In particular, under the usual dominant energy condition, we prove in all dimensions $n\\geq 3$ an optimal Penrose inequality for certain graphs in hyperbolic space $\\mathbb H^{n+1}$ whose boundary has constant mean curvature $n-1$.
Hyperbolicity of the 3+1 system of Einstein equations
Choquet-Bruhat, Y. (I.M.T.A., Paris (France)); Ruggeri, T. (Istituto di Matematica Applicata, Bologna (Italy))
1982-03-22
We obtain a hyperbolic system from the usual evolution equations of the 3+1 treatment by combining appropriately, these equations with the constraints. We obtain from these hyperbolic equations (using also the constraints and Bianchi identities) the existence theorem, in its most refined form.
Mixed elliptic and hyperbolic systems for the Einstein equations
Choquet-Bruhat, Y
1996-01-01
We analyse the mathematical underpinnings of a mixed hyperbolic-elliptic form of the Einstein equations of motion in which the lapse function is determined by specified mean curvature and the shift is arbitrary. We also examine a new recently-published first order symmetric hyperbolic form of the equations of motion.
The case for hyperbolic theories of dissipation in relativistic fluids
Anile, A M; Romano, V; Anile, Angelo Marcello; Pavon, Diego; Romano, Vittorio
1998-01-01
In this paper we higlight the fact that the physical content of hyperbolic theories of relativistic dissipative fluids is, in general, much broader than that of the hyperbolic ones. This is substantiated by presenting an ample range of dissipative fluids whose behavior noticeably departs from Navier-Stokes.
p-Capacity and p-Hyperbolicity of Submanifolds
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...
On the Coefficients of a Hyperbolic Hydrodynamic Model
Muroya, Shin
2012-01-01
Based on the Nakajima-Zubarev type nonequilibrium density operator, we derive a hyperbolic hydrodynamical equation. Microscopic Kubo-formulas for all coefficients in the hyperbolic hydrodynamics are obtained. Coefficients $\\alpha_{i}$'s and $\\beta_{i}$'s in the Israel-Stewart equation are given as current-weighted correlation lengths which are to be calculated in statistical mechanics.
Hyperbolic polaritonic crystals based on nanostructured nanorod metamaterials.
Dickson, Wayne; Beckett, Stephen; McClatchey, Christina; Murphy, Antony; O'Connor, Daniel; Wurtz, Gregory A; Pollard, Robert; Zayats, Anatoly V
2015-10-21
Surface plasmon polaritons usually exist on a few suitable plasmonic materials; however, nanostructured plasmonic metamaterials allow a much broader range of optical properties to be designed. Here, bottom-up and top-down nanostructuring are combined, creating hyperbolic metamaterial-based photonic crystals termed hyperbolic polaritonic crystals, allowing free-space access to the high spatial frequency modes supported by these metamaterials.
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 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 , 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 r 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 hyperbolicity constant in time O (n2:688). We also provide an exact algorithm to compute the hyperbolicity constant 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.
Hyperbolic orbit and its variation of deep-space probe
LIU; Lin(刘林); WANG; Xin(王歆)
2003-01-01
While approaching the target body, the deep-space probe is orbiting hyperbolically before the maneuver. We discuss the variation of perturbed hyperbolic orbit using the method similar to that used in elliptic orbit. Ephemeris calculating and orbit control will benefit from the given analytical solution.
Diffusion and dispersion of numerical schemes for Hyperbolic problems
Petit, H.A.H
2001-01-01
In the following text an overview is given of numerical schemes which can be used to solve hyperbolic partial differential equations. The overview is far from extensive and the analysis of the schemes is limited to the application on the simplest hyperbolic equation conceivable, namely the so called
The Lyapunov exponents of C~1 hyperbolic systems
无
2010-01-01
Let f be a C 1 diffeomorphisim of smooth Riemannian manifold and preserve a hyperbolic ergodic measure μ. We prove that if the Osledec splitting is dominated, then the Lyapunov exponents of μ can be approximated by the exponents of atomic measures on hyperbolic periodic orbits.
Luan, Jing; Wen, Linqing; Chen, Yanbei
2011-01-01
Electromagnetic (EM) follow-up observations of gravitational wave (GW) events will help shed light on the nature of the sources, and more can be learned if the EM follow-ups can start as soon as the GW event becomes observable. In this paper, we propose a computationally efficient time-domain algorithm capable of detecting gravitational waves (GWs) from coalescing binaries of compact objects with nearly zero time delay. In case when the signal is strong enough, our algorithm also has the flexibility to trigger EM observation before the merger. The key to the efficiency of our algorithm arises from the use of chains of so-called Infinite Impulse Response (IIR) filters, which filter time-series data recursively. Computational cost is further reduced by a template interpolation technique that requires filtering to be done only for a much coarser template bank than otherwise required to sufficiently recover optimal signal-to-noise ratio. Towards future detectors with sensitivity extending to lower frequencies, ou...
Bazeia, D; Marques, M A; Menezes, R; da Rocha, R
2016-01-01
In this work we deal with non-topological solutions of the Q-ball type in two space-time dimensions, in models described by a single complex scalar field that engenders global symmetry. The main novelty is the presence of stable Q-balls solutions that live in a compact interval of the real line and appear from a family of models controlled by two distinct parameters. We find analytical solutions and study their charge and energy, and show how to control the parameters to make the Q-balls classically and quantum mechanically stable.
Hyperbolic prisms and foams in Hele-Shaw cells
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.
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 ...
Twisted Alexander polynomials of hyperbolic knots
Dunfield, Nathan M; Jackson, Nicholas
2011-01-01
We study a twisted Alexander polynomial naturally associated to a hyperbolic knot in an integer homology 3-sphere via a lift of the holonomy representation to SL(2, C). It is an unambiguous symmetric Laurent polynomial whose coefficients lie in the trace field of the knot. It contains information about genus, fibering, and chirality, and moreover is powerful enough to sometimes detect mutation. We calculated this invariant numerically for all 313,209 hyperbolic knots in S^3 with at most 15 crossings, and found that in all cases it gave a sharp bound on the genus of the knot and determined both fibering and chirality. We also study how such twisted Alexander polynomials vary as one moves around in an irreducible component X_0 of the SL(2, C)-character variety of the knot group. We show how to understand all of these polynomials at once in terms of a polynomial whose coefficients lie in the function field of X_0. We use this to help explain some of the patterns observed for knots in S^3, and explore a potential...
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.
Hyperbolic contraction measuring systems for extensional flow
Nyström, M.; Tamaddon Jahromi, H. R.; Stading, M.; Webster, M. F.
2017-08-01
In this paper an experimental method for extensional measurements on medium viscosity fluids in contraction flow is evaluated through numerical simulations and experimental measurements. This measuring technique measures the pressure drop over a hyperbolic contraction, caused by fluid extension and fluid shear, where the extensional component is assumed to dominate. The present evaluative work advances our previous studies on this experimental method by introducing several contraction ratios and addressing different constitutive models of varying shear and extensional response. The constitutive models included are those of the constant viscosity Oldroyd-B and FENE-CR models, and the shear-thinning LPTT model. Examining the results, the impact of shear and first normal stress difference on the measured pressure drop are studied through numerical pressure drop predictions. In addition, stream function patterns are investigated to detect vortex development and influence of contraction ratio. The numerical predictions are further related to experimental measurements for the flow through a 15:1 contraction ratio with three different test fluids. The measured pressure drops are observed to exhibit the same trends as predicted in the numerical simulations, offering close correlation and tight predictive windows for experimental data capture. This result has demonstrated that the hyperbolic contraction flow is well able to detect such elastic fluid properties and that this is matched by numerical predictions in evaluation of their flow response. The hyperbolical contraction flow technique is commended for its distinct benefits: it is straightforward and simple to perform, the Hencky strain can be set by changing contraction ratio, non-homogeneous fluids can be tested, and one can directly determine the degree of elastic fluid behaviour. Based on matching of viscometric extensional viscosity response for FENE-CR and LPTT models, a decline is predicted in pressure drop for
Hyperbolic contraction measuring systems for extensional flow
Nyström, M.; Tamaddon Jahromi, H. R.; Stading, M.; Webster, M. F.
2017-02-01
In this paper an experimental method for extensional measurements on medium viscosity fluids in contraction flow is evaluated through numerical simulations and experimental measurements. This measuring technique measures the pressure drop over a hyperbolic contraction, caused by fluid extension and fluid shear, where the extensional component is assumed to dominate. The present evaluative work advances our previous studies on this experimental method by introducing several contraction ratios and addressing different constitutive models of varying shear and extensional response. The constitutive models included are those of the constant viscosity Oldroyd-B and FENE-CR models, and the shear-thinning LPTT model. Examining the results, the impact of shear and first normal stress difference on the measured pressure drop are studied through numerical pressure drop predictions. In addition, stream function patterns are investigated to detect vortex development and influence of contraction ratio. The numerical predictions are further related to experimental measurements for the flow through a 15:1 contraction ratio with three different test fluids. The measured pressure drops are observed to exhibit the same trends as predicted in the numerical simulations, offering close correlation and tight predictive windows for experimental data capture. This result has demonstrated that the hyperbolic contraction flow is well able to detect such elastic fluid properties and that this is matched by numerical predictions in evaluation of their flow response. The hyperbolical contraction flow technique is commended for its distinct benefits: it is straightforward and simple to perform, the Hencky strain can be set by changing contraction ratio, non-homogeneous fluids can be tested, and one can directly determine the degree of elastic fluid behaviour. Based on matching of viscometric extensional viscosity response for FENE-CR and LPTT models, a decline is predicted in pressure drop for
Tunable hyperbolic dispersion and negative refraction in natural electride materials
Guan, Shan; Huang, Shao Ying; Yao, Yugui; Yang, Shengyuan A.
2017-04-01
Hyperbolic (or indefinite) materials have attracted significant attention due to their unique capabilities for engineering electromagnetic space and controlling light propagation. A current challenge is to find a hyperbolic material with wide working frequency window, low energy loss, and easy controllability. Here, we propose that naturally existing electride materials could serve as high-performance hyperbolic medium. Taking the electride Ca2N as a concrete example and using first-principles calculations, we show that the material is hyperbolic over a wide frequency window from short-wavelength infrared to near infrared (from about 3.3 μ m to 880 nm). More importantly, it is almost lossless in the window. We clarify the physical origin of these remarkable properties and show its all-angle negative refraction effect. Moreover, we find that the optical properties can be effectively tuned by strain. With moderate strain, the material can even be switched between elliptic and hyperbolic for a particular frequency. Our result points out a new route toward high-performance natural hyperbolic materials, and it offers realistic materials and novel methods to achieve controllable hyperbolic dispersion with great potential for applications.
Sustaining the Internet with hyperbolic mapping
Boguna, Marian; Krioukov, Dmitri
2010-01-01
The Internet infrastructure is severely stressed. Rapidly growing overhead associated with the primary function of the Internet---routing information packets between any two computers in the world---causes concerns among Internet experts that the existing Internet routing architecture may not sustain even another decade; parts of the Internet have started sinking into black holes already. Here we present a method to map the Internet to a hyperbolic space. Guided with the constructed map, which we release with this paper, Internet routing exhibits scaling properties close to theoretically best possible, thus resolving serious scaling limitations that the Internet faces today. Besides this immediate practical viability, our network mapping method can provide a different perspective on the community structure in complex networks.
A Matrix Hyperbolic Cosine Algorithm and Applications
Zouzias, Anastasios
2011-01-01
Wigderson and Xiao presented an efficient derandomization of the matrix Chernoff bound using the method of pessimistic estimators. Based on their construction, we present a derandomization of the matrix Bernstein inequality which can be viewed as generalization of Spencer's hyperbolic cosine algorithm. We apply our construction to several problems by analyzing its computational efficiency under two special cases of matrix samples; one in which the samples have a group structure and the other in which they have rank-one outer-product structure. As a consequence of the former case, we present a deterministic algorithm that, given the multiplication table of a finite group of size n, constructs an Alon-Roichman expanding Cayley graph of logarithmic degree in O(n^2 log^3 n) time. For the latter case, we present a fast deterministic algorithm for spectral sparsification of positive semi-definite matrices (as defined in [Sri10]) which implies directly an improved deterministic algorithm for spectral graph sparsific...
Nonlinear electrodynamics as a symmetric hyperbolic system
Abalos, Fernando; Goulart, Érico; Reula, Oscar
2015-01-01
Nonlinear theories generalizing Maxwell's electromagnetism and arising from a Lagrangian formalism have dispersion relations in which propagation planes factor into null planes corresponding to two effective metrics which depend on the point-wise values of the electromagnetic field. These effective Lorentzian metrics share the null (generically two) directions of the electromagnetic field. We show that, the theory is symmetric hyperbolic if and only if the cones these metrics give rise to have a non-empty intersection. Namely that there exist families of symmetrizers in the sense of Geroch which are positive definite for all covectors in the interior of the cones intersection. Thus, for these theories, the initial value problem is well-posed. We illustrate the power of this approach with several nonlinear models of physical interest such as Born-Infeld, Gauss-Bonnet and Euler-Heisenberg.
Variable Lebesgue spaces and hyperbolic systems
2014-01-01
This book targets graduate students and researchers who want to learn about Lebesgue spaces and solutions to hyperbolic equations. It is divided into two parts. Part 1 provides an introduction to the theory of variable Lebesgue spaces: Banach function spaces like the classical Lebesgue spaces but with the constant exponent replaced by an exponent function. These spaces arise naturally from the study of partial differential equations and variational integrals with non-standard growth conditions. They have applications to electrorheological fluids in physics and to image reconstruction. After an introduction that sketches history and motivation, the authors develop the function space properties of variable Lebesgue spaces; proofs are modeled on the classical theory. Subsequently, the Hardy-Littlewood maximal operator is discussed. In the last chapter, other operators from harmonic analysis are considered, such as convolution operators and singular integrals. The text is mostly self-contained, with only some mor...
Refraction and wave matching in hyperbolic thermoelasticity
Józef Rafa
2015-03-01
Full Text Available The subject of the publication concerns the propagation of thermoelastic waves with a particular emphasis on the refraction of waves at the boundary of a layer laying (resting on a halfspace. Analogously to the effect of wave matching, which appears in the case of acoustic and electromagnetic waves, the impedance of a thermoelastic wave has been introduced and its influence and the reflection andrefraction on the boundary at media has been investigated. The model of the medium describes a mutual coupling of mechanical and thermalinteractions with a wave type propagation of heat in media taken into account.[b]Keywords[/b]: hyperbolic thermoelasticity, wave impedance of a thermoelastic medium,refraction and wave matching
Simulation of a Hyperbolic Field Energy Analyzer
Gonzalez-Lizardo, Angel
2016-01-01
Energy analyzers are important plasma diagnostic tools with applications in a broad range of disciplines including molecular spectroscopy, electron microscopy, basic plasma physics, plasma etching, plasma processing, and ion sputtering technology. The Hyperbolic Field Energy Analyzer (HFEA) is a novel device able to determine ion and electron energy spectra and temperatures. The HFEA is well suited for ion temperature and density diagnostics at those situations where ions are scarce. A simulation of the capacities of the HFEA to discriminate particles of a particular energy level, as well as to determine temperature and density is performed in this work. The electric field due the combination of the conical elements, collimator lens, and Faraday cup applied voltage was computed in a well suited three-dimensional grid. The field is later used to compute the trajectory of a set of particles with a predetermined energy distribution. The results include the observation of the particle trajectories inside the sens...
Tangent hyperbolic circular frequency diverse array radars
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.
Self-induced torque in hyperbolic metamaterials.
Ginzburg, Pavel; Krasavin, Alexey V; Poddubny, Alexander N; Belov, Pavel A; Kivshar, Yuri S; Zayats, Anatoly V
2013-07-19
Optical forces constitute a fundamental phenomenon important in various fields of science, from astronomy to biology. Generally, intense external radiation sources are required to achieve measurable effects suitable for applications. Here we demonstrate that quantum emitters placed in a homogeneous anisotropic medium induce self-torques, aligning themselves in the well-defined direction determined by an anisotropy, in order to maximize their radiation efficiency. We develop a universal quantum-mechanical theory of self-induced torques acting on an emitter placed in a material environment. The theoretical framework is based on the radiation reaction approach utilizing the rigorous Langevin local quantization of electromagnetic excitations. We show more than 2 orders of magnitude enhancement of the self-torque by an anisotropic metamaterial with hyperbolic dispersion, having negative ratio of permittivity tensor components, in comparison with conventional anisotropic crystals with the highest naturally available anisotropy.
Spin control of light with hyperbolic metasurfaces
Yermakov, Oleh Y; Bogdanov, Andrey A; Iorsh, Ivan V; Bliokh, Konstantin Y; Kivshar, Yuri S
2016-01-01
Transverse spin angular momentum is an inherent feature of evanescent waves which may have applications in nanoscale optomechanics, spintronics, and quantum information technology due to the robust spin-directional coupling. Here we analyze a local spin angular momentum density of hybrid surface waves propagating along anisotropic hyperbolic metasurfaces. We reveal that, in contrast to bulk plane waves and conventional surface plasmons at isotropic interfaces, the spin of the hybrid surface waves can be engineered to have an arbitrary angle with the propagation direction. This property allows to tailor directivity of surface waves via the magnetic control of the spin projection of quantum emitters, and it can be useful for optically controlled spin transfer.
From hyperbolic regularization to exact hydrodynamics for linearized Grad's equations.
Colangeli, Matteo; Karlin, Iliya V; Kröger, Martin
2007-05-01
Inspired by a recent hyperbolic regularization of Burnett's hydrodynamic equations [A. Bobylev, J. Stat. Phys. 124, 371 (2006)], we introduce a method to derive hyperbolic equations of linear hydrodynamics to any desired accuracy in Knudsen number. The approach is based on a dynamic invariance principle which derives exact constitutive relations for the stress tensor and heat flux, and a transformation which renders the exact equations of hydrodynamics hyperbolic and stable. The method is described in detail for a simple kinetic model -- a 13 moment Grad system.
Lower bounds on volumes of hyperbolic Haken 3-manifolds
Agol, Ian; Storm, Peter A.; Thurston, William P.
2007-10-01
We prove a volume inequality for 3-manifolds having C^{0} metrics ``bent'' along a surface and satisfying certain curvature conditions. The result makes use of Perelman's work on the Ricci flow and geometrization of closed 3-manifolds. Corollaries include a new proof of a conjecture of Bonahon about volumes of convex cores of Kleinian groups, improved volume estimates for certain Haken hyperbolic 3-manifolds, and a lower bound on the minimal volume of orientable hyperbolic 3-manifolds. An appendix compares estimates of volumes of hyperbolic 3-manifolds drilled along a closed embedded geodesic with experimental data.
Analytic hyperbolic geometry in N dimensions an introduction
Ungar, Abraham Albert
2014-01-01
The concept of the Euclidean simplex is important in the study of n-dimensional Euclidean geometry. This book introduces for the first time the concept of hyperbolic simplex as an important concept in n-dimensional hyperbolic geometry. Following the emergence of his gyroalgebra in 1988, the author crafted gyrolanguage, the algebraic language that sheds natural light on hyperbolic geometry and special relativity. Several authors have successfully employed the author's gyroalgebra in their exploration for novel results. Françoise Chatelin noted in her book, and elsewhere, that the computation la
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).
Plasmon analysis and homogenization in plane layered photonic crystals and hyperbolic metamaterials
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.
Plasmon analysis and homogenization in plane layered photonic crystals and hyperbolic metamaterials
Davidovich, M. V.
2016-12-01
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 (SiO2) 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.
Davidovich, Mikhael V.
2016-04-01
The dispersion equation and the analysis and homogenization in periodic and quasiperiodic plane layered structures with alternating dielectric layers of metal and dielectric layers, as well as a graphene sheet and SiO2 layers have been investigated. The cases are considered when these patterns become the properties of hyperbolic metamaterials, i.e., having different signs of the real parts of the tensor components of the effective dielectric constant. It is shown that usage only dielectric layers is perspective in reducing losses.
From explosive to infinite-order transitions on a hyperbolic network.
Singh, Vijay; Brunson, C T; Boettcher, Stefan
2014-11-01
We analyze the phase transitions that emerge from the recursive design of certain hyperbolic networks that includes, for instance, a discontinuous ("explosive") transition in ordinary percolation. To this end, we solve the q-state Potts model in the analytic continuation for noninteger q with the real-space renormalization group. We find exact expressions for this one-parameter family of models that describe the dramatic transformation of the transition. In particular, this variation in q shows that the discontinuous transition is generic in the regime q2 the transition immediately transforms into an infinitely smooth order parameter of the Berezinskii-Kosterlitz-Thouless type.
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...... of our recent works and demonstrate the benefits of using hyperbolic metamaterials in plasmonic waveguides and light scattering. We also discuss nonlocal topological transitions in the hyperbolic metamaterials that effectively induce a zero refractive index....
Convexity properties of generalized trigonometric and hyperbolic functions
Baricz, Árpád; Bhayo, Barkat Ali; Klén, Riku
2013-01-01
We study the power mean inequality of the generalized trigonometric and hyperbolic functions with two parameters. The generalized $p$-trigonometric and $(p, q)$-trigonometric functions were introduced by P. Lindqvist and S. Takeuchi, respectively.
The periodic domino problem is undecidable in the hyperbolic plane
Margenstern, Maurice
2007-01-01
In this paper, we consider the periodic tiling problem which was proved undecidable in the Euclidean plane by Yu. Gurevich and I. Koriakov in 1972. Here, we prove that the same problem for the hyperbolic plane is also undecidable.
OSCILLATION OF IMPULSIVE HYPERBOLIC PARTIAL DIFFERENTIAL EQUATION WITH DELAY
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.
OSCILLATION CRITERIA OF NEUTRAL TYPE IMPULSIVE HYPERBOLIC EQUATIONS
马晴霞; 刘安平
2014-01-01
In this paper, oscillatory properties of all solutions for neutral type impulsive hyperbolic equations with several delays under the Robin boundary condition are investigated and several new suﬃcient conditions for oscillation are presented.
Persistence of noncompact normally hyperbolic invariant manifolds in bounded geometry
Eldering, Jaap
2012-01-01
We prove a persistence result for noncompact normally hyperbolic invariant manifolds in Riemannian manifolds of bounded geometry. The bounded geometry of the ambient manifold is a crucial assumption in order to control the uniformity of all estimates throughout the proof.
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...
Proof mining in ${\\mathbb R}$-trees and hyperbolic spaces
Leustean, Laurentiu
2008-01-01
This paper is part of the general project of proof mining, developed by Kohlenbach. By "proof mining" we mean the logical analysis of mathematical proofs with the aim of extracting new numerically relevant information hidden in the proofs. We present logical metatheorems for classes of spaces from functional analysis and hyperbolic geometry, like Gromov hyperbolic spaces, ${\\mathbb R}$-trees and uniformly convex hyperbolic spaces. Our theorems are adaptations to these structures of previous metatheorems of Gerhardy and Kohlenbach, and they guarantee a-priori, under very general logical conditions, the existence of uniform bounds. We give also an application in nonlinear functional analysis, more specifically in metric fixed-point theory. Thus, we show that the uniform bound on the rate of asymptotic regularity for the Krasnoselski-Mann iterations of nonexpansive mappings in uniformly convex hyperbolic spaces obtained in a previous paper is an instance of one of our metatheorems.
HYPERBOLIC-PARABOLIC CHEMOTAXIS SYSTEM WITH NONLINEAR PRODUCT TERMS
Chen Hua; Wu Shaohua
2008-01-01
We prove the local existence and uniqueness of week solution of the hyperbolic-parabolic Chemotaxis system with some nonlinear product terms. For one dimensional case, we prove also the global existence and uniqueness of the solution for the problem.
Novel Hyperbolic Homoclinic Solutions of the Helmholtz-Duffing Oscillators
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.
Novel Hyperbolic Homoclinic Solutions of the Helmholtz-Duffing Oscillators
Yang-Yang Chen; Shu-Hui Chen; Wei-Wei Wang
2016-01-01
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 ...
Non strict and strict hyperbolic systems for the Einstein equations
Choquet-Bruhat, Y
2001-01-01
The integration of the Einstein equations split into the solution of constraints on an initial space like 3 - manifold, an essentially elliptic system, and a system which will describe the dynamical evolution, modulo a choice of gauge. We prove in this paper that the simplest gauge choice leads to a system which is causal, but hyperbolic non strict in the sense of Leray - Ohya. We review some strictly hyperbolic systems obtained recently.
MULTISCALE HOMOGENIZATION OF NONLINEAR HYPERBOLIC EQUATIONS WITH SEVERAL TIME SCALES
Jean Louis Woukeng; David Dongo
2011-01-01
We study the multiscale homogenization of a nonlinear hyperbolic equation in a periodic setting. We obtain an accurate homogenization result. We also show that as the nonlinear term depends on the microscopic time variable, the global homogenized problem thus obtained is a system consisting of two hyperbolic equations. It is also shown that in spite of the presence of several time scales, the global homogenized problem is not a reiterated one.
Tachyonic matter cosmology with exponential and hyperbolic potentials
Pourhassan, B.; Naji, J.
In this paper, we consider tachyonic matter in spatially flat Friedmann-Robertson-Walker (FRW) universe, and obtain behavior of some important cosmological parameters for two special cases of potentials. First, we assume the exponential potential and then consider hyperbolic cosine type potential. In both cases, we obtain behavior of the Hubble, deceleration and EoS parameters. Comparison with observational data suggest the model with hyperbolic cosine type scalar field potentials has good model to describe universe.
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.
Boundary Layer to a System of Viscous Hyperbolic Conservation Laws
2008-01-01
In this paper, we investigate the large-time behavior of solutions to the initial-boundary value problem for nxn hyperbolic system of conservation laws with artificial viscosity in the half line (0, ∞). We first show that a boundary layer exists if the corresponding hyperbolic part contains at least one characteristic field with negative propagation speed. We further show that such boundary layer is nonlinearly stable under small initial perturbation. The proofs are given by an elementary energy method.
Finite volume evolution Galerkin (FVEG) methods for hyperbolic systems
Lukácová-Medvid'ová, Maria; Morton, K.W.; Warnecke, Gerald
2003-01-01
The subject of the paper is the derivation and analysis of new multidimensional, high-resolution, finite volume evolution Galerkin (FVEG) schemes for systems of nonlinear hyperbolic conservation laws. Our approach couples a finite volume formulation with approximate evolution operators. The latter are constructed using the bicharacteristics of the multidimensional hyperbolic system, such that all of the infinitely many directions of wave propagation are taken into account. In particular, we p...
Profile of Blow-up Solution to Hyperbolic System with Nonlocal Term
Zhi Wen DUAN; Kwang Ik KIM
2007-01-01
This paper is concerned with a nonlocal hyperbolic system as follows:utt=△u+(∫Ωvdx)p for x∈RN,t＞0, utt=△v+(∫Ωvdx)q for x∈RN,t＞0,u(x,0)=u0(x),ut(x,0)=u01(x) for x∈RN,v(x,0)=u0(x),vt(x,0)=v01(x) for x∈RN,where 1 ≤ N ≤ 3, p ≥ 1, q ≥ 1 and pq > 1. Here the initial values are compactly supported andΩ(∈) RN is a bounded open region. The blow-up curve, blow-up rate and profile of the solution arediscussed.
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...
Attractors for strongly damped wave equations with nonlinear hyperbolic dynamic boundary conditions
Jameson Graber, P.; Shomberg, Joseph L.
2016-04-01
We establish the well-posedness of a strongly damped semilinear wave equation equipped with nonlinear hyperbolic dynamic boundary conditions. Results are carried out with the presence of a parameter distinguishing whether the underlying operator is analytic, α >0 , or only of Gevrey class, α =0 . We establish the existence of a global attractor for each α \\in ≤ft[0,1\\right], and we show that the family of global attractors is upper-semicontinuous as α \\to 0. Furthermore, for each α \\in ≤ft[0,1\\right] , we show the existence of a weak exponential attractor. A weak exponential attractor is a finite dimensional compact set in the weak topology of the phase space. This result ensures the corresponding global attractor also possesses finite fractal dimension in the weak topology; moreover, the dimension is independent of the perturbation parameter α. In both settings, attractors are found under minimal assumptions on the nonlinear terms.
Parracino, Stefano; Richetta, Maria; Gelfusa, Michela; Malizia, Andrea; Bellecci, Carlo; De Leo, Leonardo; Perrimezzi, Carlo; Fin, Alessandro; Forin, Marco; Giappicucci, Francesca; Grion, Massimo; Marchese, Giuseppe; Gaudio, Pasquale
2016-10-01
Urban air pollution causes deleterious effects on human health and the environment. To meet stringent standards imposed by the European Commission, advanced measurement methods are required. Remote sensing techniques, such as light detection and ranging (LiDAR), can be a valuable option for evaluating particulate matter (PM), emitted by vehicles in urban traffic, with high sensitivity and in shorter time intervals. Since air quality problems persist not only in large urban areas, a measuring campaign was specifically performed in a suburban area of Crotone, Italy, using both a compact LiDAR system and conventional instruments for real-time vehicle emissions monitoring along a congested road. First results reported in this paper show a strong dependence between variations of LiDAR backscattering signals and traffic-related air pollution levels. Moreover, time-resolved LiDAR data averaged in limited regions, directly above conventional monitoring stations at the border of an intersection, were found to be linearly correlated to the PM concentration levels with a correlation coefficient between 0.75 and 0.84.
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.
Compaction Behavior of Isomalt after Roll Compaction
2012-01-01
The suitability of the new isomalt grade galenIQ™ 801 for dry granulation and following tableting is evaluated in this study. Isomalt alone, as well as a blend of equal parts with dibasic calcium phosphate, is roll compacted and tableted. Particle size distribution and flowability of the granules and friability and disintegration time of the tablets are determined. Tensile strength of tablets is related to the specific compaction force during roll compaction and the tableting force....
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.
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.
Chen, C. -P.; Paris, R. B.
2016-01-01
In this paper, we present series representations of the remainders in the expansions for certain trigonometric and hyperbolic functions. By using the obtained results, we establish some inequalities for trigonometric and hyperbolic functions.
On Applications of a Generalized Hyperbolic Measure of Entropy
P.K Bhatia
2015-06-01
Full Text Available After generalization of Shannon‘s entropy measure by Renyi in 1961, many generalized versions of Shannon measure were proposed by different authors. Shannon measure can be obtained from these generalized measures asymptotically. A natural question arises in the parametric generalization of Shannon‘s entropy measure. What is the role of the parameter(s from application point of view? In the present communication, super additivity and fast scalability of generalized hyperbolic measure [Bhatia and Singh, 2013] of probabilistic entropy as compared to some classical measures of entropy has been shown. Application of a generalized hyperbolic measure of probabilistic entropy in certain situations has been discussed. Also, application of generalized hyperbolic measure of fuzzy entropy in multi attribute decision making have been presented where the parameter affects the preference order.
Output regulation problem for a class of regular hyperbolic systems
Xu, Xiaodong; Dubljevic, Stevan
2016-01-01
This paper investigates the output regulation problem for a class of regular first-order hyperbolic partial differential equation (PDE) systems. A state feedback and an error feedback regulator are considered to force the output of the hyperbolic PDE plant to track a periodic reference trajectory generated by a neutrally stable exosystem. A new explanation is given to extend the results in the literature to solve the regulation problem associated with the first-order hyperbolic PDE systems. Moreover, in order to provide the closed-loop stability condition for the solvability of the regulator problems, the design of stabilising feedback gain and its dual problem design of stabilising output injection gain are considered in this paper. This paper develops an easy method to obtain an adjustable stabilising feedback gain and stabilising output injection gain with the aid of the operator Riccati equation.
Hyperbolic Metamaterials and Coupled Surface Plasmon Polaritons: comparative analysis
Li, Tengfei
2016-01-01
We investigate the optical properties of sub-wavelength layered metal/dielectric structures, also known as hyperbolic metamaterials (HMMs), using exact analytical Kronig Penney (KP) model. We show that hyperbolic isofrequency surfaces exist for all combinations of layer permittivities and thicknesses, and the largest Purcell enhancements (PE) of spontaneous radiation are achieved away from the nominally hyperbolic region. Detailed comparison of field distributions, dispersion curves, and Purcell factors (PF) between the HMMs and Surface Plasmon Polaritons (SPPs) guided modes in metal/dielectric waveguides demonstrates that HMMs are nothing but weakly coupled gap or slab SPPs modes. Broadband PE is not specific to the HMMs and can be easily attained in single thin metallic layers. Furthermore, large wavevectors and PE are always combined with high loss, short propagation distances and large impedances; hence PE in HMMs is essentially a direct coupling of the energy into the free electron motion in the metal, o...
Experimental evidence of hyperbolic heat conduction in processed meat
Mitra, K.; Kumar, S.; Vedavarz, A.; Moallemi, M.K. [Polytechnic Univ., Brooklyn, NY (United States)
1995-08-01
The objective of this paper is to present experimental evidence of the wave nature of heat propagation in processed meat and to demonstrate that the hyperbolic heat conduction model is an accurate representation, on a macroscopic level, of the heat conduction process in such biological material. The value of the characteristic thermal time of a specific material, processed bologna meat, is determined experimentally. As a part of the work different thermophysical properties are also measured. The measured temperature distributions in the samples are compared with the Fourier results and significant deviation between the two is observed, especially during the initial stages of the transient conduction process. The measured values are found to match the theoretical non-Fourier hyperbolic predictions very well. The superposition of waves occurring inside the meat sample due to the hyperbolic nature of heat conduction is also proved experimentally. 14 refs., 7 figs., 2 tabs.
Relatively Hyperbolic Extensions of Groups and Cannon-Thurston Maps
Abhijit Pal
2010-02-01
Let $1→(K, K_1)→(G, N_G(K_1))→(\\mathcal{Q}, \\mathcal{Q}_1)→ 1$ be a short exact sequence of pairs of finitely generated groups with 1 a proper non-trivial subgroup of and strongly hyperbolic relative to $K_1$. Assuming that, for all $g\\in G$, there exists $k_g\\in K$ such that $gK_1g^{-1}=k_gK_1k^{-1}_g$, we will prove that there exists a quasi-isometric section $s:\\mathcal{Q}→ G$. Further, we will prove that if is strongly hyperbolic relative to the normalizer subgroup $N_G(K_1)$ and weakly hyperbolic relative to $K_1$, then there exists a Cannon–Thurston map for the inclusion $i:_K→_G$.
Hyperbolic value addition and general models of animal choice.
Mazur, J E
2001-01-01
Three mathematical models of choice--the contextual-choice model (R. Grace, 1994), delay-reduction theory (N. Squires & E. Fantino, 1971), and a new model called the hyperbolic value-added model--were compared in their ability to predict the results from a wide variety of experiments with animal subjects. When supplied with 2 or 3 free parameters, all 3 models made fairly accurate predictions for a large set of experiments that used concurrent-chain procedures. One advantage of the hyperbolic value-added model is that it is derived from a simpler model that makes accurate predictions for many experiments using discrete-trial adjusting-delay procedures. Some results favor the hyperbolic value-added model and delay-reduction theory over the contextual-choice model, but more data are needed from choice situations for which the models make distinctly different predictions.
Growth and dispersal with inertia: Hyperbolic reaction-transport systems
Méndez, Vicenç; Campos, Daniel; Horsthemke, Werner
2014-10-01
We investigate the behavior of five hyperbolic reaction-diffusion equations most commonly employed to describe systems of interacting organisms or reacting particles where dispersal displays inertia. We first discuss the macroscopic or mesoscopic foundation, or lack thereof, of these reaction-transport equations. This is followed by an analysis of the temporal evolution of spatially uniform states. In particular, we determine the uniform steady states of the reaction-transport systems and their stability properties. We then address the spatiotemporal behavior of pure death processes. We end with a unified treatment of the front speed for hyperbolic reaction-diffusion equations with Kolmogorov-Petrosvskii-Piskunov kinetics. In particular, we obtain an exact expression for the front speed of a general class of reaction correlated random walk systems. Our results establish that three out of the five hyperbolic reaction-transport equations provide physically acceptable models of biological and chemical systems.
BTZ extensions of globally hyperbolic singular flat spacetimes
Brunswic, Léo
2016-01-01
Minkowski space is the local model of 3 dimensionnal flat spacetimes. Recent progress in the description of globally hyperbolic flat spacetimes showed strong link between Lorentzian geometry and Teichm{\\"u}ller space. We notice that Lorentzian generalisations of conical singularities are useful for the endeavours of descripting flat spacetimes, creating stronger links with hyperbolic geometry and compactifying spacetimes. In particular massive particles and extreme BTZ singular lines arise naturally. This paper is three-fold. First, prove background local properties which will be useful for future work. Second, generalise fundamental theorems of the theory of globally hyperbolic flat spacetimes. Third, defining BTZ-extension and proving it preserves Cauchy-maximality and Cauchy-completeness.
Second-order hyperbolic Fuchsian systems. I. General theory
Beyer, Florian
2010-01-01
We introduce a class of singular partial differential equations, the second-order hyperbolic Fuchsian systems, and we investigate the associated initial value problem when data are imposed on the singularity. First of all, we analyze a class of equations in which hyperbolicity is not assumed and we construct asymptotic solutions of arbitrary order. Second, for the proposed class of second-order hyperbolic Fuchsian systems, we establish the existence of solutions with prescribed asymptotic behavior on the singularity. Our proof is based on a new scheme which is also suitable to design numerical approximations. Furthermore, as shown in a follow-up paper, the second-order Fuchsian framework is appropriate to handle Einstein's field equations for Gowdy symmetric spacetimes and allows us to recover (and slightly generalize) earlier results by Rendall and collaborators, while providing a direct approach leading to accurate numerical solutions. The proposed framework is also robust enough to encompass matter models ...
Enhanced and directional single photon emission in hyperbolic metamaterials
Newman, Ward D; Jacob, Zubin
2013-01-01
We propose an approach to enhance and direct the spontaneous emission from isolated emitters embedded inside hyperbolic metamaterials into single photon beams. The approach rests on collective plasmonic Bloch modes of hyperbolic metamaterials which propagate in highly directional beams called quantum resonance cones. We propose a pumping scheme using the transparency window of the hyperbolic metamaterial that occurs near the topological transition. Finally, we address the challenge of outcoupling these broadband resonance cones into vacuum using a dielectric bullseye grating. We give a detailed analysis of quenching and design the metamaterial to have a huge Purcell factor in a broad bandwidth inspite of the losses in the metal. Our work should help motivate experiments in the development of single photon sources for broadband emitters such as nitrogen vacancy centers in diamond.
Dynamical chaos and uniformly hyperbolic attractors: from mathematics to physics
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)
Visual presentation of dynamic systems with hyperbolic planar symmetry
Chen Ning [Faculty of Information and Control Engineering, Shenyang Jianzhu University, Shenyang 110168 (China)], E-mail: n_chen@126.com; Li Zichuan; Jin Yuanyuan [Faculty of Information and Control Engineering, Shenyang Jianzhu University, Shenyang 110168 (China)
2009-04-30
Hyperbolic symmetric mappings defined on hyperbolic tilings are investigated. Ljapunov exponents of the dynamic systems are computed with the Euclidean distance. The parameter combinations with great impact on the characteristics of the dynamic systems were chosen as the window coordinates for construction of generalized Mandelbrot sets. The accelerated direct search algorithm is used to search for the set of the critical points in the fundamental region. The parameter space is separated into chaotic, periodic and mixed regions by the Ljapunov exponents of the critical points. The generalized Mandelbrot sets (M-set), which are the cross-sections of the parameter space, were constructed. Three different types of hyperbolic symmetry patterns, which are chaotic attractors, filled-in Julia sets and mixed images composed of an attractor and a filled-in Julia set from the same set of parameters, were created by using parameters from this kind of M-sets.
Loeb, Peter A
2016-01-01
This textbook is designed for a year-long course in real analysis taken by beginning graduate and advanced undergraduate students in mathematics and other areas such as statistics, engineering, and economics. Written by one of the leading scholars in the field, it elegantly explores the core concepts in real analysis and introduces new, accessible methods for both students and instructors. The first half of the book develops both Lebesgue measure and, with essentially no additional work for the student, general Borel measures for the real line. Notation indicates when a result holds only for Lebesgue measure. Differentiation and absolute continuity are presented using a local maximal function, resulting in an exposition that is both simpler and more general than the traditional approach. The second half deals with general measures and functional analysis, including Hilbert spaces, Fourier series, and the Riesz representation theorem for positive linear functionals on continuous functions with compact support....
Impact of hyperbolicity on chimera states in ensembles of nonlocally coupled chaotic oscillators
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.
ON THE HYPERBOLIC OBSTACLE PROBLEM OF FIRST ORDER
无
2002-01-01
This paper presents new results for strong solutions and their coincidence sets of the obstacle problem for linear hyperbolic operators of first order. An inequality similar to the LewyStampacchia ones for elliptic and parabolic problems is shown. Under nondegeneracy conditions the stability of the coincidence set is shown with respect to the variation of the data and with respect to approximation by semilinear hyperbolic problems. These results are applied to the asymptotic stability of the evolution problem with respect to the stationary coercive problem with obstacle.
Hybrid plasmonic/semiconductor nanoparticle monolayer assemblies as hyperbolic metamaterials
Zhukovsky, Sergei; Ozel, Tuncay; Mutlugun, Evren
2014-01-01
We show that hybrid nanostructures made of alternating colloidal semiconductor quantum dot and metal nanoparticle monolayers can function as multilayer hyperbolic meta-materials. By choosing the thickness of the spacer between the quantum dot and nanoparticle layers, one can achieve the indefinite...... 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...
Weakly Nonlinear Geometric Optics for Hyperbolic Systems of Conservation Laws
Chen, Gui-Qiang; Zhang, Yongqian
2012-01-01
We establish an $L^1$-estimate to validate the weakly nonlinear geometric optics for entropy solutions of nonlinear hyperbolic systems of conservation laws with arbitrary initial data of small bounded variation. This implies that the simpler geometric optics expansion function can be employed to study the properties of general entropy solutions to hyperbolic systems of conservation laws. Our analysis involves new techniques which rely on the structure of the approximate equations, besides the properties of the wave-front tracking algorithm and the standard semigroup estimates.
Linear Weingarten surfaces in Euclidean and hyperbolic space
López, Rafael
2009-01-01
In this paper we review some author's results about Weingarten surfaces in Euclidean space $\\r^3$ and hyperbolic space $\\h^3$. We stress here in the search of examples of linear Weingarten surfaces that satisfy a certain geometric property. First, we consider Weingarten surfaces in $\\r^3$ that are foliated by circles, proving that the surface is rotational, a Riemann example or a generalized cone. Next we classify rotational surfaces in $\\r^3$ of hyperbolic type showing that there exist surfaces that are complete. Finally, we study linear Weingarten surfaces in $\\h^3$ that are invariant by a group of parabolic isometries, obtaining its classification.
ON THE DIFFUSION PHENOMENON OF QUASILINEAR HYPERBOLIC WAVES
无
2000-01-01
The authors consider the asymptotic behavior of solutions of the quasilinear hyperbolic equation with linear damping utt+ut-div(a(△u)△u)=01and show that, at least when n≤3, they tend, as t→+∞, to those of the nonlinear parabolic equation ut-div(a(△u)△u)=01in the sense that the norm ‖u(.,t)-v(.,t)‖L∞(Rn)of the difference u-v decays faster than that of either u or v. This provides another example of the diffusion phenomenon of nonlinear hyperbolic waves, first observed by Hsiao, L. and Liu Taiping (see [1,2]).
MULTIDIMENSIONAL RELAXATION APPROXIMATIONS FOR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS
Mohammed Sea(l)d
2007-01-01
We construct and implement a non-oscillatory relaxation scheme for multidimensional hyperbolic systems of conservation laws. The method transforms the nonlinear hyperbolic system to a semilinear model with a relaxation source term and linear characteristics which can be solved numerically without using either Riemann solver or linear iterations.To discretize the relaxation system we consider a high-resolution reconstruction in space and a TVD Runge-Kutta time integration. Detailed formulation of the scheme is given for problems in three space dimensions and numerical experiments are implemented in both scalar and system cases to show the effectiveness of the method.
Spherical, hyperbolic and other projective geometries: convexity, duality, transitions
Fillastre, François; Seppi, Andrea
2016-01-01
Since the end of the 19th century, and after the works of F. Klein and H. Poincar\\'e, it is well known that models of elliptic geometry and hyperbolic geometry can be given using projective geometry, and that Euclidean geometry can be seen as a "limit" of both geometries. Then all the geometries that can be obtained in this way. Some of these geometries had a rich development, most remarkably hyperbolic geometry and the Lorentzian geometries of Minkowski, de Sitter and anti-de Sitter spaces, ...
DECAY OF POSITIVE WAVES OF HYPERBOLIC BALANCE LAWS
Cleopatra Christoforou; Konstantina Trivisa
2012-01-01
Historically,decay rates have been used to provide quantitative and qualitative information on the solutions to hyperbolic conservation laws.Quantitative results include the establishment of convergence rates for approximating procedures and numerical schemes.Qualitative results include the establishment of results on uniqueness and regularity as well as the ability to visualize the waves and their evolution in time.This work presents two decay estimates on the positive waves for systems of hyperbolic and genuinely nonlinear balance laws satisfying a dissipative mechanism.The result is obtained by employing the continuity of Glimm-type functionals and the method of generalized characteristics [7,17,24].
Singularly perturbed hyperbolic problems on metric graphs: asymptotics of solutions
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.
Field-effect induced tunability in planar hyperbolic metamaterials
Papadakis, Georgia T
2015-01-01
We demonstrate that use of the field effect to tune the effective optical parameters of a layered hyperbolic metamaterial leads to topological transitions in its dispersion characteristics in the optical regime. Field effect gating electrically modulates the permittivity in transparent conductive oxides via changes in the carrier density. These permittivity changes lead to active extreme modulation of ~200% of the effective electromagnetic parameters along with active control of the anisotropic dispersion surface of hyperbolic metamaterials and enable the opening and closing of photonic band gaps.
SMOOTH CLASSIFICATION AND LINEARIZATION OF HYPERBOLIC VECTOR FIELDS ON R~3
无
2009-01-01
This paper is devoted to studying smooth normal form theory of hyperbolic vector fields. As a continuation of our previous work on smooth classification and linearization of vector fields near a hyperbolic singular point,in this paper,we deal with the case of hyperbolic vector fields on R3 by examining all possible resonant classes.
SMOOTH CLASSIFICATION AND LINEARIZATION OF HYPERBOLIC VECTOR FIELDS ON R3
Zhihua Ren
2009-01-01
This paper is devoted to studying smooth normal form theory of hyperbolic vector fields. As a continuation of our previous work on smooth classification and lineariza-tion of vector fields near a hyperbolic singular point,in this paper,we deal with the case of hyperbolic vector fields on R3 by examining all possible resonant classes.
Some Results on the Problem of Updating the Hyperbolic Matrix Factorizations
Hanyu LI; Hu YANG
2013-01-01
This paper considers the updating problem of the hyperbolic matrix factorizations.The sufficient conditions for the existence of the updated hyperbolic matrix factorizations are first provided.Then,some differential inequalities and first order perturbation expansions for the updated hyperbolic factors are derived.These results generalize the corresponding ones for the updating problem of the classical QR factorization obtained by Jiguang SUN.
Ping WANG; Jiong Sheng LI
2005-01-01
Let G be a finite simple graph with adjacency matrix A, and let P(A) be the convex closure of the set of all permutation matrices commuting with A. G is said to be compact if every doubly stochastic matrix which commutes with A is in P(A). In this paper, we characterize 3-regular compact graphs and prove that if G is a connected regular compact graph, G - v is also compact, and give a family of almost regular compact connected graphs.
Bound states in a hyperbolic asymmetric double-well
Hartmann, R. R., E-mail: richard.hartmann@dlsu.edu.ph [Physics Department, De La Salle University, 2401 Taft Avenue, Manila (Philippines)
2014-01-15
We report a new class of hyperbolic asymmetric double-well whose bound state wavefunctions can be expressed in terms of confluent Heun functions. An analytic procedure is used to obtain the energy eigenvalues and the criterion for the potential to support bound states is discussed.
Hyperbolic function method for solving nonlinear differential-different equations
Zhu Jia-Min
2005-01-01
An algorithm is devised to obtained exact travelling wave solutions of differential-different equations by means of hyperbolic function. For illustration, we apply the method to solve the discrete nonlinear (2+1)-dimensional Toda lattice equation and the discretized nonlinear mKdV lattice equation, and successfully constructed some explicit and exact travelling wave solutions.
Homogeneous Hyperbolic Systems for Terahertz and Far-Infrared Frequencies
Leonid V. Alekseyev
2012-01-01
Full Text Available We demonstrate that homogeneous naturally-occurring materials can form hyperbolic media, and can be used for nonmagnetic negative refractive index systems. We present specific realizations of the proposed approach for the THz and far-IR frequencies. The proposed structures operate away from resonance, thereby promising the capacity for low-loss devices.
INITIAL BOUNDARY VALUE PROBLEM FOR A DAMPED NONLINEAR HYPERBOLIC EQUATION
陈国旺
2003-01-01
In the paper, the existence and uniqueness of the generalized global solution and the classical global solution of the initial boundary value problems for the nonlinear hyperbolic equationare proved by Galerkin method and the sufficient conditions of blow-up of solution in finite time are given.
Classical Liouville action on the sphere with three hyperbolic singularities
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, L; Hadasz, Leszek; Jaskolski, Zbigniew
2003-01-01
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.
RIEMANN-HILBERT PROBLEMS OF DEGENERATE HYPERBOLIC SYSTEM
无
2010-01-01
This paper is concerned with the Riemann-Hilbert problems of degenerate hyperbolic system in two general domains, where the boundary curves are given by the parameter equations of the arc length s. We prove the existence and uniqueness of solutions to the Riemann-Hilbert problems by conformal deformations. The corre-sponding representations of solutions to the problems are also presented.
Hyperbolicity of the 3+1 system of Einstein equations
Choquet-Bruhat, Y.; Ruggeri, T.
1983-06-01
By a suitable choice of the lapse, which in a natural way is connected to the space metric, we obtain a hyperbolic system from the 3+1 system of Einstein equations with zero shift; this is accomplihsed by combining the evolution equations with the constraints.
Plasmonic Terahertz Amplification in Graphene-Based Asymmetric Hyperbolic Metamaterial
Igor Nefedov
2015-05-01
Full Text Available We propose and theoretically explore terahertz amplification, based on stimulated generation of plasmons in graphene asymmetric hyperbolic metamaterials (AHMM, strongly coupled to terahertz radiation. In contrast to the terahertz amplification in resonant nanocavities, AHMM provides a wide-band THz amplification without any reflection in optically thin graphene multilayers.
Physical nature of volume plasmon polaritons in hyperbolic metamaterials
Zhukovsky, Sergei; Kidwai, Omar; Sipe, J. E.
2013-01-01
We investigate electromagnetic wave propagation in multilayered metal-dielectric hyperbolic metamaterials (HMMs). We demonstrate that high-k propagating waves in HMMs are volume plasmon polaritons. The volume plasmon polariton band is formed by coupling of short-range surface plasmon polariton...
A Conformal Hyperbolic Formulation of the Einstein Equations
Alcubierre, M; Miller, M; Suen, W M; Alcubierre, Miguel; Brugmann, Bernd; Miller, Mark; Suen, Wai-Mo
1999-01-01
We propose a re-formulation of the Einstein evolution equations that cleanly separates the conformal degrees of freedom and the non-conformal degrees of freedom with the latter satisfying a first order strongly hyperbolic system. The conformal degrees of freedom are taken to be determined by the choice of slicing and the initial data, and are regarded as given functions (along with the lapse and the shift) in the hyperbolic part of the evolution. We find that there is a two parameter family of hyperbolic systems for the non-conformal degrees of freedom for a given set of trace free variables. The two parameters are uniquely fixed if we require the system to be ``consistently trace-free'', i.e., the time derivatives of the trace free variables remains trace-free to the principal part, even in the presence of constraint violations due to numerical truncation error. We show that by forming linear combinations of the trace free variables a conformal hyperbolic system with only physical characteristic speeds can a...
Plasmonic Terahertz Amplification in Graphene-Based Asymmetric Hyperbolic Metamaterial
Igor Nefedov; Leonid Melnikov
2015-01-01
We propose and theoretically explore terahertz amplification, based on stimulated generation of plasmons in graphene asymmetric hyperbolic metamaterials (AHMM), strongly coupled to terahertz radiation. In contrast to the terahertz amplification in resonant nanocavities, AHMM provides a wide-band THz amplification without any reflection in optically thin graphene multilayers.
Discontinuous Galerkin error estimation for linear symmetric hyperbolic systems
Adjerid, Slimane; Weinhart, Thomas
2009-01-01
In this manuscript we present an error analysis for the discontinuous Galerkin discretization error of multi-dimensional first-order linear symmetric hyperbolic systems of partial differential equations. We perform a local error analysis by writing the local error as a series and showing that its le
Hilbert manifold structure for asymptotically hyperbolic relativistic initial data
Fougeirol, Jérémie
2016-01-01
We provide a Hilbert manifold structure {\\`a} la Bartnik for the space of asymptotically hyperbolic initial data for the vacuum constraint equations. The adaptation led us to prove new weighted Poincar{\\'e} and Korn type inequalities for AH manifolds with inner boundary and weakly regular metric.
Convergence of rays with rational argument in hyperbolic components
Deniz, Asli
2015-01-01
In this paper, we use the Carathéodory convergence theory to prove a landing theorem of rays in hyperbolic components with rational arguments. Although the proof is done in the setting of a family of entire transcendental maps with two singular values, the method, with some modifications, can...
Nonlinear Hyperbolic-Parabolic System Modeling Some Biological Phenomena
WU Shaohua; CHEN Hua
2011-01-01
In this paper, we study a nonlinear hyperbolic-parabolic system modeling some biological phenomena. By semigroup theory and Leray-Schauder fixed point argument, the local existence and uniqueness of the weak solutions for this system are proved. For the spatial dimension N = 1, the global existence of the weak solution will be established by the bootstrap argument.
LOCAL EXACT BOUNDARY CONTROLLABILITY FOR A CLASS OFQUASILINEAR HYPERBOLIC SYSTEMS
无
2002-01-01
For a class of mixed initial-boundary value problem for general quasilinear hyperbolic systems, this paper establishes the local exact boundary controllability with boundary controls only acting on one end. As an application, the authors show the local exact boundary controllability for a kind of nonlinear vibrating string problem.
Dai, Siyuan; Ma, Qiong; Yang, Yafang; Rosenfeld, Jeremy; Goldflam, Michael D; McLeod, Alex; Sun, Zhiyuan; Andersen, Trond I; Fei, Zhe; Liu, Mengkun; Shao, Yinming; Watanabe, Kenji; Taniguchi, Takashi; Thiemens, Mark; Keilmann, Fritz; Jarillo-Herrero, Pablo; Fogler, Michael M; Basov, D N
2017-09-13
We investigated phonon-polaritons in hexagonal boron nitride-a naturally hyperbolic van der Waals material-by means of the scattering-type scanning near-field optical microscopy. Real-space nanoimages we have obtained detail how the polaritons are launched when the light incident on a thin hexagonal boron nitride slab is scattered by various intrinsic and extrinsic inhomogeneities, including sample edges, metallic nanodisks deposited on its top surface, random defects, and surface impurities. The scanned tip of the near-field microscope is itself a polariton launcher whose efficiency proves to be superior to all the other types of polariton launchers we studied. Our work may inform future development of polaritonic nanodevices as well as fundamental studies of collective modes in van der Waals materials.
Smalley, Joseph S T; Vallini, Felipe; Kanté, Boubacar; Fainman, Yeshaiahu
2014-08-25
We present a method for studying amplification of electromagnetic modes in active, circularly symmetric waveguides with hyperbolic dispersion. Using this method, we obtain a closed-form expression for the modal threshold condition. We find that modal amplification is possible in a region of the radius-wavelength phase-space with small enough radius so that propagation of the mode is permitted while modal energy and phase counter-propagate. At telecommunication frequencies, such a situation is achievable only when the absolute value of the real metal permittivity exceeds that of the active dielectric. We validate our theoretical conclusions with numerical simulations that explain the threshold condition in terms of an energy balance between the longitudinal and radial components of the electric field.
Compaction behavior of isomalt after roll compaction.
Quodbach, Julian; Mosig, Johanna; Kleinebudde, Peter
2012-09-27
The suitability of the new isomalt grade galenIQ™ 801 for dry granulation and following tableting is evaluated in this study. Isomalt alone, as well as a blend of equal parts with dibasic calcium phosphate, is roll compacted and tableted. Particle size distribution and flowability of the granules and friability and disintegration time of the tablets are determined. Tensile strength of tablets is related to the specific compaction force during roll compaction and the tableting force. In all cases, the tensile strength increases with raising tableting forces. The specific compaction force has a different influence. For isomalt alone the tensile strength is highest for tablets made from granules prepared at 2 kN/cm and 6 kN/cm and decreases at higher values, i.e., >10 kN/cm. Tensile strength of the blend tablets is almost one third lower compared to the strongest tablets of pure isomalt. Friability of pure isomalt tablets is above the limit. Disintegration time is longest when the tensile strength is at its maximum and decreases with higher porosity and lower tensile strengths. Isomalt proves to be suitable for tableting after roll compaction. Even though the capacity as a binder might not be as high as of other excipients, it is a further alternative for the formulation scientist.
Compaction Behavior of Isomalt after Roll Compaction
Peter Kleinebudde
2012-09-01
Full Text Available The suitability of the new isomalt grade galenIQ™ 801 for dry granulation and following tableting is evaluated in this study. Isomalt alone, as well as a blend of equal parts with dibasic calcium phosphate, is roll compacted and tableted. Particle size distribution and flowability of the granules and friability and disintegration time of the tablets are determined. Tensile strength of tablets is related to the specific compaction force during roll compaction and the tableting force. In all cases, the tensile strength increases with raising tableting forces. The specific compaction force has a different influence. For isomalt alone the tensile strength is highest for tablets made from granules prepared at 2 kN/cm and 6 kN/cm and decreases at higher values, i.e., >10 kN/cm. Tensile strength of the blend tablets is almost one third lower compared to the strongest tablets of pure isomalt. Friability of pure isomalt tablets is above the limit. Disintegration time is longest when the tensile strength is at its maximum and decreases with higher porosity and lower tensile strengths. Isomalt proves to be suitable for tableting after roll compaction. Even though the capacity as a binder might not be as high as of other excipients, it is a further alternative for the formulation scientist.
Okamura, Hajime; Ouchi, Masahiro
2003-01-01
Self-compacting concrete was first developed in 1988 to achieve durable concrete structures. Since then, various investigations have been carried out and this type of concrete has been used in practical structures in Japan, mainly by large construction companies. Investigations for establishing a rational mix-design method and self-compactability testing methods have been carried out from the viewpoint of making self-compacting concrete a standard concrete.
Okamura, Hajime; Ouchi, Masahiro
2003-01-01
Self-compacting concrete was first developed in 1988 to achieve durable concrete structures. Since then, various investigations have been carried out and this type of concrete has been used in practical structures in Japan, mainly by large construction companies. Investigations for establishing a rational mix-design method and self-compactability testing methods have been carried out from the viewpoint of making self-compacting concrete a standard concrete.
Federal Laboratory Consortium — Facility consists of a folded compact antenna range including a computer controlled three axis position table, parabolic reflector and RF sources for the measurement...
Compact Polarimetry Potentials
Truong-Loi, My-Linh; Dubois-Fernandez, Pascale; Pottier, Eric
2011-01-01
The goal of this study is to show the potential of a compact-pol SAR system for vegetation applications. Compact-pol concept has been suggested to minimize the system design while maximize the information and is declined as the ?/4, ?/2 and hybrid modes. In this paper, the applications such as biomass and vegetation height estimates are first presented, then, the equivalence between compact-pol data simulated from full-pol data and compact-pol data processed from raw data as such is shown. Finally, a calibration procedure using external targets is proposed.
Mechanics of tissue compaction.
Turlier, Hervé; Maître, Jean-Léon
2015-12-01
During embryonic development, tissues deform by a succession and combination of morphogenetic processes. Tissue compaction is the morphogenetic process by which a tissue adopts a tighter structure. Recent studies characterized the respective roles of cells' adhesive and contractile properties in tissue compaction. In this review, we formalize the mechanical and molecular principles of tissue compaction and we analyze through the prism of this framework several morphogenetic events: the compaction of the early mouse embryo, the formation of the fly retina, the segmentation of somites and the separation of germ layers during gastrulation.
Compact Polarimetry Potentials
Truong-Loi, My-Linh; Dubois-Fernandez, Pascale; Pottier, Eric
2011-01-01
The goal of this study is to show the potential of a compact-pol SAR system for vegetation applications. Compact-pol concept has been suggested to minimize the system design while maximize the information and is declined as the ?/4, ?/2 and hybrid modes. In this paper, the applications such as biomass and vegetation height estimates are first presented, then, the equivalence between compact-pol data simulated from full-pol data and compact-pol data processed from raw data as such is shown. Finally, a calibration procedure using external targets is proposed.
Federal Laboratory Consortium — Facility consists of a folded compact antenna range including a computer controlled three axis position table, parabolic reflector and RF sources for the measurement...
Compaction properties of isomalt
Bolhuis, Gerad K.; Engelhart, Jeffrey J. P.; Eissens, Anko C.
2009-01-01
Although other polyols have been described extensively as filler-binders in direct compaction of tablets, the polyol isomalt is rather unknown as pharmaceutical excipient, in spite of its description in all the main pharmacopoeias. In this paper the compaction properties of different types of ispoma
Compact Information Representations
2016-08-02
network traffic, information retrieval, and databases are faced with very large, inherently high-dimensional, or naturally streaming datasets. This...proposal aims at developing mathematically rigorous and general- purpose statistical methods based on stable random projections, to achieve compact...detections (e.g., DDoS attacks), machine learning, databases , and search. Fundamentally, compact data representations are highly beneficial because they
Globally hyperbolic spacetimes can be defined as 'causal' instead of 'strongly causal'
Bernal, Antonio N; Sanchez, Miguel [Departamento de GeometrIa y TopologIa, Facultad de Ciencias, Universidad de Granada, 18071-Granada (Spain)
2007-02-07
The classical definition of global hyperbolicity for a spacetime (M, g) comprises two conditions: (A) compactness of the diamonds J{sup +}(p) intersection J{sup -}(q), and (B) strong causality. Here we show that condition (B) can be replaced just by causality. In fact, we show first that the requirements on the spacetime in the classical definition of causal simplicity (i.e. to be distinguishing plus the closedness of J{sup +}(p), J{sup -}(q)) can be weakened by requiring only to be causal instead of distinguishing. So, the full consistency of the causal ladder (recently proved by the authors in a definitive way) yields directly the result. (comments, replies and notes)
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...
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...
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...
Visualising very large phylogenetic trees in three dimensional hyperbolic space
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.
Directional out-coupling from active hyperbolic metamaterials
Galfsky, Tal; Newman, Ward D; Narimanov, Evgenii; Jacob, Zubin; Menon, Vinod M
2014-01-01
Hyperbolic Metamaterials (HMMs) have recently garnered much attention because they possess the ability for broadband manipulation of the photon density of states and sub-wavelength light confinement. However, a major difficulty arises with the coupling of light out of HMMs due to strong confinement of the electromagnetic field in states with high momentum called high-k modes which become evanescent outside the structure. Here we report the first demonstration of directional out-coupling of light from high-k modes in an active HMM using a high index bulls-eye grating. Quantum dots (QDs) embedded underneath the metamaterial show highly directional emission through the propagation and out-coupling of resonance cones which are a unique feature of hyperbolic media. This demonstration of efficient out-coupling of light from active HMMs could pave the way for developing practical photonic devices using these systems.
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...
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...
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...
Hyperbolic Metamaterial Nano-Resonators Make Poor Single Photon Sources
Axelrod, Simon; Wong, Herman M K; Helmy, Amr S; Hughes, Stephen
2016-01-01
We study the optical properties of quantum dipole emitters coupled to hyperbolic metamaterial nano-resonators using a semi-analytical quasinormal mode approach. We show that coupling to metamaterial nano-resonators can lead to significant Purcell enhancements that are nearly an order of magnitude larger than those of plasmonic resonators with comparable geometry. However, the associated single photon output $\\beta$-factors are extremely low (around 10%), far smaller than those of comparable sized metallic resonators (70%). Using a quasinormal mode expansion of the photon Green function, we describe how the low $\\beta$-factors are due to increased Ohmic quenching arising from redshifted resonances, larger quality factors and stronger confinement of light within the metal. In contrast to current wisdom, these results suggest that hyperbolic metamaterial nano-structures make poor choices for single photon sources.
Tunable VO{sub 2}/Au hyperbolic metamaterial
Prayakarao, S.; Noginov, M. A., E-mail: mnoginov@nsu.edu [Center for Materials Research, Norfolk State University, Norfolk, Virginia 23504 (United States); Mendoza, B.; Devine, A. [Summer Research Program, Center for Materials Research, Norfolk State University, Norfolk, Virginia 23504 (United States); Department of Materials Science and Engineering, Cornell University, Ithaca, New York 14850 (United States); Kyaw, C. [Summer Research Program, Center for Materials Research, Norfolk State University, Norfolk, Virginia 23504 (United States); Dover, R. B. van [Department of Materials Science and Engineering, Cornell University, Ithaca, New York 14850 (United States); Liberman, V. [MIT LINCOLN Laboratory, 244 Wood Street, Lexington, Massachusetts 02420 (United States)
2016-08-08
Vanadium dioxide (VO{sub 2}) is known to have a semiconductor-to-metal phase transition at ∼68 °C. Therefore, it can be used as a tunable component of an active metamaterial. The lamellar metamaterial studied in this work is composed of subwavelength VO{sub 2} and Au layers and is designed to undergo a temperature controlled transition from the optical hyperbolic phase to the metallic phase. VO{sub 2} films and VO{sub 2}/Au lamellar metamaterial stacks have been fabricated and studied in electrical conductivity and optical (transmission and reflection) experiments. The observed temperature-dependent changes in the reflection and transmission spectra of the metamaterials and VO{sub 2} thin films are in a good qualitative agreement with theoretical predictions. The demonstrated optical hyperbolic-to-metallic phase transition is a unique physical phenomenon with the potential to enable advanced control of light-matter interactions.
Near-field energy extraction with hyperbolic metamaterials.
Shi, Jiawei; Liu, Baoan; Li, Pengfei; Ng, Li Yen; Shen, Sheng
2015-02-11
Although blackbody radiation described by Planck's law is commonly regarded as the maximum of thermal radiation, thermal energy transfer in the near-field can exceed the blackbody limit due to the contribution from evanescent waves. Here, we demonstrate experimentally a broadband thermal energy extraction device based on hyperbolic metamaterials that can significantly enhance near-field thermal energy transfer. The thermal extractor made from hyperbolic metamaterials does not absorb or emit any radiation but serves as a transparent pipe guiding the radiative energy from the emitter. At the same gap between an emitter and an absorber, we observe that near-field thermal energy transfer with thermal extraction can be enhanced by around 1 order of magnitude, compared to the case without thermal extraction. The novel thermal extraction scheme has important practical implications in a variety of technologies, e.g., thermophotovoltaic energy conversion, radiative cooling, thermal infrared imaging, and heat assisted magnetic recording.
Hyperbolic Metamaterial Feasible for Fabrication with Direct Laser Writing Processes
Zhang, Xu; Güney, Durdu Ö
2015-01-01
Stimulated emission depletion microscopy inspired direct laser writing (STED-DLW) processes can offer diffraction-unlimited fabrication of 3D-structures, not possible with traditional electron-beam or optical lithography. We propose a hyperbolic metamaterial for fabrication with STED-DLW. First, we design meandering wire structures with three different magnetic dipoles which can be excited under different incidences of light. Then, based on effective parameters corresponding to normal incidence and lateral incidence, we find that the hyperbolic dispersion relation for five-layer structure appears between 15THz to 20THz. Finally, we investigate the influence of imaginary parts of the effective parameters on the metamaterial dispersion. The proposed metamaterial structure has also potential for three-dimensionally isotropic permeability despite geometric anisotropy.
Complex geometric optics for symmetric hyperbolic systems I: linear theory
Maj, Omar
2008-01-01
We obtain an asymptotic solution for $\\ep \\to 0$ of the Cauchy problem for linear first-order symmetric hyperbolic systems with oscillatory initial values written in the eikonal form of geometric optics with frequency $1/\\ep$, but with complex phases. For the most common linear wave propagation models, this kind on Cauchy problems are well-known in the applied literature and their asymptotic theory, referred to as complex geometric optics, is attracting interest for applications. In this work, which is the first of a series of papers dedicated to complex geometric optics for nonlinear symmetric hyperbolic systems, we develop a rigorous linear theory and set the basis for the subsequent nonlinear analysis.
Plasmon-phonon coupling in graphene-hyperbolic bilayer heterostructures
Yin, Ge; Yuan, Jun; Jiang, Wei; Zhu, Jianfei; Ma, Yungui
2016-11-01
Polar dielectrics are important optical materials enabling the subwavelength manipulation of light in infrared due to their capability to excite phonon polaritons. In practice, it is highly desired to actively modify these hyperbolic phonon polaritons (HPPs) to optimize or tune the response of the device. In this work, we investigate the plasmonic material, a monolayer graphene, and study its hybrid structure with three kinds of hyperbolic thin films grown on SiO2 substrate. The inter-mode hybridization and their tunability have been thoroughly clarified from both the band dispersions and the mode patterns numerically calculated through a transfer matrix method. Our results show that these hybrid multilayer structures are of strong potentials for applications in plasmonic waveguides, modulators and detectors in infrared. Project supported by the National Natural Science Foundation of China (Grant No. 61271085) and the Natural Science Foundation of Zhejiang Province, China (Grant No. LR15F050001).
On Another Edge of Defocusing: Hyperbolicity of Asymmetric Lemon Billiards
Bunimovich, Leonid; Zhang, Hong-Kun; Zhang, Pengfei
2016-02-01
Defocusing mechanism provides a way to construct chaotic (hyperbolic) billiards with focusing components by separating all regular components of the boundary of a billiard table sufficiently far away from each focusing component. If all focusing components of the boundary of the billiard table are circular arcs, then the above separation requirement reduces to that all circles obtained by completion of focusing components are contained in the billiard table. In the present paper we demonstrate that a class of convex tables— asymmetric lemons, whose boundary consists of two circular arcs, generate hyperbolic billiards. This result is quite surprising because the focusing components of the asymmetric lemon table are extremely close to each other, and because these tables are perturbations of the first convex ergodic billiard constructed more than 40 years ago.
Finite-width plasmonic waveguides with hyperbolic multilayer cladding
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...... homogenization, we calculate the resonant eigenmodes of the finite-width cladding layers, and find agreement with the resonant features in the dispersion of the cladded waveguides. We show that at the resonant widths, the propagating modes of the waveguides are coupled to the cladding eigenmodes and hence...
Three Dimensional Numerical Relativity with a Hyperbolic Formulation
Bona, C; Seidel, E; Walker, P; Bona, Carles; Masso, Joan; Seidel, Edward; Walker, Paul
1998-01-01
We discuss a successful three-dimensional cartesian implementation of the Bona-Massó hyperbolic formulation of the 3+1 Einstein evolution equations in numerical relativity. The numerical code, which we call ``Cactus,'' provides a general framework for 3D numerical relativity, and can include various formulations of the evolution equations, initial data sets, and analysis modules. We show important code tests, including dynamically sliced flat space, wave spacetimes, and black hole spacetimes. We discuss the numerical convergence of each spacetime, and also compare results with previously tested codes based on other formalisms, including the traditional ADM formalism. This is the first time that a hyperbolic reformulation of Einstein's equations has been shown appropriate for three-dimensional numerical relativity in a wide variety of spacetimes.
Compaction properties of isomalt.
Bolhuis, Gerad K; Engelhart, Jeffrey J P; Eissens, Anko C
2009-08-01
Although other polyols have been described extensively as filler-binders in direct compaction of tablets, the polyol isomalt is rather unknown as pharmaceutical excipient, in spite of its description in all the main pharmacopoeias. In this paper the compaction properties of different types of ispomalt were studied. The types used were the standard product sieved isomalt, milled isomalt and two types of agglomerated isomalt with a different ratio between 6-O-alpha-d-glucopyranosyl-d-sorbitol (GPS) and 1-O-alpha-d-glucopyranosyl-d-mannitol dihydrate (GPM). Powder flow properties, specific surface area and densities of the different types were investigated. Compactibility was investigated by compression of the tablets on a compaction simulator, simulating the compression on high-speed tabletting machines. Lubricant sensitivity was measured by compressing unlubricated tablets and tablets lubricated with 1% magnesium stearate on an instrumented hydraulic press. Sieved isomalt had excellent flow properties but the compactibility was found to be poor whereas the lubricant sensitivity was high. Milling resulted in both a strong increase in compactibility as an effect of the higher surface area for bonding and a decrease in lubricant sensitivity as an effect of the higher surface area to be coated with magnesium stearate. However, the flow properties of milled isomalt were too bad for use as filler-binder in direct compaction. Just as could be expected, agglomeration of milled isomalt by fluid bed agglomeration improved flowability. The good compaction properties and the low lubricant sensitivity were maintained. This effect is caused by an early fragmentation of the agglomerated material during the compaction process, producing clean, lubricant-free particles and a high surface for bonding. The different GPS/GPM ratios of the agglomerated isomalt types studied had no significant effect on the compaction properties.
Non-Euclidean Fourier inversion on super-hyperbolic space
Alldridge, Alexander; Palzer, Wolfgang
2016-01-01
For the super-hyperbolic space in any dimension, we introduce the non-Euclidean Helgason--Fourier transform. We prove an inversion formula exhibiting residue contributions at the poles of the Harish-Chandra c-function, signalling discrete parts in the spectrum. The proof is based on a detailed study of the spherical superfunctions, using recursion relations and localization techniques to normalize them precisely, careful estimates of their derivatives, and a rigorous analysis of the boundary ...
The hyperbolic modular double and Yang-Baxter equation
Chicherin, D
2015-01-01
We construct a hyperbolic modular double -- an algebra lying in between the Faddeev modular double for U_q(sl_2) and the elliptic modular double. The intertwining operator for this algebra leads to an integral operator solution of the Yang-Baxter equation associated with a generalized Faddeev-Volkov lattice model introduced by the second author. We describe also the L-operator and finite-dimensional R-matrices for this model.
Inextendibilty of the Maximal Global Hyperbolic Development in Electrogowdy spacetimes
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.
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.
Einstein-Bianchi Hyperbolic System for General Relativity
Anderson, A; York, J W; Anderson, Arlen; Choquet-Bruhat, Yvonne; York, James W.
1997-01-01
By employing the Bianchi identities for the Riemann tensor in conjunction with the Einstein equations, we construct a first order symmetric hyperbolic system for the evolution part of the Cauchy problem of general relativity. In this system, the metric evolves at zero speed with respect to observers at rest in a foliation of spacetime by spacelike hypersurfaces while the curvature and connection propagate at the speed of light. The system has no unphysical characteristics, and matter sources can be included.
Asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces
Kohlenbach, Ulrich; Leuştean, Laurentiu
2007-01-01
This paper provides a fixed point theorem for asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces as well as new effective results on the Krasnoselski-Mann iterations of such mappings. The latter were found using methods from logic and the paper continues a case study in the general program of extracting effective data from prima-facie ineffective proofs in the fixed point theory of such mappings.
The Domino Problem of the Hyperbolic Plane Is Undecidable
Margenstern, Maurice
2007-01-01
In this paper, we prove that the general tiling problem of the hyperbolic plane is undecidable by proving a slightly stronger version using only a regular polygon as the basic shape of the tiles. The problem was raised by a paper of Raphael Robinson in 1971, in his famous simplified proof that the general tiling problem is undecidable for the Euclidean plane, initially proved by Robert Berger in 1966.
The quantum Ising model: finite sums and hyperbolic functions
Damski, Bogdan
2015-10-01
We derive exact closed-form expressions for several sums leading to hyperbolic functions and discuss their applicability for studies of finite-size Ising spin chains. We show how they immediately lead to closed-form expressions for both fidelity susceptibility characterizing the quantum critical point and the coefficients of the counterdiabatic Hamiltonian enabling arbitrarily quick adiabatic driving of the system. Our results generalize and extend the sums presented in the popular Gradshteyn and Ryzhik Table of Integrals, Series, and Products.
The quantum Ising model: finite sums and hyperbolic functions
Bogdan Damski
2015-01-01
We derive exact closed-form expressions for several sums leading to hyperbolic functions and discuss their applicability for studies of finite-size Ising spin chains. We show how they immediately lead to closed-form expressions for both fidelity susceptibility characterizing the quantum critical point and the coefficients of the counterdiabatic Hamiltonian enabling arbitrarily quick adiabatic driving of the system. Our results generalize and extend the sums presented in the popular Gradshteyn...
Optic axis-driven new horizons for hyperbolic metamaterials
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.
Inverse scattering at fixed energy on asymptotically hyperbolic Liouville surfaces
Daudé, Thierry; Kamran, Niky; Nicoleau, Francois
2015-12-01
In this paper, we study an inverse scattering problem on Liouville surfaces having two asymptotically hyperbolic ends. The main property of Liouville surfaces consists of the complete separability of the Hamilton-Jacobi equations for the geodesic flow. An important related consequence is the fact that the stationary wave equation can be separated into a system of radial and angular ODEs. The full scattering matrix at fixed energy associated to a scalar wave equation on asymptotically hyperbolic Liouville surfaces can be thus simplified by considering its restrictions onto the generalized harmonics corresponding to the angular separated ODE. The resulting partial scattering matrices consists in a countable set of 2 × 2 matrices whose coefficients are the so called transmission and reflection coefficients. It is shown that the reflection coefficients are nothing but generalized Weyl-Titchmarsh (WT) functions for the radial ODE in which the generalized angular momentum is seen as the spectral parameter. Using the complex angular momentum method and recent results on 1D inverse problem from generalized WT functions, we show that the knowledge of the reflection operators at a fixed non-zero energy is enough to determine uniquely the metric of the asymptotically hyperbolic Liouville surface under consideration.
Effects of nonlocal response on the density of states of hyperbolic metamaterials
Yan, Wei; Wubs, Martijn; Mortensen, N. Asger
2012-01-01
Metamaterials with a hyperbolic dispersion curve, called hyperbolic metamaterials, exhibit an amazing broad-band singularity in the photonic density of states in the usual local-response approximation. In this paper, under the framework of the hydrodynamic Drude model, we discuss the effects...... of the nonlocal response of the electron gas in the metal on the hyperbolic metamaterials. By using mean field theory, we derive the effective material parameters of the hyperbolic metamaterials. The original unbounded hyperbolic dispersion is found to be cut off at the wavevector inverse to the Fermi velocity....... 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...
Section Extension from Hyperbolic Geometry of Punctured Disk and Holomorphic Family of Flat Bundles
Siu, Yum-Tong
2011-01-01
We study the problem of constructing pluricanonical sections from flatly twisted pluricanonical sections and prove that, for a compact complex algebraic manifold X and positive integers m and q, the subvariety of flat line bundles F on X such that the complex dimension of the space of all holomorphic sections of the sum of F and the m-canonical line bundle of X is at least q is regular and is a finite union of translates of abelian subvarieties by torsion elements in the abelian variety of all flat line bundles on X. The proof uses a new extension result of Ohsawa-Takegoshi type, where the curvature current is not even semi-positive but with only mild controllable negativity. We also give a new approach to the original theorem of Ohsawa-Takegoshi. Our approach considers the origin of the open unit 1-disk as the infinite point of the hyperbolic geometry of the punctured open unit 1-disk and reduces the original theorem of Ohsawa-Takegoshi to just a simple straightforward application of the standard method of c...
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
Double-wave solutions to quasilinear hyperbolic systems of first-order PDEs
Curró, C.; Manganaro, N.
2017-10-01
A reduction procedure for determining double-wave exact solutions to first-order hyperbolic systems of PDEs is proposed. The basic idea is to reduce the integration of the governing hyperbolic set of N partial differential equations to that of a 2 × 2 reduced hyperbolic model along with a further differential constraint. Therefore, the method of differential constraints is used in order to solve the auxiliary 2 × 2 system. An example of interest to viscoelasticity is presented.
Improvement of S/N ratio of seismic data by hyperbolic filter algorithm
Xue Hao; Yue Li; Baojun Yang
2006-01-01
This paper deals with the implementation of the hyperbolic filter algorithm for noise suppression of seismic data. Known the velocity of reflection event, utilizes the resemblance of reflection signal in each seismic trace, the hyperbolic filter algorithm is effective in enhance reflection event and suppress the random noise. This algorithm is used to CDP gathers also is compared with the algorithm of τ-p transform. Simulation shows the hyperbolic filter is effective and better than τ-p transform.
Kubi's, W; Kubi\\'s, Wieslaw; Michalewski, Henryk
2005-01-01
We prove a preservation theorem for the class of Valdivia compact spaces, which involves inverse sequences of ``simple'' retractions. Consequently, a compact space of weight $\\loe\\aleph_1$ is Valdivia compact iff it is the limit of an inverse sequence of metric compacta whose bonding maps are retractions. As a corollary, we show that the class of Valdivia compacta of weight at most $\\aleph_1$ is preserved both under retractions and under open 0-dimensional images. Finally, we characterize the class of all Valdivia compacta in the language of category theory, which implies that this class is preserved under all continuous weight preserving functors.
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.
Christoforou, Cleopatra
2016-03-27
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.
Griffiths, Stewart
2003-09-30
The present invention provides compact geometries for the layout of microchannel columns through the use of turns and straight channel segments. These compact geometries permit the use of long separation or reaction columns on a small microchannel substrate or, equivalently, permit columns of a fixed length to occupy a smaller substrate area. The new geometries are based in part on mathematical analyses that provide the minimum turn radius for which column performance in not degraded. In particular, we find that straight channel segments of sufficient length reduce the required minimum turn radius, enabling compact channel layout when turns and straight segments are combined. The compact geometries are obtained by using turns and straight segments in overlapped or nested arrangements to form pleated or coiled columns.
Capability enhancement in compact digital holographic microscopy
Qu, Weijuan; Wen, Yongfu; Wang, Zhaomin; Yang, Fang; Asundi, Anand
2015-03-01
A compact reflection digital holographic microscopy (DHM) system integrated with the light source and optical interferometer is developed for 3D topographic characterization and real-time dynamic inspection for Microelectromechanical systems (MEMS). Capability enhancement methods in lateral resolution, axial resolving range and large field of view for the compact DHM system are presented. To enhance the lateral resolution, the numerical aperture of a reflection DHM system is analyzed and optimum designed. To enhance the axial resolving range, dual wavelengths are used to extend the measuring range. To enable the large field of view, stitching of the measurement results is developed in the user-friendly software. Results from surfaces structures on silicon wafer, micro-optics on fused silica and dynamic inspection of MEMS structures demonstrate applications of this compact reflection digital holographic microscope for technical inspection in material science.
Equidistribution of Zeros of Holomorphic Sections in the Non-compact Setting
Dinh, Tien-Cuong; Marinescu, George; Schmidt, Viktoria
2012-07-01
We consider tensor powers L N of a positive Hermitian line bundle ( L, h L ) over a non-compact complex manifold X. In the compact case, B. Shiffman and S. Zelditch proved that the zeros of random sections become asymptotically uniformly distributed as N→∞ with respect to the natural measure coming from the curvature of L. Under certain boundedness assumptions on the curvature of the canonical line bundle of X and on the Chern form of L we prove a non-compact version of this result. We give various applications, including the limiting distribution of zeros of cusp forms with respect to the principal congruence subgroups of SL 2(ℤ) and to the hyperbolic measure, the higher dimensional case of arithmetic quotients and the case of orthogonal polynomials with weights at infinity. We also give estimates for the speed of convergence of the currents of integration on the zero-divisors.
Equidistribution of zeros of holomorphic sections in the non compact setting
Dinh, Tien-Cuong; Schmidt, Viktoria
2011-01-01
We consider N-tensor powers of a positive Hermitian line bundle L over a non-compact complex manifold X. In the compact case, B. Shiffman and S. Zelditch proved that the zeros of random sections become asymptotically uniformly distributed with respect to the natural measure coming from the curvature of L, as N tends to infinity. Under certain boundedness assumptions on the curvature of the canonical line bundle of X and on the Chern form of L we prove a non-compact version of this result. We give various applications, including the limiting distribution of zeros of cusp forms with respect to the principal congruence subgroups of SL2(Z) and to the hyperbolic measure, the higher dimensional case of arithmetic quotients and the case of orthogonal polynomials with weights at infinity. We also give estimates for the speed of convergence of the currents of integration on the zero-divisors.
Compact Visualisation of Video Summaries
Ćalić Janko
2007-01-01
Full Text Available This paper presents a system for compact and intuitive video summarisation aimed at both high-end professional production environments and small-screen portable devices. To represent large amounts of information in the form of a video key-frame summary, this paper studies the narrative grammar of comics, and using its universal and intuitive rules, lays out visual summaries in an efficient and user-centered way. In addition, the system exploits visual attention modelling and rapid serial visual presentation to generate highly compact summaries on mobile devices. A robust real-time algorithm for key-frame extraction is presented. The system ranks importance of key-frame sizes in the final layout by balancing the dominant visual representability and discovery of unanticipated content utilising a specific cost function and an unsupervised robust spectral clustering technique. A final layout is created using an optimisation algorithm based on dynamic programming. Algorithm efficiency and robustness are demonstrated by comparing the results with a manually labelled ground truth and with optimal panelling solutions.
A cosmological context for compact massive galaxies
Stringer, Martin; Vecchia, Claudio Dalla; Martinez-Valpuesta, Inma
2015-01-01
To provide a quantitative cosmological context to ongoing observational work on the formation histories and location of compact massive galaxies, we locate and study a sample of exceptionally compact systems in the Bolshoi simulation, using the dark matter structural parameters from a real, compact massive galaxy (NGC1277) as a basis for our working criteria. We find that over 80% of objects in this nominal compact category are substructures of more massive groups or clusters, and that the probability of a given massive substructure being this compact increases significantly with the mass of the host structure; rising to ~30% for the most massive clusters in the simulation. Tracking the main progenitors of this subsample back to z=2, we find them all to be distinct structures with scale radii and densities representative of the population as a whole at this epoch. What does characterise their histories, in addition to mostly becoming substructures, is that they have almost all experienced below-average mass a...
The hyperbolic Allen-Cahn equation: exact solutions
Nizovtseva, I. G.; Galenko, P. K.; Alexandrov, D. V.
2016-10-01
Using the first integral method, a general set of analytical solutions is obtained for the hyperbolic Allen-Cahn equation. The solutions are presented by (i) the class of continual solutions described by \\tanh -profiles for traveling waves of the order parameter, and (ii) the class of singular solutions which exhibit unbounded discontinuity in the profile of the order parameter at the origin of the coordinate system. It is shown that the solutions include the previous analytical results for the parabolic Allen-Cahn equation as a limited class of \\tanh -functions, in which the inertial effects are omitted.
AD GALERKIN ANALYSIS FOR NONLINEAR PSEUDO-HYPERBOLIC EQUATIONS
Xia Cui
2003-01-01
AD (Alternating direction) Galerkin schemes for d-dimensional nonlinear pseudo-hyperbolic equations are studied. By using patch approximation technique, AD procedure is realized,and calculation work is simplified. By using Galerkin approach, highly computational accuracy is kept. By using various priori estimate techniques for differential equations,difficulty coming from non-linearity is treated, and optimal H1 and L2 convergence properties are demonstrated. Moreover, although all the existed AD Galerkin schemes using patch approximation are limited to have only one order accuracy in time increment, yet the schemes formulated in this paper have second order accuracy in it. This implies an essential advancement in AD Galerkin analysis.
Second-harmonic generation from hyperbolic plasmonic nanorod metamaterial slab
Marino, Giuseppe; Krasavin, Alexey V; Ginzburg, Pavel; Olivier, Nicolas; Wurtz, Gregory A; Zayats, Anatoly V
2015-01-01
Hyperbolic plasmonic metamaterials provide numerous opportunities for designing unusual linear and nonlinear optical properties. We show that the modal overlap of fundamental and second-harmonic light in an anisotropic plasmonic metamaterial slab results in the broadband enhancement of radiated second-harmonic intensity by up to 2 and 11 orders of magnitudes for TM- and TE-polarized fundamental light, respectively, compared to a smooth Au film under TM-polarised illumination. The results open up possibilities to design tuneable frequency-doubling metamaterial with the goal to overcome limitations associated with classical phase matching conditions in thick nonlinear crystals.
Attraction-Based Computation of Hyperbolic Lagrangian Coherent Structures
Karrasch, Daniel; Haller, George
2014-01-01
Recent advances enable the simultaneous computation of both attracting and repelling families of Lagrangian Coherent Structures (LCS) at the same initial or final time of interest. Obtaining LCS positions at intermediate times, however, has been problematic, because either the repelling or the attracting family is unstable with respect to numerical advection in a given time direction. Here we develop a new approach to compute arbitrary positions of hyperbolic LCS in a numerically robust fashion. Our approach only involves the advection of attracting material surfaces, thereby providing accurate LCS tracking at low computational cost. We illustrate the advantages of this approach on a simple model and on a turbulent velocity data set.
On hyperbolicity violations in cosmological models with vector fields
Golovnev, Alexey
2014-01-01
Cosmological models with vector fields received much attention in recent years. Unfortunately, most of them are plagued with severe instabilities or other problems. In particular, it was noted by G. Esposito-Farese, C. Pitrou and J.-Ph. Uzan in arXiv:0912.0481 that the models with a non-linear function of the Maxwellian kinetic term do always imply violations of hyperbolicity somewhere in the phase space. In this work we make this statement more precise in several respects and show that those violations may not be present around spatially homogeneous configurations of the vector field.
Spatial mode-selective waveguide with hyperbolic cladding
Tang, Y.; Xi, Z.; Xu, M.; Bäumer, S.; Adam, A. J. L.; Urbach, H. P.
2016-09-01
Hyperbolic Meta-Materials~(HMMs) are anisotropic materials with permittivity tensor that has both positive and negative eigenvalues. Here we report that by using a type II HMM as cladding material, a waveguide which only supports higher order modes can be achieved, while the lower order modes become leaky and are absorbed in the HMM cladding. This counter intuitive property can lead to novel application in optical communication and photonic integrated circuit. The loss in our HMM-Insulator-HMM~(HIH) waveguide is smaller than that of similar guided mode in a Metal-Insulator-Metal~(MIM) waveguide.
Clawpack: building an open source ecosystem for solving hyperbolic PDEs
Kyle T. Mandli
2016-08-01
Full Text Available 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.
Elliptic and Hyperbolic Dielectric Lens Antennas in mm-Waves
P. Piksa
2011-04-01
Full Text Available Dielectric lenses can substantially improve antenna parameters, especially the planarity of radiated waves and the antenna gain. The paper deals with their application in millimeter-wave band. The main goal concerns the introduction of characteristics and differences between the most commonly used types of dielectric lens antennas, i.e. elliptic and hyperbolic. Their particular features as well as behavior of radiating systems incorporating the lenses are investigated. Specific features of these lenses are discussed for both, near-field and farfield based on simulation and measurement results.
Persistence of noncompact normally hyperbolic invariant manifolds in bounded geometry
Eldering, J
2012-01-01
We prove a persistence result for noncompact normally hyperbolic invariant manifolds in the setting of Riemannian manifolds of bounded geometry. Bounded geometry of the ambient manifold is a crucial assumption required to control the uniformity of all estimates throughout the proof. The $C^{k,\\alpha}$-smoothness result is optimal with respect to the spectral gap condition involved. The core of the persistence proof is based on the Perron method. In the process we derive new results on noncompact submanifolds in bounded geometry: a uniform tubular neighborhood theorem and uniform smooth approximation of a submanifold. The submanifolds considered are assumed to be uniformly $C^k$ bounded in an appropriate sense.
Quantum error correcting codes and 4-dimensional arithmetic hyperbolic manifolds
Guth, Larry; Lubotzky, Alexander
2014-08-01
Using 4-dimensional arithmetic hyperbolic manifolds, we construct some new homological quantum error correcting codes. They are low density parity check codes with linear rate and distance nɛ. Their rate is evaluated via Euler characteristic arguments and their distance using {Z}_2-systolic geometry. This construction answers a question of Zémor ["On Cayley graphs, surface codes, and the limits of homological coding for quantum error correction," in Proceedings of Second International Workshop on Coding and Cryptology (IWCC), Lecture Notes in Computer Science Vol. 5557 (2009), pp. 259-273], who asked whether homological codes with such parameters could exist at all.
HYPERBOLIC MEAN CURVATURE FLOW:EVOLUTION OF PLANE CURVES
Kong Dexing; Liu Kefeng; Wang Zenggui
2009-01-01
In this paper we investigate the one-dimensional hyperbolic mean curvature flow for closed plane curves.More precisely, we consider a family of closed curves F: S1×[0,T)→R2 which satisfies the following evolution equationε2F/εt2(u,t)=k(u,t)-▽p(u,t),▽(u,t)∈ S1X[0,T) with the initial data F(u,0)=Fo(u) and εF/εt(u,0)=F(u)No,Where k is the mean curvature and N is the unit inner normal vector of the plane curve F(u,t)f(u) and No are the initial velocity and the unit inner normal vector of the initial convex closed curve Fo,respectively,and ▽p is given by ▽p≧(ε2F/εsε和/εF/ε和)T,in which T stands for the unit tangent vector.The above problem is an initial value problem for a system of partial differential equations for F,it can be completely reduced to an initial value problem for a single partial differential equation for its support function.The latter equation is a hyperbolic Monge-Ampere equation.Based on this,we show that there exists a class of initial velocities such that the solution of the above initial value problem exists only at the a finite time interval[0,Tmax)and when t goes to Tmax,either the solution converges to a point or shocks and other propagating discontinuities are generated.Furthermore,we also consider the hyperbolic mean curvature flow with the dissipative terms and obtain the similar equations about the support function adn the curvature of the curve.In the end,we discuss the close relationship between the hyperbolic mean curvature flow and the equations for the evolving relativistic string in the Minkowski space-timeR1,1.
Spatial mode-selective waveguide with hyperbolic cladding.
Tang, Y; Xi, Z; Xu, M; Bäumer, S; Adam, A J L; Urbach, H P
2016-09-15
Hyperbolic metamaterials (HMMs) are anisotropic materials with a permittivity tensor that has both positive and negative eigenvalues. Here we report that by using a type II HMM as a cladding material, a waveguide that only supports higher-order modes can be achieved, while the lower-order modes become leaky and are absorbed in the HMM cladding. This counter-intuitive property can lead to novel application in optical communications and photonic integrated circuits. The loss in our HMM insulator-HMM (HIH) waveguide is smaller than that of similar guided modes in a metal-insulator-metal (MIM) waveguide.
Long-range plasmonic waveguides with hyperbolic cladding.
Babicheva, Viktoriia E; Shalaginov, Mikhail Y; Ishii, Satoshi; Boltasseva, Alexandra; Kildishev, Alexander V
2015-11-30
We study plasmonic waveguides with dielectric cores and hyperbolic multilayer claddings. The proposed design provides better performance in terms of propagation length and mode confinement in comparison to conventional designs, such as metal-insulator-metal and insulator-metal-insulator plasmonic waveguides. We show that the proposed structures support long-range surface plasmon modes, which exist when the permittivity of the core matches the transverse effective permittivity component of the metamaterial cladding. In this regime, the surface plasmon polaritons of each cladding layer are strongly coupled, and the propagation length can be on the order of a millimeter.
Long-range plasmonic waveguides with hyperbolic cladding
Babicheva, Viktoriia E.; Shalaginov, Mikhail Y.; Ishii, Satoshi;
2015-01-01
We study plasmonic waveguides with dielectric cores and hyperbolic multilayer claddings. The proposed design provides better performance in terms of propagation length and mode confinement in comparison to conventional designs, such as metal-insulator-metal and insulator-metal-insulator plasmonic...... waveguides. We show that the proposed structures support long-range surface plasmon modes, which exist when the permittivity of the core matches the transverse effective permittivity component of the metamaterial cladding. In this regime, the surface plasmon polaritons of each cladding layer are strongly...
Finite-width plasmonic waveguides with hyperbolic multilayer cladding.
Babicheva, Viktoriia E; Shalaginov, Mikhail Y; Ishii, Satoshi; Boltasseva, Alexandra; Kildishev, Alexander V
2015-04-20
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 homogenization, we calculate the resonant eigenmodes of the finite-width cladding layers, and find agreement with the resonant features in the dispersion of the cladded waveguides. We show that at the resonant widths, the propagating modes of the waveguides are coupled to the cladding eigenmodes and hence, are strongly absorbed. By avoiding the resonant widths in the design of the actual waveguides, the strong absorption can be eliminated.
Parabolic Perturbation of a Nonlinear Hyperbolic Problem Arising in Physiology
Colli, P.; Grasselli, M.
We study a transport-diffusion initial value problem where the diffusion codlicient is "small" and the transport coefficient is a time function depending on the solution in a nonlinear and nonlocal way. We show the existence and the uniqueness of a weak solution of this problem. Moreover we discuss its asymptotic behaviour as the diffusion coefficient goes to zero, obtaining a well-posed first-order nonlinear hyperbolic problem. These problems arise from mathematical models of muscle contraction in the framework of the sliding filament theory.
Optical absorption of hyperbolic metamaterial with stochastic surfaces
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 ind...... of stochastically perturbed HMM compared to that of metal. (C) 2014 Optical Society of America...... 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...
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.
Compactness theorems of fuzzy semantics
无
2000-01-01
The relationship among diverse fuzzy semantics vs. the corresponding logic consequence operators has been analyzed systematically. The results that compactness and logical compactness of fuzzy semantics are equivalent to compactness and continuity of the logic consequence operator induced by the semantics respectively have been proved under certain conditions. A general compactness theorem of fuzzy semantics have been established which says that every fuzzy semantics defined on a free algebra with members corresponding to continuous functions is compact.
Totally geodesic Seifert surfaces in hyperbolic knot and link complements II
Adams, Colin; Bennett, Hanna; Davis, Christopher James;
2008-01-01
We generalize the results of Adams–Schoenfeld, finding large classes of totally geodesic Seifert surfaces in hyperbolic knot and link complements, each covering a rigid 2-orbifold embedded in some hyperbolic 3-orbifold. In addition, we provide a uniqueness theorem and demonstrate that many knots ...
On the largest component of a hyperbolic model of complex networks
Bode, Michel; Fountoulakis, Nikolaos; Müller, Tobias
2015-01-01
We consider a model for complex networks that was introduced by Krioukov et al. In this model, N points are chosen randomly inside a disk on the hyperbolic plane and any two of them are joined by an edge if they are within a certain hyperbolic distance. The N points are distributed according to a qu
Can a Hyperbolic Phase of the Brans-Dicke Field Account for Dark Matter?
Arik, M.; Çalik, M.; Çifter, F.
We show that the introduction of a hyperbolic phase of the Brans-Dicke (BD) field results in a flat vacuum cosmological solution of the Hubble parameter H and a fractional rate of change of the BD scalar field F, which asymptotically approach constant values. At later stages, the hyperbolic phase of the BD field behaves like dark matter.
Can hyperbolic phase of Brans-Dicke field account for Dark Matter?
Arik, M; Cifter, F
2008-01-01
We show that the introduction of a hyperbolic phase for Brans-Dicke (BD) field results in a flat vacuum cosmological solution of Hubble parameter H and fractional rate of change of BD scalar field, F which asymptotically approach constant values. At late stages, hyperbolic phase of BD field behaves like dark matter.
Totally geodesic Seifert surfaces in hyperbolic knot and link complements II
Adams, Colin; Bennett, Hanna; Davis, Christopher James
2008-01-01
We generalize the results of Adams–Schoenfeld, finding large classes of totally geodesic Seifert surfaces in hyperbolic knot and link complements, each covering a rigid 2-orbifold embedded in some hyperbolic 3-orbifold. In addition, we provide a uniqueness theorem and demonstrate that many knots...
Mohammed Ashraful Islam
2000-01-01
The analytic cosmological solutions of Einstein's field equations for a type of static metric representing plane, spherical and hyperbolic symmetric spaces are presented and their properties are discussed separately. A general type of solution is obtained which represents the plane, spherical and hyperbolic symmetric cosmological models. Its physical properties are also discussed in details.
Exact Boundary Controllability for a Kind of Second-Order Quasilinear Hyperbolic Systems
Ke WANG
2011-01-01
Based on the theory of semi-global C1 solution and the local exact boundary controllability for first-order quasilinear hyperbolic systems,the local exact boundary controllability for a kind of second-order quasilinear hyperbolic systems is obtained by a constructive method.
A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty
Wu, Kailiang; Tang, Huazhong; Xiu, Dongbin
2017-09-01
This paper is concerned with generalized polynomial chaos (gPC) approximation for first-order quasilinear hyperbolic systems with uncertainty. The one-dimensional (1D) hyperbolic system is first symmetrized with the aid of left eigenvector matrix of the Jacobian matrix. Then the gPC stochastic Galerkin method is applied to derive a provably symmetrically hyperbolic equations for the gPC expansion coefficients. The resulting deterministic gPC Galerkin system is discretized by a path-conservative finite volume WENO scheme in space and a third-order total variation diminishing Runge-Kutta method in time. The method is further extended to two-dimensional (2D) quasilinear hyperbolic system with uncertainty, where the symmetric hyperbolicity of the one-dimensional gPC Galerkin system is carried over via an operator splitting technique. Several numerical experiments are conducted to demonstrate the accuracy and effectiveness of the proposed gPC stochastic Galerkin method.
Boundary Causality vs Hyperbolicity for Spherical Black Holes in Gauss-Bonnet
Andrade, Tomas; Keeler, Cynthia
2016-01-01
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...
Realization of mid-infrared graphene hyperbolic metamaterials.
Chang, You-Chia; Liu, Che-Hung; Liu, Chang-Hua; Zhang, Siyuan; Marder, Seth R; Narimanov, Evgenii E; Zhong, Zhaohui; Norris, Theodore B
2016-02-04
While metal is the most common conducting constituent element in the fabrication of metamaterials, graphene provides another useful building block, that is, a truly two-dimensional conducting sheet whose conductivity can be controlled by doping. Here we report the experimental realization of a multilayer structure of alternating graphene and Al2O3 layers, a structure similar to the metal-dielectric multilayers commonly used in creating visible wavelength hyperbolic metamaterials. Chemical vapour deposited graphene rather than exfoliated or epitaxial graphene is used, because layer transfer methods are easily applied in fabrication. We employ a method of doping to increase the layer conductivity, and our analysis shows that the doped chemical vapour deposited graphene has good optical properties in the mid-infrared range. We therefore design the metamaterial for mid-infrared operation; our characterization with an infrared ellipsometer demonstrates that the metamaterial experiences an optical topological transition from elliptic to hyperbolic dispersion at a wavelength of 4.5 μm.
Adaptive aberration correction using a triode hyperbolic electron mirror.
Fitzgerald, J P S; Word, R C; Könenkamp, 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.
A Comparison of Generalized Hyperbolic Distribution Models for Equity Returns
Virginie Konlack Socgnia
2014-01-01
Full Text Available We discuss the calibration of the univariate and multivariate generalized hyperbolic distributions, as well as their hyperbolic, variance gamma, normal inverse Gaussian, and skew Student’s t-distribution subclasses for the daily log-returns of seven of the most liquid mining stocks listed on the Johannesburg Stocks Exchange. To estimate the model parameters from historic distributions, we use an expectation maximization based algorithm for the univariate case and a multicycle expectation conditional maximization estimation algorithm for the multivariate case. We assess the goodness of fit statistics using the log-likelihood, the Akaike information criterion, and the Kolmogorov-Smirnov distance. Finally, we inspect the temporal stability of parameters and note implications as criteria for distinguishing between models. To better understand the dependence structure of the stocks, we fit the MGHD and subclasses to both the stock returns and the two leading principal components derived from the price data. While the MGHD could fit both data subsets, we observed that the multivariate normality of the stock return residuals, computed by removing shared components, suggests that the departure from normality can be explained by the structure in the common factors.
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.
Realization of mid-infrared graphene hyperbolic metamaterials
Chang, You-Chia; Liu, Che-Hung; Liu, Chang-Hua; Zhang, Siyuan; Marder, Seth R.; Narimanov, Evgenii E.; Zhong, Zhaohui; Norris, Theodore B.
2016-02-01
While metal is the most common conducting constituent element in the fabrication of metamaterials, graphene provides another useful building block, that is, a truly two-dimensional conducting sheet whose conductivity can be controlled by doping. Here we report the experimental realization of a multilayer structure of alternating graphene and Al2O3 layers, a structure similar to the metal-dielectric multilayers commonly used in creating visible wavelength hyperbolic metamaterials. Chemical vapour deposited graphene rather than exfoliated or epitaxial graphene is used, because layer transfer methods are easily applied in fabrication. We employ a method of doping to increase the layer conductivity, and our analysis shows that the doped chemical vapour deposited graphene has good optical properties in the mid-infrared range. We therefore design the metamaterial for mid-infrared operation; our characterization with an infrared ellipsometer demonstrates that the metamaterial experiences an optical topological transition from elliptic to hyperbolic dispersion at a wavelength of 4.5 μm.
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.
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...
Positive temporal dependence of the biological clock implies hyperbolic discounting
Debajyoti eRay
2011-01-01
Full Text Available Temporal preferences of animals and humans often exhibit inconsistencies, whereby an earlier, smaller reward may be preferred when it occurs immediately but not when it is delayed. Such choices reflect hyperbolic discounting of future rewards, rather than the exponential discounting required for temporal consistency. Simultaneously, however, evidence has emerged that suggests that animals and humans have an internal representation of time that often differs from the calendar time used in detection of temporal inconsistencies. Here, we prove that temporal inconsistencies emerge if fixed durations in calendar time are experienced as positively related (positive quadrant dependent. Hence, what are time-consistent choices within the time framework of the decision maker appear as time-inconsistent to an outsider who analyzes choices in calendar time. As the biological clock becomes more variable, the fit of the hyperbolic discounting model improves. A recent alternative explanation for temporal choice inconsistencies builds on persistent under-estimation of the length of distant time intervals. By increasing the expected speed of our stochastic biological clock for time farther into the future, we can emulate this explanation. Ours is therefore an encompassing theoretical framework that predicts context-dependent degrees of intertemporal choice inconsistencies, to the extent that context can generate changes in autocorrelation, variability, and expected speed of the biological clock. Our finding should lead to novel experiments that will clarify the role of time perception in impulsivity, with critical implications for, among others, our understanding of aging, drug abuse and pathological gambling.
Finite Volume Evolution Galerkin Methods for Nonlinear Hyperbolic Systems
Lukáčová-Medvid'ová, M.; Saibertová, J.; Warnecke, G.
2002-12-01
We present new truly multidimensional schemes of higher order within the frame- work of finite volume evolution Galerkin (FVEG) methods for systems of nonlinear hyperbolic conservation laws. These methods couple a finite volume formulation with approximate evolution operators. The latter are constructed using the bicharacteristics of the multidimensional hyperbolic system, such that all of the infinitely many directions of wave propagation are taken into account. Following our previous results for the wave equation system, we derive approximate evolution operators for the linearized Euler equations. The integrals along the Mach cone and along the cell interfaces are evaluated exactly, as well as by means of numerical quadratures. The influence of these numerical quadratures will be discussed. Second-order resolution is obtained using a conservative piecewise bilinear recovery and the midpoint rule approximation for time integration. We prove error estimates for the finite volume evolution Galerkin scheme for linear systems with constant coefficients. Several numerical experiments for the nonlinear. Euler equations, which confirm the accuracy and good multidimensional behavior of the FVEG schemes, are presented as well.
Tangent-Impulse Interception for a Hyperbolic Target
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.
Limestone compaction: an enigma
Shinn, Eugene A.; Halley, Robert B.; Hudson, J. Harold; Lidz, Barbara H.
1977-01-01
Compression of an undisturbed carbonate sediment core under a pressure of 556 kg/cm2 produced a “rock” with sedimentary structures similar to typical ancient fine-grained limestones. Surprisingly, shells, foraminifera, and other fossils were not noticeably crushed, which indicates that absence of crushed fossils in ancient limestones can no longer be considered evidence that limestones do not compact.
Compact rotating cup anemometer
Wellman, J. B.
1968-01-01
Compact, collapsible rotating cup anemometer is used in remote locations where portability and durability are factors in the choice of equipment. This lightweight instrument has a low wind-velocity threshold, is capable of withstanding large mechanical shocks while in its stowed configuration, and has fast response to wind fluctuations.
Improving the compaction properties of roller compacted calcium carbonate.
Bacher, C; Olsen, P M; Bertelsen, P; Kristensen, J; Sonnergaard, J M
2007-09-05
The effects of roller compaction process parameters, morphological forms of calcium carbonate and particle size of sorbitol on flow, compaction and compression properties were investigated. The morphology of the calcium carbonate and the sorbitol particle size were more influential on the compaction properties than the settings of the roller compactor. The roller compaction process was demonstrated to be robust and stable in regard to flowability and compactibility. The flowability of the granules was improved adequately to facilitate compression in a production scale rotary tablet press. By adding sorbitol to the calcium carbonate, the compressibility - characterized by the Walker coefficient W(ID) - and the compactibility C(P) were improved considerably. A correlation between the consolidation characteristics was demonstrated. Compactibility data from the compaction simulator correlated with the tablet press for two of the calcium carbonates, the cubic form and the ground quality.
Mühlberger, F; Wieser, J; Ulrich, A; Zimmermann, R
2002-08-01
Fast on-line detection of organic compounds from complex mixtures, such as industrial process gas streams, require selective and sensitive analytical methods. One feasible approach for this purpose is the use of mass spectrometry (MS) with a selective and soft (fragment-free) ionization technique, such as chemical ionization (CI) or photo ionization (PI). Single photon ionization (SPI) with vacuum ultraviolet (VUV) light is a particularly sof tionization technique, well-suited for detection of both aromatic and aliphatic species. Problematic, however, is the generation of the VUV light. In general, the vacuum ultraviolet (VUV) light sources for SPI-MS are based either on lasers (e.g., 118-nm radiation generated by frequency-tripling of the third harmonic of a Nd:YAG laser) or on conventional VUV lamps, such as deuterium lamps. Althoughthe laser-based techniques are very sophisticated and expensive, the conventional lamps have serious drawbacks regarding their optical parameters, such as low-output power, low spectral power density, and broad emission bands. In this work, a novel excimer VUV light source, in which an electron beam is used to form rare gas excimer species, is used. The excimer VUV light sourceproduces brilliant and intense VUV light. The novel VUV light source was coupled to a compact and mobile time-of-flight mass spectrometer (TOFMS). A special interface design, including optical (VUV optics) as well as electronic measures (e.g., pulsed ion extraction) was realized. The use of the excimer VUV lamp for SPI will allow the realization of very compact, rugged, and sensitive SPI-TOFMS devices, which preferably will be adapted for process analytical application or monitoring issues (e.g., chemical warfare detection). The excimer VUV-lamp technology delivers VUV light with a good beam quality and high-output power at low costs. Furthermore, it allows changing the emitted wavelength as well as the bandwidth of the excimer VUV lamp in t he 100-200-nm region
Progress in Compact Toroid Experiments
Dolan, Thomas James
2002-09-01
The term "compact toroids" as used here means spherical tokamaks, spheromaks, and field reversed configurations, but not reversed field pinches. There are about 17 compact toroid experiments under construction or operating, with approximate parameters listed in Table 1.
The Riemann Problem for Hyperbolic Equations under a Nonconvex Flux with Two Inflection Points
Fossati, Marco
2014-01-01
This report addresses the solution of Riemann problems for hyperbolic equations when the nonlinear characteristic fields loose their genuine nonlinearity. In this context, exact solvers for nonconvex 1D Riemann problems are developed. First a scalar conservation law for a nonconvex flux with two inflection points is studied. Then the P-system for an isothermal version of the van der Waals gas model is examined in a range of temperatures allowing for a nonconvex pressure function. Eventually the system of the Euler equations of gasdynamics is considered for the polytropic van der Waals gas. In this case, a suitably large specific heat is considered such that the isentropes display a local loss of convexity near the saturation curve and the critical point. Such a nonconvex physical model allows for nonclassical waves to appear as a result of the change of sign of the fundamental derivative of gasdynamics. The solution of the Riemann problem for the considered real gas model reduces to a system of two nonlinear ...
Tunable absorption in graphene-based hyperbolic metamaterials for mid-infrared range
Ning, Renxia [College of Information Engineering, Huangshan University, Huangshan 245041,China (China); Key Laboratory of Radar Imaging and Microwave Photonics, Ministry of Education, College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 (China); Liu, Shaobin, E-mail: plrg@nuaa.edu.cn [Key Laboratory of Radar Imaging and Microwave Photonics, Ministry of Education, College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 (China); Zhang, Haifeng; Bian, Borui; Kong, Xiangkun [Key Laboratory of Radar Imaging and Microwave Photonics, Ministry of Education, College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 (China)
2015-01-15
Tunable absorption in periodic structure composed of graphene-based hyperbolic metamaterials (GHMMs) and isotropic medium is investigated by the transfer matrix method. The parallel part for relative permittivity of GHMMs consisting of monolayer graphene and conventional dielectric can be tuned by the chemical potential and dielectric layer thickness. The real part of the group index of GHMMs is insensitive to incident angle at the required frequency and the absorption of the periodic structure with GHMMs can be obtained nearly 100% at 22.4 terahertz (THz). The absorption peak of this frequency is almost uniform for both transverse electric (TE) and transverse magnetic (TE) polarizations. However, a new absorption peak can be observed incident angle is larger than 40 degree for TM polarization from 10 to 30 THz. The research results show that the absorption is insensitive to electromagnetic polarization at certain frequency. A new absorption peak can be found with TM polarization in low frequency region. These novel and effective GHMMs can replace metallic thin films as polarizing beam splitter for future optoelectronic applications.
Tunable absorption in graphene-based hyperbolic metamaterials for mid-infrared range
Ning, Renxia; Liu, Shaobin; Zhang, Haifeng; Bian, Borui; Kong, Xiangkun
2015-01-01
Tunable absorption in periodic structure composed of graphene-based hyperbolic metamaterials (GHMMs) and isotropic medium is investigated by the transfer matrix method. The parallel part for relative permittivity of GHMMs consisting of monolayer graphene and conventional dielectric can be tuned by the chemical potential and dielectric layer thickness. The real part of the group index of GHMMs is insensitive to incident angle at the required frequency and the absorption of the periodic structure with GHMMs can be obtained nearly 100% at 22.4 terahertz (THz). The absorption peak of this frequency is almost uniform for both transverse electric (TE) and transverse magnetic (TE) polarizations. However, a new absorption peak can be observed incident angle is larger than 40 degree for TM polarization from 10 to 30 THz. The research results show that the absorption is insensitive to electromagnetic polarization at certain frequency. A new absorption peak can be found with TM polarization in low frequency region. These novel and effective GHMMs can replace metallic thin films as polarizing beam splitter for future optoelectronic applications.
A multiband perfect absorber based on hyperbolic metamaterials.
Sreekanth, Kandammathe Valiyaveedu; ElKabbash, Mohamed; Alapan, Yunus; Rashed, Alireza R; Gurkan, Umut A; Strangi, Giuseppe
2016-05-18
In recent years, considerable research efforts have been focused on near-perfect and perfect light absorption using metamaterials spanning frequency ranges from microwaves to visible frequencies. This relatively young field is currently facing many challenges that hampers its possible practical applications. In this paper, we present grating coupled-hyperbolic metamaterials (GC-HMM) as multiband perfect absorber that can offer extremely high flexibility in engineering the properties of electromagnetic absorption. The fabricated GC-HMMs exhibit several highly desirable features for technological applications such as polarization independence, wide angle range, broad- and narrow- band modes, multiband perfect and near perfect absorption in the visible to near-IR and mid-IR spectral range. In addition, we report a direct application of the presented system as an absorption based plasmonic sensor with a record figure of merit for this class of sensors.
A decoupled system of hyperbolic equations for linearized cosmological perturbations
Ramírez, J
2002-01-01
A decoupled system of hyperbolic partial differential equations for linear perturbations around spatially flat FRW universes is obtained for the first time. The two key ingredients in obtaining this system are i) the explicit decomposition of the perturbing energy momentum tensor into two pieces: intrinsic and free, which have definite and distinct mathematical properties and physical interpretation, and ii) the introduction of a new gauge which plays a similar role as harmonic gauge does for perturbations around Minkowski space-time. The proposed formalism could be highly relevant for physical cosmology, since our universe is most likely flat. We deal with classical perturbations, but our treatment, being covariant, is also very appropriate for the description of linearized quantum gravity around cosmological backgrounds.
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.
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.
Geometrical hyperbolic systems for general relativity and gauge theories
Abrahams, A M; Choquet-Bruhat, Y; York, J W
1996-01-01
The evolution equations of Einstein's theory and of Maxwell's theory---the latter used as a simple model to illustrate the former--- are written in gauge covariant first order symmetric hyperbolic form with only physically natural characteristic directions and speeds for the dynamical variables. Quantities representing gauge degrees of freedom [the spatial shift vector \\beta^{i}(t,x^{j}) and the spatial scalar potential \\phi(t,x^{j}), respectively] are not among the dynamical variables: the gauge and the physical quantities in the evolution equations are effectively decoupled. For example, the gauge quantities could be obtained as functions of (t,x^{j}) from subsidiary equations that are not part of the evolution equations. Propagation of certain (``radiative'') dynamical variables along the physical light cone is gauge invariant while the remaining dynamical variables are dragged along the axes orthogonal to the spacelike time slices by the propagating variables. We obtain these results by (1) taking a furth...
Analysis of magnetic electron lens with secant hyperbolic field distribution
Pany, S S; 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 electron beam probe. Indicators of imaging performance of these instruments, like spatial resolution, have strong correlation with focal characteristics of the magnetic lenses which in turn have been shown to be functions of the spatial distribution of axial magnetic field generated by them. Owing to complicated design of practical lenses, empirical mathematical expressions are deemed convenient for use in physics based calculations of their focal properties. So, degree of closeness of such models to the actual field distribution determines accuracy of the calculations. Mathematical models proposed by Glaser[1] and Ramberg[1] have historically been put into extensive use. In this paper the authors discuss one such model with secant-hyperbolic type magnetic field distribution function, and present a comparison among these models, ...
Enhanced superconductivity in aluminum-based hyperbolic metamaterials
Smolyaninova, V N; Zimmerman, W; Prestigiacomo, J C; Osofsky, M S; Kim, H; Xing, Z; Qazilbash, M M; Smolyaninov, I I
2016-01-01
One of the most important goals of condensed matter physics is materials by design, i.e. the ability to reliably predict and design materials with a set of desired properties. A striking example is the deterministic enhancement of the superconducting properties of materials. Recent experiments have demonstrated that the metamaterial approach is capable of achieving this goal, such as tripling the critical temperature Tc in Al-Al2O3 epsilon near zero (ENZ) core-shell metamaterial superconductors. However, transport properties of such metamaterials remained much worse compared to conventional superconductors. Here, we demonstrate that an Al/Al2O3 hyperbolic metamaterial geometry is capable of a similar Tc enhancement, while having superior transport and magnetic properties compared to the core-shell metamaterial superconductors. This result opens up numerous new possibilities for metamaterial enhancement of Tc in other practically important simple superconductors, such as niobium and MgB2. It also indicates tha...
Edge effects on invisibility of hyperbolic multilayered nanotubes
Díaz-Aviñó, Carlos; Zapata-Rodríguez, Carlos J
2016-01-01
Invisibility of nanotubes has recently been demonstrated in highly anisotropic metamaterials in the transition regime from hyperbolic to elliptic dispersion [Sci. Rep. 5 (2015) 16027]. In such study, the characterization of a realistic multilayered metamaterial was carried out by means of an effective medium approach providing average components of the permittivity tensor and wave fields. Here, the edge effects of the metal-dielectric stratified nanotube for different combinations were thoroughly analyzed. We show how the boundary layers, which in principle remain fully irrelevant in the estimation of the effective permittivity of the nanotube, however play a critical role in the scattering spectra and the near field patterns. A dramatic enhancement of the scattered wave field is unexpectedly experienced at the frequencies of interest when a dielectric layer is chosen to be in contact with the cavity core.
Fifth international conference on hyperbolic problems -- theory, numerics, applications: Abstracts
NONE
1994-12-31
The conference demonstrated that hyperbolic problems and conservation laws play an important role in many areas including industrial applications and the studying of elasto-plastic materials. Among the various topics covered in the conference, the authors mention: the big bang theory, general relativity, critical phenomena, deformation and fracture of solids, shock wave interactions, numerical simulation in three dimensions, the level set method, multidimensional Riemann problem, application of the front tracking in petroleum reservoir simulations, global solution of the Navier-Stokes equations in high dimensions, recent progress in granular flow, and the study of elastic plastic materials. The authors believe that the new ideas, tools, methods, problems, theoretical results, numerical solutions and computational algorithms presented or discussed at the conference will benefit the participants in their current and future research.
Behavior of the Escape Rate Function in Hyperbolic Dynamical Systems
Demers, Mark
2011-01-01
For a fixed initial reference measure, we study the dependence of the escape rate on the hole for a smooth or piecewise smooth hyperbolic map. First, we prove the existence and Holder continuity of the escape rate for systems with small holes admitting Young towers. Then we consider general holes for Anosov diffeomorphisms, without size or Markovian restrictions. We prove bounds on the upper and lower escape rates using the notion of pressure on the survivor set and show that a variational principle holds under generic conditions. However, we also show that the escape rate function forms a devil's staircase with jumps along sequences of regular holes and present examples to elucidate some of the difficulties involved in formulating a general theory.
Critical coupling with graphene-based hyperbolic metamaterials
Xiang, Yuanjiang; Dai, Xiaoyu; Guo, Jun; Zhang, Han; Wen, Shuangchun; Tang, Dingyuan
2014-06-01
In order to effectively realize and control the critical coupling, a graphene-based hyperbolic metamaterial has been proposed to replace the absorbing thin film in the critically coupled resonance structure. Our calculations demonstrate that the critical coupling effect (near-perfect light absorption) can be achieved at the near-infrared wavelength by using this layered structure, while the critical coupling frequency can be tuned by varying the Fermi energy level of graphene sheets via electrostatic biasing. Moreover, we show that the critical coupling frequency can be tuned by changing the thickness of the dielectric or layer number of the graphene sheets in the unit cell of the graphene-dielectric HMM. The optimization performance has also been indicated, which may offer an opportunity towards the experimental designs of high efficient graphene based critical coupling devices.
Optimized difference schemes for multidimensional hyperbolic partial differential equations
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.
Quantum Chaos on Hyperbolic Manifolds A New Approach to Cosmology
Tomaschitz, R
1992-01-01
We consider classical and quantum motion on multiply connected hyperbolic spaces, which appear as space-like slices in Robertson-Walker cosmologies. The topological structure of these manifolds creates on the one hand bounded chaotic trajectories, and on the other hand quantal bound states whose wave functions can be reconstructed from the chaotic geodesics. We obtain an exact relation between a probabilistic quantum mechanical wave field and the corresponding classical system, which is likewise probabilistic because of the instabilities of the trajectories with respect to the initial conditions. The central part in this reconstruction is played by the fractal limit set of the covering group of the manifold. This limit set determines the bounded chaotic trajectories on the manifold. Its Hausdorff measure and dimension determine the wave function of the quantum mechanical bound state for geodesic motion. We investigate relativistic scalar wave fields in de Sitter cosmologies, coupled to the curvature scalar of...
Fano resonance engineering in slanted cavities with hyperbolic metamaterials
Vaianella, Fabio; Maes, Bjorn
2016-09-01
We present the possibility to engineer Fano resonances using multilayered hyperbolic metamaterials. The proposed cavity designs are composed of multilayers with a central slanted part. The highly tunable resonances originate from the interference between a propagating and an evanescent mode inside the slanted section. The propagating mode can reach an extremely high effective index, making the realization of deeply subwavelength cavities possible, as small as 5 nm. The evanescent mode is rarely analyzed but plays an important role here, as its contribution determines the particular shape of the cavity characteristic. Moreover, these phenomena cannot be described using effective medium theory, and we provide a more rigorous analysis. The reported resonances are very sensitive to any structural changes and could be used for sensing applications.
Enhanced superconductivity in aluminum-based hyperbolic metamaterials
Smolyaninova, Vera N.; Jensen, Christopher; Zimmerman, William; Prestigiacomo, Joseph C.; Osofsky, Michael S.; Kim, Heungsoo; Bassim, Nabil; Xing, Zhen; Qazilbash, Mumtaz M.; Smolyaninov, Igor I.
2016-01-01
One of the most important goals of condensed matter physics is materials by design, i.e. the ability to reliably predict and design materials with a set of desired properties. A striking example is the deterministic enhancement of the superconducting properties of materials. Recent experiments have demonstrated that the metamaterial approach is capable of achieving this goal, such as tripling the critical temperature TC in Al-Al2O3 epsilon near zero (ENZ) core-shell metamaterial superconductors. Here, we demonstrate that an Al/Al2O3 hyperbolic metamaterial geometry is capable of a similar TC enhancement, while having superior transport and magnetic properties compared to the core-shell metamaterial superconductors. PMID:27658850
Enhanced superconductivity in aluminum-based hyperbolic metamaterials
Smolyaninova, Vera N.; Jensen, Christopher; Zimmerman, William; Prestigiacomo, Joseph C.; Osofsky, Michael S.; Kim, Heungsoo; Bassim, Nabil; Xing, Zhen; Qazilbash, Mumtaz M.; Smolyaninov, Igor I.
2016-09-01
One of the most important goals of condensed matter physics is materials by design, i.e. the ability to reliably predict and design materials with a set of desired properties. A striking example is the deterministic enhancement of the superconducting properties of materials. Recent experiments have demonstrated that the metamaterial approach is capable of achieving this goal, such as tripling the critical temperature TC in Al-Al2O3 epsilon near zero (ENZ) core-shell metamaterial superconductors. Here, we demonstrate that an Al/Al2O3 hyperbolic metamaterial geometry is capable of a similar TC enhancement, while having superior transport and magnetic properties compared to the core-shell metamaterial superconductors.
Generalized -deformed correlation functions as spectral functions of hyperbolic geometry
Bonora, L.; Bytsenko, A. A.; Guimarães, M. E. X.
2014-08-01
We analyze the role of vertex operator algebra and 2d amplitudes from the point of view of the representation theory of infinite-dimensional Lie algebras, MacMahon and Ruelle functions. By definition p-dimensional MacMahon function, with , is the generating function of p-dimensional partitions of integers. These functions can be represented as amplitudes of a two-dimensional c = 1 CFT, and, as such, they can be generalized to . With some abuse of language we call the latter amplitudes generalized MacMahon functions. In this paper we show that generalized p-dimensional MacMahon functions can be rewritten in terms of Ruelle spectral functions, whose spectrum is encoded in the Patterson-Selberg function of three-dimensional hyperbolic geometry.
Extreme stiffness hyperbolic elastic metamaterial for total transmission subwavelength imaging
Lee, Hyuk; Oh, Joo Hwan; Seung, Hong Min; Cho, Seung Hyun; Kim, Yoon Young
2016-04-01
Subwavelength imaging by metamaterials and extended work to pursue total transmission has been successfully demonstrated with electromagnetic and acoustic waves very recently. However, no elastic counterpart has been reported because earlier attempts suffer from considerable loss. Here, for the first time, we realize an elastic hyperbolic metamaterial lens and experimentally show total transmission subwavelength imaging with measured wave field inside the metamaterial lens. The main idea is to compensate for the decreased impedance in the perforated elastic metamaterial by utilizing extreme stiffness, which has not been independently actualized in a continuum elastic medium so far. The fabricated elastic lens is capable of directly transferring subwavelength information from the input to the output boundary. In the experiment, this intriguing phenomenon is confirmed by scanning the elastic structures inside the lens with laser scanning vibrometer. The proposed elastic metamaterial lens will bring forth significant guidelines for ultrasonic imaging techniques.
Hyperbolic spin vortices and textures in exciton-polariton condensates
Manni, F.; Léger, Y.; Rubo, Y. G.; André, R.; Deveaud, B.
2013-10-01
From cosmology to the microscopic scales of the quantum world, the study of topological excitations is essential for the understanding of phase conformation and phase transitions. Quantum fluids are convenient systems to investigate topological entities because well-established techniques are available for their preparation, control and measurement. Across a phase transition, a system dramatically changes its properties because of the spontaneous breaking of certain continuous symmetries, leading to generation of topological defects. In particular, attention is given to entities that involve both spin and phase topologies. Exciton-polariton condensates are quantum fluids combining coherence and spin properties that, thanks to their light-matter nature, bring the advantage of direct optical access to the condensate order parameter. Here we report on the spontaneous occurrence of hyperbolic spin vortices in polariton condensates, by directly imaging both their phase and spin structure, and observe the associated spatial polarization patterns, spin textures that arise in the condensate.
Second-order hyperbolic Fuchsian systems and applications
Beyer, Florian
2010-01-01
We introduce a new class of singular partial differential equations, referred to as the second-order hyperbolic Fuchsian systems, and we investigate the associated initial value problem when data are imposed on the singularity. First, we establish a general existence theory of solutions with asymptotic behavior prescribed on the singularity, which relies on a new approximation scheme, suitable also for numerical purposes. Second, this theory is applied to the (vacuum) Einstein equations for Gowdy spacetimes, and allows us to recover, by more direct arguments, well-posedness results established earlier by Rendall and collaborators. Another main contribution in this paper is the proposed approximation scheme, which we refer to as the Fuchsian numerical algorithm and is shown to provide highly accurate numerical approximations to the singular initial value problem. For the class of Gowdy spacetimes, the numerical experiments presented here show the interest and efficiency of the proposed method and demonstrate t...
Bounds on integrals of the Wigner function: the hyperbolic case
Wood, J G
2004-01-01
Wigner functions play a central role in the phase space formulation of quantum mechanics. Although closely related to classical Liouville densities, Wigner functions are not positive definite and may take negative values on subregions of phase space. We investigate the accumulation of these negative values by studying bounds on the integral of an arbitrary Wigner function over noncompact subregions of the phase plane with hyperbolic boundaries. We show using symmetry techniques that this problem reduces to computing the bounds on the spectrum associated with an exactly-solvable eigenvalue problem and that the bounds differ from those on classical Liouville distributions. In particular, we show that the total ``quasiprobability'' on such a region can be greater than 1 or less than zero.
Verification of hyperbolicity for attractors of some mechanical systems with chaotic dynamics
Kuznetsov, Sergey P.; Kruglov, Vyacheslav P.
2016-03-01
Computer verification of hyperbolicity is provided based on statistical analysis of the angles of intersection of stable and unstable manifolds for mechanical systems with hyperbolic attractors of Smale-Williams type: (i) a particle sliding on a plane under periodic kicks, (ii) interacting particles moving on two alternately rotating disks, and (iii) a string with parametric excitation of standing-wave patterns by a modulated pump. The examples are of interest as contributing to filling the hyperbolic theory of dynamical systems with physical content.
Dai, Jin; Bozhevolnyi, Sergey I; Yan, Min
2016-01-01
We demonstrate the possibility of ultrabroadband super-Planckian radiative heat transfer be- tween two metal plates patterned with tapered hyperbolic metamaterial arrays. It is shown that, by employing profile-patterned hyperbolic media, one can design photonic bands to populate a desired thermal radiation window, with a spectral density of modes much higher than what can be achieved with unstructured media. For nanometer-sized gaps between two plates, the modes occupy states both inside and outside the light cone, giving rise to ultrabroadband super-Planckian radiative heat transfer. Our study reveals that structured hyperbolic metamaterial offers unprecedented potential in achieving a controllable super-Planckian radiative heat transfer.
Generalized Hyperbolic Function Solution to a Class of Nonlinear Schrödinger-Type Equations
Zeid I. A. Al-Muhiameed
2012-01-01
Full Text Available With the help of the generalized hyperbolic function, the subsidiary ordinary differential equation method is improved and proposed to construct exact traveling wave solutions of the nonlinear partial differential equations in a unified way. A class of nonlinear Schrödinger-type equations including the generalized Zakharov system, the Rangwala-Rao equation, and the Chen-Lee-Liu equation are investigated and the exact solutions are derived with the aid of the homogenous balance principle and generalized hyperbolic functions. We study the effect of the generalized hyperbolic function parameters p and q in the obtained solutions by using the computer simulation.
Nonoscillatory Central Schemes for Hyperbolic Systems of Conservation Laws in Three-Space Dimensions
Andrew N. Guarendi
2013-01-01
Full Text Available We extend a family of high-resolution, semidiscrete central schemes for hyperbolic systems of conservation laws to three-space dimensions. Details of the schemes, their implementation, and properties are presented together with results from several prototypical applications of hyperbolic conservation laws including a nonlinear scalar equation, the Euler equations of gas dynamics, and the ideal magnetohydrodynamic equations. Parallel scaling analysis and grid-independent results including contours and isosurfaces of density and velocity and magnetic field vectors are shown in this study, confirming the ability of these types of solvers to approximate the solutions of hyperbolic equations efficiently and accurately.
A non-strictly hyperbolic system for the Einstein equations with arbitrary lapse and shift
Abrahams, A M; Choquet-Bruhat, Y; York, J W; Abrahams, Andrew; Anderson, Arlen; Choquet-Bruhat, Yvonne; York, James W
1996-01-01
We obtain a system for the spatial metric and extrinsic curvature of a spacelike slice that is hyperbolic non-strict in the sense of Leray and Ohya and is equivalent to the Einstein equations. Its characteristics are the light cone and the normal to the slice for any choice of lapse and shift functions, and it admits a well-posed causal Cauchy problem in a Gevrey class of index \\alpha=2. The system becomes quasidiagonal hyperbolic if we posit a certain wave equation for the lapse function, and we can then relate the results to our previously obtained first order symmetric hyperbolic system for general relativity.
Phase change heat transfer during cryosurgery of lung cancer using hyperbolic heat conduction model.
Kumar, Ajay; Kumar, Sushil; Katiyar, V K; Telles, Shirley
2017-05-01
The paper reports a numerical study of phase change heat transfer process in lung cancer undergoing cryosurgery. A two dimensional hyperbolic bio-heat model with non-ideal property of tissue, blood perfusion and metabolism is used to analyze the problem. The governing equations are solved by finite difference method based on enthalpy formulation. Effects of relaxation time of heat flux in hyperbolic model on freezing process have been examined. A comparative investigation of two different models (hyperbolic and parabolic bio-heat models) is also presented. Copyright © 2017 Elsevier Ltd. All rights reserved.
The United Nations Global Compact
Rasche, Andreas; Waddock, Sandra; McIntosh, Malcolm
2013-01-01
This article reviews the interdisciplinary literature on the UN Global Compact. The review identifies three research perspectives, which scholars have used to study the UN Global Compact so far: a historical perspective discussing the Global Compact in the context of UN-business relations...
CERN. Geneva
2015-01-01
Fusion research is currently to a large extent focused on tokamak (ITER) and inertial confinement (NIF) research. In addition to these large international or national efforts there are private companies performing fusion research using much smaller devices than ITER or NIF. The attempt to achieve fusion energy production through relatively small and compact devices compared to tokamaks decreases the costs and building time of the reactors and this has allowed some private companies to enter the field, like EMC2, General Fusion, Helion Energy, Lawrenceville Plasma Physics and Lockheed Martin. Some of these companies are trying to demonstrate net energy production within the next few years. If they are successful their next step is to attempt to commercialize their technology. In this presentation an overview of compact fusion reactor concepts is given.
Placidi, M.; Jung, J. -Y.; Ratti, A.; Sun, C.
2014-07-25
This paper describes beam distribution schemes adopting a novel implementation based on low amplitude vertical deflections combined with horizontal ones generated by Lambertson-type septum magnets. This scheme offers substantial compactness in the longitudinal layouts of the beam lines and increased flexibility for beam delivery of multiple beam lines on a shot-to-shot basis. Fast kickers (FK) or transverse electric field RF Deflectors (RFD) provide the low amplitude deflections. Initially proposed at the Stanford Linear Accelerator Center (SLAC) as tools for beam diagnostics and more recently adopted for multiline beam pattern schemes, RFDs offer repetition capabilities and a likely better amplitude reproducibility when compared to FKs, which, in turn, offer more modest financial involvements both in construction and operation. Both solutions represent an ideal approach for the design of compact beam distribution systems resulting in space and cost savings while preserving flexibility and beam quality.
Compact fiber optic accelerometer
Feng Peng; Jun Yang; Bing Wu; Yonggui Yuan; Xingliang Li; Ai Zhou; Libo Yuan
2012-01-01
A compact fiber optic accelerometer based on a Michelson interferometer is proposed and demonstrated.In the proposed system,the sensing element consists of two single-mode fibers glued together by epoxy,which then act as a simple supported beam.By demodulating the optical phase shift,the acceleration is determined as proportional to the force applied on the central position of the two single-mode fibers.This simple model is able to calculate the sensitivity and the resonant frequency of the compact accelerometer.The experimental results show that the sensitivity and the resonant frequency of the accelerometer are 0.42 rad/g and 600 Hz,respectively.
COMPACT SUPPORT THIN PLATE SPLINE ALGORITHM
Li Jing; Yang Xuan; Yu Jianping
2007-01-01
Common tools based on landmarks in medical image elastic registration are Thin Plate Spline (TPS) and Compact Support Radial Basis Function (CSRBF). TPS forces the corresponding landmarks to exactly match each other and minimizes the bending energy of the whole image. However,in real application, such scheme would deform the image globally when deformation is only local.CSRBF needs manually determine the support size, although its deformation is limited local. Therefore,to limit the effect of the deformation, new Compact Support Thin Plate Spline algorithm (CSTPS) is approached, analyzed and applied. Such new approach gains optimal mutual information, which shows its registration result satisfactory. The experiments also show it can apply in both local and global elastic registration.
A compact PE memory for vision chips
Cong, Shi; Zhe, Chen; Jie, Yang; Nanjian, Wu; Zhihua, Wang
2014-09-01
This paper presents a novel compact memory in the processing element (PE) for single-instruction multiple-data (SIMD) vision chips. The PE memory is constructed with 8 × 8 register cells, where one latch in the slave stage is shared by eight latches in the master stage. The memory supports simultaneous read and write on the same address in one clock cycle. Its compact area of 14.33 μm2/bit promises a higher integration level of the processor. A prototype chip with a 64 × 64 PE array is fabricated in a UMC 0.18 μm CMOS technology. Five types of the PE memory cell structure are designed and compared. The testing results demonstrate that the proposed PE memory architecture well satisfies the requirement of the vision chip in high-speed real-time vision applications, such as 1000 fps edge extraction.
Pan, JianHua; Ren, YuXin
2017-08-01
In this paper, a family of sub-cell finite volume schemes for solving the hyperbolic conservation laws is proposed and analyzed in one-dimensional cases. The basic idea of this method is to subdivide a control volume (main cell) into several sub-cells and the finite volume discretization is applied to each of the sub-cells. The averaged values on the sub-cells of current and face neighboring main cells are used to reconstruct the polynomial distributions of the dependent variables. This method can achieve arbitrarily high order of accuracy using a compact stencil. It is similar to the spectral volume method incorporating with PNPM technique but with fundamental differences. An elaborate utilization of these differences overcomes some shortcomings of the spectral volume method and results in a family of accurate and robust schemes for solving the hyperbolic conservation laws. In this paper, the basic formulation of the proposed method is presented. The Fourier analysis is performed to study the properties of the one-dimensional schemes. A WENO limiter based on the secondary reconstruction is constructed.
Hydraulic conductivity of compacted zeolites.
Oren, A Hakan; Ozdamar, Tuğçe
2013-06-01
Hydraulic conductivities of compacted zeolites were investigated as a function of compaction water content and zeolite particle size. Initially, the compaction characteristics of zeolites were determined. The compaction test results showed that maximum dry unit weight (γ(dmax)) of fine zeolite was greater than that of granular zeolites. The γ(dmax) of compacted zeolites was between 1.01 and 1.17 Mg m(-3) and optimum water content (w(opt)) was between 38% and 53%. Regardless of zeolite particle size, compacted zeolites had low γ(dmax) and high w(opt) when compared with compacted natural soils. Then, hydraulic conductivity tests were run on compacted zeolites. The hydraulic conductivity values were within the range of 2.0 × 10(-3) cm s(-1) to 1.1 × 10(-7) cm s(-1). Hydraulic conductivity of all compacted zeolites decreased almost 50 times as the water content increased. It is noteworthy that hydraulic conductivity of compacted zeolite was strongly dependent on the zeolite particle size. The hydraulic conductivity decreased almost three orders of magnitude up to 39% fine content; then, it remained almost unchanged beyond 39%. Only one report was found in the literature on the hydraulic conductivity of compacted zeolite, which is in agreement with the findings of this study.
2017-04-21
illustrate some of the challenges and diversity of the threat that the United States faces in the cyber domain. Infrastructure and Systems...FBIs own definition. For example, the DOJ charged a hacker arrested by the FBI in Malaysia with cyberterrorism for stealing US service member’s
Smolyaninov, Igor I
2013-01-01
We demonstrate that high Tc superconductors exhibit hyperbolic metamaterial behavior in the far infrared and THz frequency ranges. In the THz range the hyperbolic behavior occurs only in the normal state, while no propagating modes exist in the superconducting state. Wave equation, which describes propagation of extraordinary light inside a hyperbolic metamaterial exhibits 2+1 dimensional Lorentz symmetry. The role of time in the corresponding effective 3D Minkowski spacetime is played by the spatial coordinate aligned perpendicular to the copper oxide layers. Such superconductor-based hyperbolic metamaterials exhibit a quantum phase transition at T=0, in which the effective Minkowski spacetime arise in the mixed state of the superconductor at some critical value of external magnetic field. Nucleation of Minkowski spacetime occurs via formation of quantized Abrikosov vortices, so that these vortices play the role of Minkowski spacetime quanta. Thus, the described system may be used as an experimental model of...
Hyperbolic Lagrangian coherent structures align with contours of path-averaged scalars
Farazmand, Mohammad
2015-01-01
We prove that, in area-preserving two-dimensional flows, hyperbolic Lagrangian Coherent Structures (LCS) align with the contours of path-averaged scalars, i.e. the time average of scalar fields along the trajectories of the dynamical system. The alignment is a consequence of the fact that the length of a repelling (respectively, attracting) LCS shrinks rapidly under advection in forward (respectively, backward) time. As a result, the points along a hyperbolic LCS sample similar values of the scalar field, leading to almost uniform distribution of the path-averaged scalar along the LCS. Our results illuminate the relation between the variational theory of hyperbolic LCSs and a significant subset of mixing diagnostics which are obtained as path-averaged scalars. We illustrate the theoretical results on a direct numerical simulation of two-dimensional Navier--Stokes equations. Furthermore, our results provide partial explanation for a recent observation that hyperbolic LCSs separate dynamically distinct regions ...
Oscillation of solutions to neutral nonlinear impulsive hyperbolic equations with several delays
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.
p-Trigonometric and p-Hyperbolic Functions in Complex Domain
Petr Girg
2016-01-01
Full Text Available We study extension of p-trigonometric functions sinp and cosp and of p-hyperbolic functions sinhp and coshp to complex domain. Our aim is to answer the question under what conditions on p these functions satisfy well-known relations for usual trigonometric and hyperbolic functions, such as, for example, sin(z=-i·sinhi·z. In particular, we prove in the paper that for p=6,10,14,… the p-trigonometric and p-hyperbolic functions satisfy very analogous relations as their classical counterparts. Our methods are based on the theory of differential equations in the complex domain using the Maclaurin series for p-trigonometric and p-hyperbolic functions.
Park Jong Yeoul
2007-01-01
Full Text Available We study the existence of global weak solutions for a hyperbolic differential inclusion with a source term, and then investigate the asymptotic stability of the solutions by using Nakao lemma.
Bapurao C. Dhage
2006-03-01
Full Text Available In this paper, we prove an existence theorem for hyperbolic differential equations in Banach algebras under Lipschitz and Caratheodory conditions. The existence of extremal solutions is also proved under certain monotonicity conditions.
Darboux problem for implicit impulsive partial hyperbolic fractional order differential equations
Said Abbas
2011-11-01
Full Text Available In this article we investigate the existence and uniqueness of solutions for the initial value problems, for a class of hyperbolic impulsive fractional order differential equations by using some fixed point theorems.